This help file belongs to Scala version 1.7.
Brackets indicate an optional parameter. Parentheses indicate a choice of options. Items in capital letters are commands. Words preceded by a slash are command qualifiers. Long commands and options can be abbreviated.
New users should read the sections Commands and Qualifiers for the command language format. See also About... for background info, Introduction for how you can set up things to tune electronic instruments with Scala and HELP for usage of the HELP command.
If you are looking for an operation that is not described in this file then look in the list of supplied command files.
To navigate through this page, there is a list of help items.
ADD [scalenr.]Multiply the pitches of the current scale with those in the given scale at the same degree and replace them in the current scale. This means their logarithms (value in cents) are added. The default scale is 0 (current scale), so when no number is given the pitches are multiplied with themselves. The amount of scales is set in file params.par (default 10), and shown with SHOW SETTINGS. Instead of a scale number, a filename may also be given.
/ADDInstead of multiplying the pitches, take the summation tones.
/MEDIANTInstead of multiplying the pitches, take their mediant value, i.e. (num(a) + num(b)) / (den(a) + den(b)). All pitches must be rational.
/SUMMATIONThe current scale is replaced by a scale with all sum tones of the current or given scale. If the number of notes in the given scale is n, then the size of the new scale will be n * (n + 1) / 2 - 1, but less if there are duplicate sum tones. For example, if the given scale has pitch factors 10:12:15:20 (or 1/1 6/5 3/2 2/1), then the new scale will be 22:25:27:30:32:35. Warning: the original 1/1 remains in the scale. To remove it, do DELETE 0. See also SUBTRACT/DIFFERENCE.
APPEND pitch [scalenr.]Insert a new pitch in the current (number 0) or given scale after the last position making the size of the scale increase by one. The maximum size of a scale is set in file params.par (default 100). See INSERT to insert a new pitch at another degree than after the last one.
/FACTOR factor [scalenr.]Interpret the pitch parameter as a linear factor and not as cents when it has a decimal point.
/INTERVAL interval [scalenr.]Specify the interval with the last degree instead of the absolute pitch.
/SCALE scalenr.Multiply the pitches of the given scale by the formal octave of the current scale and add them to the current scale. Instead of a scale number, a file name may also be given. Cannot be combined with other qualifiers.
APPROXIMATE [highest-prime]Replace each pitch in the current scale with the closest fraction to the pitch with numerator and denominator consisting only of prime factors used in harmonicity calculations. If the given parameter is not a prime number, then the next higher prime will be the limit. If no parameter is given, then the prime limit set with SET LIMIT is effective.
/CONSTRAINEDReplace only when there exists a fraction whose
/FLOATS_ONLYReplace only the floating point pitches (those given in cents) in the current scale.
/WEIGHTEDDoes not only take distance into account, but also the current attribute value given by SET ATTRIBUTE. The optimality criterion (which is minimised) is the sum of the absolute pitch difference and the weighting factor given by SET WEIGHTING multiplied with the attribute value of the tested ratio. For the attribute one that gives a harmonic complexity value should be chosen (like DEPTH, ENTROPY, ERLICH, EUCLID, GRADUS, HARMON, MANN, TENNEY, TRIANGLE, TR_LOG, VOGEL, WILSON) and not CENTS for example. If HARMON is chosen, the absolute inverse of it is taken into the weighed sum. If the weighting factor is higher, then the attribute value weighs more and the pitch difference less. The absolute pitch difference is weighed in cents.
/INSERT pitch [highest-prime]Insert all approximations to the given pitch in the current scale. All the same constraints of /CONSTRAINED apply here. SET MAXDIFF must be done because the initial value of 0.0 does not mean no maximum difference here, but literally zero. The range of pitches to be inserted is from pitch - max.diff. to pitch + max.diff. If highest-prime is not given, the limit set with SET LIMIT applies. Any pitches already in the current scale, will remain there. So if only the approximations are wanted, do CLEAR first. Set any exponent limits with SET EXPLIMIT. If more approximations are found than the maximum scale size, then "Overflow in scale size" will occur.
ASSUME scalenr.Make floating point pitches of the current scale into rational ones if the same pitch is present in the given scale as a rational value. This only happens if the values are exactly the same.
/COMBINATIONAlso compare the combinations (product and quotient) of the pitches in the given scale. Many more rational values can be found this way. Note that this may also find extra rational values if applied to the current scale itself (scalenumber 0) if it is partially rational.
AVERAGE patternReplace each pitch in the current scale with the geometric mean of that pitch with the pitches given by the relative offsets in the given interval pattern. For example AVERAGE 1 will take the mean of a pitch with the next degree.
BISTEP scalenr.Modify a scale in such a way that the least-squares difference with the nearest pitches in another scale is minimised. The current scale to be modified must have exactly two different interval sizes between consecutive pitches. You can check this with SHOW INTERVALS; the scale must have two intervals listed with interval class 1. The operation leaves the pattern of interval sizes intact and the formal octave also remains the same. The least-squares difference with corresponding (nearest) pitches in the given scale is minimised. The given scale does not have to have the same size as the current scale. The formal octave does not have to be the same; the difference between the formal octaves does not influence the result. The nearest pitches to the ones of the current scale will be selected for approximating them. Instead of a scale number, a filename may also be given.
/UNIQUEAs above but if the given scale has less pitches than the current scale, or if it has pitches that are closest to more than one pitch in the current scale, then those pitches are only counted once in the calculation and are ignored for approximation of pitches further removed from them.
/MATCH pitchInstead of a scale to approximate, give one pitch that must be matched in the scale. This is the same as using BISTEP/UNIQUE with the given scale containing only this given pitch.
/PERMUTATION count scalenr.Create a scale with two interval sizes in such a way that the least-squares difference with corresponding pitches in another scale is minimal. The scale will have the same size and formal octave as the given scale. The count which is given is the number of intervals with one size, while the number for the other size will be the remaining number of scale size minus count. All interval patterns (permutations of the two intervals) are tested and the one giving the lowest least-squares difference to the given scale will be taken. This is the difference with BISTEP without /PERMUTATION. For long scales it may take a lot of computing time. Instead of a scale number, a filename may also be given. The given scale may also be 0, in which case the current scale will be replaced with the approximation.
CALCULATE expressionEvaluate a given arithmetical pitch expression and show the result. The expression may consist of pitches given as a ratio, in cents, from a pitch memory or scale degree (see help of $, %, [ and Expressions), all mixed, and the following operations:
+ | : multiplication |
- | : division |
* | : power (right operand is pitch) |
^ | : power (right operand is linear value) |
\ | : root |
| | : reduction (divide the left by the right operand until the result is smaller than the right operand) |
plus | : summation |
div | : logarithmic ratio (left and right operand must have the same sign) |
abs | : if the right operand is smaller than 1/1, take the reciprocal |
lin | : specify that right operand is linear value |
min | : subtraction (see below) |
Furthermore parentheses may be given to influence the order of evaluation. It
calculates the result and shows it in various units. The result is stored in
pitch memory 0. The order of precedence of operations is first 'lin', then ^,
then * and \, then |, then +, -, 'plus' and 'abs'. Example: 3/2*12-2*7 or
3*12|2 or 3^12|2 gives the Pythagorean comma.
The difference between * and ^ is that with ^ the right operand is read as a
linear value instead of as cents, may also be negative and may not be a
parenthesized expression. With a nonnegative integer or ratio as the right
operand, * and ^ give the same result.
Strictly speaking, 'lin' is not an operation but when it is put in front of a
pitch value which contains a decimal point, then it is interpreted as a linear
factor instead of a cents value. It must not be negative.
A special operation is:
min : subtraction
When not between parentheses, it can be used only once in an expression and
has lowest precedence. The result is given as a frequency difference. The
given frequency is relative to the base frequency of SET FREQUENCY.
Example: 3/2 min 700.0. To use subtraction in an expression, put it between
parentheses.
Extra units in which the result is expressed are stored in parameter file
calcval.par and may be altered as wished. Note names can be given at the end
but it is not default. See also SET CALC_OUTPUT.
/FACTORInterpret all pitch values in the expression with a decimal point not as cents but as a linear factor. This is the same as putting the word lin in front of every pitch value.
/NOOUTPUTStore the result in pitch memory 0 only and do not show the result. See also help of :=.
/LEASTSQUAREWith this qualifier, there is no parameter. It calculates the least-squares fifth for a meantone scale (cycle of fifths). It can also be used to calculate the (formal) fifth for attaining one exactly just interval. First the size (number of notes) is asked. This is used for giving a hint for the number of fifths to be stacked to approximate the intervals. If you know this already, some value can be entered like 1 or 12. Then the formal octave is asked, usually this is 2/1. Then the degree for the fifth is asked, again for hinting the number of fifth steps. Hit return for taking the nearest equal tempered degree. Next, enter the number of pitches to be approximated. This number should include the fifth itself, even if it's not to be included in the least-squares average. Namely, the first approximant is taken to be the formal fifth. Subsequently for each one the pitch is entered, the number of steps to approximate it (for the fifth this is one) and a weighting factor, which can be given as a ratio or floating point value. Enter a weight of zero if the approximant is to be excluded from the average. For downwardly stacked fifths, enter a negative value for the number of steps. The result is shown plus the difference with the given formal fifth.
/MINIMAXAs /LEASTSQUARE except that the fifth giving the lowest maximum error is calculated instead of the least-squares error. The errors are calculated as the difference in cents times the given weight. Example: a 1/5-comma meantone fifth has the same error for 3/2 and 5/4. To calculate this enter subsequently: 12, 2, 7, 2, 3/2, 1, 1.0, 5/4, 4, 1.0
CATALOGUE [start]Show size (number of notes) and formal octave of all nonempty working scales and the pitch memories. If the start parameter is given, then it's the first scale or pitch memory to be shown. Show also whether scales consist completely of rational pitches or not, indicated with the word rational. The last column contains part of the description text and if that is absent, the first few pitches of the scale are shown.
/PITCHShow all the values in the pitch memories.
/SCALEShow the nonempty scale memories only.
CD [directory]Change the working directory to the given directory. The original directory will be restored when leaving the program. With no parameter, the current directory path appears on the screen.
CHORDS first-number last-number [size]Shows the approximations in the current scale to all just chords between the given two harmonic numbers. The size parameter is the number of notes in the chords. The default value is 3. The minimum value is 2. What is shown is first the chord, then the nearest approximation in scale degrees and then the standard deviation between the chord notes and scale notes. If the chord size is five or smaller, then the inverted chord is given too. For example if first-number is 3, last-number is 6 and size is 3, then the chords are 3:4:5, 3:4:6, 3:5:6 and 4:5:6.
/CONSTRAINEDShow only chords for which the differences with the pitches of the current scale do not exceed the maximum difference set with SET MAXDIFF. So if there is at least one note in the chord with a larger difference, then the chord will not be shown. Another constraint (if this qualifier is not given in combination with /MATCH) is that only chords whose prime exponent numbers do not exceed the limits set by SET EXPLIMIT and without primes larger than the limit set with SET LIMIT are shown.
/MATCH [position-or-name-pattern] [chord-size]Show occurrences of chords in the current scale. The chords searched are from the chord list in file chordnam.par, which must be present in order for this command to work. If the chord-size parameter is given, only chords of chord-size tones will be matched, otherwise chords of any size will be matched. If the parameter is negative, then it means that chords with at least that positive size will be matched.
* | : matches zero or more of any character. |
% | : matches exactly one of any character. |
/ALL_SHOW [name-pattern] [chord-size]Show all chords from the list if no parameter is given. If a name pattern is given, show all chords having a name that matches the pattern. In this case there is only one parameter, the pattern, which may contain spaces. If the name pattern contains spaces, it must be surrounded by double-quotes (") if the second parameter is also to be given.
/CENTS_SHOW [name-pattern] [chord-size]As above, but shows the intervals of the chords in cents, relative to the first note. Can not be combined with other qualifiers.
CLEAR [scalenr.]Empty the given scale. Default is 0 (current scale).
/ALL [last-scalenr.]Empty all scale memories, including the current scale, but not the highest ones used for UNDO. If a parameter is given then empty all scale memories from 0 (current scale) to the given last scale (may include UNDO scales). Warning: This cannot be undone with UNDO.
/MAPSet the keyboard mapping to the default values and the size to zero. This zero size will work as a linear mapping when sending a scale to a synthesizer. There is no parameter. See also SHOW MAPPING.
CLOSEClose the text file opened with FILE. It is not necessary to do this just before EXIT.
CLSClear the screen.
COLLAPSE [interval-class] [scalenr.]Replace the current or given scale with its set of unique intervals of the given interval-class. The default interval-class is 1, which means adjacent pitches (as shown by SHOW/INTERVAL). It may be any integer number. Then what were intervals will become pitches. This reduces an equal tempered scale to one note because it only has one unique interval size for an interval class. This command can among others be useful prior to FIT. If this command is repeated, it gives an effect similar as EUCLID does.
/ALL [scalenr.]Replace the current or given scale with its set of unique intervals of all interval-classes. This command may cause the scale to become very large. An equal tempered scale will stay the same. See also SHOW/TOTAL INTERVALS.
COMPARE [file-mask]Compare the current scale with all scales in memory and subsequently with files in the current directory that satisfy the file mask. For a match the scales must have equal size, and their successive intervals must be equal, but the key does not have to be equal. The key for which the scales match is displayed. See also KEY. Also if the successive intervals in reverse order are equal then this match is displayed. See also INVERT. Next, it is checked whether the pitches of the current scale form a subset of any scale. If so, if this is a known mode, then its name is given.
/MEMORY_ONLYCompare the current scale only with all scales in memory.
/SAVE_LISTSave the filenames shown by the command to be equal or inversely equal in any key to a scale list file with name comp.lst. Approximately equal files are not added. This list file is used when '@comp' is given instead of a filename mask. For instance to do a much quicker compare against the same files a second time, or to load them all into memory, or to invoke an operation on all of them using ITERATE. Cannot be combined with /MEMORY_ONLY.
/SUPERSETAlso indicate the cases when the current scale is a superset of the scales it is compared with.
/PITCH pitch [file-mask]Search for the given pitch in the files that satisfy the file mask. The scale degree where the pitch was found is given and the size of the scale. Can only be combined with /SAVE_LIST in which case the list file is named search.lst. Use this list file with '@search'.
CONVERGENTS factorShow the convergents (continued fraction) of a nonnegative linear factor. At the left it is shown whether the displayed fraction is higher or lower than the given number by a plus or a minus sign, or if it's equal (within the computer's floating point resolution) with an equal sign. For every convergent the total number of (semi-)convergents is then displayed, followed by the fraction. Then the continued fraction expansion is shown. If an asterisk appears, then the ratio is too large to be displayed and only the fractional part (between 0 and 1) is shown.
/CENTSShow the convergents and interpret the factor as being a cents value. A rational number will also be taken as a cents value.
/LOGARITHMICTake first the binary logarithm of the given factor and then show the convergents. It must be 1.0 or larger. For a pitch memory or scale degree it is the same as /CENTS.
COPY scalenr. scalenr.Copy the first to the second given scale. The current scale is number 0. The number of scale memories and UNDO scale copies is set in params.par. The total number of scales is the sum of these two. To undo a scale operation, UNDO or COPY can be used. Copying scales into the UNDO memories should be avoided. See also PUSH, POP and UNDO.
/PITCH pitch pitchnr.Assign a pitch to the given pitch memory. Warning: it is not copying one pitch memory to another. To do that, use a $-value with the first pitch (see help of $). The highest pitch memory is set in params.par (default 10). See also help of :=.
CPSCreate a Wilson Combination Product Set. First is asked Enter number of factors to select from:, which is the number of factors the set will be taken from. Then Enter combination count:, which is the number of factors in each product. Subsequently all the factors must be entered which can have any ratio or cents value.
/SCALE [scalenr.]Instead of entering the factors one by one, the current or given scale is used. If the current scale is used, it will be replaced with the result. Only the combination count needs to be entered. Degree 0 with 1/1 is not used, so if a factor of 1/1 is desired, there needs to be an extra one in the scale besides degree 0.
