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Frets are already on equal temperament on the vast majority of mainstream guitars; you're not getting away from equal temperament unless all you play is open strings, like a koto/harp.

If octaves are perfect with one string in between, the in between string can be slightly detuned from equal temperament to provide a clean fifth, free of beats. Then it also provides a clean fourth up to the octave. That's a useful thing that will make certain chords sound good.

by dahart12 hours ago|

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That’s not very helpful. You can only do that one string, and it breaks the perfect octave starting on the detuned string. As soon as you also try to detune the next string up, you break the octave you started from. This is a house of cards idea that falls apart immediately.

by kazinator11 hours ago|

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The detuned string in between likewise has a perfect octave relationship to strings that are two removed.

The E, D and B strings are turned such that they yield clean octaves (and other equal-temperament intervals).

Then so are the A, G and E.

But these two groups are slightly detuned, so that the fifths are clean from the E to A string, D to G, and B to E.

by dahart9 hours ago|

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Have you actually tried this? What songs work? To me this sounds totally impractical and useless, like it’s a logical technicality for the purposes of this discussion and not something a real musician would ever do. You’re making tuning a pain, breaking the E-E octaves (all barre chords), breaking octaves with 2 strings between, breaking the next-string octaves, breaking a lot of scales and jazz chords, and to top it off it would still only work for certain keys and not others. I’ll pass.

by kazinator7 hours ago|

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1. Yes; I've been tuning along those lines for nearly four decades. What songs work: anything with power chords that benefit from sounding sharp, free of flutter.

2. The error between the equal temperament perfect fifth and the pure one (3/2) is just less than 2 cents. So the difference I'm talking about is at the same level of accuracy as that of pretty excellent guitar intonation. The corrections are not simply for equal temperament; they are not separable from the condition of the instrument and its intonation. The given instrument is what it is, and to get those 1-5-8 power chords to sound clean you do whatever you have to.