User:FloraC/Fumica's edo impressions: Difference between revisions
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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 – | * 16 – Workable as a temperament of the 2.5.7 subgroup, a subgroup that calls for novel chord structures such as 4:7:10. 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 hold much water. D-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. | * 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. | ||
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* 22 – The least evil solution to porcupine and less so to superpyth. I happen to have experience working with porcupine and it felt quite alright, except that I often found myself struggling to combat its out-of-tune nature. B-tier. | * 22 – The least evil solution to porcupine and less so to superpyth. I happen to have experience working with porcupine and it felt quite alright, except that I often found myself struggling to combat its out-of-tune nature. B-tier. | ||
* 23 – Potentially useful as every other step of 46edo. D-tier. | * 23 – Potentially useful as every other step of 46edo. D-tier. | ||
* 24 – This is kind of a normie's edo, but also the most accessible. Quartertones in my otherwise 12edo works often go unnoticed by the audience. A natural next step of 12edo with a structurally beautiful 2.3.5.11.17.19 subgroup interpretation. A-tier. | * 24 – This is kind of a normie's edo, but also the most accessible. Quartertones in my otherwise 12edo works often go unnoticed by the audience. A natural next step of 12edo with a structurally beautiful 2.3.5.11.17.19-subgroup interpretation. A-tier. | ||
* 25 – | * 25 – Like 16edo, workable as a temperament of the 2.5.7 subgroup. D-tier. | ||
* 26 – Just as 19edo is the point separating meantone and flattone, this is the point separating flattone and a meantone extension that implies an even flatter fifth. Therefore it should share all the advantages of 12edo and 19edo, at least theoretically, that is if not for its poor intonation in the 5-limit. C-tier. | * 26 – Just as 19edo is the point separating meantone and flattone, this is the point separating flattone and a meantone extension that implies an even flatter fifth. Therefore it should share all the advantages of 12edo and 19edo, at least theoretically, that is if not for its poor intonation in the 5-limit. C-tier. | ||
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* 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. | * 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 sixth tones to plain 12edo music | * 36 – This edo is more difficult to use than it appears. The idea of adding sixth tones to plain 12edo music might be interesting, but I generally find them to sound forced. Added to this fact is that I think of 12edo as a complete 7-limit system, so the alternative mapping of harmonic 7 only serves to create mental dissonance. C-tier. | ||
* 37 – | * 37 – This edo offers good approximation to harmonics 5, 7, 11 and 13. The last two primes adds the much needed variety to the otherwise pretty dull sound of the 2.5.7 subgroup. 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. | * 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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| 41 | | 41, 58 | ||
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! A-tier | ! A-tier | ||
| 46 | | 46, 62 | ||
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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 the similarity 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 | * 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 septischismic 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 apparently 2.3.5.7.11.19.29.31 thanks to the unique uniform tunings for the harmonic segments 18::22 and 27::33 – a fact related to the vanish of 100/99 (S10) and 243/242 (S9/S11) – but prime 13 is just as plausible. I consider it the first edo to deal with the all-important 2.3.5.7.11.13.19.29 subgroup. The beauty of this edo goes beyond the structure, but 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. | ||
* 44 – This edo adds decent approximation to harmonic 13 on top of 22edo's 11-limit, which is pretty tense to start with. At this point it just all breaks down. D-tier. | * 44 – This edo adds decent approximation to harmonic 13 on top of 22edo's 11-limit, which is pretty tense to start with. At this point it just all breaks down. D-tier. | ||
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* 55 – This edo is out of the optimal range of meantone. Septimal meantone feels dumb here since we know 43edo is sharp enough. It can be used for mohaha, but that feels so similar to 24edo that I'd just go with the latter. D-tier. | * 55 – This edo is out of the optimal range of meantone. Septimal meantone feels dumb here since we know 43edo is sharp enough. It can be used for mohaha, but that feels so similar to 24edo that I'd just go with the latter. D-tier. | ||
* 56 – A hemicommatic edo with a rather messed-up tuning profile. Nothing notable about it. D-tier. | * 56 – A hemicommatic edo with a rather messed-up tuning profile. Nothing notable about it. D-tier. | ||
* 58 – The fourth essential comma-level edo. Being the first edo with full 11-odd-limit distinction, this one is easily adorable. Whereas 41edo tunes the fifth to 24 steps, this edo tunes the fourth to 24 steps, and the implication is its 2.3.5.7.13.29 subgroup is analogous to 41edo's 2.3.5.7.11.19 subgroup. | * 58 – The fourth essential comma-level edo. Being the first edo with full 11-odd-limit distinction, this one is easily adorable. Whereas 41edo tunes the perfect fifth to 24 steps, this edo tunes the perfect fourth to 24 steps, and the implication is its 2.3.5.7.13.29 subgroup is analogous to 41edo's 2.3.5.7.11.19 subgroup. Due to this, it would seem like it is most useful as a temperament of above plus prime 11, but it has more to offer – the 19 and 23 in the 58hi val are surprisingly convincing, and although the 17 doesn't blend quite well it at least looks good on paper. So like 41edo, it deals adequately with everything in the 2.3.5.7.11.13.19.29 subgroup, making it essentially a dual. Best tuned with a pure perfect twelfth. S-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. | * 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. | ||
=== Subcomma-size === | |||
* 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, and 19, and paves the path to the 23 from 31edo. I find these additions to 31edo's 11-limit very favorable. A-tier. | * 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. | ||
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* 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. | ||
* 67 – A disastrous meantone tuning. F-tier. | * 67 – A disastrous meantone tuning. F-tier. | ||
* 68 – While this edo contains 17edo and if we compare it with 51edo, it clearly hits more harmonic targets, it should be noted that linearly dividing the steps into four is a weaker move than into two or three, as quarter-step offsets don't tend to create new categories, unlike third- or half-step offsets. This is especially true of this edo, as 34edo hits lots of harmonic targets already. Another obvious flaw is the awkward situation with prime 11. C-tier. | * 68 – While this edo contains 17edo and if we compare it with 51edo, it clearly hits more harmonic targets, it should be noted that linearly dividing the steps into four is a weaker move than into two or three, as quarter-step offsets don't tend to create new categories, unlike third- or half-step offsets. This is especially true of this edo, as 34edo hits lots of harmonic targets already. Another obvious flaw is the awkward situation with prime 11. C-tier. | ||
* 70 – As every other step of 140edo, this edo's structure allows lots of niche uses. Unfortunately none of them is interesting enough to make me stay very long. C-tier. | * 70 – As every other step of 140edo, this edo's structure allows lots of niche uses. Unfortunately none of them is interesting enough to make me stay very long. C-tier. | ||