/CORNERCreate a larger Combination Product Set by also taking combinations of the generating intervals themselves. So once one interval is selected, it is put back in the set so it can be taken again (drawing with replacement). The lattice of the result scale is then in the form of a corner. It is similar to /SUPERSTELLATED, a one-sided form of it. Use the LATTICE command to see the difference. Can not be combined with /EXPANDED, /STELLATED and /SUPERSTELLATED.
/EXPANDEDCreate an expanded Combination Product Set by taking several combination counts of the generating intervals. First enter the number of factors. Then the first combination count (default 1) and the last combination count. All combination counts from the first until the last will be combined in the scale. If all counts from 1 to the number of factors is taken then it produces an Euler-Fokker genus. Cannot be combined with /CORNER, /STELLATED and /SUPERSTELLATED. See also EULERFOKKER.
/STELLATEDCreate a stellated Combination Product Set. The input values are given as with a normal CPS. A stellated CPS is a CPS where all otonal (harmonic) and utonal (subharmonic) chords are completed by adding missing tones. For example in a 2 out of 4 CPS (Hexany), there are 6 tones forming 4 otonal and 4 utonal triads. These are completed to tetrads, so 8 tones are added making a total of 14. If the Hexany is pictured as a tetrahedron, the added tones are points above the faces, giving a starlike shape, hence the name. If the number of factors is not twice the combination count, then the otonal and utonal chords are not equal in number but stellation is still possible.
/SUPERSTELLATEDCreate a superstellated Combination Product Set. This is a CPS which results from CPS/STELLATED, but where the incomplete chords formed by the extra tones of the stellation are also completed; and if that forms new incomplete chords, they are also completed, and so on. Note that this operation is how Erv Wilson defined "stellation". Perhaps confusingly, the names in this program have been chosen to distinguish and characterise the two kinds of stellation.
/FACTORCreate a Combination Product Set by giving the generating intervals as linear factors which need not have a period. This qualifier is not allowed in combination with /PRIMES and /SCALE.
/PRIMESCreate a Combination Product Set from a set of prime numbers. First is asked Enter number of factors to select from: and Enter combination count:. Subsequently the first factor must be entered which must be an integer number and then the number of primes to be skipped each time for the next prime to be taken. For instance if the first is 3 and then 2 are skipped the next prime will be 7. With 0 the same prime is used again, and with 1 the next prime is taken. Can not be combined with /SCALE and /FACTOR. <
DELETE position [scalenr.]Delete the pitch at the given position (degree) from the current or given scale. The position may not be higher than the number of notes in the scale. If degree 0 with the value 1/1 is deleted, then all pitches shift downward by the amount of degree 1. See also INSERT.
/START position [scalenr.]Delete all pitches at the given position and higher from the current or given scale. The same operation can be done with EXTEND.
/INTERVAL position [scalenr.]Delete the interval at the given position (degree) from the current or given scale. The position may not be higher than the number of notes in the scale. The pitches above the given position will then shift downward.
/EQUAL pitch [scalenr.]Delete the given pitch from the current or given scale. If there are more degrees with the same pitch, then these are all deleted.
/GREATER pitch [scalenr.]Delete all pitches from the current or given scale that are greater than the given pitch.
/SMALLER pitch [scalenr.]Delete all pitches from the current or given scale that are smaller than the given pitch.
/FLOATSDelete all floating point pitches from the current scale. There is no parameter.
/MODEL scalenr.For each pitch in the given scale, the nearest pitch from the current scale will be deleted. The formal octave will not be deleted. Instead of a scale number, a filename may also be given. See also SELECT/MODEL.
/EGALIZEThere is no parameter. Deletes one pitch from the current scale so as to make the scale more equal tempered. If the scale would not become more equal tempered by deleting one pitch, then nothing happens. All interval classes are considered in this. The sum of absolute logarithmic differences of all intervals with the equal tempered intervals is minimised. Note this is not the same as the average distance from equal tempered shown by SHOW DATA. The formal octave will not be deleted.
DIFFERENCE scalenr. [scalenr.]Remove pitches that are both in the first scale and the second scale from the second scale. If no second parameter is given, it will be the current scale. The first parameter may also be a filename. See also INTERSECT and MERGE. For the exclusive-or of two scales (i.e. obtain the pitches not contained in both) see command file xor.cmd.
DIRECTORY [file-mask] [scale-size]Present a directory of the files that satisfy the given filename pattern. If it is omitted, the file mask will be *.scl. It will show the scale size and first part of the description with the name. If no filename extension is given, '.scl' will be assumed. If the scale size parameter is also given, then files which conform to the file mask and which have this scale size are given. The scale size must be a positive number. If only a scale size is given and no file mask then all scale files with that number of notes are given.
/NAME_ONLY [file-mask]This will only display the filenames, which is quicker. Scales cannot be selected by size, only file mask.
/SAVE_LIST [file-mask] [output-filename] [scale-size]Save the filenames shown by the command to a scale list file with the given name or dir.lst, which is default. This list file is used when '@dir' is given instead of a filename mask. For instance to do a much quicker compare against these files, or to load them all into memory, or to invoke an operation on all of them using ITERATE.
DISCARD marginFind clusters of notes that are within the given range from each other, and delete all but the one with the highest absolute harmonicity value. The margin can be given in cents or as a ratio. If there are notes with equal harmonicity values which are highest, they are kept. The harmonicity value of a floating point pitch is considered to be zero, so they are always deleted if there is a rational pitch within the margin. If all notes are floating point pitches then the lowest scale degree will be kept.
/SMALLESTUse as margin the smallest interval of the scale. There is no parameter. This is equivalent to doing DISCARD %si. To see what is the smallest interval SHOW DATA can be done. Cannot be combined with /EQUAL.
/EQUAL intervalDelete from all intervals in the current scale which are equal to the given interval the pitch with the lowest absolute harmonicity value. If the harmonicity values are equal then the highest pitch will be deleted. The harmonicity value of a floating point pitch is considered to be zero. After doing this command, the notes will be in ascending order and unique. Cannot be combined with /SMALLEST.
DIVIDE interval count [lower-bound]Show divisions of the given interval in superparticular ratios where the second parameter is the number of ratios. The first parameter must be given as a ratio. Only one permutation of each division is given; the interval sizes are in descending order.
/FIND interval [octave] [maximum-difference]Show the equal tempered divisions of the given octave wherein a scale degree approximates the given interval. If the octave parameter is not given, 2/1 is the default. If no maximum difference parameter is given, then successively better approximations will be shown, multiples of earlier shown divisions will not be shown, and three dots will indicate that all intermediate temperaments successively approximate the given interval better and better until the one on the next line. If a maximum difference is given in cents or as a ratio, then all divisions will be given with a deviation less than the one given.
/ALLFIND interval [octave]As above, but show all successive equal tempered divisions.
/CONSISTENT interval [octave] [maximum-difference]As /FIND, but instead of the best direct approximation, the best consistent approximation is given. The given interval must be rational. Consistent approximation means that the constituent prime factors of the interval ratio are approximated to the nearest step in each successive division, and these step numbers are added to approximate the ratio. This usually gives a different result than the direct approximation.
DOUBLE [interval-class] [expansion]Double the number of pitches in the current scale by inserting a mean between pitches separated by the given interval-class. The default interval-class is 1, which means adjacent pitches. It may be any integer number. The default expansion factor is 2, i.e. doubling. To triple by inserting two means, do DOUBLE 1 3. Expansion may be any positive number.
/GEOMETRICUses the geometric mean, i.e. sqrt(a * b). This divides an interval equally.
/HARMONICUses the harmonic mean, i.e. 2 * a * b / (a + b). Densifying a scale by inserting harmonic or arithmetic means is also known as katapyknosis.
/ARITHMETICUses the arithmetic mean, i.e. (a + b) / 2. Densifying a scale by inserting harmonic or arithmetic means is also known as katapyknosis.
/SUBC_HARMONICUses the subcontrary to harmonic mean, i.e. (a^2 + b^2) / (a + b).
/LOGARITHMICUses the logarithmic mean, i.e. log(mean) = (b * log(a) + a * log(b)) / (a + b).
/COUNTER_LOGUses the counterlogarithmic mean, i.e. log(mean) = (a * log(a) + b * log(b)) / (a + b).
/RMS [interval-class]Uses the root mean square, i.e. sqrt((a^2 + b^2) / 2). Specifying another expansion factor is not allowed.
/MEDIANT [interval-class]Uses the mediant, i.e. (num(a) + num(b)) / (den(a) + den(b)). All pitches must be rational. Specifying another expansion factor is not allowed.
ECHO [text]Writes the given text to the screen. This is useful for displaying text in external command files. Without text, an empty line will be written. This command can also be used to display pitch values on the screen or simultaneously display them and write them to an output file. The following lexical functions exist:
EGALIZE factorMove the pitches of the current scale towards or away from the equally tempered value. If the given factor is zero, the resulting scale will be an equal-tempered scale, if it is 1.0, the scale will remain unchanged. A factor larger than 1.0 increases the unevenness of the scale. The factor linearly influences the logarithmic difference of the scale pitches and the corresponding equally tempered pitch. The formal octave remains the same. The factor may be given as a fraction or as a floating point value and may also be negative. A value of -1 will reverse the sign of the difference with the equal-tempered value. To view the effect of this command do SET ATTRIBUTE DIFF_ET.
/MODEL [scalenr.] [maximum-difference]Temper the intervals of the current scale to get as many of them as close as possible to the pitches in the given scale. All intervals which are within the distance of the given maximum difference to one of the approximants in the given scale are taken into account. The quadratic error of these intervals will be minimised. All intervals of the current scale except the formal octave are subject to approximation. To see them, use SHOW INTERVALS.
EQUALTEMP division [octave] [scale-size]Create an equal-tempered scale with the given formal octave (also called modulus or interval of equivalence) divided into the given number of steps (division). The division may be either a positive integer or floating point number. If the octave parameter is not given, 2/1 is assumed. If a scale size is given, the resulting scale will have that number of notes, otherwise it will be the same as the division, or if the division was given as a floating point number, the nearest integer above that. So to create a scale by giving a step size rather than dividing an octave, enter 1 for division, the step size for octave and the scale size as the last parameter.
/DATA division [octave] [alternative-fifth]Shows structural properties of the temperament and relations between several intervals. The best approximations to major third, perfect fifth and harmonic seventh are shown and other interval sizes derived from them. If another octave than 2/1 is entered, the given comma sizes are with respect to the nearest octave approximation.
/SHORTDATA division [octave] [alternative-fifth]As above, with the difference that possible diatonic and other subscales are not shown.
EUCLID iterationsPerforms the Euclidean algorithm on the current scale with the given number of iterations and shows the results. The second largest pitch is subtracted from the largest pitch as many times as goes in each iteration. If this is more than one time, the intermediate result is also shown, indicated by an apostrophe on the first line. Iteration stops if one of the two largest intervals have become zero. The scale must have at least 2 pitches. If the current scale has rational intervals, they are also shown as rationals. If multiple instances of the same interval occur, only one row will be displayed. A plus sign in the first column indicates a change of the smallest "defining" interval. Also the sum count of all but the smallest interval is given and the remainder being the sum size of the smallest interval. See also CONVERGENTS.
EULERFOKKERCreate an Euler-Fokker genus. This is a scale with a rectangular lattice. See also LATTICE. With this command however the factors are not restricted to being prime, or even integer or rational. The first question is Enter number of dimensions: that is for the resulting lattice to have. Then Enter factor 1 which need not be an integer but can be any pitch. Then Enter multiplicity 1: that is the number of lattice steps in the first dimension. Then it goes on for the remaining dimensions and the concluding question is Enter formal octave (return for none): for an eventual separate last degree as interval of equivalence. For example to create a genus [33355] enter: 2, 3/1, 3, 5/1, 2, 2/1 and then do NORMALIZE. See also CPS.
EXAMPLE input-file [output-file]Create a MIDI-file with a piece of music using the current scale as default scale. The MIDI-file makes use of pitch bend messages for tuning. Because pitch bend messages affect all notes on a MIDI channel, this command's algorithm chooses channels on a kind of round-robin basis. All channels will be used if necessary unless some are explicitly excluded specified in the input file. If the amount of channels (16 or less) is not sufficient, i.e. there are too many simultaneous notes, then no output file will be generated. The algorithm tries to minimise the number of pitch bend messages in the output file. The instrument to be used must be tuned to 12-tone equal temperament and be using the default standard pitch bend range of +/- 2 semitones.
/MIDI input-file output-fileUse a MIDI-file as input file. It will be translated into another MIDI-file with an extra track containing pitch bend messages, using the current scale. The same algorithm as above is employed. The instrument to be used must be tuned to 12-tone equal temperament and be using the default standard pitch bend range of +/- 2 semitones. If there are MIDI channels which should not be retuned, these channel numbers should be entered first with the command SET EXCLUDE (for a drum track for example).
EXCHANGE position positionExchange two positions in the current scale. The positions may not be higher than the number of notes in the scale. If degree 0 with the value 1/1 is exchanged, then all pitches will shift.
/INTERVALExchange the two intervals at the given positions in the current scale. The positions must be positive and not higher than the number of notes in the scale.
/EQUAL interval and-intervalReplace the given interval(s) in the current scale with the given other interval and vice versa. The scale must be non-empty. It is not necessary that both intervals occur in the scale. If only one occurs, it works the same as REPLACE/EQUAL.
EXITLeave the program. Under Unix or Linux it can also be left by pressing Ctrl/D when prompted for input.
EXPONENTIATE power [base]Change all pitches of the current scale by the given power. The default base is 2. The base-logarithmic values of the pitches are raised to the given power. Both power and base may be a fraction or a floating point value. If the base is 2, octaves will remain the same, because 2/1 has a logarithmic value of 1. If the power is greater than 1, pitches greater than the base will become higher and pitches below lower and conversely. The base must be larger than 1/1. See also MULTIPLY and STRETCH.
EXTEND size [scalenr.]Change the number of notes in the current or given scale to the given size. If the size is smaller than the current size, the degrees above the size are removed. If the size is greater, extra notes are added with respect to the formal octave (equivalence interval) of the scale. If the scale is equal tempered, it will remain so with the same step size.
/CHORD interval add-intervalChecks in the current scale on each degree if the first given interval exists on that degree and then adds the second given interval there if the second interval is absent. The command does only one run, so if the added pitch(es) create new instances of the first given interval, then those will not be considered. This command therefore completes partial triads. The intervals must match within 0.5 cent. Comparisons are made up and down to twice the number of notes in the scale.
/CHILDRENThere is no parameter. Adds the Farey child fractions of all rational pitches in the current scale to the current scale. To get the child fractions of the next level, repeat this command.
/PARENTSThere is no parameter. Adds the Farey parent fractions of all rational pitches in the current scale to the current scale. To get the parent fractions of the next level, repeat this command. To get all parent fractions, repeat this command until no more pitches are added. Note that it is possible to create a scale by starting with a scale of size one with 1/1 at degree 1. Afterwards NORMALIZE can be used.
FAREY orderReplace each pitch in the current scale with the closest fraction to the pitch with denominator smaller than or equal to the given order. A Farey order is the maximum denominator. This is a rational approximation that is different from the method used with APPROXIMATE. See also ASSUME and FIT/HARMONIC. Warning: if the order is high then this takes a lot of computing time.
/BEATSReplace each pitch in the current scale with the fraction which gives the lowest beat frequency with the scale pitch, where the denominator is smaller than or equal to the given order. Note that giving a high order is meaningless since the beating partials could be so high that they are inaudible. See also RATIO/FAREY.
/FLOATS_ONLYReplace only the floating point pitches (those shown in cents) in the current scale.
/MINIMAXReplace each pitch in the current scale with a fraction approximating the pitch with denominator smaller than or equal to the given order, where all pitches have the same denominator. The denominator giving the smallest maximum logarithmic difference for all intervals (between each pair of pitches) will be chosen. Cannot be combined with other qualifiers. See also FIT/HARMONIC.
FILE filenameCreates a text file with the given name. Then subsequent program output will be written to the file as well as to the screen. To end this use command CLOSE.
