Collection of EDO impressions - Revision history

FloraC: Update

2026-08-30T09:55:30Z

Update

MisterShafXen at 20:55, 18 May 2026

2026-05-18T20:55:44Z

← Older revision		Revision as of 20:55, 18 May 2026
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	:: 1. next-smallest EDO that has something resembling [[3/2]]. This sounds like an "equalized" diatonic scale, so that there are no more "major" or "minor" thirds, but just "thirds." 7-EDO is also notable for being an equalized version of a number of scales, including but not limited to: the diatonic scale, [[mohajira]]/[[maqamic]][7] and its [[MODMOS]]'s, [[porcupine]][7], [[tetracot]][7], and [[mavila]][7]. Anyone who's familiar with any of these scales will be able to hear echos of them in 7-EDO. Additionally, if you [[octave stretching\|stretch the octaves]] to about 1230 [[cents]], you get something which is like every other step of the popular nonoctave [[88cET]], and which can also be thought of as a nonoctave version of [[tetracot]] temperament, with really good [[2:3:5]] chords.		:: 1. next-smallest EDO that has something resembling [[3/2]]. This sounds like an "equalized" diatonic scale, so that there are no more "major" or "minor" thirds, but just "thirds." 7-EDO is also notable for being an equalized version of a number of scales, including but not limited to: the diatonic scale, [[mohajira]]/[[maqamic]][7] and its [[MODMOS]]'s, [[porcupine]][7], [[tetracot]][7], and [[mavila]][7]. Anyone who's familiar with any of these scales will be able to hear echos of them in 7-EDO. Additionally, if you [[octave stretching\|stretch the octaves]] to about 1230 [[cents]], you get something which is like every other step of the popular nonoctave [[88cET]], and which can also be thought of as a nonoctave version of [[tetracot]] temperament, with really good [[2:3:5]] chords.
	:: 2. equidiatonic, which is trippy		:: 2. equidiatonic, which is trippy
			:'''MisterShafXen:''' Yay, diatonic! Oh no, it's all neutral (2.3.11.13.29 subgroup, anyone?)
	: '''Yourmusic Productions:''' The emancipation from harmony, but now with recognisable, if bland diatonic melodies.		: '''Yourmusic Productions:''' The emancipation from harmony, but now with recognisable, if bland diatonic melodies.
	: '''Carmen14edo/Bragtime:''' The basis of [[knowsur]]'s melody and harmony on the [[14edo]] album ''NANA WODORI'', and thus one of my personal favorites.		: '''Carmen14edo/Bragtime:''' The basis of [[knowsur]]'s melody and harmony on the [[14edo]] album ''NANA WODORI'', and thus one of my personal favorites.

Eufalesio: Changed impressions

2026-04-19T12:00:03Z

Changed impressions

Show changes

BudjarnLambeth: /* 30edo */ expanded my yapping here

2026-04-11T11:21:31Z

30edo: expanded my yapping here

← Older revision		Revision as of 11:21, 11 April 2026
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	: '''Yourmusic Productions:''' [[6edo\|Whole tone]] + [[Blackwood]]. Like [[24edo]], mainly just adds more ways to sound bad compared to [[15edo]] and not worth the hassle.		: '''Yourmusic Productions:''' [[6edo\|Whole tone]] + [[Blackwood]]. Like [[24edo]], mainly just adds more ways to sound bad compared to [[15edo]] and not worth the hassle.
	: '''Fumica:''' Potentially useful as every other step of [[60edo]]. D-tier.		: '''Fumica:''' Potentially useful as every other step of [[60edo]]. D-tier.
	: '''Budjarn Lambeth:''' The most simple [[dual-fifth]] edo, ~~but~~ not as "in-tune" as ~~others~~.		: '''Budjarn Lambeth:''' The most simple [[dual-fifth]] edo, not as "in-tune" as bigger ones, but a good introduction to the dual-fifth concept. It's kind of underrated because, while it doesn't have the same precise, luminous [[JI]] chords as 29 or 31, its [[wolf interval]]s are fewer and have less bite than 29 or 31 - so 30edo is actually relatively easy to noodle around in without hitting any ''really sour'' notes. It's not a good system for the JI-centric, regular temperament-centric approach that works for other big edos - but if you meet 30edo ''on its own terms'', it's actually surprisingly approachable, and you can get a surprising amount of sweetness out of it. It kind of sounds like if JI was muffled underwater, if that makes sense? Everything's a little murky, but in a 'smooth' way - not necessarily unpleasant. [[Bryan Deister]] has lots of good [[Lumatone]] pieces in 30edo. Don't get me wrong, it's not ''as'' useful as 29 or 31, but it's much more useful than it's made out to be.
	: '''Eufalesio:''' Useless. FF.		: '''Eufalesio:''' Useless. FF.

