User:Astaryuu/15edo Notes/Notes and chords: Difference between revisions

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==Inside you are two fifths (and two tritones)==

15edo... doesn't really have a fifthy fifth. 12edo's fifth sounds the way it does because it's an extremely good estimation of a so-called "perfect fifth". The best fifth in 15edo is 9\15, but that sounds notably sharp. Again, you can probably get used to it, but it'll mean 12edo strategies might sound a bit off in it. That's not what it means to be "wolf", though.

15edo... doesn't really have a fifthy fifth. 12edo's fifth sounds the way it does because it's an extremely good estimation of a so-called "perfect fifth" (in technical terms, it's 1.9¢ flat of [[3/2]], the second-smallest numerator and denominator you can put in an interval non-trivially). The best fifth in 15edo is 9\15, but that sounds notably sharp. Again, you can probably get used to it, but it'll mean 12edo strategies might sound a bit off in it. That's not what it means to be "wolf", though.

The actual wolf fifth, is the valentine semitone ''below'' that 720¢ interval. At 640¢, meet 8\15, the wolf fifth. You could think of this as four neutral seconds stacked on top of each other, but at that point the margin between the neutral second and 2\15 goes beyond the diesis. This is actually also a tritone. Since 15 is odd, there is no true position halfway between octaves - but 7\15 and 8\15 bracket that midpoint.

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This means we end up calling 9\15 the major fifth, 8\15 the minor fifth and major tritone, 7\15 the minor tritone, and 2\15 the perfect second. (Note that in 12edo, the tritone is probably best described as neutral, like the neutral second described earlier.) After all, our "neutral second" isn't really neutral either. Usually neutral seconds are defined as 150¢ specifically. Thirds and fourths are still somewhat normal relative to 12edo, so they don't flip even though there are audible differences.

Of course, chords are named after the third, so we can't just call them major and minor based on which fifth they use. Instead, we call chords built using the "major" fifth natural, while ones built with the "minor" wolf fifth are "wolf." For example, 0-5-9 is the major chord, while 0-5-8 is the wolfmajor chord. Since the wolf fifth is a tritone, wolf chords can be used for similar tritone-y stuff as the 12edo tritone - but note that neither this tritone nor the previous one are as dissonant as the 12edo tritone. Even edos perfectly hit the ~~1 to square root~~ of 2 ~~interval that~~ defines the tritone, while odd edos can't.

Of course, chords are named after the third, so we can't just call them major and minor based on which fifth they use. Instead, we call chords built using the "major" fifth natural, while ones built with the "minor" wolf fifth are "wolf." For example, 0-5-9 is the major chord, while 0-5-8 is the wolfmajor chord. Since the wolf fifth is a tritone, wolf chords can be used for similar tritone-y stuff as the 12edo tritone - but note that neither this tritone nor the previous one are as dissonant as the 12edo tritone. Even edos perfectly hit the midpoint of [[2/1]], which defines the tritone, while odd edos can't do that.

==Sixths and sevenths==

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 ==Inside you are two fifths (and two tritones)==
-edo... doesn't really have a fifthy fifth. 12edo's fifth sounds the way it does because it's an extremely good estimation of a so-called "perfect fifth". The best fifth in 15edo is 9\15, but that sounds notably sharp. Again, you can probably get used to it, but it'll mean 12edo strategies might sound a bit off in it. That's not what it means to be "wolf", though.
+edo... doesn't really have a fifthy fifth. 12edo's fifth sounds the way it does because it's an extremely good estimation of a so-called "perfect fifth" (in technical terms, it's 1.9¢ flat of [[3/2]], the second-smallest numerator and denominator you can put in an interval non-trivially). The best fifth in 15edo is 9\15, but that sounds notably sharp. Again, you can probably get used to it, but it'll mean 12edo strategies might sound a bit off in it. That's not what it means to be "wolf", though.
 The actual wolf fifth, is the valentine semitone ''below'' that 720¢ interval. At 640¢, meet 8\15, the wolf fifth. You could think of this as four neutral seconds stacked on top of each other, but at that point the margin between the neutral second and 2\15 goes beyond the diesis. This is actually also a tritone. Since 15 is odd, there is no true position halfway between octaves - but 7\15 and 8\15 bracket that midpoint.
@@ Line 31: / Line 31: @@
 This means we end up calling 9\15 the major fifth, 8\15 the minor fifth and major tritone, 7\15 the minor tritone, and 2\15 the perfect second. (Note that in 12edo, the tritone is probably best described as neutral, like the neutral second described earlier.) After all, our "neutral second" isn't really neutral either. Usually neutral seconds are defined as 150¢ specifically. Thirds and fourths are still somewhat normal relative to 12edo, so they don't flip even though there are audible differences.
-Of course, chords are named after the third, so we can't just call them major and minor based on which fifth they use. Instead, we call chords built using the "major" fifth natural, while ones built with the "minor" wolf fifth are "wolf." For example, 0-5-9 is the major chord, while 0-5-8 is the wolfmajor chord. Since the wolf fifth is a tritone, wolf chords can be used for similar tritone-y stuff as the 12edo tritone - but note that neither this tritone nor the previous one are as dissonant as the 12edo tritone. Even edos perfectly hit the 1 to square root of 2 interval that defines the tritone, while odd edos can't.
+Of course, chords are named after the third, so we can't just call them major and minor based on which fifth they use. Instead, we call chords built using the "major" fifth natural, while ones built with the "minor" wolf fifth are "wolf." For example, 0-5-9 is the major chord, while 0-5-8 is the wolfmajor chord. Since the wolf fifth is a tritone, wolf chords can be used for similar tritone-y stuff as the 12edo tritone - but note that neither this tritone nor the previous one are as dissonant as the 12edo tritone. Even edos perfectly hit the midpoint of [[2/1]], which defines the tritone, while odd edos can't do that.
 ==Sixths and sevenths==