I tried to tune the 12 tones differently to gain more harmony. Rather than equal temperament or just intonation, I picked 7-limit tuning. Here're the tones:

    C = 1/1
    C♯ = 21/20
    D = 10/9
    D♯/E♭ = 7/6
    E = 5/4
    F = 4/3
    F♯/G♭ = 7/5
    G = 3/2
    A♭ = 14/9
    A = 5/3
    A♯ = 7/4
    C♭ = 28/15

This places the tones in a 3×2×2 grid, and approximates 12-TET well. (Like just intonation does in a 4×3 grid)

My questions are:

  1. Is G major chord out of tune in this tuning?
  2. Does B mean C♭?
  3. Are C7 chord and F7 chord enough to have a chord progression?
  4. What is the name of D♯-F♯-A♯-C chord?
  • 1
    4. Cm7b5 is one name. But not with those note names, just the sound.
    – Tim
    Aug 8 '19 at 14:53
  • @Tim -- I might be more inclined to call that an Ebm6 (or possibly a D#m6); respelling needed in any case....
    – ex nihilo
    Aug 9 '19 at 2:06
  1. No. The B is 56:45 above the G, which is rather lower than a just major third at 5:4. It's about 8 cents low, which is less of a difference than the difference between the just major third and the equal tempered major third. That might be acceptable. But the ratio between G and D, after adjusting the octave, is 40:27 rather than 3:2, which is in my opinion unusable as a consonant perfect fifth.

  2. Yes.

  3. I don't understand this question.

  4. I'll leave this for others to argue about.

I'll also note that with most attempts to tune a keyboard to "just intonation" some intervals are too dissonant to be useful as a perfect fifth. The E to B interval here, for example,

  • 3. I mean whether it's possible to have chord progression such as I - V - vi - IV? The only harmonic seventh chords are C7 and F7. Aug 8 '19 at 15:24
  • @DannyuNDos I wrote this answer having read the question carelessly and thinking that you were using 9:8 for D. I do not think the G-to-D fifth is useable if D is 10:9. I've edited the answer accordingly.
    – phoog
    Aug 8 '19 at 15:50

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