Keenan's EDO impressions - Revision history

FloraC: Some basic formatting work

2025-09-11T04:42:27Z

Some basic formatting work

← Older revision		Revision as of 04:42, 11 September 2025
Line 1:		Line 1:
	[[1edo\|1]] ~~–~~ People ought to write more 2-limit music. (Or not.)		* [[1edo\|1]] – People ought to write more 2-limit music. (Or not.)
			* [[2edo\|2]] – Boring
	[[2edo\|2]] ~~–~~ Boring		* [[3edo\|3]] – Boring
			* [[4edo\|4]] – Boring
	[[3edo\|3]] ~~–~~ Boring		* [[5edo\|5]] (aka [[8edt]]) – Smallest useful EDO, and it's really cool. Basically 2.3.7 limit (no hint of the 5th harmonic at all), and a great candidate for a scale people can just bang away on. Regular temperament model of slendro.
			* [[6edo\|6]] – Boring as a subset of 12edo, but useful as a very simple 2.9.5.7 temperament. Most of the good 2.9.... scales have 6-note MOSes for this reason.
	[[4edo\|4]] ~~–~~ Boring		* [[7edo\|7]] (aka [[11edt]]) – Cool in many of the ways that 5 is. Regular temperament model of a scale used in Thai music.
			* [[8edo\|8]] – A very weird edo. It has passable 10:11:12:14 chords, but nothing "rooted" (unless 750 cents is an acceptable 3/2).
	[[5edo\|5]] (aka [[~~8edt\|~~8edt]]) ~~–~~ Smallest useful EDO, and it's really cool. Basically 2.3.7 limit (no hint of the 5th harmonic at all), and a great candidate for a scale people can just bang away on. Regular temperament model of slendro.		* [[9edo\|9]] (aka [[14edt]]) – On the one hand you can treat the 667 cent intervals as 3/2, yielding an extreme version of [[mavila]] (or 7-limit [[armodue (temperament)\|armodue]]) which is a very acceptable tuning for pelog selisir. On the other hand you can treat it has having no 3rd harmonics, as something like a 2.5.7/3 temperament. (Treating it as a super-accurate 2.27/25.7/3 temperament makes no sense to me.) First EDO with '''recognizable''' "major" and "minor" chords.
			* [[10edo\|10]] (aka [[16edt]], "blackwood semitones") – Like [[blackwood]], except with neutral thirds. Or, blackwood intersects [[dicot]]. Same circle-of-3/2s structure as 5edo, but now there are 360-cent "neutral thirds" and 600-cent "tritones". It's easy to trick people into thinking that [[decimal]] MODMOSes are the familiar "blues scale" (and for that matter, that 0 360 960 cents is a "dominant seventh").
	[[6edo\|6]] ~~–~~ Boring as a subset of 12edo, but useful as a very simple 2.9.5.7 temperament. Most of the good 2.9.... scales have 6-note MOSes for this reason.		* [[11edo\|11]] – Every other note of [[22edo\|22]]. This makes it a great 2.9.7.11 temperament. Includes [[machine]], [[orgone]], [http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11] and [http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11]
			* [[12edo\|12]] (aka [[19edt]], "standard semitones") – Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular [[dominant (temperament)\|dominant]] temperament. Also [[augmented (temperament)\|augmented]] and [[diminished (temperament)\|diminished]]. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.
	[[7edo\|7]] (aka [[~~11edt\|~~11edt]]) ~~– Cool~~ in many of the ways that 5 is. Regular temperament model of a scale used in Thai music.		* [[13edo\|13]] – Every other note of [[26edo\|26]]. This makes it a good temperament for a subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including [[uncle]] and [[dicot]].
			* [[14edo\|14]] (aka "whitewood semitones") – [[Jamesbond]], [[bug]]/[[semaphore]], etc. (Quite bad whitewood tuning.) Pretty much misses "minor" and "major" thirds entirely, going straight from "subminor" to "neutral" to "supermajor", which makes it very xenharmonic (thought not necessarily pleasant). Also don't forget the presence of DTMF ("touch tone") tones. Any phone number is a two-part piece of music!
	[[8edo\|8]] ~~–~~ A very weird edo. It has passable 10:11:12:14 chords, but nothing "rooted" (unless 750 cents is an acceptable 3/2).		* [[15edo\|15]] (aka 24edt, "blackwood 1/3-tones") – Very interesting for [[blackwood]], [[porcupine]], and others. A good all-around EDO. If you want to internalize [[porcupine intervals\|porcupine interval categories]], use 15edo.
			* [[16edo\|16]] (aka 25edt, "armodue semitones") – [[Mavila]]/armodue. Really versatile and interesting – if you don't mind the lack of reasonable 3/2s. On the other hand you can treat it as an all-encompassing gamelan EDO where the beating fifths are an advantage. (The one advantage it has over 9edo in this respect is its slendro approximation, [[gorgo]].)
	[[9edo\|9]] (aka [[~~14edt\|~~14edt]]) ~~–~~ On the one hand you can treat the 667 cent intervals as 3/2, yielding an extreme version of [[~~Mavila\|~~mavila]] (or 7-limit [[~~Armodue~~\|armodue]]) which is a very acceptable tuning for pelog selisir. On the other hand you can treat it has having no 3rd harmonics, as something like a 2.5.7/3 temperament. (Treating it as a super-accurate 2.27/25.7/3 temperament makes no sense to me.) First EDO with '''recognizable''' "major" and "minor" chords.		* [[17edo\|17]] (aka [[27edt]], "superpyth 1/3-tones") – Really good no-5's system; [[supra]], [[bleu]], etc. The lack of 5-limit harmony forces you to think xenharmonically, but the nice accurate 3/2s form a solid familiar backbone you can depend on when things get too crazy. Also, neutral third scales are awesome. Compatible (not perfectly, of course) with a large number of maqamat.
			* [[18edo\|18]] – Almost totally useless.
	[[10edo\|10]] (aka [[~~16edt\|~~16edt]], "blackwood semitones") ~~–~~ Like [[~~Blackwood\|~~blackwood]], except with neutral thirds. Or, blackwood intersects [[~~Dicot\|~~dicot]]. Same circle-of-3/2s structure as 5edo, but now there are 360-cent "neutral thirds" and 600-cent "tritones". It's easy to trick people into thinking that [[~~Decimal\|~~decimal]] MODMOSes are the familiar "blues scale" (and for that matter, that 0 360 960 cents is a "dominant seventh").		* [[19edo\|19]] (aka 30edt, "meantone 1/3-tones") – First EDO with a meantone diatonic scale (5L2s proper), but not only meantone! [[Negri]] is awesome, [[godzilla]] is awesome, [[sensi]] is awesome, and [[keemun]] and [[magic]] are both quite interesting. Excellent EDO to promote to newcomers because it works beautifully with standard meantone notation and familiar meantone harmony is possible, but again, it's so much more than meantone. Xenharmonic scales and comma pumps abound.
			* [[20edo\|20]] (aka "blackwood 1/4-tones") – More-complicated version of [[blackwood]], not much else. Instead of [5edo interval], minor, major, [5edo interval] it now goes [5edo interval], minor, neutral, major, [5edo interval]. Big deal. I'd choose 15 over 20 any day because it has porcupine.
	[[11edo\|11]] ~~–~~ Every other note of [[22edo\|22]]. This makes it a great 2.9.7.11 temperament. Includes [[~~Machine\|~~machine]], [[~~Orgone\|~~orgone]], [http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&~~amp;~~limit=2_9_7_11] and [http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&~~amp;~~limit=2_9_7_11]		* [[21edo\|21]] (aka "whitewood 1/3-tones") – First usable (sub-optimal) [[whitewood]] EDO, not much else.
			* [[22edo\|22]] (aka 35edt, "superpyth 1/4-tones") – Amazing and mind-blowing; many great [[22edo #Rank-2 temperaments\|temperaments]]. Not much reason to use more notes per octave than this, if you ask me.
	[[12edo\|12]] (aka [[~~19edt\|~~19edt]], "standard semitones") ~~–~~ Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular [[dominant (temperament)\|dominant]] temperament. Also [[augmented\|augmented]] and [[~~Diminished~~\|diminished]]. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.		* [[23edo\|23]] (aka "hornbostel 1/3-tones") – Mavila system similar to 16, but has [[superpelog]] in addition. Nothing to write home about.
			* [[24edo\|24]] (aka 38edt, "standard 1/4-tones") – Very worthwhile, and underrated because of its long history of "microtonal" (rather than "xenharmonic") use. Really nails the 2.3.11 subgroup, and has all the familiar meantone harmony (and diatonic scale) of 12edo. The basis of much low-level maqam music theory (maqamat are often presented as quarter tones).
	[[13edo\|13]] ~~–~~ Every other note of [[26edo\|26]]. This makes it a good temperament for a subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including [[~~Uncle\|~~uncle]] and [[~~Dicot\|~~dicot]].		* [[25edo\|25]] (either "blackwood 1/5-tones" or "armodue 1/3-tones") – Can be treated in two different ways (blackwood or mavila/armodue) depending on which interval you consider "the fifth" or "3/2". Too many notes for either one of them – why not use 15 or 16 instead?
			* [[26edo\|26]] (aka 41edt, "flattone 1/4-tones") – The forgotten meantone EDO, and the first true [[flattone]] EDO. Flattone is amazing because 8/7 and 7/6 are swapped from their roles in 7-limit meantone temperament, and because [[flattone12\|flattone[12]]] is much easier to hear as unequal than meantone[12]. Also has [[injera]] and [[cynder]]/[[mothra]].
	[[14edo\|14]] (aka "whitewood semitones") ~~–~~ [[Jamesbond~~\|Jamesbond]~~], [[~~Bug\|~~bug]]/[[~~Semaphore\|~~semaphore]], etc. (Quite bad whitewood tuning.) Pretty much misses "minor" and "major" thirds entirely, going straight from "subminor" to "neutral" to "supermajor", which makes it very xenharmonic (thought not necessarily pleasant). Also don't forget the presence of DTMF ("touch tone") tones. Any phone number is a two-part piece of music!		* [[27edo\|27]] (aka 43edt, "superpyth 1/5-tones") – First true [[tetracot]]/[[modus]] EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs.