FIT [scalenr.]Show the best least-squares fittings of an equal tempered scale to the given scale with decreasing step sizes, so that each pitch in the scale is approximately an integer multiple of this step, not all necessarily different. All scale pitches must be greater than 1/1. If the scale is not in non-descending order, it will be sorted first. You can give a pitch more weight by including it more than once in the given scale. Approximations are shown with step sizes down to about one twelfth of the smallest interval in the scale. Only successively better approximations are shown. The linear least-squares approximation which is given first is the value for which degree one is one step, degree two, two steps, etc. This value does not necessarily occur in the list that follows. Subdivisions of the given approximations are not given since their standard deviation is not better but equal. See also CALCULATE/LEASTSQUARE.
/MINIMAXIn addition to the best least-squares fittings explained above, also give the best minimax fittings, i.e. for which the maximum deviation among the steps is minimal. The linear minimax approximation which is given first is the value for which degree one is one step, degree two, two steps, etc. FIT/MINIMAX works slower then FIT only. See also CALCULATE/MINIMAX.
/MODE [division] [scalenr.]Show the best least-squares fittings of modes of increasingly larger equal tempered scales compared to the current scale, where the octaves are the same. Displayed are:
/HARMONIC [first-harmonic] [scalenr.]Show the best least-squares fittings of harmonic scales with increasingly higher first harmonic. If the number of notes in the scale is fifteen or less then the matched harmonics are shown, otherwise only the first and last harmonic and the amount of harmonics matched. An unmatched pitch is indicated with an 'x'. A harmonic will only match one pitch of the scale; the one that is closest to it. If all consecutive intervals of the harmonic scale are superparticular then this is indicated by the letter S. The standard deviation is also shown in cents.
FLIP first-prime second-primeExchange for all rational pitches in the current scale the exponents of the two given prime factors. This will cause the lattice to be mirrored in the main diagonal between the two prime axes. For example if the primes are 5 and 7, and there's a pitch 28/25 (2.2.7/5.5) it will become 20/49 (2.2.5/7.7).
HARMONIC first-harmonic last-harmonic [step]Create a harmonic scale with all harmonic numbers between and including the given ones. To create a subharmonic scale, do INVERT afterwards or reverse the parameters. Degree 0 will represent the first harmonic. If parameter step is given then harmonics are skipped by that amount if it is higher than 1. This value may also be noninteger (>= 1.0), in which case the harmonics will obey this formula : first-harmonic + floor(n * step), n >= 0.
HELP [subject]Give information on the subject. If no subject is given, all help topics will be displayed. Subjects may be abbreviated, like commands and qualifiers. Square brackets indicate an optional parameter. Often the number and meaning of parameters depend on the command qualifier (see help items Commands and Qualifiers). This is the case if in the help texts there are parameters on the same line after the qualifier. If not, then the parameters are the same as for the command without a qualifier, unless explicitly stated that there are no parameters.
IMPORT filenameThe default qualifier is /JICALC. See also LOAD/UNFORMATTED and LOAD/CENTS which can read text files with linear factors and cents values respectively. SAVE/CENTS does the opposite.
/JICALCConverts a JI Calc text file to a set of Scala scale files. For each scale in the file, the description will be displayed and the number of notes. Then a filename will be prompted for to store the scale in. If a file with the same name already exists, then it will be asked if it is to be replaced or another name is wanted. The description of the scale can be changed. To do so, enter an empty filename. Then a new description can be entered, and then the filename again. To skip one scale, enter an empty description and then again an empty filename. To stop converting the input file, press Control-C and the return key.
INPUT [scalenr.]Input a scale by hand. The pitches may be given as a rational or in cents. Those to be given in cents must contain a decimal point. Degree 0 (1/1) is not entered. If this is to be other than 1, use MOVE with the inverse amount afterwards. The default scale is 0 (current scale). See also LOAD.
/FACTORInput a scale by giving relative, linear factors. They can be the frequencies of the notes or factors proportional to them. The numbers do not have to have a decimal point. Degree 0 is also to be entered whereto all subsequent factors are relative.
/INTERVALInput a scale by giving the intervals relative to the previous degree. Can be combined with /FACTOR.
/LINEInput a scale by giving all pitches on one line at once. The number of notes does not have to be entered separately. Pitches are separated by spaces. But they can be separated by colons as well. In that case the values with decimal points are read as linear factors instead of cents values, for example: 4:5:6:7:8. Can be combined with /INTERVAL but not with /FACTOR.
INSERT position pitchInsert a new pitch in the current scale at the given position. All pitches at a higher position shift up and the size of the scale increases by one. The position must be a number not higher than the number of notes in the scale plus one. If insertion is done at degree 0, the given pitch must be lower than 1/1 in order for the scale to remain monotonic. See also DELETE.
/INTERVAL position intervalSplit the interval in the current scale between the given and next position by inserting another interval. The position must be not higher than the number of notes in the scale.
/FREQUENCY position frequencyInsert a new pitch by specifying the frequency relative to the base frequency (see SET FREQUENCY and SHOW/FREQUENCY).
/NEAREST pitchInsert a new pitch in the current scale after the highest pitch smaller than the given pitch.
/LARGEST intervalSplit the largest interval(s) in the current scale by inserting the given interval. The scale may not be empty.
INTERSECT scalenr. [scalenr.]Remove pitches that are not in the first scale from the second scale. The current scale is default for the second parameter. The first parameter may also be a filename. See also MERGE and DIFFERENCE.
INVERT [position] [position]Reverse the order of the intervals in the current scale. If one position is given, reverse the order of the intervals between degree 0 and the given position. If two positions are given, reverse the intervals between the two given scale degrees. To view the effect of this command do SHOW/INTERVAL, or SET ATTRIBUTE INTERVAL and then SHOW. Warning: the last pitch is assumed to be the formal octave so it does not change with this operation. If the current scale does not have a formal octave (yet) -which may be the case if a CPS scale has been created- then it must first be added with APPEND or NORMALIZE.
/INTERVAL positionExchange intervals pairwise in the current scale. The interval at the given position remains the same. The interval at position-1 is exchanged with the interval at position+1, the one at position-2 with position+2, etc. Positions are modulo the scale size. If the scale is inversionally symmetric in the given interval position, then it remains the same, see also SHOW DATA. To view the effect of this command do SHOW/INTERVAL, or SET ATTRIBUTE INTERVAL and then SHOW.
ITERATE command [file-mask] [scalenr.]Will load successively scale files with filenames that match the given file mask to a scale memory and execute the given command for each of them. So it visits each scale in a set defined by the file mask and does an operation on it. For each loaded file, the filename and description is shown. The default scale memory where each file is loaded into is number 0 (current scale). Any previous scale in the given scale memory will be lost. Files that are not scale files are silently ignored. If the command contains more than one word, it must be surrounded by double- quotes ("). Example: ITERATE "SHOW DATA" mean*.scl The command can be an external command, see help for @. ITERATE commands can be nested, but then double-quotes must be used. Another example: to compare the current scale against a set of scale files do: ITERATE "SHOW DIFFERENCE 1" *.scl 1.
/COMBINATION command [scalenr.]Will apply the given command to all different combinations of pitches of the current or given scale. The pitch count of the combination is asked for separately. Of course it may not exceed the size of the scale. The combinations will be consecutively put in the current scale, which will lose its previous contents, and then the command applied. The "parent" scale, if it is another one than number 0, will not be affected. Afterwards, the last combination will remain in the current scale. For quoting the command, see above.
/KEY command [scalenr.]Will apply the given command to all different keys of the current or given scale. The original key will be restored afterwards. For quoting the command, see above.
/MEMORY command [first-scalenr.]Will copy each nonempty scale memory with the given scale number and higher to scale number 0 (current scale) and execute the given command for each of them. The default scale number is 1. The highest scale memories which are used for UNDO will not be visited.
/MODE command [scalenr.]Like /COMBINATION with the difference that the last pitch (formal octave) is always present. It is included in the pitch count of the combination which is asked for.
/REPEAT command countWill execute the given command a number of times. The second parameter is the number of times. If it is "n" then it equals the number of notes.
/SCALE command [scalenr.]Will traverse the current or given scale and execute the given command for each degree in it. The degree will be copied to pitch memory 1, so that the command can reference it with $1. The original contents of pitch memory 1 will be lost. Instead of a scale number, a filename may also be given.
KEY [steps]Change the key (tonic) of the current scale to the given degree. This cycles the intervals downwards by the given number of positions. The value given will be taken modulo the scale size. Any integer value is allowed, also a negative one. The default value is 1. To transpose a scale by changing all frequencies without changing the interval pattern, use SET FREQUENCY. Warning: the last pitch is assumed to be the formal octave so it does not change with this operation. If the current scale does not have a formal octave (yet) -which may be the case if a CPS scale has been created- then it must first be added with APPEND or NORMALIZE. Alternatively without adding a formal octave, the command MOVE/KEY can be used to change the key of an octaveless scale.
/ALLCopy all keys of the current scale to scale memories 1 and further. The current scale itself remains the same. There is no parameter. Warning: all scale memories from 1 until the scale size minus one will be overwritten.
/EGALIZEChange the key of the current scale so that is it as close as possible to an equal tempered scale. The sum of absolute differences between the pitches and a corresponding equal tempered pitch is minimised. A parameter may not be given. For rational scales, this operation tends to move the tonic towards the centre of the lattice, depending on the actual primes.
/MATCH scalenr.Change the key of the current scale to make it match that of the given scale as closely as possible. Both scales must have the same number of notes. The sum of absolute differences between the degrees of the two scales is minimised. Instead of a scale number, a filename may also be given.
LATTICE horizontal-factor vertical-factor [depth-prime]Show the lattice (Carthesian model) of a rational scale. All rational pitches in the scale must be a combination of the two given factors for the primes they contain. The optional third parameter must be a prime not being in one of the other two factors. It controls the third dimension which is layed out horizontally, unless the diagram would become too wide in which case the planes are above one another. If there are non-rational pitches (i.e. floating point pitches) in the scale, then the message Not all pitches mapped will be given. If the error message No such lattice is given then it means that neither factors given are present in the scale, or that no one- or two-dimensional lattice can be created for the scale with the given factors. So one or more two-dimensional projections will be shown and the ignored primes will be listed. If only a one-dimensional projection is wanted, then a factor of 1/1 can be given. The total number of different primes in the scale must not be more than 12.
/DIAMONDThere are no parameters. It shows for the current scale a diagram like a Partch diamond. Horizontally the odd numerators are shown and vertically the odd denominators. Octave relations do not play a role. The positions indicating 1/1 are marked with a '0', a pitch with a '*' and with a '.' the positions that have a common factor in numerator and denominator and which are present in the scale. Numbers above 75 are not shown. A Partch diamond is usually drawn turned 45 degrees clockwise.
/LOAD horizontal-factor vertical-factor filenameCreate a scale using a lattice that is drawn in a text file. The format of the lattice is the same as shown by LATTICE, but can have only two dimensions. This means a lattice picture can be saved using the commands FILE and CLOSE and then be changed with a text editor, or created with a text editor. Each line counts for one vertical factor and two horizontal positions for one horizontal factor. The *'s must be separated by one space on a line. A zero character must indicate the origin (1/1). An empty last line is recommended. With this qualifier it is easy to create a multilinear temperament for instance like:
* * * * * * * * 0 * * *The factors can be rational or floating point pitches. Afterwards the scale can be reduced by an octave, sorted and have an octave appended with NORMALIZE. Cannot be combined with other qualifiers.
/NOTATION horizontal-factor vertical-factor [depth-prime]Instead of the asterisks, show the note names of the pitches. The shortest name is taken for the current notation system (if there are enharmonic equivalents). If the equivalents have the same length, then names which are closer to C in the cycle of fifths have priority, so Eb comes before D# for example. The current notation system is set with the command SET NOTATION. Any notation system may be chosen, but because the scale has to be rational for the LATTICE command, a useful one is JI.
/TRIANGULAR horizontal-factor vertical-factor [depth-prime]As without qualifiers, but show the lattice (Carthesian model) in a slanted way. The vertical factor will be shifted to the right going upwards. So if the horizontal factor is 3 and the vertical factor 5, then major triads are shown as triangles like this:
* 0 *And minor triads are down pointing triangles. If there is not enough space with three factors for a horizontal arrangement of the layers, then try without this qualifier. Cannot be combined with other qualifiers.
LIMIT [number]Change rational pitches into floating point pitches that have a prime limit higher than the prime number given. If the number is 1 then all rational pitches in the current scale will be made floating point numbers. If the given number is not prime, the first lower prime is taken. If no parameter is given, the value set with SET LIMIT is taken. To actually change pitches to those of a lower limit, use APPROXIMATE. See also PROJECT.
/DELETERemove the pitches from the current scale that have a limit higher than the number given.
/ODDChange rational pitches into floating point pitches that have an odd number limit higher than the number given. If the given number is not odd, the number one less is taken. Can only be combined with /DELETE.
/MAX_ATTRIBDelete pitches from the current scale which have an attribute value higher than the given number. The attribute is set with SET ATTRIBUTE. From attribute values which can also be negative, the absolute value will be taken for the comparison. Only attributes which give a numerical value are allowed, so attributes like FRACTION or VECTOR are not allowed and give the message "Invalid argument for operation". INTERVAL and OTHER_SCALE are also not allowed.
/MIN_ATTRIBLike above, but pitches with an attribute value lower than the given number will be deleted.
LOAD filename [scalenr.]Read a scale from a scale file on disk and store it to the given scale number. The default scale is 0 (current scale). If the given filename has no extension, the extension '.scl' will be assumed. If a wildcard is given in the filename then the first scale that matches the name will be loaded. This works only for scale files. See also IMPORT.
/ALL filename [first-scalenr.]Interpret the given filename as a file mask and load all the scales that match into available scale memories. If a scale number is given this scale will be the first where a scale is stored, next scales go in subsequent higher memories. A list file can also be used, for example if the list filename is dir.lst then do LOAD/ALL @dir .
/UNFORMATTED filename [first-scalenr.]Reads a text file with all pitches for a scale on one line. The values are considered to be linear factors. The first number will represent degree 0 and the other factors are relative to that. The number of notes will therefore be one less than the number of factors. If the text file has more than one line then next scales go in subsequent higher memories.
/CENTS filename [scalenr.]Reads a text file with pitches in cents on separate lines. The first number will represent degree 1. Lines with no readable number will be skipped. All text on a line will be ignored, except the first readable number. This can be used to write command files for converting tuning files from other programs. See also IMPORT.
/CHORD name-patternCopy the first chord that matches the given name pattern to the first non-empty scale memory. To explore the available chords, use the command SHOW MAPPING and CLEAR/MAP. This is an example mapping:
! Template for a keyboard mapping ! ! Size of map (greater than or equal to the number of notes in the scale ! to be mapped). The pattern repeats every so many keys: 12 ! First MIDI note number to retune: 0 ! Last MIDI note number to retune: 127 ! Middle note where scale degree 0 is mapped to: 60 ! Reference note for which frequency is given: 69 ! Frequency to tune the above note to (floating point e.g. 440.0): 440.0 ! Scale degree to consider as formal octave (determines difference in pitch ! between adjacent mapping patterns): 12 ! Mapping. ! The numbers represent scale degrees mapped to keys. The first degree is for ! the given middle note, the next for subsequent higher keys. ! For an unmapped key, put in an "x". At the end, unmapped keys may be left out. 0 1 2 3 4 5 6 7 8 9 10 11
/PITCH filename [first-pitchnr.]Read one or more pitch values from a text file on disk and store them to the given pitch memory and beyond. The default pitch memory is 0. Pitch memories are used to store single pitch values and hold intermediate results of pitch calculations, not in the context of a scale.
MERGE scalenr. [scalenr.]Merge the first scale into the second scale. All duplicate pitches will be removed. In set-terms: take the union of the first and second scale. The resulting scale (given by the second parameter) will be in ascending order. With no second parameter, it is the current scale. The first parameter may also be a filename. See also DIFFERENCE and INTERSECT.
MODE name-pattern-or-modeSelects a mode from the current scale. If the parameter is a name pattern, the mode is searched from the mode list in file modenam.par, which must then be present in order for the command to work. The first occurrence of a match with the given name pattern is taken, unless the number of notes doesn't match with the scale size in which case the search continues. The following special characters are recognised:
* | : matches zero or more of any character. |
% | : matches exactly one of any character. |
This is a link to the list of presupplied modes.
