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What happens when this passage is repeated in just intonation?

My answer to this question is the pitch drifts up by a syntonic comma because of the F# being close to the E. I am not sure how to elaborate on this, but is this correct or is my reasoning correct?

  • 2
    My guess is that a correct answer to this question requires numbers. What are the frequency ratios for the intervals in the passage?
    – phoog
    Nov 22, 2021 at 3:53
  • Why wouldn't we get no drift at all if we play this on a piano tuned with just intonation? (Alternately, we get a great singer to sing this.)
    – Dekkadeci
    Nov 22, 2021 at 12:12
  • @Dekkadeci indeed, there's no reason that it has to drift.
    – phoog
    Nov 22, 2021 at 17:03

1 Answer 1


Let’s say we do each interval just. Then e-a is 4:3 and a-f# is 5/4 : 3/2 = 5:6. So finally we get e-f# becomes 4:3·5:6 = 10:9.

So we get the so called small whole step, which is slightly smaller (by one syntonic comma) than the big whole step at 9:8 (9:8 / 10:9 = 81/80 is the syntonic comma).

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