	[[15edo\|15]] (aka 24edt, "blackwood 1/3-tones") ~~–~~ Very interesting for [[~~Blackwood\|~~blackwood]], [[~~Porcupine\|~~porcupine]], and others. A good all-around EDO. If you want to internalize [[~~Porcupine_intervals~~\|porcupine interval categories]], use 15edo.

	[[16edo\|16]] (aka 25edt, "armodue semitones") ~~–~~ [[~~Mavila\|~~Mavila]]/armodue. Really versatile and interesting ~~–~~ if you don't mind the lack of reasonable 3/2s. On the other hand you can treat it as an all-encompassing gamelan EDO where the beating fifths are an advantage. (The one advantage it has over 9edo in this respect is its slendro approximation, [[~~Gorgo\|~~gorgo]].)

	[[17edo\|17]] (aka [[~~27edt\|~~27edt]], "superpyth 1/3-tones") ~~–~~ Really good no-5's system; [[~~Supra\|~~supra]], [[~~Bleu\|~~bleu]], etc. The lack of 5-limit harmony forces you to think xenharmonically, but the nice accurate 3/2s form a solid familiar backbone you can depend on when things get too crazy. Also, neutral third scales are awesome. Compatible (not perfectly, of course) with a large number of maqamat.

	[[18edo\|18]] ~~–~~ Almost totally useless.

	[[19edo\|19]] (aka 30edt, "meantone 1/3-tones") ~~–~~ First EDO with a meantone diatonic scale (5L2s proper), but not only meantone! [[~~Negri\|~~Negri]] is awesome, [[~~Godzilla\|~~godzilla]] is awesome, [[~~Sensi\|~~sensi]] is awesome, and [[~~Keemun\|~~keemun]] and [[~~Magic\|~~magic]] are both quite interesting. Excellent EDO to promote to newcomers because it works beautifully with standard meantone notation and familiar meantone harmony is possible, but again, it's so much more than meantone. Xenharmonic scales and comma pumps abound.

	[[20edo\|20]] (aka "blackwood 1/4-tones") ~~–~~ More-complicated version of [[~~Blackwood\|~~blackwood]], not much else. Instead of [5edo interval], minor, major, [5edo interval] it now goes [5edo interval], minor, neutral, major, [5edo interval]. Big deal. I'd choose 15 over 20 any day because it has porcupine.

	[[21edo\|21]] (aka "whitewood 1/3-tones") ~~–~~ First usable (sub-optimal) [[~~Whitewood\|~~whitewood]] EDO, not much else.

	[[22edo\|22]] (aka 35edt, "superpyth 1/4-tones") ~~–~~ Amazing and mind-blowing; many great [[22edo#~~Theory~~-~~Properties of 22 equal temperament-Linear Temperaments~~\|temperaments]]. Not much reason to use more notes per octave than this, if you ask me.

	[[23edo\|23]] (aka "hornbostel 1/3-tones") ~~–~~ Mavila system similar to 16, but has [[~~superpelog\|~~superpelog]] in addition. Nothing to write home about.

	[[24edo\|24]] (aka 38edt, "standard 1/4-tones") ~~–~~ Very worthwhile, and underrated because of its long history of "microtonal" (rather than "xenharmonic") use. Really nails the 2.3.11 subgroup, and has all the familiar meantone harmony (and diatonic scale) of 12edo. The basis of much low-level maqam music theory (maqamat are often presented as quarter tones).

	[[25edo\|25]] (either "blackwood 1/5-tones" or "armodue 1/3-tones") ~~–~~ Can be treated in two different ways (blackwood or mavila/armodue) depending on which interval you consider "the fifth" or "3/2". Too many notes for either one of them ~~–~~ why not use 15 or 16 instead?

	[[26edo\|26]] (aka 41edt, "flattone 1/4-tones") ~~–~~ The forgotten meantone EDO, and the first true [[~~Flattone\|~~flattone]] EDO. Flattone is amazing because 8/7 and 7/6 are swapped from their roles in 7-limit meantone temperament, and because [[flattone12\|flattone[12]]] is much easier to hear as unequal than meantone[12]. Also has [[~~Injera\|~~injera]] and [[~~Cynder\|~~cynder]]/[[~~Mothra\|~~mothra]].

	[[27edo\|27]] (aka 43edt, "superpyth 1/5-tones") ~~–~~ First true [[~~Tetracot\|~~tetracot]]/[[~~Modus\|~~modus]] EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs.

	[[Category:EDO theory pages]]		[[Category:EDO theory pages]]
	[[Category:~~impression~~]]		[[Category:Impression]]

ArrowHead294 at 18:45, 26 December 2024

2024-12-26T18:45:22Z

Bcmills at 18:54, 23 August 2024

2024-08-23T18:54:43Z

← Older revision		Revision as of 18:54, 23 August 2024
Line 21:		Line 21:
	[[11edo\|11]] - Every other note of [[22edo\|22]]. This makes it a great 2.9.7.11 temperament. Includes [[Machine\|machine]], [[Orgone\|orgone]], [http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11] and [http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11]		[[11edo\|11]] - Every other note of [[22edo\|22]]. This makes it a great 2.9.7.11 temperament. Includes [[Machine\|machine]], [[Orgone\|orgone]], [http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11] and [http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11]

	[[12edo\|12]] (aka [[19edt\|19edt]], "standard semitones") - Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular [[dominant\|dominant]] temperament. Also [[augmented\|augmented]] and [[Diminished\|diminished]]. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.		[[12edo\|12]] (aka [[19edt\|19edt]], "standard semitones") - Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular [[dominant (temperament)\|dominant]] temperament. Also [[augmented\|augmented]] and [[Diminished\|diminished]]. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.