/COMPLEMENTAs above but selects the complementary mode from the current scale.
/CREATECreate a scale with the given mode. The pattern is matched as above. For each number of steps that is in the given mode, a corresponding interval must be given, as a ratio or in cents. If the scale doesn't come out with the right octave, then do MULTIPLY/ABSOLUTE afterwards to stretch or shrink it.
/EQUALCreate an octave-based subset of an equal temperament with the given mode. The division of the equal temperament is equal to the sum of the interval steps in the mode. You can do FIT/MODE afterwards to check which equal division the resulting scale is a subset of. Also both a name and a mode pattern in numbers may be given.
/FACTORCreate a scale with the given mode. For each number of steps that is in the given mode, a corresponding factor must be given. These factors are relative and may be given as a ratio or floating point value. To obtain the same mode equal tempered, the same number as the number of steps can be given. Then the octave is asked for. You can do FIT/MODE afterwards to check which equal temperament the resulting scale is a subset of.
/SHOWShow the given mode. Only the first occurrence of a match is shown. To show all modes that match the pattern, use /ALL_SHOW instead. Note that a mode or a name-pattern may be given. If a mode is given for which there is no name, then only the same mode is displayed. The current scale remains unaffected. See also FIT/MODE.
/ALL_SHOW [name-pattern-or-number] [number-of-notes]Show all modes from the file if no parameter is given. If a name pattern is given, show all modes having a name that matches the pattern. In this case there is only one parameter, the pattern, which may contain spaces. If a number is given, show all modes with the sum of their step count equal to that number, for example to show all 19 tone modes do MODE/ALL 19. This can be restricted further to only give modes with a given number of notes. To show all modes with a certain number of notes, make the first parameter 0, for example to show all modes with 10 notes do MODE/ALL 0 10.
MODULATEMake a scale containing the frequencies of the spectrum of (a) modulated sine wave(s). In general, the spectra resulting from amplitude or frequency modulation are inharmonic.
/GENERATOR position [steps]Make a different distribution of the scale intervals by doing an exchange of two intervals in the cycle of a given generating interval. One of them is the interval that has the most extreme size and which is unique in the cycle. This may either be the smallest or the largest, whichever one is unique or has the highest difference from the average interval of the cycle. If there is no such interval then you will be notified. To see if there is one beforehand, use SHOW INTERVALS.
/INTERVALThis changes intervals of the current scale according to the sine function. Values of the sine function are added in cents to the intervals. The parameters are given interactively. The order in which degrees are mapped to the angle parameter is determined by the generator. This must be a positive number which has no common factors with the size of the scale. For example if the size is 12 and the generator 7 then the order of the degrees is that from the circle of fifths. The next parameter is the count downwards for the generator. It has the same function as with the command PYTHAGOREAN. Default value is 0. Then the interval class must be given. This determines which interval's size will be modulated. The default value is the same as the generator. Another value may be given, but it may also not have a factor in common with the scale size. Then the amplitude is asked, it may be a ratio or a cents value. Subsequently the relative frequency must be given. This is the angular frequency for the sine function. If the default value one is given, then there is one revolution for the number of notes in the scale. Two will give two revolutions, but any positive ratio or fraction may be given. If it is an integer number then the earlier given count downwards doesn't matter. Then the phase offset must be given. This will be the phase for the interval on degree 0. It must be given in degrees. So if 90.0 is given, then the maximum value is added to the interval at degree 0, or if -90.0 is given then the maximum value will be subtracted from that interval.
MORPH scalenr. factorMove the vector orientation of the current scale towards or away from another scale. If the factor parameter is zero, the scale will remain unchanged. A factor of 1.0 will make it equal to the given scale. Any other factor will replace each pitch with a weighted average of the current value and the value in the same degree of the given scale. The scales don't have to have the same size; octave extension is assumed.
/ABSOLUTE scalenr. position pitchInstead of giving a factor, enter a desired pitch for a given position in the current scale. The operation will be the same and the factor will be implicitly calculated from the difference of pitches at the given position in the two scales. These two pitches may not be the same, otherwise the factor would be infinite. The given position may lie outside the scale's range since octave extension is assumed. It may not be degree zero.
MOSGenerates a Moment Of Symmetry from the current scale. The program asks first the generating interval, which must be a scale degree number and have no common factor with the scale size. Then the series index is asked which must be a natural number and indicates which scale in the MOS series is desired. You can do MOS/SHOW or MOS/ALL_SHOW first to see the modes, and decide which index of the series you want. Note that this command deletes pitches from the current scale. See also MODE. MOS and Myhill's property are equivalent. Another way to create a scale with this property is using PYTHAGOREAN. See also FIT/MODE.
/CREATECreate a Moment Of Symmetry scale by giving two intervals. The program asks first the scale size and then the generator, which must be a scale degree number and have no common factor with the scale size. Then the first interval is asked which will be the first pitch in the scale and subsequently the second generating interval. Afterwards you can stretch or shrink the scale to give it another formal octave with the command MULTIPLY/ABSOLUTE. See also MODE/CREATE.
/SHOW parent-size generatorShow successive members of a MOS series. The first parameter is the number of notes the MOS is taken from and the second the generating scale degree. The numbers shown are interval sizes in number of steps. The number of notes of the resulting scale is shown between parentheses. The current scale is not affected.
/ALL_SHOW parent-size [number-of-notes]As above but show MOS series for all possible generators. If the second parameter is given, only show the MOS with the given number of tones, for all possible generators. The current scale is not affected.
MOVE interval [first-degree]Increase the pitches of the current scale with the given interval. The default first degree is 1 (all pitches). If another first degree is specified, only that and subsequent degrees will be altered. It must be greater than or equal to 0. If it is 0, then a new 1/1 note will be inserted. The second parameter can also be combined with /ABSOLUTE, but not with other qualifiers.
/ABSOLUTE pitch [first-degree]Increase the pitches of the current scale such that the formal octave will become the given pitch value. If another first degree is specified, only that and subsequent degrees will be altered.
/KEY degreeDecrease all pitches of the current scale with the pitch of the given degree. The resulting 1/1 of that and possibly other degrees will be removed from the scale. The degree parameter may be any integer value. Cannot be combined with other qualifiers.
/LENGTH partIncrease all reciprocal pitches (cf. string lengths) with the given part, including degree 0. The part may be a rational or floating point number and be positive and negative but not less than -1.0. It is considered relative to the 1/1 of degree 0. The effect of this operation is that of moving the bridge on a string instrument. Can be combined with /ABSOLUTE.
/FREQUENCY partIncrease all frequencies with the given part including degree 0. This is done by addition. The part may be a rational or floating point number and be positive and negative but not less than -1.0. It is considered relative to the 1/1 of degree 0. The effect is that intervals become smaller when their frequencies are increased with the same value. Can be combined with /ABSOLUTE.
MULTIPLY factorChange all pitches of the current scale logarithmically by the given factor. The values in cents are multiplied with the factor which may be given as a fraction, a floating point value, or a pitch memory. For example if the scale in cents is 0-100-300-500, then a multiply with 11/10 makes it 0-110-330-550. Rational values will therefore turn into floating point values if the factor is non-integer. See also EXPONENTIATE and STRETCH.
/ABSOLUTE pitchChange all pitches of the current scale by a factor that is such that the formal octave will become the given pitch value. The parameter must have the same sign as the formal octave of the current scale, i.e. both larger or both smaller than 1/1.
/MATCH scalenr.Change all pitches of the current scale by a factor that is such that the least-squares difference with the nearest pitches in another scale is minimal. The given scale may have a different size than the current scale. Instead of a scale number, a filename may also be given. See also PROJECT/MATCH.
NORMALIZE [octave] [scalenr.]Reduce all pitches of the current or given scale with the given octave, sort and take unique values, and append the octave if it's absent. This command is a shortcut for the combination of commands that do the above operations. The default is 2/1. It is useful for doing after CPS, HARMONIC, LATTICE/LOAD, PIPEDUM, etc. See also REDUCE.
PAUSE [duration]When no duration is given, prompts for the return key to be pressed. Otherwise, waits the given number of seconds. This is useful for in external command files.
PERMUTE [count]Take the next permutation of the scale intervals for count equals 1 which is default. For -1 the previous permutation is taken, larger values give further permutations. The permutation order is the lexicographic one. If the count is too high or low, the message "no more permutations" will be given and the scale be left unchanged.
/EGALIZETake a permutation of the scale intervals such that the scale has the minimum deviation from equal tempered with the first pitch unchanged. There is no parameter. By doing repeatedly KEY and PERMUTE/EGALIZE one may find a permutation with a slightly less deviation.
/GENERATOR position [count]Take a permutation of the scale intervals by doing a rotation of a cycle of a given generating interval. The first parameter is the interval class of the generator. It must be a positive scale degree that has no common factor with the scale size. The second parameter is the cycle count for the rotation, which may be any integer number, and is taken modulo the scale size. The default value is 1.
/MATCH scalenr.Take a permutation of the scale intervals in such a way that the least-squares difference with the nearest pitches in another scale is minimal. The given scale may have a different size than the current scale. For scales with many different interval sizes it may take a lot of computing time. Instead of a scale number, a filename may also be given. See also BISTEP/PERMUTATION.
/RANDOMTake a random permutation of the scale intervals. There is no parameter. Each permutation has the same probability. See also SEED.
PIPEDUM [scalenr.]Create a scale with the lattice in the form of the inside of a parallelepiped (Fokker periodicity block). A number of rational defining intervals must be given, whose prime components represent the homophonic vectors that span up the parallelepiped. The number of different primes in the defining intervals must be equal to the given number of intervals, or one prime more that can be ignored (default is 2/1, to have octave equivalence. If this is the case, one would do NORMALIZE 2/1 afterwards). Defining intervals are the intervals considered to vanish in the scale, usually commas or other small intervals. For instance when the syntonic comma (81/80 = 3^4.5^-1) is given, the homophonic vector is (4, -1) with octave equivalence, namely four fifths up and a major third down.
| | 7 | 6 | | |
| | -4 | -2 | | |
/SCALE [scalenr.]Does not ask for the defining intervals, but gets them from the current or given scale. Prime number 2 will be ignored. The resulting scale will be put in the current scale. Can be combined with /TETRA and /VERTICES.
/TETRADoes not get a whole parallelepiped but instead only the notes that represent the lattice points inside the tetrahedron (or triangle, etc.) with the origin 1/1 as a vertex. Cannot be combined with /VERTICES.
/VERTICESAlso include the other parallelepiped's vertices in the scale, besides 1/1. This gives a choice of equivalent pitches for degree 0. Cannot be combined with /TETRA.
POLYNOMIAL [scalenr.]Create a scale where the pitches are defined by a polynomial of some order. First the size of the scale is asked. Then the order (highest power in a term) of the polynomial is asked, followed by the coefficients of the terms from high to low order. The coefficients may be entered as a fraction or floating point value. A term in the polynomial is the coefficient times the scale degree to some power. Coefficient number 0 is the constant term. For instance a harmonic scale will result if one takes order 1 and coefficient number 1 equal to 1.0. After the coefficients, an operand offset can be given. The default value is 0 which means that the operand for degree 1 is 1, etc. An offset of 5 for example will cause the operand for degree 1 to be 6. If the created scale contains pitches below 1/1, they can be deleted with DELETE/SMALLER.
/LOGARITHMICSame as the above except that the polynomial is not evaluated as being linear, but logarithmical with base 2. For instance an equal tempered scale will result if one takes order 1 and coefficient number 0 equal to 0. For 12-tET, coefficient 1 equals 1/12.
/POWEREnables entry of all the powers in the terms. Strictly speaking the expression is not a polynomial anymore, because in a polynomial the powers are non-negative integers. The powers may be entered as a fraction or floating point value. Coefficient number 0 is a constant term. Use this qualifier if negative exponents are present. Can be combined with /LOGARITHMIC and /SOLVE.
/SOLVEDoes not create a scale but tries to find a nonnegative real root of the polynomial. If one is found, it is stored in pitch memory 0. A second solution will be tried. If found, it is stored in pitch memory 1. Solving a polynomial equation is sometimes required for calculating the fifth of a meantone scale with certain properties (regarding beat rates or otherwise). For other cases, see CALCULATE/LEASTSQUARE. Can be combined with /LOGARITHMIC and with /POWER but not with both. Solving with /POWER is sometimes needed for calculating non-octave equal temperaments with certain beat rate properties.
POPCopy scale number 1 to 0, 2 to 1, etc. The current scale will be lost. The highest scale memory is set in params.par (default 10). See also COPY.
/PITCHCopy pitch number 1 to 0, 2 to 1, etc. The current pitch will be lost. The highest pitch memory is set in params.par (default 10). See also COPY/PITCH.
PRODUCT [scalenr.]Calculate the 'Carthesian product' of the current scale and the given scale by multiplying each pitch of the current scale with all other pitches from the given scale. This is also called a cross-product set. The result will be sorted and identical pitches removed. If no scale is given, the current scale is multiplied with itself. To do division of each pitch instead of multiplication, do INVERT and REVERSE first on the other scale.
/ADDInstead of multiplying the pitches, take the summation tones.
/MEDIANTInstead of multiplying the pitches, take their mediant value, i.e. (num(a) + num(b)) / (den(a) + den(b)). All pitches must be rational.
/POWERInstead of multiplying the pitches, take the pitches of the current scale to the power of all pitches of the given scale.
PROJECT factor new-value [factor new-value ...]All instances of the given factor in the rational pitches of the current scale will be replaced by the new value. How much a pitch changes depends on how many multiples it has of the factor. If after division by the given factor still factors with the primes involved remain, then nothing happens, because replacement cannot be done unambiguously.
/MATCH prime scalenr.All instances of the given prime factor in the rational pitches of the current scale will be replaced by a new value which minimizes the least squares difference with the nearest pitches in the given scale. Pitches without the given prime factor and floating point pitches will not be affected. Any prime may be used, 2 included. This can be used to change rational scales into well temperaments. Instead of a scale number, a filename may also be given. See also CALCULATE/LEASTSQUARE and MULTIPLY/MATCH.
PUSHCopy scale number 0 to 1, 1 to 2, etc. The scale with the highest number will be lost. The current scale will be unchanged. See also COPY.
/PITCHCopy pitch number 0 to 1, 1 to 2, etc. The pitch with the highest number will be lost. The current pitch will be unchanged. See also COPY/PITCH.
PYTHAGOREAN [scalenr.]Create a Pythagorean scale in the current or given scale. The program asks first the scale size and then the formal octave. Next the position of the formal fifth in the scale must be given. If instead 0 is entered, the order of pitches is determined by their size (monotonically ascending). This is also default when just the return key is pressed. Otherwise the range is indicated where the formal fifth must be in, for the resulting scale to be monotonic. Then the formal fifth is entered. The default value for this is pitch memory 0. Subsequently the count downwards, i.e. the number of fifths that are stacked in the downward direction is entered which is by default 0. This gives a scale in another key. Defining it here can prevent pitches from becoming a floating point value if ratios overflow.
/GIVENBEATSLike above, but the actual fifths are varied so that they exhibit a constant beat rate, except for the "wolf" fifth at the end of the cycle. The formal fifth must be a rational value. The beat rate to be entered is given in Hertz and relative to the base frequency set with SET FREQUENCY. If it is positive, then the actual fifths will be larger than the formal fifth; for a negative beat frequency they will be smaller. See also SHOW BEATS.
/EQUALBEATSLike above, but there is no "wolf" fifth that is different. Instead, the beat rate is calculated to be equal for all fifths. The formal fifth to be approximated must be a rational value. The number of notes must not be less than two. If the fifth is not a proper generator for a full cycle of the given number of notes then the resulting scale may not be correct (for example 5/4 and 12). This doesn't mean that an equal beating scale cannot be generated, but that it must be assembled from more than one cycle, or that the number of tones and the octave must be chosen differently. The algorithm may also fail if the average formal fifth is too remote from the just value, in which case wrapping around the octave occurs at wrong places.
