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Jun 12, 2020 at 18:07 comment added Joe Bloggs @AlexP: Fair enough. All I could remember was that Ancient Greek tuning sounded bad to modern ears, and they liked perfect fourths while disliking thirds. I equated the two.
Jun 12, 2020 at 17:25 comment added awe lotta @AlexP I disagree with your justification for the harmony of perfect fourths. Octave equivalence doesn't imply that the same interval inverted or in different octaves have the same consonance. Subjectively, for example, a perfect 11th (3:8) is more dissonant than a perfect fifth (2:3), since it has higher numbers / least common multiple. Though in terms of counterpoint, the categories of consonance and dissonance would refer to different things, I think.
Jun 12, 2020 at 15:04 comment added AlexP @JoeBloggs: Perfect fourths are harmonious. (They cannot be not harmonious when fifths are harmonious and octaves are equivalent.) (Octaves, perfect fifths and perfect fourths are the only intervals which sound the same in the tuning used in the antiquity and our post-Renaissance equal temperament tuning.) Ancient Greeks used Pythagorean tuning, and Pythagorean major thirds do indeed sound bad (and are different at various points on the scale, to boot). Basically, their thirds and our thirds are not the same.
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Jun 8, 2020 at 11:36 comment added David258 I think the problem you'll have is not explaining why 1:3 does sound equivalent (An octave+5th sounds very harmonious to me), but explaining why 1:2 does not. I think it would be hard to find a system where 1:2 is distasteful but other numeric ratios are fine.
Jun 8, 2020 at 10:56 comment added Joe Bloggs Related but not actually useful: Ancient Greeks found perfect fourths harmonious and thirds distasteful, suggesting that ‘harmony’ is cultural.
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