	[[13edo\|13]] - Every other note of [[26edo\|26]]. This makes it a good temperament for a subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including [[Uncle\|uncle]] and [[Dicot\|dicot]].		[[13edo\|13]] - Every other note of [[26edo\|26]]. This makes it a good temperament for a subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including [[Uncle\|uncle]] and [[Dicot\|dicot]].

Fredg999 category edits: Removing from Category:Overview using Cat-a-lot

2023-03-06T22:14:11Z

Removing from Category:Overview using Cat-a-lot

← Older revision		Revision as of 22:14, 6 March 2023
Line 54:		Line 54:
	[[Category:EDO theory pages]]		[[Category:EDO theory pages]]
	[[Category:impression]]		[[Category:impression]]
	~~[[Category:overview]]~~

Keenan Pepper category edits: Moving from Category:Edo to Category:EDO theory pages using Cat-a-lot

2020-12-04T23:20:49Z

Moving from Category:Edo to Category:EDO theory pages using Cat-a-lot

← Older revision		Revision as of 23:20, 4 December 2020
Line 52:		Line 52:

	[[27edo\|27]] (aka 43edt, "superpyth 1/5-tones") - First true [[Tetracot\|tetracot]]/[[Modus\|modus]] EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs.		[[27edo\|27]] (aka 43edt, "superpyth 1/5-tones") - First true [[Tetracot\|tetracot]]/[[Modus\|modus]] EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs.
	[[Category:~~edo~~]]		[[Category:EDO theory pages]]
	[[Category:impression]]		[[Category:impression]]
	[[Category:overview]]		[[Category:overview]]

Keenan Pepper at 23:36, 28 October 2018

2018-10-28T23:36:51Z

← Older revision		Revision as of 23:36, 28 October 2018
Line 54:		Line 54:
	[[Category:edo]]		[[Category:edo]]
	[[Category:impression]]		[[Category:impression]]
	~~[[Category:keenan]]~~
	[[Category:overview]]		[[Category:overview]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes

Wikispaces>xenwolf: Imported revision 521675128 - Original comment:

2014-09-10T15:36:18Z

**Imported revision 521675128 - Original comment: **

Wikispaces>keenanpepper: Imported revision 373737258 - Original comment:

2012-10-16T21:00:17Z

**Imported revision 373737258 - Original comment: **

Show changes

Wikispaces>mbattaglia1: Imported revision 337249226 - Original comment:

2012-05-19T04:31:55Z

**Imported revision 337249226 - Original comment: **

← Older revision		Revision as of 04:42, 11 September 2025
Line 1:		Line 1:
	[[1edo\|1]] ~~–~~ People ought to write more 2-limit music. (Or not.)		* [[1edo\|1]] – People ought to write more 2-limit music. (Or not.)
			* [[2edo\|2]] – Boring
	[[2edo\|2]] ~~–~~ Boring		* [[3edo\|3]] – Boring
			* [[4edo\|4]] – Boring
	[[3edo\|3]] ~~–~~ Boring		* [[5edo\|5]] (aka [[8edt]]) – Smallest useful EDO, and it's really cool. Basically 2.3.7 limit (no hint of the 5th harmonic at all), and a great candidate for a scale people can just bang away on. Regular temperament model of slendro.
			* [[6edo\|6]] – Boring as a subset of 12edo, but useful as a very simple 2.9.5.7 temperament. Most of the good 2.9.... scales have 6-note MOSes for this reason.
	[[4edo\|4]] ~~–~~ Boring		* [[7edo\|7]] (aka [[11edt]]) – Cool in many of the ways that 5 is. Regular temperament model of a scale used in Thai music.
			* [[8edo\|8]] – A very weird edo. It has passable 10:11:12:14 chords, but nothing "rooted" (unless 750 cents is an acceptable 3/2).
	[[5edo\|5]] (aka [[~~8edt\|~~8edt]]) ~~–~~ Smallest useful EDO, and it's really cool. Basically 2.3.7 limit (no hint of the 5th harmonic at all), and a great candidate for a scale people can just bang away on. Regular temperament model of slendro.		* [[9edo\|9]] (aka [[14edt]]) – On the one hand you can treat the 667 cent intervals as 3/2, yielding an extreme version of [[mavila]] (or 7-limit [[armodue (temperament)\|armodue]]) which is a very acceptable tuning for pelog selisir. On the other hand you can treat it has having no 3rd harmonics, as something like a 2.5.7/3 temperament. (Treating it as a super-accurate 2.27/25.7/3 temperament makes no sense to me.) First EDO with '''recognizable''' "major" and "minor" chords.
			* [[10edo\|10]] (aka [[16edt]], "blackwood semitones") – Like [[blackwood]], except with neutral thirds. Or, blackwood intersects [[dicot]]. Same circle-of-3/2s structure as 5edo, but now there are 360-cent "neutral thirds" and 600-cent "tritones". It's easy to trick people into thinking that [[decimal]] MODMOSes are the familiar "blues scale" (and for that matter, that 0 360 960 cents is a "dominant seventh").
	[[6edo\|6]] ~~–~~ Boring as a subset of 12edo, but useful as a very simple 2.9.5.7 temperament. Most of the good 2.9.... scales have 6-note MOSes for this reason.		* [[11edo\|11]] – Every other note of [[22edo\|22]]. This makes it a great 2.9.7.11 temperament. Includes [[machine]], [[orgone]], [http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11] and [http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11]
			* [[12edo\|12]] (aka [[19edt]], "standard semitones") – Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular [[dominant (temperament)\|dominant]] temperament. Also [[augmented (temperament)\|augmented]] and [[diminished (temperament)\|diminished]]. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.
	[[7edo\|7]] (aka [[~~11edt\|~~11edt]]) ~~– Cool~~ in many of the ways that 5 is. Regular temperament model of a scale used in Thai music.		* [[13edo\|13]] – Every other note of [[26edo\|26]]. This makes it a good temperament for a subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including [[uncle]] and [[dicot]].
			* [[14edo\|14]] (aka "whitewood semitones") – [[Jamesbond]], [[bug]]/[[semaphore]], etc. (Quite bad whitewood tuning.) Pretty much misses "minor" and "major" thirds entirely, going straight from "subminor" to "neutral" to "supermajor", which makes it very xenharmonic (thought not necessarily pleasant). Also don't forget the presence of DTMF ("touch tone") tones. Any phone number is a two-part piece of music!
	[[8edo\|8]] ~~–~~ A very weird edo. It has passable 10:11:12:14 chords, but nothing "rooted" (unless 750 cents is an acceptable 3/2).		* [[15edo\|15]] (aka 24edt, "blackwood 1/3-tones") – Very interesting for [[blackwood]], [[porcupine]], and others. A good all-around EDO. If you want to internalize [[porcupine intervals\|porcupine interval categories]], use 15edo.
			* [[16edo\|16]] (aka 25edt, "armodue semitones") – [[Mavila]]/armodue. Really versatile and interesting – if you don't mind the lack of reasonable 3/2s. On the other hand you can treat it as an all-encompassing gamelan EDO where the beating fifths are an advantage. (The one advantage it has over 9edo in this respect is its slendro approximation, [[gorgo]].)
	[[9edo\|9]] (aka [[~~14edt\|~~14edt]]) ~~–~~ On the one hand you can treat the 667 cent intervals as 3/2, yielding an extreme version of [[~~Mavila\|~~mavila]] (or 7-limit [[~~Armodue~~\|armodue]]) which is a very acceptable tuning for pelog selisir. On the other hand you can treat it has having no 3rd harmonics, as something like a 2.5.7/3 temperament. (Treating it as a super-accurate 2.27/25.7/3 temperament makes no sense to me.) First EDO with '''recognizable''' "major" and "minor" chords.		* [[17edo\|17]] (aka [[27edt]], "superpyth 1/3-tones") – Really good no-5's system; [[supra]], [[bleu]], etc. The lack of 5-limit harmony forces you to think xenharmonically, but the nice accurate 3/2s form a solid familiar backbone you can depend on when things get too crazy. Also, neutral third scales are awesome. Compatible (not perfectly, of course) with a large number of maqamat.
			* [[18edo\|18]] – Almost totally useless.
	[[10edo\|10]] (aka [[~~16edt\|~~16edt]], "blackwood semitones") ~~–~~ Like [[~~Blackwood\|~~blackwood]], except with neutral thirds. Or, blackwood intersects [[~~Dicot\|~~dicot]]. Same circle-of-3/2s structure as 5edo, but now there are 360-cent "neutral thirds" and 600-cent "tritones". It's easy to trick people into thinking that [[~~Decimal\|~~decimal]] MODMOSes are the familiar "blues scale" (and for that matter, that 0 360 960 cents is a "dominant seventh").		* [[19edo\|19]] (aka 30edt, "meantone 1/3-tones") – First EDO with a meantone diatonic scale (5L2s proper), but not only meantone! [[Negri]] is awesome, [[godzilla]] is awesome, [[sensi]] is awesome, and [[keemun]] and [[magic]] are both quite interesting. Excellent EDO to promote to newcomers because it works beautifully with standard meantone notation and familiar meantone harmony is possible, but again, it's so much more than meantone. Xenharmonic scales and comma pumps abound.
			* [[20edo\|20]] (aka "blackwood 1/4-tones") – More-complicated version of [[blackwood]], not much else. Instead of [5edo interval], minor, major, [5edo interval] it now goes [5edo interval], minor, neutral, major, [5edo interval]. Big deal. I'd choose 15 over 20 any day because it has porcupine.
	[[11edo\|11]] ~~–~~ Every other note of [[22edo\|22]]. This makes it a great 2.9.7.11 temperament. Includes [[~~Machine\|~~machine]], [[~~Orgone\|~~orgone]], [http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&~~amp;~~limit=2_9_7_11] and [http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&~~amp;~~limit=2_9_7_11]		* [[21edo\|21]] (aka "whitewood 1/3-tones") – First usable (sub-optimal) [[whitewood]] EDO, not much else.
			* [[22edo\|22]] (aka 35edt, "superpyth 1/4-tones") – Amazing and mind-blowing; many great [[22edo #Rank-2 temperaments\|temperaments]]. Not much reason to use more notes per octave than this, if you ask me.
	[[12edo\|12]] (aka [[~~19edt\|~~19edt]], "standard semitones") ~~–~~ Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular [[dominant (temperament)\|dominant]] temperament. Also [[augmented\|augmented]] and [[~~Diminished~~\|diminished]]. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.		* [[23edo\|23]] (aka "hornbostel 1/3-tones") – Mavila system similar to 16, but has [[superpelog]] in addition. Nothing to write home about.
			* [[24edo\|24]] (aka 38edt, "standard 1/4-tones") – Very worthwhile, and underrated because of its long history of "microtonal" (rather than "xenharmonic") use. Really nails the 2.3.11 subgroup, and has all the familiar meantone harmony (and diatonic scale) of 12edo. The basis of much low-level maqam music theory (maqamat are often presented as quarter tones).
	[[13edo\|13]] ~~–~~ Every other note of [[26edo\|26]]. This makes it a good temperament for a subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including [[~~Uncle\|~~uncle]] and [[~~Dicot\|~~dicot]].		* [[25edo\|25]] (either "blackwood 1/5-tones" or "armodue 1/3-tones") – Can be treated in two different ways (blackwood or mavila/armodue) depending on which interval you consider "the fifth" or "3/2". Too many notes for either one of them – why not use 15 or 16 instead?
			* [[26edo\|26]] (aka 41edt, "flattone 1/4-tones") – The forgotten meantone EDO, and the first true [[flattone]] EDO. Flattone is amazing because 8/7 and 7/6 are swapped from their roles in 7-limit meantone temperament, and because [[flattone12\|flattone[12]]] is much easier to hear as unequal than meantone[12]. Also has [[injera]] and [[cynder]]/[[mothra]].
	[[14edo\|14]] (aka "whitewood semitones") ~~–~~ [[Jamesbond~~\|Jamesbond]~~], [[~~Bug\|~~bug]]/[[~~Semaphore\|~~semaphore]], etc. (Quite bad whitewood tuning.) Pretty much misses "minor" and "major" thirds entirely, going straight from "subminor" to "neutral" to "supermajor", which makes it very xenharmonic (thought not necessarily pleasant). Also don't forget the presence of DTMF ("touch tone") tones. Any phone number is a two-part piece of music!		* [[27edo\|27]] (aka 43edt, "superpyth 1/5-tones") – First true [[tetracot]]/[[modus]] EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs.

