User:FloraC/Fumica's edo impressions: Difference between revisions

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* 15 – The error of the fifth is getting quite large for its step size, particularly if you compare it with 10edo. Either this or 10edo can be viewed as the opposite of 14edo, so I think of this as the direct competitor of 10edo. As for which I prefer? I have no idea. A-tier.

* 16 – Potentially useful as every other step of 32edo. Besides that, it has armodue, basically an extremely flat fifth that doesn't sound like the 3rd harmonic at all. "Fifthiness" is useless if not for approximating the 3rd harmonic, so I'm afraid I don't consider this approach to have much value. D-tier.

* 17 – This edo ~~contains an impressive~~ diatonic scale ~~which is nice for both melody~~ and harmony~~. Semiquartal~~ harmony, that is using the contrast between 7/4 and 12/7 as the basis of tonality, ~~works exceptionally well in this system~~. S-tier.

* 17 – This edo is characterized by its hard diatonic scale, with more contrasting step sizes than 12edo's basic diatonic scale. This gives it more intense voice leading and more cathartic resolutions. Traditional tertian harmony works pretty well here, but semiquartal harmony, that is using the contrast between 7/4 and 12/7 as the basis of tonality, does even better. S-tier.

* 18 – Potentially useful as every other step of 36edo. D-tier.

* 19 – This edo is where my microtonal journey began. Extremely versatile yet friendly to beginners. Using it as a tuning of meantone, the tuning profile is sort of opposite to 12edo, but with seven more pitch classes, the expressive possibility explodes. Presence of an exact hemitwelfth sets it apart from many other meantone edos. Octave stretch solves the intonational problem to a large extent. S-tier.

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* 32 – 27edo but worse. F-tier.

* 33 – 26edo but worse. F-tier.

* 34 – This is to 17edo what 24edo is to 12edo. While 17edo is often good enough, this offers some more sophisticated solutions such as tetracot. Even the harmonics 7 and 11, commonly cited as poor in this edo, are convincing enough to me, since when I worked with modus I never had a problem with the intonation at all, unlike with porcupine. The sound is better than the structure. B-tier.

* 34 – This is to 17edo what 24edo is to 12edo. While 17edo is often good enough, this offers some more sophisticated solutions such as tetracot. Even the harmonics 7 and 11, which come from 17edo and are commonly cited as relatively poor in this edo, are convincing enough to me, since when I worked with modus I never had a problem with the intonation at all, unlike with porcupine. The sound is better than the structure. B-tier.

* 35 – Potentially useful as every other step of 70edo. D-tier.

* 36 – The idea of adding ~~third~~ tones to plain 12edo music is interesting, but none of my attempts have been successful as I generally find them to sound forced. I think this edo is more difficult to use than it appears. C-tier.

* 36 – The idea of adding sixth tones to plain 12edo music is interesting, but none of my attempts have been successful as I generally find them to sound forced. I think this edo is more difficult to use than it appears. C-tier.

* 37 – Potentially useful as every other step of 74edo. Besides that, it has a good 2.5.7.11.13 subgroup interpretation, tho I have no idea how harmony in this subgroup is supposed to work. D-tier.

* 38 – This is to 19edo what 24edo is to 12edo. On paper it adds decent approximation to harmonics 11, 17, and 19, but in practice I never had a situation where I felt I needed these additional notes when working with 19edo. C-tier.

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=== Comma-size ===

* 39 – 1/5-comma quasisuper, most notable for tuning the minor second to 28/27 (with the 39d val) which I feel is where the tension peaks for voice leading. Such an overlooked system despite ~~being similar~~ to 27edo in many ways. B-tier.

* 39 – 1/5-comma quasisuper, most notable for tuning the minor second to 28/27 (with the 39d val) which I feel is where the tension peaks for voice leading. Such an overlooked system despite the similarity to 27edo in many ways. B-tier.

* 41 – The first of the five essential comma-level edos, and the first edo to achieve 9-odd-limit distinction and consistency. This is most significant for providing three flavors for each chromatic category: classical, Pythagorean, and septimal. In this case it is a schismic and garischismic system, so that all three kinds are separated by the same comma step and can be found on a stack of fifths. The comma step is somewhat larger than just, making the differences more pronounced, which is part of why I think this edo is pretty deep – the step isn't only a comma, but many things at once, including but not limited to the septimal dieses, as well as the chroma of the archaeotonic scale, the scale of Tetracot[7]. The best subgroup of this edo is, actually, 2.3.5.7.11.19. Prime 13 is certainly plausible, but prime 19 fits way better. There's a unique uniform tuning for the harmonic segment 18::22, a fact related to the vanish of s10 = 100/99 and s9/s11 = 243/242. The beauty of this edo goes even beyond the structure, but also to the intonation: it has a very slightly sharp 3 and a more noticeably flat 5, making a flat, more stable 15; that is ideal for my music. Finally, it's an ideal tuning for the magic temperament. I can't compliment it enough. S-tier.

* 43 – 1/5-comma meantone, not a bad meantone tuning in the 5-limit. The 3 and 5 are equally off, making up a beautifully pure 15. Unfortunately the diesis is too small to achieve good septimal and undecimal harmony. B-tier.