/VARIEDCreate a Pythagorean scale with regularly varied fifths. It works like above except that an initial fifth size is asked and then an accumulating variation which is added to each subsequent fifth. For instance suppose the initial value is 698.0 cents and the variation 1.0 cent, then the fifths will be 698, 699, 700, 701, etc. cents. For the fifths in the downward direction the variation is in the opposite direction, so the variation is not monotonic over the cycle of fifths.
QUANTIZE resolutionReplace all pitches in the current scale with a near multiple of a small interval which is 1200 cents divided by the given logarithmic resolution. The resolution may be given as a fraction or floating point value. To round off all pitches to the nearest whole cents value one does QUANTIZE 1200. To make the scale a subset of the 31-tone equal division of the octave for instance one does QUANTIZE 31.
/PITCH stepProvide the step size as a ratio or in cents instead of as an octave division. For instance to quantise in schismas one does QUANTIZE/PITCH $s. This qualifier can be combined with all qualifiers below, except /LINEAR.
/ROUNDThis is the default quantisation method. The nearest interval step is chosen.
/TRUNCATEThe interval step that is lower than or equal to the pitch is chosen.
/BESTThe formal octave of the current scale must be a multiple of the step size that belongs to the resolution. It finds the least-squares optimal quantisation. It uses the same algorithm as FIT/MODE.
/CONSISTENTFor floating point pitches the nearest interval step is chosen. For rational pitches the step will be the sum of the rounded approximations to the constituent primes. If for one of the scale pitches this is not the same step as the nearest rounded step, then a message is given that the quantisation is not consistent, but it is made anyway. See also DIVIDE/CONSISTENT.
/LINEAR stepReplace all pitches in the current scale with a near multiple of a small interval which is the given linear step. The default quantisation method is rounding: the nearest step is chosen. For truncation, combine this qualifier with /TRUNCATE. It may not be combined with other qualifiers than /ROUND and /TRUNCATE. The parameter may be a ratio or floating point value. It must be positive. When step is of the form 1/n, then n will be a common denominator of the resulting scale. So a common fundamental is set. To set a common guide tone instead, do INVERT prior to and after QUANTIZE/LINEAR. Quantisation to zero will not take place. See also FIT/HARMONIC.
RATIO pitch [highest-prime]Approximate the given pitch with the closest fraction for successive prime limits and show the results. The first fraction is the best 3-limit approximation, the next the best 5-limit, and so on. With the /CONTRAINED qualifier one can limit the search to a certain range for the prime exponents. If the prime parameter is not a prime number, then the next higher prime will be the limit. The prime count is set up in params.par. The last approximation is stored in pitch memory 0 and an intermediate one if the command is interrupted. See also APPROXIMATE.
/CONSTRAINEDConsider only the fractions in which the prime exponents of numerator and denominator do not exceed the limits set by SET EXPLIMIT.
/NOOUTPUTStores the last approximation in pitch memory 0 only and does not show the results.
/SUPER pitchApproximates the pitch with a superparticular ratio. Shows the ratio lower than or equal and the one above the given pitch. The best approximation is stored in pitch memory 0. Cannot be combined with /CONSTRAINED and /FAREY.
/CHILDREN pitchThe given pitch must be rational. Shows the two children of the ratio in the Farey tree, also called Stern-Brocot tree. Can only be combined with /PARENTS. If combined with /PARENTS, then first the parents and then the children are shown.
/PARENTS pitchThe given pitch must be rational. Shows the parents of the ratio in the Stern-Brocot tree. If the value is an integer number then there are no parents, otherwise there are two. Can only be combined with /CHILDREN. If combined with /CHILDREN, then first the parents and then the children will be shown.
/FAREY pitch highest-order [prime-limit]Approximates the pitch with Farey fractions up to the given order. A Farey order is the maximum denominator. Also shown are the differences in cents, the factorisation and the continued fraction representation. The best approximation is stored in pitch memory 0.
/STERN pitch [maximum-depth]Shows all the convergents of the given pitch following the Stern-Brocot tree. An 'L' indicates branches to the left, an 'R' to the right. If no maximum depth is given, then the pitch will be approximated until the difference is very small, otherwise no more approximations than the given number will be given. If the given pitch is rational and no maximum depth is given, approximation will continue until the result is exact. The last approximation is stored in pitch memory 0.
RECTANGLECreate a rational scale with combinations of numerators and denominators which are in a given range. The parameters are given in the following order: lower bound numerator, higher bound numerator, numerator step (default 1), lower bound denominator, higher bound denominator, denominator step (default 1). If a step is given, then numbers are skipped if it is higher than 1. For example: If the numerator is in 7 .. 9 and the denominator in 4 .. 6 then the scale will be 7/4 8/4 9/4 7/5 8/5 9/5 7/6 8/6 9/6.
REDUCE pitchDivide all pitches in the current scale with the given pitch as many times as needed to make the resulting pitch lower than the given pitch. Otherwise if a scale pitch is smaller than 1/1, it is multiplied so the result is greater than or equal to 1/1. The given pitch parameter must be greater than 1. See also NORMALIZE.
/UPPERDoes the above except that pitches below 1/1 are not changed.
REMOVE filenameRemove the file with the given name from disk. There is no default file extension.
REPLACE position pitchReplace the pitch in the current scale at the given position with another pitch. The position must be a number not higher than the number of notes in the scale. If degree 0, the 1/1 is changed then all pitches shift by the inverse of the given amount. See also help of :=.
/INTERVALReplace the interval in the current scale at the given position with another interval. The position must be greater than 0 and not higher than the number of notes in the scale. To see the current scale intervals, do SHOW/INTERVAL.
/FREQUENCY position frequencyReplace the pitch by specifying the frequency relative to the base frequency (see SET FREQUENCY and SHOW/FREQUENCY).
/NEAREST pitchReplace the pitch in the current scale with the smallest absolute difference from the given pitch, with the given pitch. The scale may not be empty. Degree 0 will not be replaced even if 1/1 is closest to the given pitch.
/LARGEST new-intervalReplace the largest interval(s) in the current scale with the given new interval. The scale must be non-empty.
/SMALLEST new-intervalReplace the smallest interval(s) in the current scale with the given new interval. The scale must be non-empty.
/EQUAL interval new-intervalReplace the given interval(s) in the current scale with the given new interval. The scale must be non-empty. See also EXCHANGE/EQUAL.
/MODEL scalenr.Replace the pitches in the current scale with the nearest pitches in the given scale. This means that for each pitch in the given scale, the nearest pitch from the current scale is replaced. This only happens if the pitch in the given scale is also the nearest pitch for the current scale. So there may be pitches in the current scale that remain unchanged. Instead of a scale number, a filename may also be given. The file intnam.par is useful because it contains many rational pitches. See also SELECT/MODEL and SHOW/NEAREST DIFFERENCE.
/NOTATION source-notation target-notationReplace the pitches in the current scale with pitches having the same notation in a different notation system. The pitch is replaced with the corresponding value for that name in the target notation system. If the target system does not contain the name, then the pitch is not replaced. If the source system has no name for the pitch, then it is not replaced either. Note that whether a notation system contains a certain name can depend on the value set by SET TOLERANCE. For each pitch the shortest name is taken for the given source notation system (if there are enharmonic equivalents). If the equivalents have the same length, then names which are closer to C in the cycle of fifths have priority, so Eb comes before D# for example.
REVERSEReverse the order of all pitches in the current scale. To take the reciprocal of all pitches: do INVERT after REVERSE.
SAMPLE patternSelect degrees according to a mode pattern from the current scale and delete the intermediate degrees. Degree 0 and the last degree (formal octave) will not be deleted. For instance if a single number is given it means that every so many pitches are taken from the scale and the rest deleted.
/COMPLEMENTAs above but selects the complementary pattern.
/RANDOM countTake a random sample of the scale degrees from the current scale. Each degree has the same probability. If the scale is not in ascending order then the order is not preserved. The last degree may be deleted. Degree 0 will be unaffected and is also not counted. See also SIEVE/RANDOM and SEED.
SAVE filename [scalenr.]Write the given or current scale to a file on disk with the given filename. If a filename without extension is given, the extension will be '.scl'. A description no longer than 80 characters must be given. A longer decription can be added with an editor if the lines begin with an exclamation mark.
/KEEP_TEXTIf the scale has been loaded from disk, retain the description that it had, unless the description is empty.
/CENTSWrite the given or current scale to a text file on disk with the given filename. The filename has no default extension. The pitch values are written in cents, one value per line. The first line will contain the description. The file can so be used as input file for spreadsheet or other programs. For rational pitches the value is also written in cents, but followed by the numerator and denominator of the fraction. The numbers are separated by horizontal tabs. In a spreadsheet, this will get the numbers in adjacent columns (if the tab character is selected as separator). Such a file can be loaded again with LOAD/CENTS, but only as floating point values.
SEED [number]Gives the random number generator that is used for the aleatoric commands a new seed to prevent getting the same sequence of results each time the program is started. The number must be an integer number. If it is omitted, the computer's clock is used to obtain a value. It's also used for TIP. See also PERMUTE/RANDOM, SAMPLE/RANDOM, SIEVE/RANDOM and VARY.
SELECT [scalenr.]Enter a set of scale degrees to keep for the given or current scale and delete the degrees not entered. This is sometimes a more convenient way of deleting pitches from a scale than with the DELETE command. Modes can also be selected with the MODE command. See also SAMPLE and SIEVE.
/MODEL scalenr.Change the current scale to the structure of the given scale. This means that for each pitch in the given scale, the nearest pitch from the current scale is taken. So there may be pitches from the current scale removed or duplicates inserted. If two pitches are equally distant from a pitch in the given scale, (within half a cent) then the highest one will consistently be selected. After the operation the current scale has the amount of notes of the given scale. Instead of a scale number, a filename may also be given. See also REPLACE/MODEL.
SEND [parameters]Send a tuning over MIDI to a synthesizer. This command is equivalent to @SEND, so the command file send.cmd must be present in the current directory. The contents of send.cmd will be different depending on the computer type used. Any parameters given will be passed to the command file.
/FILE filename [scalenr.]Write the tuning data as one or more system tuning messages to a MIDI-file with the given filename, using the current keyboard mapping and according to the currently selected synthesizer type. Warning: the MIDI-file will not contain anything audible, just tuning messages.
/CPS_FILE filename [scalenr.]Write the tuning data to a CPS-file useable by MIDI2CS, a program to convert a MIDI-file to a Csound score file. The current keyboard mapping is used. The file contains a list of MIDI note numbers and frequencies. The default file extension is '.cps'.
/HEXADECIMAL filename [scalenr.]Write the tuning data to a text file with the given filename, using the current keyboard mapping and according to the currently set synthesizer type. The synthesizer type can only be one defined in synth.par, see SET SYNTHESIZER. This is used to create tuning dumps for unsupported synthesizer types. Only the MIDI tuning numbers will be written to the file, in hexadecimal format. MIDI codes in synth.par for prefix and suffix are ignored. The file written can then be included in another file containing a text representation of surrounding MIDI system exclusive codes. Then it can be transformed into a MIDI-file with the program T2MF (text to MIDI-file).
/SCREEN [scalenr.]Write the scale data in numbers to the screen so putting them in the synthesizer can be done by hand. If a tuning number is inappropriate (i.e. too high, too low, or too far from the equal tempered value for the synthesizer) then it is marked with an asterisk. The keyboard map determines which note numbers will be shown. In order to write the data to a file, for example to print, use command FILE first. Instead of a scale number a filename can also be given.
SET (ATTRIBUTE | CALC_OUTPUT | CONTROLLER | DESCRIPTION | DIFF_DEGREE | EXCLUDE | EXPLIMIT | FIRST | FREQUENCY | HARMCONST | INDEX | INT_STEPS | LIMIT | MAP_FREQ | MAXDIFF | MIDDLE | NAME | NOTATION | OFFSET | ONERROR | PAUSE | PROGRAM | RECIPROCAL | SEPARATOR | STEP_UNIT | SYNTHESIZER | TOLERANCE | UNIT | WEIGHTING)
SET ATTRIBUTE optionChange the pitch attribute shown with SHOW SCALE or SHOW/INTERVAL SCALE.
CENTS | : show the cents value |
DEPTH | : show the length of the continued fraction expansion [1] |
DIFF_ET | : show the difference in cents with the equal tempered value [2] |
DISSONANCE | : show the sensory dissonance of the dyad with 1/1 [3] |
ENTROPY | : show the Erlich harmonic entropy value [4] |
ERLICH | : show the Erlich harmonic distance value |
EUCLID | : show the rectangular distance in lattice space (less factor 2) |
FRACTION | : show the continued fraction expansion |
FACTOR | : show the frequency ratio as a linear decimal factor [5] |
GRADUS | : show the Gradus Suavitatis of Euler |
HARMON | : show the Barlow harmonicity value [6] |
INTERVAL | : show the interval with previous or other position in cents [7] |
INV_HARMON | : show the absolute reciprocal of Barlow's harmonicity value |
LIMIT | : show the prime limit |
LOG_FRACT | : show the number of octaves as a ratio [8] |
MANN | : show the average of numerator and denominator |
MULTIPLE | : show the integer multiple (all values under denominator 1) |
NONE | : show no attribute |
NOTATION | : show name and accidentals according to a given system [9] |
OCTAVE | : show the number of octaves (oct value of Csound) |
OTHER_SCALE | : show the same degree of another scale [10] |
PITCH_BEND | : show the semitone roundoff and pitch bend value (-2048..2047) [11] |
PRIMES | : show the prime factorisation |
RECIPROCAL | : show the reciprocal ratio with degree 0, (rel. string length) [12] |
SEMITONE | : show the semitone roundoff value and remainder (-50..49 c.) |
SEP_PRIMES | : show the prime factors except 2 all separately (i.e. 3.3.5.7) |
STEP_DIFF | : show the difference in cents with the nearest e.t. step [13] |
STERN | : show the length of the path in the Stern-Brocot tree |
SUBMULTIPLE | : show the inverse multiple (all values under numerator 1) [14] |
TENNEY | : show the Tenney harmonic distance value: log(num*den) |
TRIANGLE | : show the distance in triangular lattice space (less factor 2) |
TR_LOG | : show the triangular logarithmic complexity (less factor 2) |
TWELVE | : show the nearest semitone name and difference (-50..49 c.) |
VECTOR | : show the harmonic vector of primes other than 2 |
VOGEL | : show the Vogel harmonic complexity value: num+den |
WILSON | : show the Wilson harmonic complexity value |
<number> | : show the interval size in number per octave units [15] |
Remarks:
SET CALC_OUTPUT (ALL | LONG | SHORT | NONE)
Modify the amount of values given by the CALCULATE command. Default option at
startup is LONG. SHORT only gives the linear and log values of the result and
the interval name, if any. With NONE it gives no output, like when the
/NOOUTPUT qualifier is used. With ALL it is like LONG plus the note names of
all implemented notation systems. The pitch must not be further removed from a
degree than the part of the corresponding step size set with SET
TOLERANCE. Otherwise no name will be given.
See also SET NOTATION. The parameter cannot be abbreviated.
SET CONTROLLER (ON | OFF)
Influences the command EXAMPLE/MIDI. If it is OFF, then no MIDI parameter
(control) messages will be put in the output file. The initial setting is ON.
SET DESCRIPTION [scalenr.]
Change the description line for the current or given scale. This line is shown
with SHOW SCALE and CATALOGUE among others and replaced when LOAD is done.
It can be saved with the scale, see SAVE/KEEP_TEXT.
SET DIFF_DEGREE position
Change the base class for the comparison of the scale with an equal tempered
scale. The initial setting is 0, which means that for degree 0 a zero
difference will be shown. For example with a twelve tone scale if the
differences are to be shown with respect to A instead of C, then do SET
DIFF_DEGREE 9. Remember to do SET ATTRIB DIFF_ET after this for SHOW SCALE.
SET EXCLUDE [list-of-midi-channels]
Influences the command EXAMPLE/MIDI. Enter the MIDI channel numbers (between 1
and 16) that are not to be used by this command. Initially no channels are
excluded. If you have a soundcard with a standard channel for drum sounds,
usually 10, but sometimes 16 (on Soundblaster cards), then use this command to
exclude it before doing EXAMPLE/MIDI. Or put it in the startup command file.
To view the excluded channels do SHOW SETTINGS.
It does not influence the command EXAMPLE, since with that excluded channels
are set in the input file.