	[[15edo\|15]] (aka 24edt, "blackwood 1/3-tones") ~~–~~ Very interesting for [[~~Blackwood\|~~blackwood]], [[~~Porcupine\|~~porcupine]], and others. A good all-around EDO. If you want to internalize [[~~Porcupine_intervals~~\|porcupine interval categories]], use 15edo.

	[[16edo\|16]] (aka 25edt, "armodue semitones") ~~–~~ [[~~Mavila\|~~Mavila]]/armodue. Really versatile and interesting ~~–~~ if you don't mind the lack of reasonable 3/2s. On the other hand you can treat it as an all-encompassing gamelan EDO where the beating fifths are an advantage. (The one advantage it has over 9edo in this respect is its slendro approximation, [[~~Gorgo\|~~gorgo]].)

	[[17edo\|17]] (aka [[~~27edt\|~~27edt]], "superpyth 1/3-tones") ~~–~~ Really good no-5's system; [[~~Supra\|~~supra]], [[~~Bleu\|~~bleu]], etc. The lack of 5-limit harmony forces you to think xenharmonically, but the nice accurate 3/2s form a solid familiar backbone you can depend on when things get too crazy. Also, neutral third scales are awesome. Compatible (not perfectly, of course) with a large number of maqamat.

	[[18edo\|18]] ~~–~~ Almost totally useless.

	[[19edo\|19]] (aka 30edt, "meantone 1/3-tones") ~~–~~ First EDO with a meantone diatonic scale (5L2s proper), but not only meantone! [[~~Negri\|~~Negri]] is awesome, [[~~Godzilla\|~~godzilla]] is awesome, [[~~Sensi\|~~sensi]] is awesome, and [[~~Keemun\|~~keemun]] and [[~~Magic\|~~magic]] are both quite interesting. Excellent EDO to promote to newcomers because it works beautifully with standard meantone notation and familiar meantone harmony is possible, but again, it's so much more than meantone. Xenharmonic scales and comma pumps abound.

	[[20edo\|20]] (aka "blackwood 1/4-tones") ~~–~~ More-complicated version of [[~~Blackwood\|~~blackwood]], not much else. Instead of [5edo interval], minor, major, [5edo interval] it now goes [5edo interval], minor, neutral, major, [5edo interval]. Big deal. I'd choose 15 over 20 any day because it has porcupine.

	[[21edo\|21]] (aka "whitewood 1/3-tones") ~~–~~ First usable (sub-optimal) [[~~Whitewood\|~~whitewood]] EDO, not much else.

	[[22edo\|22]] (aka 35edt, "superpyth 1/4-tones") ~~–~~ Amazing and mind-blowing; many great [[22edo#~~Theory~~-~~Properties of 22 equal temperament-Linear Temperaments~~\|temperaments]]. Not much reason to use more notes per octave than this, if you ask me.

	[[23edo\|23]] (aka "hornbostel 1/3-tones") ~~–~~ Mavila system similar to 16, but has [[~~superpelog\|~~superpelog]] in addition. Nothing to write home about.

