3 ms·
>The difference between a Pythagorean fifth and an equal temperament fifth is not enough to bother any but the fussiest listeners, but it is detectable to some.
by placebo 12y ago
>The difference between a Pythagorean fifth and an equal temperament fifth is not enough to bother any but the fussiest listeners, but it is detectable to some.
Thought experiment: Suppose someone with perfect pitch were to sing out all the notes on a scale which they feel sounds perfect, while someone else would measure the frequencies of each note they sing. Obviously, the result would not show a counter example to the fundamental theorem of arithmetic, but I'd be curious to know what it would show...
- ajross 12y agoMostly likely the person with perfect pitch would be singing the "correct" scale they were taught to sing, which almost certainly would be equitempered. But in principle it's not impossible to imagine someone (someone impossibly talented anyway) singing their way around the cicle of fifths and landing in a key that doesn't quit match the one they started in. And the point in the article that temperment cannot be heard is sort of wrong anyway. You can write some quick code to generate both chords, and the difference is notable. Perfect tuning is something we actually hear regularly in things like tight vocal harmony. It's not alien.
- baddox 12y agoIn fact, I think an unaccompanied trained singer would tend to sing a scale in just intonation, with or without perfect pitch.