SET EXPLIMIT [prime exponent-limit]
Modify any exponent limit(s) per prime for rational approximation. Without
parameters, a list of prime and exponent limit pairs can be given, ended by
entering a zero. Otherwise one pair is given on the command line. See
APPROXIMATE.
SET FACTOR factor
This is a multiplication factor for the factor shown with SET ATTRIBUTE
FACTOR. The initial value is 1.0. The given factors represent relative
frequencies. Remember to do SET ATTRIB FACTOR after this. The value set is the
same as used for SET ATTRIBUTE RECIPROCAL so this command is synonymous with
SET RECIPROCAL.
SET FIRST degree
Set the lowest scale degree that will be shown with the SHOW SCALE command.
It can be any integer. This overrides the default value in params.par.
SET FREQUENCY frequency
Change the base frequency. The frequency is entered in Hertz.
This influences the SHOW/FREQUENCY commands, SHOW BEATS, SHOW DISTANCE,
CATALOGUE/PITCH and the beat frequencies calculated with CALCULATE. This value
and other settings can be viewed with SHOW SETTINGS.
The parameter can also be a pitch memory or scale degree (see help items of $
and %). Then the value is interpreted as a change from the current value, so
for instance if pitch memory nr.0 contains 3/2 and $0 is given, the frequency
will become a fifth higher. The frequency of middle C corresponding to an A of
440 Hz is 261.6255653 Hz.
To change the reference frequency of the keyboard mapping, see SET MAP_FREQ.
SET HARMCONST [prime coefficient]
Modify any coefficient(s) of the harmonicity function. This influences among
other things the harmonicity values shown when SET ATTRIBUTE HARMON is done,
or SET ATTRIBUTE INV_HARMON. Also the harmonicity values of SHOW DATA. If the
coefficients are set to be equal to the prime number, the Gamma-prime
function, a modified version of Euler's function is obtained. With no
parameters, the coefficients are set interactively. See also SHOW
HARMCONST and APPROXIMATE/WEIGHTED.
SET INDEX (ON | OFF)
Enable or disable showing the scale degree index with the SHOW SCALE commands.
The initial setting is ON.
SET INT_STEPS number
Change the relative position of the scale degree with which the interval is
shown with SHOW SCALE and SHOW/INTERVAL SCALE. The initial setting is -1,
which means the previous degree. Remember to do SET ATTRIB INTERVAL after this
for SHOW SCALE; it's not necessary for SHOW/INTERVAL SCALE.
SET LIMIT prime-limit
Change the default prime limit for the commands APPROXIMATE, CHORDS and
LIMIT. If 0 is given, the highest prime is taken (set in params.par).
SET MAP_FREQ frequency [note_number]
Change the reference frequency of the current keyboard mapping. Influences the
SEND command. See the current value with SHOW MAPPING.
The initial value is 261.6256 Hz. The frequency parameter can also be a pitch
memory or scale degree (see help items of $ and %). Then the
value is interpreted as a change from the current value, so for instance if
pitch memory nr.0 contains 3/2 and $0 is given, the frequency will become a
fifth higher. With the optional second parameter, the MIDI note number to
which the reference frequency is mapped, can be changed. The initial value is
60 (C). Use 69 for mapping to A. Don't type something like "69.A", but only
the number, for example: SET MAP_FREQ 440.0 69
This command does not change the frequency alterable by SET FREQUENCY.
See also SET MIDDLE.
SET MAXDIFF difference
Change the maximum difference for approximated pitches. The value can be given
as ratio or in cents (or with $ or %). To set no maximum, give 0.0 as the
value. Example: to set the schisma as maximum do SET MAXDIFF $s, but depending
on the accuracy of the scale, a slightly higher value may be required.
This value and other settings can be viewed with SHOW SETTINGS.
See also APPROXIMATE and EGALIZE/MODEL.
SET MIDDLE note_number
Change the middle key of the current keyboard mapping where scale degree 0 is
mapped to. The parameter is a MIDI note number. The initial value is 60
(middle C). It influences the SEND command. See the current value with
SHOW MAPPING. See also SET MAP_FREQ.
SET NAME (ON | OFF)
Choose whether an interval name will be given with SHOW SCALE for rational
intervals. The initial setting is ON.
SET NOTATION notation_system
This is an abbrevation for SET ATTRIBUTE NOTATION. Legal values are:
Octave based equal temperaments: E5, E7, E9, W9, E10, S10, E11, C12, D12, E12,
N12, S12, R13, W13, E14, E15, E16, M16, W16, E17, W18, E19, Y19, E20, Z20,
E21, C22, E22, P22, E23, W23, E24, P24, E25, E26, E27, E28, E29, E30, E31,
F31, S31, E32, E33, E34, E35, E36, E37, E38, E39, E40, E41, E42, E43, S43,
E44, E45, E46, E47, E48, A48, E49, E50, E51, E52, E53, E54A, E55, E56, E57,
E58, E59A, E60, E61, E62, E63, E64, E65, E66A, E67, E68, E69, E70, E71A, E72,
R72, E73, E74, E75, E76, E77, E78A, E79, E80, E81, E82, E84, E85A, E87, E88,
E89, E91, E94, E96, E98, E103.
Tritave (3/1) based equal temperaments: BP, KL, KD, KG.
Not equal temperaments: S5, P7, A17, P17, I22, T24, JI, JI2.
Names beginning with an E are for equal temperaments with that number of notes
per octave and give the note name (C, D, etc.) followed by accidentals.
Rapoport's notation system is used which is consistent with Fokker's for
31-tET and Blackwood's for 15-tET. For 16-tET Blackwood's notation is used.
For 20-tET and 25-tET a notation of mine is used. Names beginning with an E
and ending with an A have for G one step lower than the best fifth, to avoid a
very large syntonic comma.
Names beginning with a W are Wilson's note names for equal temperaments. Its
Greek letters are written out or abbreviated with two letters.
S5 | gives the Central-Javanese note names for slendro. |
P7 | gives the Central-Javanese note names for pelog. |
S10 | gives Sethares' 10-tET names. |
C12 | gives Carnatic note names for the 12-tone mela system. |
D12 | gives the German note names for 12-tET. |
N12 | gives the Dutch note names for 12-tET. |
S12 | gives solmisation names for 12-tET (Dutch). |
R13 | gives Rapoport's 13-tET names. |
M16 | gives Miller's 16-tET names. |
A17 | gives the Arabic note names for the Arabic 17-tone scale. |
P17 | gives the Persian note names for the Persian 17-tone scale. |
Y19 | gives Yasser's 19-tET names. |
Z20 | gives Zweifel's 20-tET names. |
C22 | gives Op de Coul's note names for 22-tET. |
I22 | gives the Indian sruti names. |
P22 | gives Paul Erlich's note names for 22-tET. |
P24 | gives the Persian note names for 24-tET. |
T24 | gives Turkish names of the Arel-Ezgi system. |
F31 | gives Fokker's names for 31-tET notes. |
S31 | gives Suppig's names for 31-tET notes. |
S43 | gives Sauveur's names for 43-tET notes. |
A48 | gives another 48-tET name system. |
R72 | gives Richter Herf's 72-tET names. |
BP | gives Bohlen's new names for the Bohlen-Pierce scale. |
KL | gives Bohlen's names based on the Lambda mode of the Bohlen-Pierce scale. |
KD | gives Bohlen's names based on the Delta mode of the Bohlen-Pierce scale. |
KG | gives Bohlen's names based on the Gamma mode of the Bohlen-Pierce scale. |
JI | gives a commatic notation for just intervals. The pitch must be rational. |
JI2 | gives a commatic notation for just intervals with other commas. |
# | semitone sharp (Pythagorean semitone) |
b | semitone flat (Pythagorean semitone) |
x | two semitones sharp |
bb | two semitones flat |
| | semitone fraction sharp (1/n semitone = one step) |
; | semitone fraction flat (1/n semitone = one step) |
#| | 1+1/n semitone sharp |
b; | 1+1/n semitone flat |
/ | comma sharp |
\ | comma flat |
) | diesis sharp |
( | diesis flat |
For the Persian system P17 Vaziri's notation is used:
# | sharp (about +100 cents) |
b | flat (about -100 cents) |
> | sori (about +70 cents) |
p | koron (about -70 cents) |
For the Turkish system T24 the Arel-Ezgi notation is used. These are the chosen equivalents for the graphic symbols:
| | one comma sharp (about 23 cents), a vertical line with two horizontal lines through |
d | one comma flat (about -23 cents), a reversed flat sign |
# | small semitone sharp (4 commas, 90 cents) |
b- | small semitone flat (-4 commas), a flat sign with one horizontal line through |
#| | large semitone sharp (5 commas, 114 cents), a vertical line with three horizontal lines |
b | large semitone flat (-5 commas) |
## | small whole tone sharp (8 commas, 180 cents), two vertical lines with three horizontal lines |
b= | small whole tone flat (-8 commas), a flat sign with two horizontal lines |
x | large whole tone sharp (9 commas, 204 cents) |
bb | large whole tone flat (-9 commas) |
The notation systems JI and JI2 give names for exact rational pitches with primes not higher than 31. There is no range of tolerance. The 3-limit names are Pythagorean. The accidentals following represent higher limit commas. It's similar to Eitz's notation system. These symbols were chosen; for primes 17 and higher, system JI2 uses different comma's than system JI:
/ | comma sharp, 81/80 | |
\ | comma flat, 80/81 | |
) | diesis sharp, 128/125 | |
( | diesis flat, 125/128 | |
7 | septimal comma sharp, 64/63 | |
L | septimal comma flat, 63/64 | |
^ | 33/32 | |
v | 32/33 | |
| | 27/26 | |
; | 26/27 | JI2: |
#' | 17/16 | 2187/2176 |
b' | 16/17 | 2176/2187 |
% | 19/18 | 513/512 |
d | 18/19 | 512/513 |
@ | 24/23 | 736/729 |
* | 23/24 | 729/736 |
#! | 29/27 | 261/256 |
b! | 27/29 | 256/261 |
|' | 32/31 | 248/243 |
;' | 31/32 | 243/248 |
SET OFFSET [notename-or-pitch]
Specify the note name to use for scale degree 0 of 1/1. The notation system
must be set first with SET NOTATION. The notename parameter must be a name in
the current notation system. The pitch belonging to the name will subsequently
be used as offset wherever a note name is displayed. Instead of a name, a
ratio or value in cents may also be given. Without parameter, the offset is
reset to 1/1 which is C in notation systems beginning with an E. When changing
notation systems, it is wise to do SET OFFSET again, although this is not
always required. If the notation system is JI, a rational offset value must be
given, otherwise no names will be displayed.
This command does not influence the commands ECHO, EXAMPLE, REPLACE/NOTATION.
SET ONERROR (STOP | CONT)
Specify to stop or to continue in case of an error while executing an external
command file (see @) or ITERATE command. The initial setting is STOP.
SET PAUSE (ON | OFF)
Enable or disable the pause during scrolling. The initial setting is ON.
SET PROGRAM (ON | OFF)
For the command EXAMPLE/MIDI. If it is OFF, then no MIDI program change
messages will be put in the output file. This can be useful for instruments
that have a slow response to these messages which causes notes to be lost.
The initial setting is ON.
SET RECIPROCAL factor
This is a multiplication factor for the factor shown with SET ATTRIBUTE
RECIPROCAL. The initial value is 1.0. If it is set to the string length for
degree 0 of 1/1, then the given factors represent absolute string lengths.
Remember to do SET ATTRIB RECIPROCAL after this. Remark: more accurate string
lengths may be obtained with SHOW STRINGLEN. For lengths of organ pipes, the
values are inadequate since they require an end correction. However if the
pipes have the same width and shape, a constant end correction can be
subtracted from the reciprocal values.
This value is the same as used for SET ATTRIBUTE FACTOR, so this command is
synonymous with SET FACTOR.
SET SEPARATOR [string]
Set a string to be used as separator between output of subsequent commands.
Initial value is a vertical bar (|). Default value is an empty string, which
gives no separation.
SET STEP_UNIT pitch
This is the equal tempered step size for the difference shown with SET
ATTRIBUTE STEP_DIFF. The initial value is 100 cents. Remember to do SET ATTRIB
STEP after this. See also SHOW ET_DIFF for a similar operation without this
attribute setting.
SET SYNTHESIZER synthesizer-number
Set the current synthesizer type. It must be either 0 or a number which is
defined in parameter file synth.par. These definitions are called external.
There are also internal definitions in the program and their number is 101 or
higher. The default type can be set in file params.par, otherwise it is 0.
See also SHOW SYNTHESIZER and SEND.
SET TOLERANCE factor
Set the tolerance value for notation. The value is relative to the
corresponding equal tempered step size of the selected notation system. The
initial value is 1/3. It means that the absolute logarithmic difference
between a pitch and the nearest pitch in the notation system may not exceed
the given factor times the step size, or no name will be given. So for an
exact match use 0. This value has no effect for notation systems not for equal
temperaments which are S5, P7, P17, I22, JI and JI2. Otherwise this value
affects all situations where a notation system is used. See also SET NOTATION,
SHOW NOTATION and REPLACE/NOTATION.
SET UNIT (ON | OFF)
Enable or disable displaying a unit name after a value, like "cents" or
"Hertz" for the commands SHOW SCALE, SHOW CYCLE and SHOW BESTCYCLE.
The initial setting is ON.
SET WEIGHTING factor
Change the weighting factor used in the command APPROXIMATE/WEIGHTED.
If the weighting factor is higher, then the harmonicity value weighs more and
the pitch difference less. This value and other settings can be viewed with
SHOW SETTINGS.
SHOW (SCALE | BEATS | BESTCYCLE | COMBINATION | CYCLE | DATA | DIFFERENCE | DISTANCE | ET_DIFF | EXPLIMIT | HARMCONST | INTERVALS | LOCATIONS | MAPPING | NOTATION | PITCH | SETTINGS | STRINGLEN | SYNTHESIZER | TEMPERINGS | TRANSPOSE)
SHOW SCALE [scalenr.]Show the pitches of the given or current scale with the attribute that was set with the command SET ATTRIBUTE and interval name if rational. The option SCALE is default so a SHOW or SH command is enough to show the current scale or a scale memory. Instead of a scale number a filename can be given which then shows the scale in the file, without affecting the current scale. The first degree to be shown can be set with SET FIRST or given in params.par. See also SET INDEX, SET NAME and SET UNIT. Pitches can be left-justified or centred, see params.par.
/CENTSShow the pitches in cents with the interval name if rational. Can be used in combination with /LINE and /INTERVAL.
/INTERVALShow the intervals between two scale degrees with a constant number of steps in between. The initial setting is between a degree and the previous one. This can be changed by doing SET INT_STEPS. See also SET ATTRIBUTE INTERVAL. The values of attributes shown correspond to the displayed interval sizes. Can be used in combination with /CENTS, /LINE and /INTERVAL. See also SHOW/LINE INTERVALS to see intervals grouped by scale degree.
/FREQUENCYShow the absolute frequency of the pitches in Hertz and in number of octaves above 1.021975 Hertz. The latter is the same as the oct value of Csound. The base frequency used is the one set with SET FREQUENCY. The default base frequency is set in params.par (default 261.6255653 Hertz). Cannot be combined with other qualifiers.
/HERTZAs with /FREQUENCY but shows only the value in Hertz. Cannot be combined with other qualifiers.
/OCTCPSAs with /FREQUENCY but shows only the Csound cpsoct value. Cannot be combined with other qualifiers.
/CHORDThe scale must be rational. Shows the frequency multiples like 4:5:6. Cannot be combined with other qualifiers.
/LINEShow pitches or intervals consecutively on one or more text lines. Can be used in combination with /CENTS and /INTERVAL.
/ATTRIBUTEDoes not show the pitches but only the attribute value for each degree. Afterwards it shows arithmetical averages of the attribute values. If the attribute is not numerical then the averages are zero and can be ignored. Can only be combined with /INTERVAL.
SHOW BEATS interval-list
Show the beat frequencies on each tone of the current scale for the given
interval(s). The intervals in the list with a maximum of 12 are separated by
spaces and only ratios are allowed. But they can be separated by colons as
well. In that case the values are read as linear factors, for example:
4:5:6:7. See also CHORDS. If the interval list is enclosed in parentheses,
then this means the inversion, for example (4:5:6) means 10:12:15.