	[[24edo\|24]] (aka 38edt, "standard 1/4-tones") ~~–~~ Very worthwhile, and underrated because of its long history of "microtonal" (rather than "xenharmonic") use. Really nails the 2.3.11 subgroup, and has all the familiar meantone harmony (and diatonic scale) of 12edo. The basis of much low-level maqam music theory (maqamat are often presented as quarter tones).

	[[25edo\|25]] (either "blackwood 1/5-tones" or "armodue 1/3-tones") ~~–~~ Can be treated in two different ways (blackwood or mavila/armodue) depending on which interval you consider "the fifth" or "3/2". Too many notes for either one of them ~~–~~ why not use 15 or 16 instead?

	[[26edo\|26]] (aka 41edt, "flattone 1/4-tones") ~~–~~ The forgotten meantone EDO, and the first true [[~~Flattone\|~~flattone]] EDO. Flattone is amazing because 8/7 and 7/6 are swapped from their roles in 7-limit meantone temperament, and because [[flattone12\|flattone[12]]] is much easier to hear as unequal than meantone[12]. Also has [[~~Injera\|~~injera]] and [[~~Cynder\|~~cynder]]/[[~~Mothra\|~~mothra]].

	[[27edo\|27]] (aka 43edt, "superpyth 1/5-tones") ~~–~~ First true [[~~Tetracot\|~~tetracot]]/[[~~Modus\|~~modus]] EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs.

	[[Category:EDO theory pages]]		[[Category:EDO theory pages]]
	[[Category:~~impression~~]]		[[Category:Impression]]

← Older revision		Revision as of 18:54, 23 August 2024
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	[[11edo\|11]] - Every other note of [[22edo\|22]]. This makes it a great 2.9.7.11 temperament. Includes [[Machine\|machine]], [[Orgone\|orgone]], [http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11] and [http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11]		[[11edo\|11]] - Every other note of [[22edo\|22]]. This makes it a great 2.9.7.11 temperament. Includes [[Machine\|machine]], [[Orgone\|orgone]], [http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11] and [http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11]

	[[12edo\|12]] (aka [[19edt\|19edt]], "standard semitones") - Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular [[dominant\|dominant]] temperament. Also [[augmented\|augmented]] and [[Diminished\|diminished]]. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.		[[12edo\|12]] (aka [[19edt\|19edt]], "standard semitones") - Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular [[dominant (temperament)\|dominant]] temperament. Also [[augmented\|augmented]] and [[Diminished\|diminished]]. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.

	[[13edo\|13]] - Every other note of [[26edo\|26]]. This makes it a good temperament for a subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including [[Uncle\|uncle]] and [[Dicot\|dicot]].		[[13edo\|13]] - Every other note of [[26edo\|26]]. This makes it a good temperament for a subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including [[Uncle\|uncle]] and [[Dicot\|dicot]].

← Older revision		Revision as of 18:45, 26 December 2024
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	[[1edo\|1]] - People ought to write more 2-limit music. (Or not.)		[[1edo\|1]] – People ought to write more 2-limit music. (Or not.)

	[[2edo\|2]] - Boring		[[2edo\|2]] – Boring

	[[3edo\|3]] - Boring		[[3edo\|3]] – Boring

	[[4edo\|4]] - Boring		[[4edo\|4]] – Boring

	[[5edo\|5]] (aka [[8edt\|8edt]]) - Smallest useful EDO, and it's really cool. Basically 2.3.7 limit (no hint of the 5th harmonic at all), and a great candidate for a scale people can just bang away on. Regular temperament model of slendro.		[[5edo\|5]] (aka [[8edt\|8edt]]) – Smallest useful EDO, and it's really cool. Basically 2.3.7 limit (no hint of the 5th harmonic at all), and a great candidate for a scale people can just bang away on. Regular temperament model of slendro.

	[[6edo\|6]] - Boring as a subset of 12edo, but useful as a very simple 2.9.5.7 temperament. Most of the good 2.9.... scales have 6-note MOSes for this reason.		[[6edo\|6]] – Boring as a subset of 12edo, but useful as a very simple 2.9.5.7 temperament. Most of the good 2.9.... scales have 6-note MOSes for this reason.

	[[7edo\|7]] (aka [[11edt\|11edt]]) - Cool in many of the ways that 5 is. Regular temperament model of a scale used in Thai music.		[[7edo\|7]] (aka [[11edt\|11edt]]) – Cool in many of the ways that 5 is. Regular temperament model of a scale used in Thai music.

	[[8edo\|8]] - A very weird edo. It has passable 10:11:12:14 chords, but nothing "rooted" (unless 750 cents is an acceptable 3/2).		[[8edo\|8]] – A very weird edo. It has passable 10:11:12:14 chords, but nothing "rooted" (unless 750 cents is an acceptable 3/2).

	[[9edo\|9]] (aka [[14edt\|14edt]]) - On the one hand you can treat the 667 cent intervals as 3/2, yielding an extreme version of [[Mavila\|mavila]] (or 7-limit [[Armodue\|armodue]]) which is a very acceptable tuning for pelog selisir. On the other hand you can treat it has having no 3rd harmonics, as something like a 2.5.7/3 temperament. (Treating it as a super-accurate 2.27/25.7/3 temperament makes no sense to me.) First EDO with '''recognizable''' "major" and "minor" chords.		[[9edo\|9]] (aka [[14edt\|14edt]]) – On the one hand you can treat the 667 cent intervals as 3/2, yielding an extreme version of [[Mavila\|mavila]] (or 7-limit [[Armodue\|armodue]]) which is a very acceptable tuning for pelog selisir. On the other hand you can treat it has having no 3rd harmonics, as something like a 2.5.7/3 temperament. (Treating it as a super-accurate 2.27/25.7/3 temperament makes no sense to me.) First EDO with '''recognizable''' "major" and "minor" chords.

	[[10edo\|10]] (aka [[16edt\|16edt]], "blackwood semitones") - Like [[Blackwood\|blackwood]], except with neutral thirds. Or, blackwood intersects [[Dicot\|dicot]]. Same circle-of-3/2s structure as 5edo, but now there are 360-cent "neutral thirds" and 600-cent "tritones". It's easy to trick people into thinking that [[Decimal\|decimal]] MODMOSes are the familiar "blues scale" (and for that matter, that 0 360 960 cents is a "dominant seventh").		[[10edo\|10]] (aka [[16edt\|16edt]], "blackwood semitones") – Like [[Blackwood\|blackwood]], except with neutral thirds. Or, blackwood intersects [[Dicot\|dicot]]. Same circle-of-3/2s structure as 5edo, but now there are 360-cent "neutral thirds" and 600-cent "tritones". It's easy to trick people into thinking that [[Decimal\|decimal]] MODMOSes are the familiar "blues scale" (and for that matter, that 0 360 960 cents is a "dominant seventh").

	[[11edo\|11]] - Every other note of [[22edo\|22]]. This makes it a great 2.9.7.11 temperament. Includes [[Machine\|machine]], [[Orgone\|orgone]], [http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11] and [http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11]		[[11edo\|11]] – Every other note of [[22edo\|22]]. This makes it a great 2.9.7.11 temperament. Includes [[Machine\|machine]], [[Orgone\|orgone]], [http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_14&limit=2_9_7_11] and [http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11 http://x31eq.com/cgi-bin/rt.cgi?ets=11_20&limit=2_9_7_11]

	[[12edo\|12]] (aka [[19edt\|19edt]], "standard semitones") - Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular [[dominant (temperament)\|dominant]] temperament. Also [[augmented\|augmented]] and [[Diminished\|diminished]]. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.		[[12edo\|12]] (aka [[19edt\|19edt]], "standard semitones") – Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular [[dominant (temperament)\|dominant]] temperament. Also [[augmented\|augmented]] and [[Diminished\|diminished]]. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.

	[[13edo\|13]] - Every other note of [[26edo\|26]]. This makes it a good temperament for a subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including [[Uncle\|uncle]] and [[Dicot\|dicot]].		[[13edo\|13]] – Every other note of [[26edo\|26]]. This makes it a good temperament for a subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including [[Uncle\|uncle]] and [[Dicot\|dicot]].

