Collection of EDO impressions: Difference between revisions

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: '''Bozu:''' Hyperpent augmented with a lot of notes.

: '''Nicolai:''' You either get mavila or superpyth, there is no middle.

: '''Fumica:''' 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.

== [[40edo]] ==

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: '''Bozu:''' Lots of notes, but all of the bases seem to be covered. Probably the only edo between 35 and 49 worth all of the trouble of dealing with so many notes.

: '''Nicolai:''' Smaller version of 53EDO.

: '''Fumica:''' 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.

== [[42edo]] ==

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: '''Bozu:''' Hypopent composite. Looks great on paper, but is a lot of notes and is either difficult to use or perhaps not as good in practice as it ought to be.

: '''Nicolai:''' The other step-sibling of meantone.

: '''Fumica:''' 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.

== [[44edo]] ==

: '''Bozu:''' Amphipent diminished.

: '''Fumica:''' 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.

== [[45edo]] ==

: '''Bozu:''' Amphipent augmented.

: '''Fumica:''' The only legit edo tuning for flattone. Otherwise it has little utility. It has this weird structure of 9/8~10/9~11/10 all tempered together as a characteristic of flattone, but meanwhile the septimal comma is tuned to two steps, which feels a bit ugly. D-tier.

== [[46edo]] ==

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: '''Bozu:''' Hyperpent composite. Same thing where it looks great on paper, but I feel underwhelmed noodling around with it.

: '''Nicolai:''' You either get 5EDO or 7EDO, but there is a middle.

: '''Fumica:''' The second essential comma-level edo. Five more notes than 41edo, offering the distinction of two types of neutral intervals at the cost of a narrower septimal diesis. As an eighth-tone system, it has a true quartertone. With that and all the accurate approximations, the expressive possibilities are endless. Best as a 2.3.5.7.11.17.23-subgroup temperament. A-tier.

== [[47edo]] ==

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: '''Bozu:''' 12edo eighth-tones.

: '''Nicolai:''' 12EDO, but more fancy.

: '''Fumica:''' More appropriate as an interval category scheme than anything else. C-tier.

== [[49edo]] ==

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: '''Bozu:''' This is a great option for meantone. Notations seems to be less of a pain, but 53edo is almost better in every way.

: '''Nicolai:''' I consider this an optimal meantone EDO, due to a wealthy collection of notes here.

: '''Fumica:''' Close to 2/7-comma meantone so it has a niche. Has the same problem as 45edo, though less severe. C-tier.

== [[51edo]] ==

: '''Bozu:''' Not as versatile as 50edo.

: '''Fumica:''' 17edo with a major third from the augmented temperament, which can be a useful combo. Otherwise it has little tone efficiency. C-tier.

== [[52edo]] ==

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: '''Bozu:''' Generally the stopping point. If you are comfortable with >50 tones, then this tuning offers almost everything you will need. If not, stick with 31edo or something smaller.

: '''Nicolai:''' JI: The Book.

: '''Fumica:''' The third essential comma-level edo. This one is kinda overrated. The best thing about it is the distinction of 15/13 and 13/10 from nearby septimal intervals, which neither 41- nor 46edo does. What bugs me is that the fifth feels undertempered for pretty much every purpose, and while the 5-limit approximation is praiseworthy the rest deserves more love. Compared to 41- or 46edo, it feels slack and doesn't convey a sense of tightly packed well-compromisedness. B-tier.

== [[55edo]] ==

: '''ArrowHead:''' A standardisation and representation of 1/6-comma meantone, proposed by Telemann as a theoretical basis for analysing the intervals of meantone. Works well for most of Western music written since the Renaissance and even works today for songs that don't presuppose 12edo's enharmonics, but in practice I think it's really best suited for certain classical works as it's gotten to the point of diminishing returns. For non-classical musicians, the sound is likely to be far too similar to 12edo to justify the significant extra complexity, especially since 43 and 50 are already pushing it.

: '''Fumica:''' 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.

== [[56edo]] ==

: '''Fumica:''' A hemicommatic edo with a rather messed-up tuning profile. Nothing notable about it. D-tier.

== [[58edo]] ==

: '''Fumica:''' 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. This edo is best as a 2.3.5.7.11.13.29-subgroup system, but it has more to offer. Specifically, the harmonics 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. Everything considered, it is virtually the first full 23-limit system. All that bugs me is the minor fact that 11/8 and 7/5 are tuned too close to each other, only one comma apart. A-tier.

== [[59edo]] ==

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== [[60edo]] ==

: '''Bozu:''' 12edo, with each note sliced into five pieces. Not a bad option, except for the myriad of notes to navigate.

: '''Fumica:''' 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.

== [[61edo]] ==

: '''Fumica:''' Can be used to tune modus. Otherwise not bearing much utility. D-tier.