The frequencies are given in Hertz and relative to the base frequency set with
SET FREQUENCY. The beats are given for the nearest pitch in the scale that
is the given interval away from each degree. If it's lower, then the frequency
has a minus sign. Example: to show the beat frequencies of fifths, fourths
and major thirds type: SHOW BEATS 3/2 4/3 5/4
To see the beats of more octaves, do EXTEND first with a multiple of the
current scale size. Warning: for sounds with an inharmonic spectrum, perceived
beat frequencies may be different. See also SHOW TEMPERINGS.
SHOW BESTCYCLE [scalenr.]
Show the difference of the fifths in the current scale from a least-squares
optimal fifth. Enter the fifth degree. The difference between each fifth and
the optimal fifth is given in cents. Also given is the best starting point
for the cycle of fifths and the resulting standard deviation which was
optimised.
SHOW COMBINATION interval [scalenr.]
Show all pairs of pitches in the current or given scale whose sums or
differences are equal to the given interval. This can also be done for pairs
of intervals in file intnam.par. Instead of a scale number a filename
can be given. You can do first LOAD intnam.par but this is not necessary. For
example: SHOW COMBINATION 25/24 intnam.par
Number of notes | |
Smallest interval | |
Average interval | |
Average / smallest interval | |
Largest interval | |
Largest / average interval | |
Largest / smallest interval | |
Least-squares average interval | |
Median interval of one step | |
n>1 | Most common interval of one step |
Interval standard deviation | |
Interval skew | |
Whether scale has Rothenberg's propriety: strictly proper, proper or not | |
n>1 | Whether scale has Myhill's property and which are possible generators |
n>1 | Whether scale has maximal or distributional evenness |
Whether scale consists of repeating interval blocks or is equal tempered | |
n>1 | Whether scale is a mode of an equal temperament |
n>1 | Whether scale is a Winograd deep scale |
n=7 | Whether scale is an octave species of an abstract tetrachord and which one(s) |
n>=7 | Whether scale contains two identical tetrachords |
n=12 | Whether scale is well-tempered and how many different fifths it has. It means no fifths larger than and major thirds smaller than pure. |
n=12 | Whether scale has a monotonous distribution of thirds proceeding over the circle of fifths, i.e. growing and shrinking only once |
n>2 | Whether scale is sum-free |
n>1 | Whether scale is an addition chord |
n=2..120 | Whether scale is a Constant Structure (Wilson) |
n=2..120 | Number of different intervals and ratio to n-1 Abortable by Control-C. |
n=2..120 | Smallest interval difference (if not equal temperament) |
n=2..120 | Most common interval and amount (its inverse is equally common) |
n=2..120 | Number of recognisable fifths (between 4/7 and 3/5 octave) and their average size |
n=4..120 | Whether scale is a chain of identical triads |
n=4..120 | Most common triad and amount |
n=2..120 | Rothenberg stability (if proper) |
n>1 | Lumma instability |
n>1 | Impropriety factor (if not proper) |
n>1 | Rothenberg efficiency (if computing time not prohibitive) Abortable by Control-C. |
rat | Prime number limit |
rat | Odd number limit, otonal and utonal odd limit |
rat | Barlow's harmonicity |
rat | Barlow's average harmonicity |
rat | Barlow's specific harmonicity |
rat | Common denominator and fundamental frequency |
rat | Common multiple and guide tone frequency |
rat | Exponens Consonantiae |
rat | Euler's gradus suavitatis |
rat | Wille's k value |
rat | Vogel's harmonic complexity |
rat | Wilson's harmonic complexity |
rat | Rectangular lattice dimensions |
rat | Triangular lattice dimensions |
rat | Whether scale is a complete genus musicum and which one |
rat | Whether scale is superparticular |
rat | Prime exponents range and averages |
Limited transpositions | |
Inversional symmetry on degrees | |
Inversional symmetry on intervals | |
Average distance from equal tempered | |
Standard deviation from equal tempered | |
Maximum distance from equal tempered | |
Geometric average of pitches 0..n | |
Arithmetic average of pitches 0..n | |
Harmonic average of pitches 0..n | |
Geometric average of pitches 1..n | |
Arithmetic average of pitches 1..n | |
Harmonic average of pitches 1..n | |
n>1 | Geometric average of pitches 1..n-1 |
n>1 | Arithmetic average of pitches 1..n-1 |
n>1 | Harmonic average of pitches 1..n-1 |
SHOW DIFFERENCE scalenr.
Show the differences of the pitches in the current scale with those of the
given scale. If the scales do not have the same number of notes, the amount
compared is the maximum of the two scale sizes. Average values are also given.
The differences shown are those that would result from a SUBTRACT operation.
Instead of a scale number a filename can be given.
/FREQUENCY
Show the differences of the pitches in terms of beat frequencies. These are
calculated relative to the value given with SET FREQUENCY.
/NEARESTShow the differences not between corresponding scale degrees but between each pitch of the current scale and its nearest counterpart in the given scale. The degree numbers of both scales are shown. The beat frequencies are also shown. At the end the number of pitches which are different is given and the mode is displayed which forms the selection of nearest pitches from the given scale. See also MODE.
SHOW DISTANCE pitch [position]
Show the distance of the given pitch to the nearest pitches and intervals in
the current scale and the beat frequencies. The given pitch may be in octaves
higher than the scale, but below 1/1 no near degrees will be found unless the
scale contains them. This is in case no position parameter is given, the
default is degree zero and the pitch is relative to 1/1. Another position can
be given to find the degree of the nearest interval starting on that position,
which can also be negative.
The beat frequency is calculated relative to the value given with SET
FREQUENCY. If the given pitch is rational, then the beat frequencies between
the corresponding partials will also be given.
SHOW ET_DIFF division [octave]
Show for each pitch in the current scale the nearest step of the given equal
temperament. This ET is the given formal octave (also called modulus or
interval of equivalence) divided into the given number of steps (division).
The division may be either a positive integer or floating point number. If the
octave parameter is not given, 2/1 is assumed. The differences are given in
cents and number of steps. Average values are also given. See also SHOW
DIFFERENCE and DIVIDE/FIND.
SHOW EXPLIMIT
Show the exponent limit(s) of the primes used for rational approximation. The
initial limits are 31 for all primes. Note that the practical limits are lower
for each prime other than 2 because the highest integer is 2^31 - 1.
Also the default prime limit is given, see SET LIMIT. See also APPROXIMATE.
SHOW HARMCONST
Show the harmonicity coefficient(s) of the primes used. See also SET
HARMCONST.
SHOW INTERVALS [scalenr.]
Show all intervals between all pairs of pitches in the given or current scale.
They are grouped by interval class (distance in position).
Instead of a scale number a filename can be given which then shows the
intervals of the scale in the file, without affecting the current scale.
/LINE
Show the intervals grouped by scale degree consecutively on lines. First given
is the pitch of the starting degree followed by all the intervals relative to
that degree. Cannot be combined with /TOTAL.
/CENTS
In combination with /LINE, show the intervals in cents.
/TOTAL
Shows all intervals between all pairs of pitches in the given or current scale
but they are not grouped by interval class but by interval size. If an
interval size is unique to one interval class, then the class number is also
given and an asterisk if it is not (then it's called ambiguous). The total
number of incidences of each interval is given with it. If there are ambiguous
intervals, the number of different ones, and the total number of them is
given. Cannot be combined with /LINE.
SHOW LOCATIONS interval-list
Show the degree(s) where the given interval combination (chord) is present in
the current scale. For each occurrence the number of steps and the begin and
end degree is shown. A comparison is made up and down to twice the number of
notes in the scale. If one of the intervals only approximates an interval in
the scale, the difference(s) are also given, with a maximum of one sixth of
the average one-step interval in the scale. The intervals in the list are
separated by spaces. But they can be separated by colons as well. In that case
the values with decimal points are read as linear factors instead of cents
values, for example: 4:5:6:7. See also CHORDS. If the interval list is
enclosed in parentheses, then this means the inversion, for example (4:5:6)
means 10:12:15.
If the current attribute is notation then an extra line is shown with the
note names of the chord position. See also SET NOTATION.
Then the total, average and highest differences are given which is the sum
over one chord.
/MODE name-pattern-or-mode
Instead of an interval list, give a mode pattern as used in the MODE command.
A mode name can also be given. The intervals which are selected from the
current scale by the mode will be looked for. The combination at degree 0 will
therefore always be found.
/EQUALMODE name-pattern-or-mode
Instead of an interval list, give a mode pattern of an equal temperament. The
current scale must be a mode of an equal temperament. To see if it is, use
FIT/MODE and look if the last scale given has a SD of 0.00 cents.
This will also indicate the division selected for this command. A mode name
can also be given. Example: check the positions of tetrads with relative
interval sizes: SHOW/EQUALMODE LOCATION 2 2 1.
If the standard deviation shown with FIT/MODE is not zero, then QUANTIZE
can be done first.
/SCALE scalenr.Instead of an interval list, give a scale number or filename.
SHOW MAPPING [filename]
Show the current keyboard mapping if no filename is given, otherwise show the
mapping in the file without affecting the current mapping. Middle indicates
the MIDI note number to which scale degree 0 is mapped. The initial value is
60. Reference indicates the master frequency and the note number which will
receive this frequency. The initial values are 261.6256 Hertz to note number
60. Octave degree is the degree which is considered to be the formal octave.
This formal octave is the difference in pitch between two adjacent instances
of the mapping pattern. A value of 0 means that the last pitch of the current
scale is considered to be the formal octave. The initial value is 0. If the
current mapping is not linear, you will see in the left column a list of scale
degrees for each key. An unused key is indicated with two hyphens. The right
column contains a list of keys for each mapped scale degree. A linear mapping
means that successive scale degrees are mapped to successive keys.
See also LOAD/MAP, SET MIDDLE.
SHOW NOTATION
Show the names of all notation systems. Also show the current active system,
even if the attribute is not set to notation. See also SET NOTATION.
To view all the note names in one of these systems, use SET NOTATION to select
the system, then get the corresponding equal tempered scale with the EQUALTEMP
command (except for the Indian names) and do SHOW. For the Bohlen-Pierce scale
do EQUAL 13 3. For the Indian names use LOAD to obtain one from file, or you
can do EQUAL 53. For the Persian names do LOAD persian, or do EQUAL 36.
The notation offset and tolerance are also shown, see SET OFFSET and
SET TOLERANCE. The tolerance is the maximum allowed deviation for the
name to be given. It is shown here in cents, not relative to the step size in
which it is set.
SHOW PITCH [pitchnr.]
Show the value in the given or default pitch memory both in cents and in Hertz
relative to the base frequency. See also CATALOGUE to show the values of all
used pitch memories.
/CENTSShow the value in cents only.
SHOW SETTINGS
Show the current values and settings of changeable parameters. To make
different settings at startup, the files params.par and startup.cmd
can be edited.
SHOW STRINGLEN [string-file] [last-degree]
Show the positions where frets are to be placed for the degrees of the current
scale with high precision. This command needs to read the string length and
other parameters of the string and the instrument from a file. The default
name of this file can be set in params.par. The name can also be given as
parameter.
The pitch of the open string must correspond to scale degree 0. If this is not
the case, i.e. degree 0 is also at a fret, then first insert the pitch of the
open string (relative to the the current 1/1) to degree 0, see INSERT.
If more frets than scale degrees are to be shown, enter the count as second
parameter (in this case the filename must be given too).
In the first column are the distances relative to the nut, in the plane of the
fingerboard towards the bridge. The second column has the distance of the
point where the string starts to vibrate at the bridge to the fret position.
Accurate results are only obtained for metal strings, or strings of a material
with a fixed spring constant. Unattainable pitches will be indicated with
dashes.
SHOW SYNTHESIZER
Show the names of the synthesizer types defined in parameter file synth.par
and the ones defined internally. The current synthesizer type is indicated
with an arrow.
SHOW TEMPERINGS interval-list
Show the differences for the nearest interval on each tone of the current
scale with the given interval(s). The intervals in the list with a maximum of
12 are separated by spaces. But they can be separated by colons as well. In
that case any values with decimal points are read as linear factors, for
example: 4:5:6:7. See also CHORDS.
The differences are shown in cents and are relative to the nearest pitch in
the scale that is the given interval away from each degree. See also
SHOW BEATS.
SHOW TRANSPOSE [scalenr.]
Show how many pitches of the given or current scale are different resp.
identical for the same scale in different keys. The count in the second column
is the number of pitches different resp. identical in degree order, and in the
third column the number that is different in any order. It then shows the
largest deviation, and the average deviation for the degrees that are
different in order. Lastly, the normalised autocorrelation values for the
logarithmic intervals between consecutive pitches. It is a measure how similar
the interval sequence is when the scale is transposed to the given key. A
value of 1.0 means identical, a value of 0.0 means no similarity. If a
notation attribute was set, the note names are given too.
For equal tempered scales, obvious values are not given. Instead of a scale
number a filename can be given.
/SORTED
Show the results sorted by key in order of ascending number of pitches
different.
SIEVE pattern
Select pitches from the current scale and delete the intermediate pitches.
The numbers in the given pattern come in pairs. The first one is the number
of steps to proceed upwards with each selected degree. The second one is the
degree to start on which has 0 as default value (may also be negative). For
more than one given pair, the union is taken. Degree 0 and the last degree
(formal octave) will not be deleted. For instance if a single number is given
it means that every so many pitches are taken from the scale and the rest
deleted (then it does the same as SAMPLE).
Example: with 12-tone equal temperament, doing SIEVE 2 1 will give the
degrees 1 3 5 7 9 11 12. Or SIEVE 3 0 4 0 will give 3 4 6 8 9 12.
See also MODE and SAMPLE.
/COMPLEMENT
As above but instead the selected pitches are not kept but deleted.
/RANDOM probability
Take a random selection of the scale degrees from the current scale. Each
degree has the given probability of being selected. So the number of notes is
not known in advance.
The parameter must be a floating point number or ratio between 0 and 1
inclusive. The last degree may be deleted. Cannot be combined with
/COMPLEMENT. See also SAMPLE/RANDOM and SEED.
SORT [scalenr.]
Sort the pitches in the given or current scale in ascending order.
For descending order, do REVERSE afterwards.
/INTERVALSort the consecutive intervals in the given or current scale in ascending order. For descending order, do INVERT afterwards.
SPAWN commandExecute an operating system (shell) command and return to the program after it has been completed. To work interactively with the operating system enter
for MS-DOS | : spawn command |
for Unix | : spawn sh (or any other shell name) |
for VMS | : spawn spawn |
for Windows 9x/NT | : spawn command |
/DETACHEDExecute the operating system command in the background (as a separate process) and/or run it concurrently in a separate window. Control is returned to Scala before the system command has been completed. Not possible under MS-DOS.
SQUARECreate a scale like a Novaro-Partch tonality diamond. This is the Carthesian product of a set of factors with their reciprocals. The diagonal of the diamond consists of only 1/1's. These redundant notes will not be included in the scale. Scales like this are self-inverse.
STRETCH intervalIncrease the formal octave of the current scale with the given interval and all other pitches with a logarithmic proportional part of it with respect to their scale degree. If the number of notes in the current scale is n, then the first degree will be incremented with the 1/n part of the given interval, the second degree with the 2/n part, etc. For example if the scale in cents is 0-100-300-500, then a stretch with 90 cents makes it 0-130-360-590. The given interval may also be smaller than 1/1. See also EXPONENTIATE and MULTIPLY.
/ABSOLUTE pitchChange the formal octave of the current scale to the given pitch and increase all other pitches with a logarithmic proportional part of the increment to the formal octave.
/MATCH scalenr.Stretch the current scale by an interval such that the least-squares difference with the corresponding degrees in another scale is minimal. The given scale may have a different size than the current scale. Instead of a scale number, a filename may also be given. See also MULTIPLY/MATCH.
SUBTRACT scalenr.Divide the pitches of the current scale by the corresponding scale degrees of the given scale. Instead of a scale number, a filename may also be given.
/SUBTRACTInstead of dividing the pitches, take the difference tones.