	[[14edo\|14]] (aka "whitewood semitones") - [[Jamesbond\|Jamesbond]], [[Bug\|bug]]/[[Semaphore\|semaphore]], etc. (Quite bad whitewood tuning.) Pretty much misses "minor" and "major" thirds entirely, going straight from "subminor" to "neutral" to "supermajor", which makes it very xenharmonic (thought not necessarily pleasant). Also don't forget the presence of DTMF ("touch tone") tones. Any phone number is a two-part piece of music!		[[14edo\|14]] (aka "whitewood semitones") – [[Jamesbond\|Jamesbond]], [[Bug\|bug]]/[[Semaphore\|semaphore]], etc. (Quite bad whitewood tuning.) Pretty much misses "minor" and "major" thirds entirely, going straight from "subminor" to "neutral" to "supermajor", which makes it very xenharmonic (thought not necessarily pleasant). Also don't forget the presence of DTMF ("touch tone") tones. Any phone number is a two-part piece of music!

	[[15edo\|15]] (aka 24edt, "blackwood 1/3-tones") - Very interesting for [[Blackwood\|blackwood]], [[Porcupine\|porcupine]], and others. A good all-around EDO. If you want to internalize [[Porcupine_intervals\|porcupine interval categories]], use 15edo.		[[15edo\|15]] (aka 24edt, "blackwood 1/3-tones") – Very interesting for [[Blackwood\|blackwood]], [[Porcupine\|porcupine]], and others. A good all-around EDO. If you want to internalize [[Porcupine_intervals\|porcupine interval categories]], use 15edo.

	[[16edo\|16]] (aka 25edt, "armodue semitones") - [[Mavila\|Mavila]]/armodue. Really versatile and interesting - if you don't mind the lack of reasonable 3/2s. On the other hand you can treat it as an all-encompassing gamelan EDO where the beating fifths are an advantage. (The one advantage it has over 9edo in this respect is its slendro approximation, [[Gorgo\|gorgo]].)		[[16edo\|16]] (aka 25edt, "armodue semitones") – [[Mavila\|Mavila]]/armodue. Really versatile and interesting – if you don't mind the lack of reasonable 3/2s. On the other hand you can treat it as an all-encompassing gamelan EDO where the beating fifths are an advantage. (The one advantage it has over 9edo in this respect is its slendro approximation, [[Gorgo\|gorgo]].)

	[[17edo\|17]] (aka [[27edt\|27edt]], "superpyth 1/3-tones") - Really good no-5's system; [[Supra\|supra]], [[Bleu\|bleu]], etc. The lack of 5-limit harmony forces you to think xenharmonically, but the nice accurate 3/2s form a solid familiar backbone you can depend on when things get too crazy. Also, neutral third scales are awesome. Compatible (not perfectly, of course) with a large number of maqamat.		[[17edo\|17]] (aka [[27edt\|27edt]], "superpyth 1/3-tones") – Really good no-5's system; [[Supra\|supra]], [[Bleu\|bleu]], etc. The lack of 5-limit harmony forces you to think xenharmonically, but the nice accurate 3/2s form a solid familiar backbone you can depend on when things get too crazy. Also, neutral third scales are awesome. Compatible (not perfectly, of course) with a large number of maqamat.

	[[18edo\|18]] - Almost totally useless.		[[18edo\|18]] – Almost totally useless.

	[[19edo\|19]] (aka 30edt, "meantone 1/3-tones") - First EDO with a meantone diatonic scale (5L2s proper), but not only meantone! [[Negri\|Negri]] is awesome, [[Godzilla\|godzilla]] is awesome, [[Sensi\|sensi]] is awesome, and [[Keemun\|keemun]] and [[Magic\|magic]] are both quite interesting. Excellent EDO to promote to newcomers because it works beautifully with standard meantone notation and familiar meantone harmony is possible, but again, it's so much more than meantone. Xenharmonic scales and comma pumps abound.		[[19edo\|19]] (aka 30edt, "meantone 1/3-tones") – First EDO with a meantone diatonic scale (5L2s proper), but not only meantone! [[Negri\|Negri]] is awesome, [[Godzilla\|godzilla]] is awesome, [[Sensi\|sensi]] is awesome, and [[Keemun\|keemun]] and [[Magic\|magic]] are both quite interesting. Excellent EDO to promote to newcomers because it works beautifully with standard meantone notation and familiar meantone harmony is possible, but again, it's so much more than meantone. Xenharmonic scales and comma pumps abound.

	[[20edo\|20]] (aka "blackwood 1/4-tones") - More-complicated version of [[Blackwood\|blackwood]], not much else. Instead of [5edo interval], minor, major, [5edo interval] it now goes [5edo interval], minor, neutral, major, [5edo interval]. Big deal. I'd choose 15 over 20 any day because it has porcupine.		[[20edo\|20]] (aka "blackwood 1/4-tones") – More-complicated version of [[Blackwood\|blackwood]], not much else. Instead of [5edo interval], minor, major, [5edo interval] it now goes [5edo interval], minor, neutral, major, [5edo interval]. Big deal. I'd choose 15 over 20 any day because it has porcupine.

	[[21edo\|21]] (aka "whitewood 1/3-tones") - First usable (sub-optimal) [[Whitewood\|whitewood]] EDO, not much else.		[[21edo\|21]] (aka "whitewood 1/3-tones") – First usable (sub-optimal) [[Whitewood\|whitewood]] EDO, not much else.

	[[22edo\|22]] (aka 35edt, "superpyth 1/4-tones") - Amazing and mind-blowing; many great [[22edo#Theory-Properties of 22 equal temperament-Linear Temperaments\|temperaments]]. Not much reason to use more notes per octave than this, if you ask me.		[[22edo\|22]] (aka 35edt, "superpyth 1/4-tones") – Amazing and mind-blowing; many great [[22edo#Theory-Properties of 22 equal temperament-Linear Temperaments\|temperaments]]. Not much reason to use more notes per octave than this, if you ask me.

	[[23edo\|23]] (aka "hornbostel 1/3-tones") - Mavila system similar to 16, but has [[superpelog\|superpelog]] in addition. Nothing to write home about.		[[23edo\|23]] (aka "hornbostel 1/3-tones") – Mavila system similar to 16, but has [[superpelog\|superpelog]] in addition. Nothing to write home about.

	[[24edo\|24]] (aka 38edt, "standard 1/4-tones") - Very worthwhile, and underrated because of its long history of "microtonal" (rather than "xenharmonic") use. Really nails the 2.3.11 subgroup, and has all the familiar meantone harmony (and diatonic scale) of 12edo. The basis of much low-level maqam music theory (maqamat are often presented as quarter tones).		[[24edo\|24]] (aka 38edt, "standard 1/4-tones") – Very worthwhile, and underrated because of its long history of "microtonal" (rather than "xenharmonic") use. Really nails the 2.3.11 subgroup, and has all the familiar meantone harmony (and diatonic scale) of 12edo. The basis of much low-level maqam music theory (maqamat are often presented as quarter tones).

	[[25edo\|25]] (either "blackwood 1/5-tones" or "armodue 1/3-tones") - Can be treated in two different ways (blackwood or mavila/armodue) depending on which interval you consider "the fifth" or "3/2". Too many notes for either one of them - why not use 15 or 16 instead?		[[25edo\|25]] (either "blackwood 1/5-tones" or "armodue 1/3-tones") – Can be treated in two different ways (blackwood or mavila/armodue) depending on which interval you consider "the fifth" or "3/2". Too many notes for either one of them – why not use 15 or 16 instead?

