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Author Topic: Making N-notes Equal Temperament scales  (Read 1020 times)


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Making N-notes Equal Temperament scales
« on: March 21, 2021, 08:45:59 pm »
Until we hopefully get alternative scales, we can make N notes Equal Temperament scales using the mod matrix Key/Seq to Global Pitch.

To do this, assign Key/Seq to Global Pitch in the mod matrix to adjust the key tracking for the oscillator pitch. The mod amount in semitones needed is:

semitones = (128 * 12) / N - 128

where N is the number of notes in an octave.

E.g.for 24TET we need to halve the control voltage range, and we do this by subtracting 64 semitones from the 128 semitone control range, which takes us from 12 to 24 semitones per octave. The maximum for a mod matrix slot is +/- 60 semitones, and this is where "stacking" modulators comes in; we need to assign Key/Seq twice to the Global Pitch, one assignment with the max of -60, and one with -4, to get to -64 semitones in total. For 31TET we need -78.45 semitones, and to achieve this we need to use 3 slots because for values above 12 semitones the amount is in whole semitones - so we use slots of -60, -18 and -0.45 to get to -78.45.

When the scale has been stretched or compressed the common key is the middle E.

We can also retune the synth to get a different common key. To hit e.g. middle C as the common key, for 24TET -2 semitones is needed, for 48TET 3 semitones is needed. For N that aren't doublings of 12, we'll not hit the right tuning, so a tweak of the Fine tune is needed - e.g. for the in between 36TET, -2.5 semitones is needed - so a little fiddly for those.

The attached ZIP archive contains these N-TET template patches:
19TET_E, 24TET_E, 31TET_E, 36TET_E, 48TET_E
19TET_C, 24TET_C, 31TET_C, 36TET_C, 48TET_C

For 24TET_C and 48TET_C, the absolute tuning is spot on, for 19TET_C, 31TET_C and 36TET_C a tweak of Fine Tune is needed. For 36TET it's a full semitone up, for 19TET and 31TET it's a little less - I've set the VCO 1 and 2 tunings so that the Fine Tune must be increased to hit the standard tuning for middle C for those. We could potentially use the Mod Envelope to create the tuning offset, but it's nice to save that envelope for sound design.

These patches use page 4 of the mod matrix to keep the tuning stuff "out of the way". The sound is the standard Init sound, ready for making new microtonal patches from scratch. Since all it consists of is 2 or 3 mod slots and a little tuning of the VCOs, those things can also easily be copied into existing patches to make them ET microtonal.

Edit: changed to include the scales with common keys as both middle E and C
« Last Edit: June 06, 2021, 09:21:38 am by DrJustice »


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Re: Making N-notes Equal Temperament scales
« Reply #1 on: April 10, 2021, 02:55:56 pm »
Awesome, thanks!
Still hoping for support of .scl files  ;)


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