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This virtual piano is the best I’ve found. Sadly, though it uses shift to hit the black keys. And

Standard equal tempermant scale has each note go up by $2^{1/12}$

Pythagorean Tuning constructs the ratios from pure perfect fifths (3:2) and octaves (2:1).

If you have a note and the other notes with frequency $n$ times as fast, the lowest note, will be percived as the actual note being played, and the higher overtones will change the timbre.

In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids, the fundamental frequency is the lowest frequency sinusoidal in the sum.

Since the fundamental is the lowest frequency and is also perceived as the loudest, the ear identifies it as the specific pitch of the musical tone [harmonic spectrum]…. The individual partials are not heard separately but are blended together by the ear into a single tone.

I could set things up using columns instead of rows. And have each column be a tetrachord

What I’ve been trying to do is Additive Synthesis

From the 12 tones equal temperment, we can tweak to get just tunings:

  • C = 0 up, baseline
  • 💿 = 1 up $\approx$ 16/15 (Just diatonic semitone)
  • D = 2 up $\approx$ 9/8 (Major Tone)
  • 🇩🇪 = 3 up $\approx$ 6/5 (just minor third)
  • E = 4 up $\approx$ 5/4 (Just major third)
  • F = 5 up $\approx$ 4/3 (Just perfect fourth)
  • 🐸 = 6 up $\approx$ 45/32 (Just augmented fourth) or $\approx$ 64/45 (Just diminished 5th)
  • G = 7 up $\approx$ 3/2 = $\frac{4}{3}\frac{9}{8}$ (just perfect fifth)
  • 🇬🇦 = 8 up $\approx$ 8/5 (Just minor sixth)
  • A = 9 up $\approx$ 5/3 = $\frac{4}{3}\frac{5}{4}$ or 27/16 (Just major sixth)
  • 🆎 = 10 up $\approx$ 7/4 (Harmonic seventh)
  • B = 11 up $\approx$ 15/8 = $\frac{4}{3}\frac{5}{4}$ (just major seventh)

Major tone is 9:8. Minor tone is 10:9.
Just diatonic semitone is 16:15

In Five-limit tuning, a power of 2 moves up an octave, a power of 3 moves up an octave and a perfect fifth, and a power of 5 moves up two octaves plus a major third.

Pretty close to what I was trying to do.

Maybe should use 7 limit tuning

Possibilities for note between F and G

  • 64/45 = 4/3 * 16/15

Software that basically already does what I spent hours doing