User:FloraC/Fumica's edo impressions: Difference between revisions
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== Small == | == Small == | ||
These edos are where the steps tend to separate distinct interval categories rather than functioning as commatic inflections. I classify them into semitone-size, subsemitone-size (third-tone and quartertone), and diesis-size (fifth-tone and sixth-tone) edos. | |||
{| class="wikitable" | {| class="wikitable" | ||
|+ Tier list for small edos (10–38) | |+ Tier list for small edos (10–38) | ||
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|- | |- | ||
! A-tier | ! A-tier | ||
| 10, 15, 24, 31 | | 10, 15, 24, 27, 31 | ||
|- | |- | ||
! B-tier | ! B-tier | ||
| 11, 14, 22, | | 11, 14, 22, 34 | ||
|- | |- | ||
! C-tier | ! C-tier | ||
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=== Subsemitone-size === | === Subsemitone-size === | ||
* 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. | * 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 | * 16 – Potentially useful as every other step of 32edo or every third step of 48edo. Besides that, it has armodue, basically an extremely flat fifth that doesn't sound like the 3rd harmonic at all. "Fifthiness" is pointless 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 | * 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. | * 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. | * 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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=== Diesis-size === | === Diesis-size === | ||
* 27 – The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 subgroup with the sole exception of harmonic 15 tuned way too sharp, for I prefer a flat tuning of 15 or at least no sharper than 12edo's to improve its stability as a consonant major seventh. Other than that it's pretty good. | * 27 – The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 subgroup with the sole exception of harmonic 15 tuned way too sharp, for I prefer a flat tuning of 15 or at least no sharper than 12edo's to improve its stability as a consonant major seventh. Other than that it's pretty good. Octave compression gives better intonation. A-tier. | ||
* 28 – Potentially useful as every other step of 56edo. D-tier. | * 28 – Potentially useful as every other step of 56edo. D-tier. | ||
* 29 – The first edo that sounds like Pythagorean tuning with distinct chromatic and diatonic semitones, such that most contemporary 12edo music will sound alright if retempered to this through dominant. The patent-val interpretation is underwhelming. Otherwise it's a good framework as every other step of 58edo and every third step of 87edo. C-tier. | * 29 – The first edo that sounds like Pythagorean tuning with distinct chromatic and diatonic semitones, such that most contemporary 12edo music will sound alright if retempered to this through dominant. The patent-val interpretation is underwhelming. Otherwise it's a good framework as every other step of 58edo and every third step of 87edo. C-tier. | ||
* 30 – Potentially useful as every other step of 60edo. D-tier. | * 30 – Potentially useful as every other step of 60edo. D-tier. | ||
* 31 – This is a great edo | * 31 – This is a great edo. Too great it's a little unfun to work with. It has a tuning profile close to what I consider the optimal tuning of meantone, and migration, the meantone extension that maps harmonic 11 to the semi-augmented fourth, works almost perfectly in this system. Octave stretch gives better intonation. A-tier. | ||
* 32 – 27edo but worse. F-tier. | * 32 – 27edo but worse. F-tier. | ||
* 33 – 26edo 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 | * 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. | * 35 – Potentially useful as every other step of 70edo. D-tier. | ||
* 36 – The idea of adding | * 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. | * 37 – Potentially useful as every other step of 74edo or every third step of 111edo. 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. | * 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. | ||
== Medium == | == Medium == | ||
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=== Comma-size === | === 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 | * 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. | * 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. | * 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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* 60 – This edo has a particularly problematic fifth, in that it closes after twelve steps, tempering out the Pythagorean comma. As the first thing I leave meantone is to look for a fifth that leads to a positive Pythagorean comma, this edo is clearly not my thing. C-tier. | * 60 – This edo has a particularly problematic fifth, in that it closes after twelve steps, tempering out the Pythagorean comma. As the first thing I leave meantone is to look for a fifth that leads to a positive Pythagorean comma, this edo is clearly not my thing. C-tier. | ||
* 61 – Can be used to tune modus. Otherwise not bearing much utility. D-tier. | * 61 – Can be used to tune modus. Otherwise not bearing much utility. D-tier. | ||
* 62 – The ultimate 23-limit meantone tuning. It re-tunes harmonics 13, 17, 19, and 23 | * 62 – The ultimate 23-limit meantone tuning. It re-tunes harmonics 13, 17, and 19, and paves the path to the 23 from 31edo. I find these additions to 31edo's 11-limit very favorable. A-tier. | ||
* 63 – Similar to 56edo, nothing notable about it. D-tier. | * 63 – Similar to 56edo, nothing notable about it. D-tier. | ||
* 65 – As every other step of 130edo, this edo is excellent in the 2.3.5.11.19.23-subgroup, but the contrast between that and the poor approximations to 7 and 13 is fatal. Still, it allows a dual-7 dual-13 approach, not very satisfying at this level but better than nothing. C-tier. | * 65 – As every other step of 130edo, this edo is excellent in the 2.3.5.11.19.23-subgroup, but the contrast between that and the poor approximations to 7 and 13 is fatal. Still, it allows a dual-7 dual-13 approach, not very satisfying at this level but better than nothing. C-tier. | ||
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== Large == | == Large == | ||
Starting from here, it'd be better to adopt a more systematic approach, for which I'm planning an essay where I'll investigate the 2.3.5.7.11.13.19-subgroup JI and temperaments. | Starting from here, it'd be better to adopt a more systematic approach, for which I'm planning an essay where I'll investigate the 2.3.5.7.11.13.19.29-subgroup JI and temperaments. | ||