adding or modifying existing scales is easy and doesn’t require programming skills. it boils down to adding or editing the scale definitions, which are basically just ordered lists of numbers from 0 - 1536, as described below.

• the preset scales are defined in braids_quantizer_scales.h, with their corresponding names in OC_scales.cpp.

• for example, the Phrygian scale looks like this:

// Phrygian
{ 12 << 7, 7, { 0, 128, 384, 640, 896, 1024, 1280} }

• technically, a scale is a simple struct (defined in braids_quantizer.h), consisting of three members: span, num_notes, and notes[16]:

struct Scale {
   int16_t span;
   size_t num_notes;
   int16_t notes[16];
};

• where
  • span is the scale span, namely 12 << 7 (= 1536 = 1.0V = 1 octave = 1200cents),
  • num_notes the number of notes per scale, and
  • notes[16] is an array containing the actual note values within that span, with a maximum of 16 notes per scale (and a minimum of 4).

• in other words, in terms of the preset scales, each octave has a resolution of 1536 steps, each step corresponding to 1/128th of a semitone (or 0.78125 cents, or 0.65mV).

• Conversely, 1 cent translates to 1.28 steps, 1 semitone to 128 steps. for converting ratios, use this formula:

  1536 * Log(ratio)/Log(2) (further reading).

• for 12-TET scales, the note values thus will be multiples of span divided by 12:

  1536 / 12 = 128 (= 83.33mV = 1 semitone = 100 cents).

• Or taking the chromatic scale as an example: in this case, span = 1536, num_notes = 12, and notes is an array consisting of 12 elements at semitone intervals from 0 - 1408:

// Semitones
{ 12 << 7, 12, { 0, 128, 256, 384, 512, 640, 768, 896, 1024, 1152, 1280, 1408} }

• correspondingly, scales with fewer notes will have the same span but fewer elements, e.g. Pentatonic minor with only 5 notes:

// Pentatonic minor
{ 12 << 7, 5, { 0, 384, 640, 896, 1280} }

• where:
  • 0 = 0 * 128 = 0 * 0.78125 cents = 0 cents,
  • 384 = 3 * 128 = 384 * 0.78125 cents = 300 cents (minor third),
  • 640 = 5 * 128 = 640 * 0.78125 cents = 500 cents (fourth),
  • 896 = 7 * 128 = 896 * 0.78125 cents = 700 cents (fifth), and
  • 1280 = 10 * 128 = 1280 * 0.78125 cents = 1000 cents (minor seventh)).

• non-12-TET scales/intonations work much the same way, except the intervals won’t be multiples of 128; for example:

// bairagi 
{ 12 << 7, 5, { 0, 115, 637, 899, 1275} }

• where span = 12 << 7 = 1536 (as before), num_notes = 5, and

  • 0 = 0 cents,
  • 115 = 115 * 0.78125 cents =~ 90 cents,
  • 637 = 637 * 0.78125 cents =~ 498 cents, and so on.

• the displayed names (short and long version) are stored in two arrays: const char* const scale_names[] and const char* const scale_names_short[], with their names given at the index corresponding to the actual scale definition in const Scale scales[].

• to add your own scale, you’ll simply have to:

  • A) add the suitable scale definition to const Scale scales[], as well as
  • B) add (at the corresponding array position) the short and long versions of the scale name to scale_names[] and scale_names_short[], respectively.
  • C) re-compile as per method B here.

Note: do not edit the USER1 to USER4 scales in the code. They are intended for editing via the module user interface only. You can rename them in the code if you wish.

Note: You can specify non-octaval scales by specifying a scale range other than 12 << 7 (i.e. 1536). However, the octave settings and buttons will then not transpose or shift by one full scale repetition (such as by one tritave) - they will still shift by one octave, which is probably not a note in the non-octaval scale. Therefore, special scaling factors are hard-coded to support specific non-octaval scaling schemes. Currently, if the firmware has been compiled with the BUCHLA_SUPPORT directive set to true, there is support for the Wendy Carlos alpha, beta and gamma microtonal non-octaval scalings, and the tritave macrotonal scaling as used by the popular (ahem) Bohlen-Pierce scale, amongst other.