/MEDIANTInstead of dividing the pitches, take the subtractive mediant value, i.e. the absolute value of (num(a) - num(b)) / (den(a) - den(b)). All pitches must be rational. If either the numerator or denominator becomes zero, then a 1/1 is inserted. If this has happened, you can do UNIQUE to delete them.
/DIFFERENCE [scalenr.]The current scale is replaced by a scale with all difference tones of the current or given scale. If the number of notes in the given scale is n, then the size of the new scale will be n * (n + 1) / 2 - 1, but less if there are duplicate difference tones. For example, if the given scale has pitch factors 10:12:15:20 (or 1/1 6/5 3/2 2/1), then the new scale will be 2:3:5:8:10 (or 1/1 3/2 5/2 4/1 5/1). Warning: the original 1/1 remains in the scale. To remove it, do DELETE 0. See also ADD/SUMMATION.
SWAP scalenr. [scalenr.]Interchange the first with the second given scale. To select another scale as the current scale, use only one parameter with the other scale's number. The command to interchange notes inside a scale is EXCHANGE.
/PITCH pitchnr. [pitchnr.]Interchange the first with the second given pitch memory. Pitch number 0 is the default.
SYMMETRIZE positionMake the current scale symmetrical in some way around the given position. The qualifiers determine in which way. It can be done by replacing pitch pairs around the given position so that their average distance to the pitch at the given position is the same. Or one can be replaced by the other or pitches can be copied to the other side. /GEOMETRIC is default by absence. Qualifiers cannot be combined.
/GEOMETRICUses the geometric mean, i.e. sqrt(a * b). When this is used the symmetry is recognised by the SHOW DATA command.
/HARMONICUses the harmonic mean, i.e. 2 * a * b / (a + b).
/ARITHMETICUses the arithmetic mean, i.e. (a + b) / 2.
/SUBC_HARMONICUses the subcontrary to harmonic mean, i.e. (a^2 + b^2) / (a + b).
/LOGARITHMICUses the logarithmic mean, i.e. log(mean) = (b * log(a) + a * log(b)) / (a + b).
/COUNTER_LOGUses the counterlogarithmic mean, i.e. log(mean) = (a * log(a) + b * log(b)) / (a + b).
/RMSUses the root mean square, i.e. sqrt((a^2 + b^2) / 2).
/MEDIANTUses the mediant, i.e. (num(a) + num(b)) / (den(a) + den(b)). All pitches must be rational.
/FIRSTDoes not average two pitches but just replaces the second by the first. When this is used the symmetry is recognised by the SHOW DATA command.
/SECONDDoes not average two pitches but just replaces the first by the second. When this is used the symmetry is recognised by the SHOW DATA command.
/INSERTDoes not average two pitches but inserts all the octave inversions. Afterwards the command UNIQUE can be used to delete eventual double pitches. However this may change the position of symmetry. When this is used the inversional symmetry is recognised by the SHOW DATA command.
TIP [tipnr.]Provide a tip-of-the-day. With no parameter given, a random tip is provided. Tips are written in the file tips.par.
TYPE file-maskRead a text file. It can be useful to read a command file or keyboard mapping file or something else before executing or loading it. If the file parameter contains a wildcard, all the matching files will be typed. If the file does not exist, then no error message will be given.
UNCYCLE position [down-count]The position must be a scale degree that has no common factor with the scale size. This command reorders the pitches by putting them in "fifths-order" by considering the current scale to be a cycle of fifths. The given position is the degree of the formal fifth. The down-count is the number of fifths in the downward direction with default value 0.
UNDOAfter doing a command that changes the current scale, this command can be invoked to get back the scale as it was before the last command. Each time when a command is used that changes the current scale, it is first copied to the first UNDO scale memory. The number of UNDO scale copies is set in file params.par, default is 1. If it's more than one (see SHOW SETTINGS), then UNDO can be invoked repeatedly to get earlier states of the current scale back. Use the CATALOGUE or SHOW SCALE command to examine the contents of the UNDO memories. The command works cyclically so the state before UNDO is not lost.
UNIQUE [scalenr.]Deletes all double pitches from the current or given scale and sorts the scale in ascending order. Pitches are considered equivalent if their difference is less than approximately the numerical accuracy of floating point numbers in the computer.
UNRAT positionChange the pitch at the given position (degree) in the current scale from a rational to a floating point value. This cannot be done for degree 0. To do this with all pitches, use VARY 0.0 or LIMIT 1.
VARY deviationAdds a random value with an absolute maximum of the given value to all pitches in the current scale except the last one (formal octave). The random values are distributed uniformly between minus and plus the deviation logarithmically. If the last degree is to be changed too, then append an extra temporary degree before doing this command.
/INTERVALAs above but adds a random value to each interval instead of each pitch. The last degree will be affected too.
/LINEARAdds a random frequency value with an absolute maximum of the given value to all pitches in the current scale except the last one (formal octave). The random values are distributed uniformly between minus and plus the deviation linearly. The given frequency is relative to the base frequency of SET FREQUENCY.
@<filespec> [parameters]An @ preceding a filename executes commands in an external text file called a command file (or "script"). The command file must have one command per line. Execution stops when an empty line is encountered or an error occurs. Do not execute command files from within themselves or create endless loops otherwise, because the program will then consume all available memory and stop, losing any unsaved scales. The default extension for command files is '.cmd'. Lines beginning with an exclamation mark (!) are ignored and can be used for comments. An example:
! Average the pitches of scale 0 with those of scale 1 add 1 multiply 1/2
With commands like INPUT or PYTHAGOREAN that ask for values, the values must
be put separately on lines following the command or alternatively command
lines with question marks ('?') will cause prompting for user input, once for
each question mark causing each one to be replaced by the response given.
Prompting can also be done for parameters that are normally taken from the
command line.
A line with two question marks ('??') will cause prompting for user input for
all the rest of the parameters. See also help ?.
Command files can be used to store scales by definition, versus by value.
It is possible to pass parameters from the invoking command line to the command file. Parameters on the command line are separated by spaces and assigned to symbols p1, p2, .., p9. To translate these symbols inside the command file, surround them by single quote characters. An example: spawn search *.scl 'p1'. However this translation can only be done in lines with commands, not in lines containing input data to commands which ask for values. The example will do a text search in scale files, searching for the text of the given parameter, provided the operating system knows the command "search". Another useful command file to make, for instance to edit keyboard mappings is spawn edit 'p1'.kbm
Nesting invocations of other command files inside command files can be done to a maximum depth of 10.
If the first command in a command file is ECHO, then this text will be displayed as description with the command DIR *.cmd.
This is a link to the list of presupplied command files.
See the directory with the command files.
@list-fileAn @ can also be used in front of a filename, where a file mask can be given. The given name must be the name of a file with a list of filenames inside, one on every line. The default extension of such a list file is '.lst'. The commands to which this can be used as file parameter are COMPARE, DIRECTORY, ITERATE and LOAD/ALL. A set of scale files can be defined this way. A list file can be created with a text editor, with COMPARE/SAVE_LIST or DIRECTORY/SAVE_LIST.
$
A $ preceding a natural number smaller than or equal to the number of pitch
memories can be used wherever the user enters a pitch. It means that the value
of the corresponding pitch memory will be taken instead of a literal value.
The highest pitch memory is set in params.par (default 10).
A $ preceding any of the following letters can be used as a synonym wherever a
pitch is entered.
p | : Pythagorean (ditonic) comma | 23.46 cents |
k | : syntonic comma | 21.51 cents |
s | : schisma | 1.95 cents |
q | : diaschisma | 19.55 cents |
c | : major diesis | 62.57 cents |
d | : minor diesis | 41.06 cents |
w | : Würschmidt's comma | 11.45 cents |
y | : kleisma | 8.11 cents |
f | : golden section (phi) | 833.09 cents |
e | : base of natural logarithm (e) | 1731.23 cents |
See also % for symbols beginning with a %-character and help for expressions.
%
A % preceding an integer number can be used wherever the user enters a pitch.
It means that the value of the corresponding degree in the current scale will
be taken instead of a literal value. The degree may be outside the scale,
a negative value is also allowed, which will give a value properly offset by a
number of formal octaves.
Other symbols are:
%n | : the formal octave (pitch of highest degree) of the current scale. |
%si | : the smallest interval between consecutive pitches of the current scale. |
%li | : the largest interval between consecutive pitches of the current scale. |
%ai | : the average interval between consecutive pitches of the current scale. |
The symbol n or N can be used to get the number of notes which can be entered where a scale degree or an amount of notes is the parameter. See also ECHO for the lexical functions with %-character useable in ECHO output. And see $ for symbols beginning with a $-character and help for expressions.
[ ]
A pitch expression surrounded by square brackets gets the value of the nearest
pitch in the current scale. It can be used wherever the user enters a pitch.
The range of the scale is octave extended, so for equal temperaments the
number of notes is irrelevant. Warning: if the current scale is not in
ascending order then a wrong value may result for degrees outside the scale
range. See also help for expressions.
:=
Assign the result of an arithmetical pitch expression to a pitch memory or
scale degree. The left hand side must be a number preceded by a $ or a % for a
pitch memory or scale degree respectively. The right hand size can be a pitch
expression or arithmetical expression as described under CALCULATE. See help
of $, %, Expressions. It does not provide extra functionality but is there for
syntactic convenience.
The command CALCULATE/NOOUT 3/2+5/4 is equivalent to $0 := 3/2+5/4.
The command COPY/PITCH $0 1 is equivalent to $1 := $0.
With REPLACE there are two differences. One is that when := is used, this
cannot be undone with UNDO. The second is with the latter, the position may be
one higher than the number of notes, so := can also be used instead of APPEND.
REPLACE 7 3/2 is equivalent to %7 := 3/2.
!
A ! at the beginning of a command line from user input or a command file or
parameter file will cause the line to be ignored.
?
A line with only a question mark in a command file will cause the input of a
parameter or part of a command line to be input from the keyboard instead of
the command file itself. See @.
If two question marks are put inside a command file at the beginning of a line below a command requiring user input, this will cause the rest of the user input to be queried directly, instead of read from the command file. For example, commands like INPUT and CPS ask for a variable amount of pitches. In these cases ?? can be used because with single question marks the amount required cannot be known beforehand.
About...
Scala is the word for scale in Italian (scalae is Latin for ladder). In
Dutch it stands for "a wide range" of things, usually possibilities. This is
what the program hopes to offer, a large amount of useful functions to suit
most needs of both beginners and experts.
Scala was written in the programming language Ada. This makes the code very
readable, maintainable, bugs very scarce and saves me lots of precious time.
If you find a bug nonetheless, please report this with an accurate description
of what you were doing and which type of computer you are using to the author
(Manuel Op de Coul) at e-mail address coul@computer.org. If the program ends
with an exception (error code), then please mail which one it was and include
any text that is in the exception message. Suggestions for improvements are
also welcome.
As an engineer, the author is unable to place appearance above function, so
that's the reason for the absence of a more fancy user interface, however he
thinks it's quite adequate and works much faster after a while than a GUI.
Currently there are versions of Scala for MS-DOS, Windows 9x/NT, Unix, Linux and VAX/VMS.
Disclaimer: Scala is freeware without warranty and may not be sold, modified or distributed for sale in combination with commercial products.
Commands
Commands must be entered as follows. First comes the command verb which may be
abbreviated to the smallest unambiguous length. Then any desired qualifiers
follow which must be preceded with a slash (/) and may also be abbreviated.
Then parameters follow to be separated by at least one space. Nonoptional
parameters not given on the command line are prompted for. Qualifiers must
always precede and not follow the parameters.
This is a link to the list of all commands.
Errors
If the program ends with exception Storage_Error raised, it means there is
insufficient memory. To decrease memory consumption, change file
params.par to have fewer or smaller scales in memory (or both). If that
doesn't help, rename the help file help.htm to another name. This
disables the HELP command but saves memory. Under Windows 9x, check the memory
options from the DOS-icon properties.
When a wrong parameter value is given by the user, this is indicated with the message Illegal parameter. Sometimes a more specific message is given, like Illegal generator value, Illegal directory or some such.
When an operation inserts more notes in a scale than the maximum value in file params.par allows, then the message Overflow in scale size is given. When a scale is empty, and an operation expects a non-empty scale, then Scale is empty is given.
Numeric overflows abort the running operation and give the message Computation error. They will never produce meaningless results. They will neither abort the program, unless there is a bug.
Expressions
Pitch expressions can be:
Interruption
The execution of a command can be interrupted by pressing Ctrl/C. This does
not end the program, only the last command. It may take a short while before
the actual interruption occurs. If Ctrl/C is pressed when the program is
waiting for user input, this will not be noticed by the program until a
return is given. Under Windows NT and most Unix versions pressing Ctrl/C
does not end the command, but the whole program. Under Windows 9x it works
ok.
To cancel a long output, either press Ctrl/C or type 'q' followed by return when the program asks to hit the return key when it is pausing to scroll.
If an end-of-file character like Ctrl/Z is typed when the program is waiting for user input, the program stops (not for MS-DOS). Be sure not to have unsaved scales.
Introduction
Recipe for new users to retune their synthesizer or sampler. For synthesizers
or samplers without tuning table and soundcards, see below.
What if it didn't work?
spawn gsplay xxx.midinto:
spawn gsplay tempo 50 xxx.midThis sets the MIDI transfer rate to 50%. Take a lower value if the problem persists.
With a PC soundcard:
For soundcards and synthesizers without a tuning table:
Pitches
The representation of a pitch can be either a floating point value (shown in
cents or as a factor) or a ratio. The program does composite arithmetic which
means that rational values are kept in rational form whenever possible. If
not, for example when an operation gives a numerator or denominator that is
too large, then the representation is automatically switched to floating
point. This also happens with operations acting on both a rational and
floating point pitch. Operations will never produce junk numbers.
Important: where a pitch is entered by the user it may be given as a rational
or in cents. If a value entered contains a decimal point, it is interpreted as
a value in cents, otherwise not (even if it's zero), unless explicitly stated
in the help text. Floating point values may not start with a decimal point,
i.e. there is no implicit leading zero. They may however end with one.
See also Scales, $, % and CALCULATE.
Qualifiers
Qualifiers alter the action of a particular command. They are preceded by a
slash (/) and may be abbreviated like commands. On the command line they
immediately follow the command verb and precede the parameters, if any.
Commands with qualifiers may have different parameters than the command
without them.
Scales
A scale consists of zero or more pitches. The terms pitch, note, tone and
scale degree are being used interchangeably here.
The size of scales (number of notes) is bounded, but the maximum size is
configurable. The same goes for the amount of scales.
Both values are set in file params.par, and can be shown with SHOW SETTINGS.
Each scale memory has a number, and scale number 0 is called the current scale. This is always the default scale upon which commands act. Some, not all commands can also act on other scales than the current one. Also some commands can take scale filenames as parameter, as well as scale numbers.
The last note (with the highest degree number) of a scale serves as the formal octave. The terms octave, formal octave and interval of equivalence are also used interchangeably. This can be value 2/1 but also any other value. This value is important when the scale is extended and when notes are used outside the range of degrees from 0 to the last degree.
The value of the first note (degree 0) is always 1/1 or 0 cents.
With respect to scales which are generated by a fifth, we use the terms fifth, formal fifth and generator interchangeably.
This is a link to download a large archive of scales.
Screen dimensions
The number of lines and columns of the screen that the program works with is
for MS-DOS | : 25 x 80 |
for Linux | : set automatically at startup |
for Unix | : defined in parameter file termsize.par, default 24 x 80 |
for VMS | : set automatically at startup |
for Windows 9x/NT | : set automatically at startup |
24 80
Startup
At program startup, command line parameters can be given. By invocation with no
parameters, an external command file startup.cmd is searched in the current
directory and if it is found, the commands in it are executed, prior to giving
control to the user. In it, you can put commands to CD to a scale directory,
do SET ATTRIBUTE, give a TIP, or whatever more.
One or more parameters can be given which must be names of existing files. The
filename's extension must be .scl, .kbm or .cmd. Depending on the extension
a scale is loaded, a keyboard mapping is loaded or an external command file
executed. The extension cannot be left away like with the LOAD command. The
command line is read from left to right.