I’ve finished the original transcription of the Bach 1st English Suite Allamende, parts one and two. To make this, I’ve expanded the number of modes in the 31-limit tonality diamond to 189 different triads, each with a 16 note scale derived from either an otonality or utonality taken at different starting positions. Previous versions used only the otonality or utonality right from the diamond. But the modulation from one key to another was rather jarring. Now I have many more keys I can chose from.
For example, I’ve created a relatively normal sounding A major diatonic scale from the notes in the F major Otonality by starting at the 3rd scale step, which is A at 5:3, then a 5:4 third above that as a C# at 23/12, and a 3:2 above the A as an E at 25:24. Relative to the A, we have 1:1, 5:4, 3:2 triad. Other notes in the 16 in the otonlality round out the other notes in the scales.
Bach used several modulations in the piece, from A major, B major, E major, and F# major in the first part, and a few other keys in the second. The D major needs work, as it’s not really where it should be to my ears. But this is a start.
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