	== [[31edo]] ==		== [[31edo]] ==

Jerdle: /* 27edo */Minor formatting fix

2026-03-17T10:05:23Z

27edo: Minor formatting fix

← Older revision		Revision as of 10:05, 17 March 2026
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	: '''Aura:''' Not going to lie, given how underexplored this EDO is, I felt it necessary to try working with a [[159edo]]-based retuning of it. Judging from my experience with that, it should suffice to say that working with Superlocrian in this EDO is another interesting experience.		: '''Aura:''' Not going to lie, given how underexplored this EDO is, I felt it necessary to try working with a [[159edo]]-based retuning of it. Judging from my experience with that, it should suffice to say that working with Superlocrian in this EDO is another interesting experience.
	: '''Bozu:''' Comte [[hyperpent]]. Another one with tons of usable tonal possibilities that seems to get little actual use.		: '''Bozu:''' Comte [[hyperpent]]. Another one with tons of usable tonal possibilities that seems to get little actual use.
	: '''Nicolai:''' Amazing approximations of intervals like [[7/6]], [[6/5]], [[5/4]] (but its the same as [[12edo\|12EDO]]), [[3/2]], [[5/3], and [[7/4]]. Its weird how it manages to work this much with being a power of 3.		: '''Nicolai:''' Amazing approximations of intervals like [[7/6]], [[6/5]], [[5/4]] (but its the same as [[12edo\|12EDO]]), [[3/2]], [[5/3]], and [[7/4]]. Its weird how it manages to work this much with being a power of 3.
	: '''Keenan:''' First true tetracot/[[modus]] EDO. Otherwise, it has an interesting combination of things ([[superpyth]], [[neutral third]]s, [[augene]], [[sensi]]), which, however, all exist in smaller EDOs.		: '''Keenan:''' First true tetracot/[[modus]] EDO. Otherwise, it has an interesting combination of things ([[superpyth]], [[neutral third]]s, [[augene]], [[sensi]]), which, however, all exist in smaller EDOs.
	: '''Yourmusic Productions:''' Like all pure powers of 3, unusually good for it's size. All the melodic coolness of 9 plus decent minor and [[neutral]] intervals and an acceptable 5th. Definitely my favourite superpyth system of manageable size.		: '''Yourmusic Productions:''' Like all pure powers of 3, unusually good for it's size. All the melodic coolness of 9 plus decent minor and [[neutral]] intervals and an acceptable 5th. Definitely my favourite superpyth system of manageable size.