	[[26edo\|26]] (aka 41edt, "flattone 1/4-tones") - The forgotten meantone EDO, and the first true [[Flattone\|flattone]] EDO. Flattone is amazing because 8/7 and 7/6 are swapped from their roles in 7-limit meantone temperament, and because [[flattone12\|flattone[12]]] is much easier to hear as unequal than meantone[12]. Also has [[Injera\|injera]] and [[Cynder\|cynder]]/[[Mothra\|mothra]].		[[26edo\|26]] (aka 41edt, "flattone 1/4-tones") – The forgotten meantone EDO, and the first true [[Flattone\|flattone]] EDO. Flattone is amazing because 8/7 and 7/6 are swapped from their roles in 7-limit meantone temperament, and because [[flattone12\|flattone[12]]] is much easier to hear as unequal than meantone[12]. Also has [[Injera\|injera]] and [[Cynder\|cynder]]/[[Mothra\|mothra]].

			[[27edo\|27]] (aka 43edt, "superpyth 1/5-tones") – First true [[Tetracot\|tetracot]]/[[Modus\|modus]] EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs.

	[[27edo\|27]] (aka 43edt, "superpyth 1/5-tones") - First true [[Tetracot\|tetracot]]/[[Modus\|modus]] EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs.
	[[Category:EDO theory pages]]		[[Category:EDO theory pages]]
	[[Category:impression]]		[[Category:impression]]

← Older revision		Revision as of 15:36, 10 September 2014
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	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:~~keenanpepper~~\|~~keenanpepper~~]] and made on <tt>~~2012~~-10~~-16 21~~:00:17 UTC</tt>.<br>		: This revision was by author [[User:xenwolf\|xenwolf]] and made on <tt>2014-09-10 15:36:18 UTC</tt>.<br>
	: The original revision id was <tt>~~373737258~~</tt>.<br>		: The original revision id was <tt>521675128</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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	[[24edo\|24]] (aka 38edt, "standard 1/4-tones") - Very worthwhile, and underrated because of its long history of "microtonal" (rather than "xenharmonic") use. Really nails the 2.3.11 subgroup, and has all the familiar meantone harmony (and diatonic scale) of 12edo. The basis of much low-level maqam music theory (maqamat are often presented as quarter tones).		[[24edo\|24]] (aka 38edt, "standard 1/4-tones") - Very worthwhile, and underrated because of its long history of "microtonal" (rather than "xenharmonic") use. Really nails the 2.3.11 subgroup, and has all the familiar meantone harmony (and diatonic scale) of 12edo. The basis of much low-level maqam music theory (maqamat are often presented as quarter tones).
	[[25edo\|25]] (either "blackwood 1/5-tones" or "armodue 1/3-tones") - Can be treated in two different ways (blackwood or mavila/armodue) depending on which interval you consider "the fifth" or "3/2". Too many notes for either one of them - why not use 15 or 16 instead?		[[25edo\|25]] (either "blackwood 1/5-tones" or "armodue 1/3-tones") - Can be treated in two different ways (blackwood or mavila/armodue) depending on which interval you consider "the fifth" or "3/2". Too many notes for either one of them - why not use 15 or 16 instead?
	[[26edo\|26]] (aka 41edt, "flattone 1/4-tones") - The forgotten meantone EDO, and the first true [[flattone]] EDO. Flattone is amazing because 8/7 and 7/6 are swapped from their roles in 7-limit meantone temperament, and because flattone[12] is much easier to hear as unequal than meantone[12]. Also has [[injera]] and [[cynder]]/[[mothra]].		[[26edo\|26]] (aka 41edt, "flattone 1/4-tones") - The forgotten meantone EDO, and the first true [[flattone]] EDO. Flattone is amazing because 8/7 and 7/6 are swapped from their roles in 7-limit meantone temperament, and because [[flattone12\|flattone[12]]] is much easier to hear as unequal than meantone[12]. Also has [[injera]] and [[cynder]]/[[mothra]].
	[[27edo\|27]] (aka 43edt, "superpyth 1/5-tones") - First true [[tetracot]]/[[modus]] EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs.</pre></div>		[[27edo\|27]] (aka 43edt, "superpyth 1/5-tones") - First true [[tetracot]]/[[modus]] EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs.</pre></div>
	<h4>Original HTML content:</h4>		<h4>Original HTML content:</h4>
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	<a class="wiki_link" href="/24edo">24</a> (aka 38edt, &quot;standard 1/4-tones&quot;) - Very worthwhile, and underrated because of its long history of &quot;microtonal&quot; (rather than &quot;xenharmonic&quot;) use. Really nails the 2.3.11 subgroup, and has all the familiar meantone harmony (and diatonic scale) of 12edo. The basis of much low-level maqam music theory (maqamat are often presented as quarter tones).<br />		<a class="wiki_link" href="/24edo">24</a> (aka 38edt, &quot;standard 1/4-tones&quot;) - Very worthwhile, and underrated because of its long history of &quot;microtonal&quot; (rather than &quot;xenharmonic&quot;) use. Really nails the 2.3.11 subgroup, and has all the familiar meantone harmony (and diatonic scale) of 12edo. The basis of much low-level maqam music theory (maqamat are often presented as quarter tones).<br />
	<a class="wiki_link" href="/25edo">25</a> (either &quot;blackwood 1/5-tones&quot; or &quot;armodue 1/3-tones&quot;) - Can be treated in two different ways (blackwood or mavila/armodue) depending on which interval you consider &quot;the fifth&quot; or &quot;3/2&quot;. Too many notes for either one of them - why not use 15 or 16 instead?<br />		<a class="wiki_link" href="/25edo">25</a> (either &quot;blackwood 1/5-tones&quot; or &quot;armodue 1/3-tones&quot;) - Can be treated in two different ways (blackwood or mavila/armodue) depending on which interval you consider &quot;the fifth&quot; or &quot;3/2&quot;. Too many notes for either one of them - why not use 15 or 16 instead?<br />
	<a class="wiki_link" href="/26edo">26</a> (aka 41edt, &quot;flattone 1/4-tones&quot;) - The forgotten meantone EDO, and the first true <a class="wiki_link" href="/flattone">flattone</a> EDO. Flattone is amazing because 8/7 and 7/6 are swapped from their roles in 7-limit meantone temperament, and because flattone[12] is much easier to hear as unequal than meantone[12]. Also has <a class="wiki_link" href="/injera">injera</a> and <a class="wiki_link" href="/cynder">cynder</a>/<a class="wiki_link" href="/mothra">mothra</a>.<br />		<a class="wiki_link" href="/26edo">26</a> (aka 41edt, &quot;flattone 1/4-tones&quot;) - The forgotten meantone EDO, and the first true <a class="wiki_link" href="/flattone">flattone</a> EDO. Flattone is amazing because 8/7 and 7/6 are swapped from their roles in 7-limit meantone temperament, and because <a class="wiki_link" href="/flattone12">flattone[12</a>] is much easier to hear as unequal than meantone[12]. Also has <a class="wiki_link" href="/injera">injera</a> and <a class="wiki_link" href="/cynder">cynder</a>/<a class="wiki_link" href="/mothra">mothra</a>.<br />
	<a class="wiki_link" href="/27edo">27</a> (aka 43edt, &quot;superpyth 1/5-tones&quot;) - First true <a class="wiki_link" href="/tetracot">tetracot</a>/<a class="wiki_link" href="/modus">modus</a> EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs.</body></html></pre></div>		<a class="wiki_link" href="/27edo">27</a> (aka 43edt, &quot;superpyth 1/5-tones&quot;) - First true <a class="wiki_link" href="/tetracot">tetracot</a>/<a class="wiki_link" href="/modus">modus</a> EDO. Otherwise, it has an interesting combination of things (superpyth, neutral thirds, augene, sensi), which, however, all exist in smaller EDOs.</body></html></pre></div>

