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April 20

11th overtone on C; is it F or F♯??

Sources are disagreeing on whether the 11th overtone on C is F or F♯. Which is correct?? Georgia guy (talk) 00:56, 20 April 2020 (UTC)[reply]

I think it will depend on what instrument, especially whether string or wind. See overtone. Also is very possible that it falls between F and F♯.--Shantavira|^{feed me} 08:14, 20 April 2020 (UTC)[reply]

According to one of the illustrations in Harmonic series (music) it's 49 cents flat from F♯, so almost exactly halfway between F and F♯. AndrewWTaylor (talk) 09:13, 20 April 2020 (UTC)[reply]

Very close to F-half-sharp (see Quarter tone), being only 1 cent off from ~~just-intonation~~ equal tempered quarter tone. If you want to know more about microtonal music like this, musician Jacob Collier does a lot of it on his YouTube channel, as do Adam Neely [1] and David Bruce [2] --Jayron 32 17:49, 20 April 2020 (UTC)[reply]

If I'm right, the uses of an octave and a fifth as important musical intervals arose from the statement that they are 1/2 and 2/3 of the full string. The use of 12 semitones arose from the statement that the logarithm of 1 1/2 in base 2 is approximately 7/12. Any fraction that's even closer with a larger denominator?? (Please use the smallest denominator that results in a fraction with this criterion.) Georgia guy (talk) 17:54, 20 April 2020 (UTC)[reply]

It depends on whether you mean just intonation or any of the various temperament systems, especially on what you want your tuning system to do for you. Just intonation itself introduces musical paradoxes like the comma pump (here is a good demonstration of it), so how you fix that is you use intervals that correct for the problem, but which knock you off just intonation. The system you are describing, using a fixed ratio of the 12th root of 2, is called twelve tone equal temperament, and is what most modern instruments use. It does a pretty good job, but some intervals are a mess; for example the rather important major third is like 15 cents off from the just major third, that's basically 1/6 of a semitone, and definitely within the range of discernment of most ears. So why use it? Because 12-TET optimizes transposeability. Because it is built on a regular-sized semitone ratio, you can transpose any key to any other key, and they all sound the same. If you don't value that particular property, there are MANY MANY other temperament systems you can use that do other things well. Want to maintain the sanctity of the perfect fifth? Pythagorean tuning is the way to go. Want better thirds, but are willing to give a little bit on having perfect fifths? Meantone temperaments are your thing. The use of 12 semitones comes from the minimum number of notes necessary to get back to an octave following the circle of fifths. Basically, if you start on a note, and go a fifth up or down from that note, and keep stacking fifths, you get very close to a perfect octave only after going through 12 other notes (over 7 octaves) (of course, because of the comma pump problem, you're a little more than 1 cent off on that octave, specifically 12 stacked fifths is 531441/4096 which is damned close to 128/1, which is the answer you get if you stack 7 octaves). That's how we get to 12 notes. --Jayron 32 18:35, 20 April 2020 (UTC)[reply]

Nicely stated! --jpgordon^{𝄢𝄆 𝄐𝄇} 23:55, 20 April 2020 (UTC)[reply]

I am sceptical that the 15 cent difference for the major third is actually noticeable. In isolation, comparing the 5/4 major third to the equal-tempered one? Certainly, yes. In the context of actual music? With all the vibrato going on and expressive intonation, not a chance. Double sharp (talk) 03:25, 21 April 2020 (UTC)[reply]

You're right about that. Which is why I always take the music theory wonks who claim these sorts of things are a big deal with a grain of salt. --Jayron 32 16:13, 21 April 2020 (UTC)[reply]

Jayron, what is just-intonation quarter tone? —Tamfang (talk) 05:13, 23 April 2020 (UTC)[reply]

Ooops. So fixed. --Jayron 32 12:22, 23 April 2020 (UTC)[reply]