Zhenlige: /* 72edo */ fix typo

2026-03-11T12:19:49Z

72edo: fix typo

← Older revision		Revision as of 12:19, 11 March 2026
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	: '''Aura:''' While I don't recall making many songs with this EDO, I did compile a private list of [[JI\|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]], with the latter being inherited from [[36edo]]. However, the fifth is not [[telic]], which is a problem for me in its own right.		: '''Aura:''' While I don't recall making many songs with this EDO, I did compile a private list of [[JI\|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]], with the latter being inherited from [[36edo]]. However, the fifth is not [[telic]], which is a problem for me in its own right.
	: '''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 [[41edo\|41-]] and [[58edo]]. B-tier.		: '''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 [[41edo\|41-]] and [[58edo]]. B-tier.
	: '''Zhenlige:''' The ultimate extension of [[12edo]] and [[24edo]]. Its [[11-limit]] is very accurate with a slightly ~~sharp~~ tendency that works well with 12edo's flat [[3/1\|3]], and some higher limit intervals are also usable. [[Compton]] which is useful in 12edo-based programs. The only notable [[13-limit]] non-[[akea]] EDO around this size. A powerful tool for modulating quartertones, which can be difficult in 24edo itself. Good for [[miracle]]. Suitable for octave stretching if only [[17-limit]] or below is used. Playable by using three 24edo instruments or six 12edo instruments.		: '''Zhenlige:''' The ultimate extension of [[12edo]] and [[24edo]]. Its [[11-limit]] is very accurate with a slightly flat tendency that works well with 12edo's flat [[3/1\|3]], and some higher limit intervals are also usable. [[Compton]] which is useful in 12edo-based programs. The only notable [[13-limit]] non-[[akea]] EDO around this size. A powerful tool for modulating quartertones, which can be difficult in 24edo itself. Good for [[miracle]]. Suitable for octave stretching if only [[17-limit]] or below is used. Playable by using three 24edo instruments or six 12edo instruments.
	: '''Eufalesio:''' The first compton edo that achieves any semblance of JIoid goodness. This was one of the first finer edos I've composed in. It has an astounding 11-limit, and decent 19-limit! It's also a multiple of 12, so it is very transposing-friendly and building it is trivial! It's a miracle, and it also supports it! SSS.		: '''Eufalesio:''' The first compton edo that achieves any semblance of JIoid goodness. This was one of the first finer edos I've composed in. It has an astounding 11-limit, and decent 19-limit! It's also a multiple of 12, so it is very transposing-friendly and building it is trivial! It's a miracle, and it also supports it! SSS.

	== [[73edo]] ==		== [[73edo]] ==

FloraC: Minor style unification. Linking.

2026-03-09T10:46:40Z

Minor style unification. Linking.

Show changes

Eufalesio: More impressions!

2026-03-08T17:50:26Z

More impressions!

Show changes

Zhenlige: update to version 225320

2026-03-07T17:26:21Z

update to version 225320

Show changes

FloraC: Update

2026-02-26T12:06:41Z

Update

← Older revision		Revision as of 12:06, 26 February 2026
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	: '''Carmen14edo/Bragtime:''' I want [[Easley Blackwood]]'s "16 notes: Andantino" to play at my funeral		: '''Carmen14edo/Bragtime:''' I want [[Easley Blackwood]]'s "16 notes: Andantino" to play at my funeral
	: '''Deja Igliashon:''' There's lots of cool stuff happening in 16edo, but a surprising amount of it is basically just inherited from [[8edo]]. What 16edo adds to the mix is a nice [[5-limit]] major 3rd and a nice approximation to the 7th harmonic, and also the freaky-funky [[Mavila]][7] [[antidiatonic\|inside-out diatonic]] (where major chords become minor, minor chords become major, diminished chords become augmented, and mice chase cats). But IDK, despite my high tolerance for tunings with awful or non-existent perfect 5ths, I've yet to find anything I can do in 16edo that I don't feel like I can do better in a different tuning.		: '''Deja Igliashon:''' There's lots of cool stuff happening in 16edo, but a surprising amount of it is basically just inherited from [[8edo]]. What 16edo adds to the mix is a nice [[5-limit]] major 3rd and a nice approximation to the 7th harmonic, and also the freaky-funky [[Mavila]][7] [[antidiatonic\|inside-out diatonic]] (where major chords become minor, minor chords become major, diminished chords become augmented, and mice chase cats). But IDK, despite my high tolerance for tunings with awful or non-existent perfect 5ths, I've yet to find anything I can do in 16edo that I don't feel like I can do better in a different tuning.
	: '''Fumica:''' Potentially useful as every other step of [[32edo]]. Besides that, it has [[armodue (temperament)\|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.		: '''Fumica:''' Potentially useful as every other step of [[32edo]] or every third step of [[48edo]]. Besides that, it has [[armodue (temperament)\|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.
	: '''Vector:''' Definitive proof that a fifth doesn't need to be a 3/2. (TBA)		: '''Vector:''' Definitive proof that a fifth doesn't need to be a 3/2. (TBA)
	: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".		: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".
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	: '''Bozu:''' [[Amphipent]] with a lot of notes.		: '''Bozu:''' [[Amphipent]] with a lot of notes.
	: '''Nicolai:''' Same situation as [[35edo\|35EDO]], but the [[5edo\|5EDO]] fifth is now just a [[superpyth]] fifth. Also good approximations of intervals.		: '''Nicolai:''' Same situation as [[35edo\|35EDO]], but the [[5edo\|5EDO]] fifth is now just a [[superpyth]] fifth. Also good approximations of intervals.
	: '''Fumica:''' 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.		: '''Fumica:''' 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.
	: '''Budjarn Lambeth:''' A very good [[dual-fifth]] edo.		: '''Budjarn Lambeth:''' A very good [[dual-fifth]] edo.
	: '''Zhenlige:''' Everything but prime [[3/1\|3]].		: '''Zhenlige:''' Everything but prime [[3/1\|3]].