← Older revision		Revision as of 04:31, 19 May 2012
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	<h2>IMPORTED REVISION FROM WIKISPACES</h2>		<h2>IMPORTED REVISION FROM WIKISPACES</h2>
	This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>		This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
	: This revision was by author [[User:~~keenanpepper~~\|~~keenanpepper~~]] and made on <tt>2012-03-27 19:14:44 UTC</tt>.<br>		: This revision was by author [[User:mbattaglia1\|mbattaglia1]] and made on <tt>2012-05-19 04:31:55 UTC</tt>.<br>
	: The original revision id was <tt>~~315241882~~</tt>.<br>		: The original revision id was <tt>337249226</tt>.<br>
	: The revision comment was: <tt></tt><br>		: The revision comment was: <tt></tt><br>
	The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>		The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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	[[12edo\|12]] (aka [[19edt]], "standard semitones") - Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular [[dominant]] temperament. Also [[augmented]] and [[diminished]]. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.		[[12edo\|12]] (aka [[19edt]], "standard semitones") - Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular [[dominant]] temperament. Also [[augmented]] and [[diminished]]. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of "non-xenharmonic" ensembles.
	[[13edo\|13]] - Every other note of [[26edo\|26]]. This makes it a good temperament for a large subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including [[uncle]] and [[dicot]].		[[13edo\|13]] - Every other note of [[26edo\|26]]. This makes it a good temperament for a large subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including [[uncle]] and [[dicot]].
	[[14edo\|14]] (aka "whitewood semitones") - [[Jamesbond]], [[bug]]/[[~~semiphore~~]], etc. (Quite bad whitewood tuning.) Pretty much misses "minor" and "major" thirds entirely, going straight from "subminor" to "neutral" to "supermajor", which makes it very xenharmonic (thought not necessarily pleasant).		[[14edo\|14]] (aka "whitewood semitones") - [[Jamesbond]], [[bug]]/[[semaphore]], etc. (Quite bad whitewood tuning.) Pretty much misses "minor" and "major" thirds entirely, going straight from "subminor" to "neutral" to "supermajor", which makes it very xenharmonic (thought not necessarily pleasant).
	[[15edo\|15]] (aka 24edt, "blackwood 1/3-tones") - Very interesting for [[blackwood]], [[porcupine]], and others. A good all-around EDO. If you want to internalize [[Porcupine intervals\|porcupine interval categories]], use 15edo.		[[15edo\|15]] (aka 24edt, "blackwood 1/3-tones") - Very interesting for [[blackwood]], [[porcupine]], and others. A good all-around EDO. If you want to internalize [[Porcupine intervals\|porcupine interval categories]], use 15edo.
	[[16edo\|16]] (aka 25edt, "armodue semitones") - [[Mavila]]/armodue; those Italians love it. Really versatile and interesting - if you don't mind the lack of reasonable 3/2s. On the other hand you can treat it as an all-encompassing gamelan EDO where the beating fifths are an advantage. (The one advantage it has over 9edo in this respect is its slendro approximation, [[gorgo]].)		[[16edo\|16]] (aka 25edt, "armodue semitones") - [[Mavila]]/armodue; those Italians love it. Really versatile and interesting - if you don't mind the lack of reasonable 3/2s. On the other hand you can treat it as an all-encompassing gamelan EDO where the beating fifths are an advantage. (The one advantage it has over 9edo in this respect is its slendro approximation, [[gorgo]].)
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	<a class="wiki_link" href="/12edo">12</a> (aka <a class="wiki_link" href="/19edt">19edt</a>, &quot;standard semitones&quot;) - Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular <a class="wiki_link" href="/dominant">dominant</a> temperament. Also <a class="wiki_link" href="/augmented">augmented</a> and <a class="wiki_link" href="/diminished">diminished</a>. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of &quot;non-xenharmonic&quot; ensembles.<br />		<a class="wiki_link" href="/12edo">12</a> (aka <a class="wiki_link" href="/19edt">19edt</a>, &quot;standard semitones&quot;) - Excellent 5-limit temperament with strong hints of 7. The ideal tuning for the wildly popular <a class="wiki_link" href="/dominant">dominant</a> temperament. Also <a class="wiki_link" href="/augmented">augmented</a> and <a class="wiki_link" href="/diminished">diminished</a>. Currently used as a basis for adaptive tuning, as well as directly, by a huge number of &quot;non-xenharmonic&quot; ensembles.<br />
	<a class="wiki_link" href="/13edo">13</a> - Every other note of <a class="wiki_link" href="/26edo">26</a>. This makes it a good temperament for a large subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including <a class="wiki_link" href="/uncle">uncle</a> and <a class="wiki_link" href="/dicot">dicot</a>.<br />		<a class="wiki_link" href="/13edo">13</a> - Every other note of <a class="wiki_link" href="/26edo">26</a>. This makes it a good temperament for a large subgroup containing the primes 5, 11, and 13 (but not 3). Alternatively, the ~738 cent interval could be treated as 3/2, giving a few high-error 5-limit temperaments, including <a class="wiki_link" href="/uncle">uncle</a> and <a class="wiki_link" href="/dicot">dicot</a>.<br />
	<a class="wiki_link" href="/14edo">14</a> (aka &quot;whitewood semitones&quot;) - <a class="wiki_link" href="/Jamesbond">Jamesbond</a>, <a class="wiki_link" href="/bug">bug</a>/<a class="wiki_link" href="/~~semiphore~~">~~semiphore~~</a>, etc. (Quite bad whitewood tuning.) Pretty much misses &quot;minor&quot; and &quot;major&quot; thirds entirely, going straight from &quot;subminor&quot; to &quot;neutral&quot; to &quot;supermajor&quot;, which makes it very xenharmonic (thought not necessarily pleasant).<br />		<a class="wiki_link" href="/14edo">14</a> (aka &quot;whitewood semitones&quot;) - <a class="wiki_link" href="/Jamesbond">Jamesbond</a>, <a class="wiki_link" href="/bug">bug</a>/<a class="wiki_link" href="/semaphore">semaphore</a>, etc. (Quite bad whitewood tuning.) Pretty much misses &quot;minor&quot; and &quot;major&quot; thirds entirely, going straight from &quot;subminor&quot; to &quot;neutral&quot; to &quot;supermajor&quot;, which makes it very xenharmonic (thought not necessarily pleasant).<br />
	<a class="wiki_link" href="/15edo">15</a> (aka 24edt, &quot;blackwood 1/3-tones&quot;) - Very interesting for <a class="wiki_link" href="/blackwood">blackwood</a>, <a class="wiki_link" href="/porcupine">porcupine</a>, and others. A good all-around EDO. If you want to internalize <a class="wiki_link" href="/Porcupine%20intervals">porcupine interval categories</a>, use 15edo.<br />		<a class="wiki_link" href="/15edo">15</a> (aka 24edt, &quot;blackwood 1/3-tones&quot;) - Very interesting for <a class="wiki_link" href="/blackwood">blackwood</a>, <a class="wiki_link" href="/porcupine">porcupine</a>, and others. A good all-around EDO. If you want to internalize <a class="wiki_link" href="/Porcupine%20intervals">porcupine interval categories</a>, use 15edo.<br />
	<a class="wiki_link" href="/16edo">16</a> (aka 25edt, &quot;armodue semitones&quot;) - <a class="wiki_link" href="/Mavila">Mavila</a>/armodue; those Italians love it. Really versatile and interesting - if you don't mind the lack of reasonable 3/2s. On the other hand you can treat it as an all-encompassing gamelan EDO where the beating fifths are an advantage. (The one advantage it has over 9edo in this respect is its slendro approximation, <a class="wiki_link" href="/gorgo">gorgo</a>.)<br />		<a class="wiki_link" href="/16edo">16</a> (aka 25edt, &quot;armodue semitones&quot;) - <a class="wiki_link" href="/Mavila">Mavila</a>/armodue; those Italians love it. Really versatile and interesting - if you don't mind the lack of reasonable 3/2s. On the other hand you can treat it as an all-encompassing gamelan EDO where the beating fifths are an advantage. (The one advantage it has over 9edo in this respect is its slendro approximation, <a class="wiki_link" href="/gorgo">gorgo</a>.)<br />