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Comment by hunter2_ | Hacker News Reader

No, my entire comment is about tuning a typical fretted guitar. Playing a unison as you say, and turning the peg until beating completely disappears, yields integer ratios instead of equal temperament ratios. The result of that can sound nicer than equal temperament for some keys/chords but terrible for other keys/chords.

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I played classical guitar for years, and am a physicist, and feel a bit sheepish to say that I never realized this.

Unison means same sound. There's no ratio, unless you mean 1:1.

Ah shoot. I screwed up (only in the comment you're questioning, not my earlier comment per se). Of course the frets are positioned according to equal temperament, so when fretting a note for tuning the next string, indeed you end up at equal temperament when getting the beating down to nothing as you play the unison.

Rather, I'm talking from a point of view of playing two adjacent open strings. Or harmonics thereof (as some people like to tune with 7th fret harmonics and so forth). If you aren't fretting and you minimize beating down to nothing, then you end up with integer ratios.

IIRC harmonics ignore frets. You use the fret to approach the point where it happens, but its exact position is a function of the whole string lenght and it's therefore not equal temperament related.

I think you're right about the "beating"... in general this post has been extremely instructive for me. My teachers were piano players. Either they didn't know better (because they didn't need it) or they didn't bother to explain the fine details to me. Even the books I consulted later don't tell the whole story. That's the magic of the Internet :-)

Correct! Tuning open strings (listening to an interval) and tuning by harmonics (listening to a unison without using frets) both result in a lack of equal temperament if you eliminate the beating entirely. Only good piano tuners are really experienced in landing at the correct beat frequencies without electronic aid.

Yes, in this case that is correct. It is common to play the same note on two different guitar strings in order to tune them together.

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