← Older revision		Revision as of 09:55, 30 August 2026
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	: '''Carmen14edo/Bragtime:''' I want [[Easley Blackwood]]'s "16 notes: Andantino" to play at my funeral		: '''Carmen14edo/Bragtime:''' I want [[Easley Blackwood]]'s "16 notes: Andantino" to play at my funeral
	: '''Deja Igliashon:''' There's lots of cool stuff happening in 16edo, but a surprising amount of it is basically just inherited from [[8edo]]. What 16edo adds to the mix is a nice [[5-limit]] major 3rd and a nice approximation to the 7th harmonic, and also the freaky-funky Mavila[7] [[antidiatonic\|inside-out diatonic]] (where major chords become minor, minor chords become major, diminished chords become augmented, and mice chase cats). But IDK, despite my high tolerance for tunings with awful or non-existent perfect 5ths, I've yet to find anything I can do in 16edo that I don't feel like I can do better in a different tuning.		: '''Deja Igliashon:''' There's lots of cool stuff happening in 16edo, but a surprising amount of it is basically just inherited from [[8edo]]. What 16edo adds to the mix is a nice [[5-limit]] major 3rd and a nice approximation to the 7th harmonic, and also the freaky-funky Mavila[7] [[antidiatonic\|inside-out diatonic]] (where major chords become minor, minor chords become major, diminished chords become augmented, and mice chase cats). But IDK, despite my high tolerance for tunings with awful or non-existent perfect 5ths, I've yet to find anything I can do in 16edo that I don't feel like I can do better in a different tuning.
	: '''Fumica:''' ~~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.		: '''Fumica:''' 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.
	: '''Vector:''' Definitive proof that a fifth doesn't need to be a 3/2. (TBA)		: '''Vector:''' Definitive proof that a fifth doesn't need to be a 3/2. (TBA)
	: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".		: '''Budjarn Lambeth:''' Offers exciting melodic shapes, but requires careful attention to [[timbre]] to prevent it sounding "out of tune".
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	: '''Yourmusic Productions:''' The whole-tone version of [[50edo\|50EDO]]'s [[golden meantone]]. Lots and lots of bad options but like [[6edo\|6]] vs [[12edo\|12]], missing most of the good combinations.		: '''Yourmusic Productions:''' The whole-tone version of [[50edo\|50EDO]]'s [[golden meantone]]. Lots and lots of bad options but like [[6edo\|6]] vs [[12edo\|12]], missing most of the good combinations.
	: '''Deja Igliashon:''' 25edo might be "the one that got away" for me. It bears a lot of similarities to [[23edo]] by virtue of being half the notes of a large very-accurate ET (50edo), having half of the nice 2nds, 3rds, 6ths, and 7ths, but not the nice 4ths and 5ths. Lots of nice harmony to be had, but no 5-limit triads (or at least, none that are very nice). I've thought about having a [[guitar]] made in 25edo multiple times but always ended up going with something else for some reason. Anyway, it's really really good for 8:9:10:14:17:19:23:25 chords, as well as 11:12:13:15:21:27 chords, but you can't put the two together unless you are in 50edo.		: '''Deja Igliashon:''' 25edo might be "the one that got away" for me. It bears a lot of similarities to [[23edo]] by virtue of being half the notes of a large very-accurate ET (50edo), having half of the nice 2nds, 3rds, 6ths, and 7ths, but not the nice 4ths and 5ths. Lots of nice harmony to be had, but no 5-limit triads (or at least, none that are very nice). I've thought about having a [[guitar]] made in 25edo multiple times but always ended up going with something else for some reason. Anyway, it's really really good for 8:9:10:14:17:19:23:25 chords, as well as 11:12:13:15:21:27 chords, but you can't put the two together unless you are in 50edo.
	: '''Fumica:''' ~~Potentially useful~~ as ~~every other step~~ of ~~50edo~~. D-tier.		: '''Fumica:''' Like 16edo, workable as a temperament of the [[2.5.7 subgroup]]. D-tier.
	: '''Eufalesio:''' Having no diatonic fifths is useless to me.		: '''Eufalesio:''' Having no diatonic fifths is useless to me.