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 * 15 – The error of the fifth is getting quite large for its step size, particularly if you compare it with 10edo. Either this or 10edo can be viewed as the opposite of 14edo, so I think of this as the direct competitor of 10edo. As for which I prefer? I have no idea. A-tier.
 * 16 – Potentially useful as every other step of 32edo. Besides that, it has armodue, basically an extremely flat fifth that doesn't sound like the 3rd harmonic at all. "Fifthiness" is useless if not for approximating the 3rd harmonic, so I'm afraid I don't consider this approach to have much value. D-tier.
-* 17 – This edo contains an impressive diatonic scale which is nice for both melody and harmony. Semiquartal harmony, that is using the contrast between 7/4 and 12/7 as the basis of tonality, works exceptionally well in this system. S-tier.
+* 17 – This edo is characterized by its hard diatonic scale, with more contrasting step sizes than 12edo's basic diatonic scale. This gives it more intense voice leading and more cathartic resolutions. Traditional tertian harmony works pretty well here, but semiquartal harmony, that is using the contrast between 7/4 and 12/7 as the basis of tonality, does even better. S-tier.
 * 18 – Potentially useful as every other step of 36edo. D-tier.
 * 19 – This edo is where my microtonal journey began. Extremely versatile yet friendly to beginners. Using it as a tuning of meantone, the tuning profile is sort of opposite to 12edo, but with seven more pitch classes, the expressive possibility explodes. Presence of an exact hemitwelfth sets it apart from many other meantone edos. Octave stretch solves the intonational problem to a large extent. S-tier.
@@ Line 66: / Line 66: @@
 * 32 – 27edo but worse. F-tier.
 * 33 – 26edo but worse. F-tier.
-* 34 – This is to 17edo what 24edo is to 12edo. While 17edo is often good enough, this offers some more sophisticated solutions such as tetracot. Even the harmonics 7 and 11, commonly cited as poor in this edo, are convincing enough to me, since when I worked with modus I never had a problem with the intonation at all, unlike with porcupine. The sound is better than the structure. B-tier.
+* 34 – This is to 17edo what 24edo is to 12edo. While 17edo is often good enough, this offers some more sophisticated solutions such as tetracot. Even the harmonics 7 and 11, which come from 17edo and are commonly cited as relatively poor in this edo, are convincing enough to me, since when I worked with modus I never had a problem with the intonation at all, unlike with porcupine. The sound is better than the structure. B-tier.
 * 35 – Potentially useful as every other step of 70edo. D-tier.
-* 36 – The idea of adding third tones to plain 12edo music is interesting, but none of my attempts have been successful as I generally find them to sound forced. I think this edo is more difficult to use than it appears. C-tier.
+* 36 – The idea of adding sixth tones to plain 12edo music is interesting, but none of my attempts have been successful as I generally find them to sound forced. I think this edo is more difficult to use than it appears. C-tier.
 * 37 – Potentially useful as every other step of 74edo. Besides that, it has a good 2.5.7.11.13 subgroup interpretation, tho I have no idea how harmony in this subgroup is supposed to work. D-tier.
 * 38 – This is to 19edo what 24edo is to 12edo. On paper it adds decent approximation to harmonics 11, 17, and 19, but in practice I never had a situation where I felt I needed these additional notes when working with 19edo. C-tier.
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 === Comma-size ===
-* 39 – 1/5-comma quasisuper, most notable for tuning the minor second to 28/27 (with the 39d val) which I feel is where the tension peaks for voice leading. Such an overlooked system despite being similar to 27edo in many ways. B-tier.
+* 39 – 1/5-comma quasisuper, most notable for tuning the minor second to 28/27 (with the 39d val) which I feel is where the tension peaks for voice leading. Such an overlooked system despite the similarity to 27edo in many ways. B-tier.
 * 41 – The first of the five essential comma-level edos, and the first edo to achieve 9-odd-limit distinction and consistency. This is most significant for providing three flavors for each chromatic category: classical, Pythagorean, and septimal. In this case it is a schismic and garischismic system, so that all three kinds are separated by the same comma step and can be found on a stack of fifths. The comma step is somewhat larger than just, making the differences more pronounced, which is part of why I think this edo is pretty deep – the step isn't only a comma, but many things at once, including but not limited to the septimal dieses, as well as the chroma of the archaeotonic scale, the scale of Tetracot[7]. The best subgroup of this edo is, actually, 2.3.5.7.11.19. Prime 13 is certainly plausible, but prime 19 fits way better. There's a unique uniform tuning for the harmonic segment 18::22, a fact related to the vanish of s10 = 100/99 and s9/s11 = 243/242. The beauty of this edo goes even beyond the structure, but also to the intonation: it has a very slightly sharp 3 and a more noticeably flat 5, making a flat, more stable 15; that is ideal for my music. Finally, it's an ideal tuning for the magic temperament. I can't compliment it enough. S-tier.
 * 43 – 1/5-comma meantone, not a bad meantone tuning in the 5-limit. The 3 and 5 are equally off, making up a beautifully pure 15. Unfortunately the diesis is too small to achieve good septimal and undecimal harmony. B-tier.