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Tuning of the day

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    #51
    Tuning of the day

    For instruments with fixed tuning, namely keyboards, a tricky tradeoff operates in the battle for supremacy between pure fifths and pure thirds. Why? Start at C and start tuning pure fifths upward: C-G, G-D, D-A, A-E. At E, we've arrived at our first major third from C, and we'd like it to sound good. The trouble is, four perfect fifths don't add up to a nice major third: 3/2^4 = 81/64, which is quite a bit wider an interval than 5/4 (or 80/64). It may not look like much, but even relatively untrained ears will reliably hear the difference in a blind test. 81/64 sounds pretty shit. (It's often not even called a major third because of this, rather a "Pythagorean ditone.")
    This isn't quite right, to be pedantic about it: (3/2)^4 is 81/16. You need to come down a couple of octaves to get 81/64.

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