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	: '''Nicolai:''' 12EDO, but better.		: '''Nicolai:''' 12EDO, but better.
	: '''Yourmusic Productions:''' 12, only with lots of extra harmonic options that actually sound good and are much easier to slip into an otherwise normal track than 24's.		: '''Yourmusic Productions:''' 12, only with lots of extra harmonic options that actually sound good and are much easier to slip into an otherwise normal track than 24's.
	: '''Fumica:''' 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.		: '''Fumica:''' 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 unfortunately the alternative mapping of harmonic 7 only serves to create mental dissonance for me. C-tier.
	: '''Budjarn Lambeth:''' Along with 24edo, it is one of the two possible ways to extend 12edo while preserving equal spacing, and keeping the number of notes somewhat manageable. 36edo is ideal if you want to add intervals involving the 7th harmonic into 12edo, while 24edo is ideal if you want to add intervals involving the 11th harmonic. Comparing and contrasting 24edo and 36edo can help you get a feel for the difference between the "vibe" of the 11th harmonic, and the "vibe" of the 7th harmonic. I recommend dipping your toes into each of the two. — Try using familar 12edo intervals in lower registers of your instrument(s)/mix, while mixing in some of the strange new 36edo intervals in the higher registers. Thus will mimic the shape of the [[harmonic series]] and sound nice and glittery.		: '''Budjarn Lambeth:''' Along with 24edo, it is one of the two possible ways to extend 12edo while preserving equal spacing, and keeping the number of notes somewhat manageable. 36edo is ideal if you want to add intervals involving the 7th harmonic into 12edo, while 24edo is ideal if you want to add intervals involving the 11th harmonic. Comparing and contrasting 24edo and 36edo can help you get a feel for the difference between the "vibe" of the 11th harmonic, and the "vibe" of the 7th harmonic. I recommend dipping your toes into each of the two. — Try using familar 12edo intervals in lower registers of your instrument(s)/mix, while mixing in some of the strange new 36edo intervals in the higher registers. Thus will mimic the shape of the [[harmonic series]] and sound nice and glittery.
	: '''Zhenlige:''' Good for 2.3.7.13.17.19.23.29 subroup. Avoid [[5/1\|5]] here because it is almost completely missed. Otherwise incomplete [[72edo]].		: '''Zhenlige:''' Good for 2.3.7.13.17.19.23.29 subroup. Avoid [[5/1\|5]] here because it is almost completely missed. Otherwise incomplete [[72edo]].
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	: '''Bozu:''' [[Amphipent]] with a lot of notes.		: '''Bozu:''' [[Amphipent]] with a lot of notes.
	: '''Nicolai:''' Same situation as [[35edo\|35EDO]], but the [[5edo\|5EDO]] fifth is now just a [[superpyth]] fifth. Also good approximations of intervals.		: '''Nicolai:''' Same situation as [[35edo\|35EDO]], but the [[5edo\|5EDO]] fifth is now just a [[superpyth]] fifth. Also good approximations of intervals.
	: '''Fumica:''' ~~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.		: '''Fumica:''' This edo offers good approximation to [[harmonic]]s [[5/1\|5]], [[7/1\|7]], [[11/1\|11]] and [[13/1\|13]]. The last two primes add the much needed variety to the otherwise pretty dull sound of the [[2.5.7 subgroup]]. C-tier.
	: '''Budjarn Lambeth:''' A very good [[dual-fifth]] edo.		: '''Budjarn Lambeth:''' A very good [[dual-fifth]] edo.
	: '''Zhenlige:''' A strong no-[[3/1\|3]] system, which is kinda hard to use since the only isoharmonic chords are subsets of the 3n+1 and 3n+2 series, and there are not many useful scales.		: '''Zhenlige:''' A strong no-[[3/1\|3]] system, which is kinda hard to use since the only isoharmonic chords are subsets of the 3n+1 and 3n+2 series, and there are not many useful scales.
