I’ve been looking at different adaptive tuning systems, and none do what I want. My preference, which is probably crazy, is a tuning that will find the optimum tuning for a chord, on my terms. In this case, I want the ratios between notes in a chord to use the lowest possible integer ratios. That means I will favor 7/4 of 9/5, even though it’s typical for a just flatted 7th to use a 9/5. I also favor 7/5 over 10/7, even though it might create some awkward moments.
I brought this about with some python code the attempts to find the 72 EDO tuning for each chord that minimizes the size of the ratios between the notes in a chord. The source material is a real Bach chorale used in the St. Matthew Passion, known as Herzliebster. All chorales have four notes. So I wrote code that evaluated a chord by looking at the ratio distance from each note to every other note. That’s six compares: Given soprano, alto, tenor, bass as SATB, then the combinations to evaluate are S to A, S to T, S to B, A to T, A to B, and T to B.
Then I did the same after changing one of the voices by on 72 EDO step, and scored that. I continued that so that I evaluated all six combinations modified by -3 to +3 72 EDO steps, or 50 cents up and 50 cents down, in 16.67 cent steps. The result was a Vertically Adaptive Tuning of Herzliebster. Vertical means I only looked at each chord all by itself. I haven’t written the code that would permit evaluation of one chord to the previous or succeeding step, which is Horizontal Adaptive Tuning. But it’s a start.
There may be some notes that sound strange here:
