Talk:159edo/Notation: Difference between revisions

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In response to your comment [[User_talk:Xenwolf#Another_Comma|here]], Xenwolf, I'm glad you think this picture is clear. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:26, 14 October 2020 (UTC)

: Saw all this and thought I'd mention that the idea that there is only one type of semitone is a modern idea arising directly from 12-edo. In Pythagorean tunings, there are two types of semitone. The diatonic semitone is a minor 2nd 256/243, and the chromatic semitone is the augmented unison 2187/2048. The two add up to exactly a whole tone 9/8. The two semitones are obviously notated completely differently, since one is a 2nd and one isn't. Meantone tunings draw the same distinction, but of course the semitones are tuned differently.

: In 5-limit JI, both semitones can be altered by 81/80, making even more semitones, e.g. 135/128, 25/24, 16/15 and 27/25. Each of these is either diatonic or chromatic, and corresponding pairs add up to a whole tone.

: Once you make the distinction between chromatic and diatonic semitones, it becomes clear that the sharp sign that represents the chromatic semitone was never meant to denote exactly half a whole tone. It represents a whole tone minus a minor 2nd.

: BTW something similar happened to the term tritone. In modern times, it means exactly half an octave, but in the past it literally meant the aug 4th, which at the time was distinct from the dim 5th.

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 In response to your comment [[User_talk:Xenwolf#Another_Comma|here]], Xenwolf, I'm glad you think this picture is clear. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:26, 14 October 2020 (UTC)
+: Saw all this and thought I'd mention that the idea that there is only one type of semitone is a modern idea arising directly from 12-edo. In Pythagorean tunings, there are two types of semitone. The diatonic semitone is a minor 2nd 256/243, and the chromatic semitone is the augmented unison 2187/2048. The two add up to exactly a whole tone 9/8. The two semitones are obviously notated completely differently, since one is a 2nd and one isn't. Meantone tunings draw the same distinction, but of course the semitones are tuned differently.
+: In 5-limit JI, both semitones can be altered by 81/80, making even more semitones, e.g. 135/128, 25/24, 16/15 and 27/25. Each of these is either diatonic or chromatic, and corresponding pairs add up to a whole tone.
+: Once you make the distinction between chromatic and diatonic semitones, it becomes clear that the sharp sign that represents the chromatic semitone was never meant to denote exactly half a whole tone. It represents a whole tone minus a minor 2nd.
+: BTW something similar happened to the term tritone. In modern times, it means exactly half an octave, but in the past it literally meant the aug 4th, which at the time was distinct from the dim 5th.