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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.		: '''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\|53EDO]].		: '''Nicolai:''' Smaller version of [[53edo\|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 diesis\|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]] [[13/1\|13]] is certainly plausible, but prime [[19/1\|19]] fits way better~~. ~~There's a~~ unique uniform ~~tuning~~ for the [[harmonic segment]] 18::22, a fact related to the vanish of [[S-expression\|~~s10~~]] = [[~~100~~/99]] ~~and~~ [[S-expression\|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.		: '''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 [[septischismic]] system, so that all three kinds are separated by the same [[comma]] step and can be found on a chain of [[3/2\|perfect 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 diesis\|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 series segment\|harmonic segments]] 18::22 and 27::33 – a fact related to the vanish of [[100/99]] ([[S-expression\|S10]]) and [[243/242]] ([[S-expression\|S9/S11]]) – but [[prime interval\|prime]] [[13/1\|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 [[3/1\|3]] and a more noticeably flat [[5/1\|5]], making a flat, more stable [[15/1\|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.
	: '''Zhenlige:''' Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Containing [[Bohlen-Pierce scale]]. Good for magic. The [[Kite guitar]] shows its elegance, with many simple intervals evenly spaced. Also [[garibaldi]] and [[miracle]]. The largest problem is its relatively inaccurate [[5~~/1\|5]]~~. From here on, most EDOs with good [[13-limit]] [[support]] [[akea]].		: '''Zhenlige:''' Prime octave and highly composite fifth, opposite from [[12edo]], thus good for fifth-dividing temperaments. Containing [[Bohlen-Pierce scale]]. Good for magic. The [[Kite guitar]] shows its elegance, with many simple intervals evenly spaced. Also [[garibaldi]] and [[miracle]]. The largest problem is its relatively inaccurate 5. From here on, most EDOs with good [[13-limit]] [[support]] [[akea]].
	: '''Eufalesio:''' The first usable [[schismic]] edo ([[29edo]] and [[17edo]] don't count because their [[5/4]]'s are wack). Still manageable grain, hyperaccurate fifths and the non-meantoneness is definitely welcome. It is the first edo to introduce a comma accidental framework, which in my opinion is one of the best frameworks for composition. The yazala is marvelous (pun intended) but the [[yazalatha]] is... lacking. However, since it tempers so many things together, it is extremely useful. Still, even if the ya is not that accurate, since the innacuracy is flatwards, I think it's much more enjoyable, as I like wide minor thirds. Also supports Bohlen Pierce, which is also incredibly cool. Rank: AC, not for air conditioner, but for ''accuracy'' and ''cool''.		: '''Eufalesio:''' The first usable [[schismic]] edo ([[29edo]] and [[17edo]] don't count because their [[5/4]]'s are wack). Still manageable grain, hyperaccurate fifths and the non-meantoneness is definitely welcome. It is the first edo to introduce a comma accidental framework, which in my opinion is one of the best frameworks for composition. The yazala is marvelous (pun intended) but the [[yazalatha]] is... lacking. However, since it tempers so many things together, it is extremely useful. Still, even if the ya is not that accurate, since the innacuracy is flatwards, I think it's much more enjoyable, as I like wide minor thirds. Also supports Bohlen Pierce, which is also incredibly cool. Rank: AC, not for air conditioner, but for ''accuracy'' and ''cool''.

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	== [[58edo]] ==		== [[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 ~~[[harmonic]]s~~ [[19/1\|19]] and [[23/1\|23]] in the 58hi [[val]] are surprisingly convincing, and although the [[17/1\|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.		: '''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 [[3/2\|perfect fifth]] to 24 steps, this edo tunes the [[4/3\|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 interval\|prime]] [[11/1\|11]], but it has more to offer – the [[19/1\|19]] and [[23/1\|23]] in the 58hi [[val]] are surprisingly convincing, and although the [[17/1\|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 [[3/1\|perfect twelfth]]. S-tier.

	== [[59edo]] ==		== [[59edo]] ==