Creates an offset matrix from a scale table. An offset matrix is used to retune an octave for synthesizers that support such retunings, like the Korg Minilogue XD and the Dirtywave M8 tracker.
Value
the offset matrix. Columns represent key names in 12-tone equal temperament. Rows represent note names from the scale table. The value of a matrix cell is the offset in cents you need to apply to the column name's key to get the row name's scale note.
Details
The columns of an offset matrix represent key names in 12-tone equal temperament. Rows represent note names from a scale table. The value of a matrix cell is the offset in cents you need to apply to the column name's key to get the row name's scale note.
For example, if the value in row "3x9" and column "C#" is 104, you would tune the "C#" key up 104 cents to have it play "3x9". If the value in row "1x7", column "D#" is -33, you would tune the "D#" key down 33 cents.
Keep in mind that you can only use each 12-TET key once, and you have to end up with a key for all the notes in the scale. The strategy I use is:
For scales with seven or fewer notes, I retune the white keys starting with C, and retune any left-over white keys to the last note in the scale. For a hexany, it's fun to stick an extra note in somewhere.
For scales with 8 to 12 notes, I retune the keys from left to right,
again sometimes adding notes to fill up to 12. There's an example of this
in Microtonality and the Tuning Systems of Erv Wilson, pages 127 - 131.
This example is worked out in examples grady_a and grady_b for the
function ps_scale_table.