== [[62edo]] ==

: '''Fumica:''' The ultimate 23-limit meantone tuning. It re-tunes harmonics 13, 17, 19, and 23 for 31edo. I find these additions to 31edo's 11-limit very favorable. A-tier.

== [[63edo]] ==

: '''Fumica:''' Similar to 56edo, nothing notable about it. D-tier.

== [[65edo]] ==

: '''Bozu:''' There are so many tonal options, but many of them are very useful. Maybe this could rival 53edo for versatility. There are some limitations, though.

: '''Fumica:''' 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.

== [[67edo]] ==

: '''Fumica:''' A disastrous meantone tuning. F-tier.

== [[68edo]] ==

: '''Fumica:''' 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.

== [[70edo]] ==

: '''Fumica:''' 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.

== [[72edo]] ==

: '''Aura:''' While I don't recall making many songs with this EDO, I did compile a private list of Just Intervals, and I was quite fascinated with it for a time, as this EDO has better 5-limit and 7-limit approximations than both 12edo and 24edo.

: '''Fumica:''' The last essential comma-level edo. Has the same problem as 60edo. Even tho it approximates JI way better and thus qualifies for an essential comma-level edo, most of its structural features have been provided by 41- and 58edo. B-tier.

== [[73edo]] ==

: '''Fumica:''' A strange sharp-tending hemicommatic system that seems to allow some niche uses. C-tier.

== [[74edo]] ==

: '''Fumica:''' A good meantone tuning. Not much else to offer. D-tier.

== [[75edo]] ==

: '''Fumica:''' A good tetracot tuning. Otherwise nothing notable. D-tier.

== [[77edo]] ==

: '''Fumica:''' This edo is very sophisticated and hard to evaluate. It's an ideal tuning for the valentine temperament, obviously. It also seems to be capable of somewhat approximating the full 23-limit. Overall, the structure is a tight fit, with lots of quirks, but that's not too troublesome – they may as well be turned into advantages in the right circumstances. B-tier.

== [[79edo]] ==

: '''Fumica:''' A disastrous non-meantone tuning. F-tier.

== [[84edo]] ==

@@ Line 404: / Line 404: @@
 : '''Bozu:''' Hyperpent augmented with a lot of notes.
 : '''Nicolai:''' You either get mavila or superpyth, there is no middle.
+: '''Fumica:''' 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.
 == [[40edo]] ==
@@ Line 412: / Line 413: @@
 : '''Bozu:''' Lots of notes, but all of the bases seem to be covered. Probably the only edo between 35 and 49 worth all of the trouble of dealing with so many notes.
 : '''Nicolai:''' Smaller version of 53EDO.
+: '''Fumica:''' 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.
 == [[42edo]] ==
@@ Line 421: / Line 423: @@
 : '''Bozu:''' Hypopent composite. Looks great on paper, but is a lot of notes and is either difficult to use or perhaps not as good in practice as it ought to be.
 : '''Nicolai:''' The other step-sibling of meantone.
+: '''Fumica:''' 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.
 == [[44edo]] ==
 : '''Bozu:''' Amphipent diminished.
+: '''Fumica:''' 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.
 == [[45edo]] ==
 : '''Bozu:''' Amphipent augmented.
+: '''Fumica:''' The only legit edo tuning for flattone. Otherwise it has little utility. It has this weird structure of 9/8~10/9~11/10 all tempered together as a characteristic of flattone, but meanwhile the septimal comma is tuned to two steps, which feels a bit ugly. D-tier.
 == [[46edo]] ==
@@ Line 432: / Line 437: @@
 : '''Bozu:''' Hyperpent composite. Same thing where it looks great on paper, but I feel underwhelmed noodling around with it.
 : '''Nicolai:''' You either get 5EDO or 7EDO, but there is a middle.
+: '''Fumica:''' The second essential comma-level edo. Five more notes than 41edo, offering the distinction of two types of neutral intervals at the cost of a narrower septimal diesis. As an eighth-tone system, it has a true quartertone. With that and all the accurate approximations, the expressive possibilities are endless. Best as a 2.3.5.7.11.17.23-subgroup temperament. A-tier.
 == [[47edo]] ==
@@ Line 440: / Line 446: @@
 : '''Bozu:''' 12edo eighth-tones.
 : '''Nicolai:''' 12EDO, but more fancy.
+: '''Fumica:''' More appropriate as an interval category scheme than anything else. C-tier.
 == [[49edo]] ==
@@ Line 448: / Line 455: @@
 : '''Bozu:''' This is a great option for meantone. Notations seems to be less of a pain, but 53edo is almost better in every way.
 : '''Nicolai:''' I consider this an optimal meantone EDO, due to a wealthy collection of notes here.
+: '''Fumica:''' Close to 2/7-comma meantone so it has a niche. Has the same problem as 45edo, though less severe. C-tier.
 == [[51edo]] ==
 : '''Bozu:''' Not as versatile as 50edo.
+: '''Fumica:''' 17edo with a major third from the augmented temperament, which can be a useful combo. Otherwise it has little tone efficiency. C-tier.
 == [[52edo]] ==
@@ Line 460: / Line 469: @@
 : '''Bozu:''' Generally the stopping point. If you are comfortable with >50 tones, then this tuning offers almost everything you will need. If not, stick with 31edo or something smaller.
 : '''Nicolai:''' JI: The Book.
+: '''Fumica:''' The third essential comma-level edo. This one is kinda overrated. The best thing about it is the distinction of 15/13 and 13/10 from nearby septimal intervals, which neither 41- nor 46edo does. What bugs me is that the fifth feels undertempered for pretty much every purpose, and while the 5-limit approximation is praiseworthy the rest deserves more love. Compared to 41- or 46edo, it feels slack and doesn't convey a sense of tightly packed well-compromisedness. B-tier.
 == [[55edo]] ==
 : '''ArrowHead:''' A standardisation and representation of 1/6-comma meantone, proposed by Telemann as a theoretical basis for analysing the intervals of meantone. Works well for most of Western music written since the Renaissance and even works today for songs that don't presuppose 12edo's enharmonics, but in practice I think it's really best suited for certain classical works as it's gotten to the point of diminishing returns. For non-classical musicians, the sound is likely to be far too similar to 12edo to justify the significant extra complexity, especially since 43 and 50 are already pushing it.
+: '''Fumica:''' 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.
+== [[56edo]] ==
+: '''Fumica:''' A hemicommatic edo with a rather messed-up tuning profile. Nothing notable about it. D-tier.
+== [[58edo]] ==
+: '''Fumica:''' 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. This edo is best as a 2.3.5.7.11.13.29-subgroup system, but it has more to offer. Specifically, the harmonics 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. Everything considered, it is virtually the first full 23-limit system. All that bugs me is the minor fact that 11/8 and 7/5 are tuned too close to each other, only one comma apart. A-tier.
 == [[59edo]] ==
@@ Line 469: / Line 486: @@
 == [[60edo]] ==
 : '''Bozu:''' 12edo, with each note sliced into five pieces. Not a bad option, except for the myriad of notes to navigate.
+: '''Fumica:''' 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.
+== [[61edo]] ==
+: '''Fumica:''' Can be used to tune modus. Otherwise not bearing much utility. D-tier.
+== [[62edo]] ==
+: '''Fumica:''' The ultimate 23-limit meantone tuning. It re-tunes harmonics 13, 17, 19, and 23 for 31edo. I find these additions to 31edo's 11-limit very favorable. A-tier.
+== [[63edo]] ==
+: '''Fumica:''' Similar to 56edo, nothing notable about it. D-tier.
 == [[65edo]] ==
 : '''Bozu:''' There are so many tonal options, but many of them are very useful. Maybe this could rival 53edo for versatility. There are some limitations, though.
+: '''Fumica:''' 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.
+== [[67edo]] ==
+: '''Fumica:''' A disastrous meantone tuning. F-tier.
+== [[68edo]] ==
+: '''Fumica:''' 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.
+== [[70edo]] ==
+: '''Fumica:''' 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.
 == [[72edo]] ==
 : '''Aura:''' While I don't recall making many songs with this EDO, I did compile a private list of Just Intervals, and I was quite fascinated with it for a time, as this EDO has better 5-limit and 7-limit approximations than both 12edo and 24edo.
+: '''Fumica:''' The last essential comma-level edo. Has the same problem as 60edo. Even tho it approximates JI way better and thus qualifies for an essential comma-level edo, most of its structural features have been provided by 41- and 58edo. B-tier.
+== [[73edo]] ==
+: '''Fumica:''' A strange sharp-tending hemicommatic system that seems to allow some niche uses. C-tier.
+== [[74edo]] ==
+: '''Fumica:''' A good meantone tuning. Not much else to offer. D-tier.
+== [[75edo]] ==
+: '''Fumica:''' A good tetracot tuning. Otherwise nothing notable. D-tier.
+== [[77edo]] ==
+: '''Fumica:''' This edo is very sophisticated and hard to evaluate. It's an ideal tuning for the valentine temperament, obviously. It also seems to be capable of somewhat approximating the full 23-limit. Overall, the structure is a tight fit, with lots of quirks, but that's not too troublesome – they may as well be turned into advantages in the right circumstances. B-tier.
+== [[79edo]] ==
+: '''Fumica:''' A disastrous non-meantone tuning. F-tier.
 == [[84edo]] ==