User:Eboone/EDO Impressions: Difference between revisions

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[[File:EDO Tier List.png|alt=A tier list of EDOs. S Tier - 12, 34, 31, 53, 72, 50, 22, 17, 15, 26, 19. A Tier - 27, 10, 46, 21, 20, 7, 16, 41, 55. B Tier - 18, 24, 36, 48, 65, 58, 25, 63, 13, 11, 56, 29, 23, 9, 5, 8. C Tier - 40, 43, 28, 14, 70, 68, 57, 37, 30, 60, 54, 49, 47, 44, 38, 67, 59, 35, 6. F Tier - 52, 62, 66, 71, 64, 39, 51, 61, 32, 39, 42, 45, 33.|thumb|Ebooone's tier list of EDOs 5-72, available at https://tiermaker.com/list/personal/numbers-0-100-15569788/3966935.]]

I, at least currently, work strictly in [[EDO|edos]]. I don't tend to go any higher than 72edo in my own works, so here are my impressions of all the edos ~~from 5~~ to 72.

I, at least currently, work strictly in [[EDO|'''edos''']]. I don't tend to go any higher than '''72edo''' in my own works, so here are my impressions of all the positive integer edos up to 72.

Additionally, I will be referencing the tier list I made (see above).

Additionally, I will be referencing the '''tier list''' I made (see above). Of course, this tier list is subject to change in the future, as are all of the impressions on this page.

''~~Yes, this page currently has no impressions.~~ I ~~will be back shortly~~.''

''EDOs I haven't gotten to yet are marked with "placeholder."''

== Categorization ==

I have split these edos into categories based on step size:

* 1-4edo — '''Trivial''' (subset of 12edo)

* 5-9edo — '''Macrotonal''' (133.33-240¢)

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* 20-29edo — '''Large Diesitonal''' (41.38-60¢)

* 30-39edo — '''Small Diesitonal''' (30.77-40¢)

* 40-72edo — '''~~Commatonal~~''' (16.67-~~30¢~~)

* 40-55edo — '''Supra-syntonic''' (21.82-30¢)

* 56-72edo — '''Sub-syntonic''' (16.67-21.43¢)

''These terms are not standard in any way. I just made them up.''

== Trivial ==

=== [[1edo]] ===

''Tier: '''N/A'''''

Honestly, can this one even be called an edo? I mean, "equal divisions of the octave" implies that the octave is divided. Anyway, this edo is pretty lame because the whole point of using different temperaments is to access certain melodic and harmonic properties, and this edo doesn't allow any of that. The only way to make this edo musical is through rhythm, dynamics, form, etc... stuff that isn't related to tuning.

=== [[2edo]] ===

''Tier: '''N/A'''''

This edo is literally just a tritone. And, in this case, it isn't really that great of a tritone. It's the 600¢ hemioctave tritone, the only one with no octave complement, so the melodic and harmonic capabilities of this tritone in isolation are pretty bare. That being said, this is the smallest edo with any dissonance, so that's a bonus.

=== [[3edo]] ===

''Tier: '''N/A'''''

This edo is just an augmented triad, but specifically one that closes the octave and, as such, cannot be inverted. This means that, once again, the melodic and harmonic capabilities of this edo are pretty limited. Nothing much else to say.

=== [[4edo]] ===

''Tier: '''N/A'''''

This edo is just straight up a better version of 2edo. It's a diminished tetrad, but specifically one that closes the octave and, as such, cannot be inverted. It's so metal it has 2 tritones.

== Macrotonal ==

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''Tier: '''B-'''''

~~placeholder~~

This is the first edo with a perfect fifth, but it's pretty sharp, coming in at 720¢ (18.04¢ sharp of [[3/2]]). This means 5edo works best in timbres with quick decay, like a marimba, so that the dissonance of the fifth is softened. Although, the sharp fifth when used melodically has quite a desirable "uplifting" quality to it that brings it out amidst the texture of the rest of the scale. This edo also features [[Interseptimal interval|interseptimal intervals]], giving melodies an "open" quality. It's a bit reminiscent of the minor pentatonic scale of 12edo, making it quite familiar to unaccustomed ears, but still with a tang of xen. Overall, this is a fun edo to work in, it's just that it suffers from the same problem that all very small edos have; there just aren't enough notes. It isn't a very versatile edo, so you usually have to rely on nontonal musical factors such as rhythm, dynamics, and form to create an interesting piece.

=== [[6edo]] ===

''Tier: '''C-'''''

~~placeholder~~

This is technically a trivial edo, but I'd say it's much more interesting than 1-4edo because it contains a whole tone (6edo being the familiar whole tone scale of 12edo). There are many pieces that make use of the whole tone scale, but very few that strictly exist in 6edo. [[wikipedia:Claude_Debussy|Claude Debussy]] is well known for his use of this scale. Overall, this is a very interesting color to use while working in 6n-edos, but a very limiting scale to use in isolation. The best 6edo pieces I could find are the prelude and invention from [[Aaron Andrew Hunt]]'s "[https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard The Equal Tempered Keyboard]," and honestly they are pretty interesting.

=== [[7edo]] ===

''Tier: '''A'''''

~~placeholder~~

This is the first edo with a perfect fifth and a third. The fifth is pretty flat, coming in at 685.71¢ (16.25¢ flat of 3/2), and the third is a supraminor third of 342.86¢. It's a bit reminiscent of the dorian scale of 12edo, but not really. The 2nd, 3rd, 6th, and 7th are all neutral, so this edo has a very distinct (and very xen) sound. It may seem quite limiting to only have one third, but honestly this is a very fun edo to work in. Quartal and quintal structures have a distinct "underwater" quality to them, which I really like. Overall, a very nice edo and one that is trivially easy to notate.

=== [[8edo]] ===

''Tier: '''B-'''''

~~placeholder~~

This edo does not have a perfect fifth, but it does have 2 flavors of thirds... kind of. Because 8 is divisible by 4, it contains the 300¢ minor third, but it also includes a 450¢ interval that could be used either as an ultramajor third or a very flat fourth. This dual purpose actually makes it a pretty interesting interval to work with harmonically. This edo also has a neutral second, but one that much more closely approximates [[12/11]] than 7edo, giving melodies a pretty distinct neutral sound. This edo actually works surprisingly well on organ, producing a very sinister, foreboding sound. Overall, a decent edo to work in but one that I don't find myself using often.

=== [[9edo]] ===

''Tier: '''B-'''''

~~placeholder~~

This edo, while I put it in low B tier, is actually a very fun edo. It is, what most people would say, the first edo with 2 flavors of thirds, featuring the familiar 400¢ major third because it's divisible by 3, but also a scarily close approximation of 7/6. In fact, this edo approximates many septimal intervals down to the decimal point, which is quite strange, but definitely contributes to the sound of this tuning. The fifth is heinously flat (over 30¢ flat of 3/2), but I've found that even this fifth can be softened via the use of a honky-tonk piano timbre. The distinct septimal resonance of the subminor third juxtaposed with the abhorrently flat fifth is an almost ineffable combination, but one that creates some of the most beautiful harmonies. The only reason I put this temperament so low is because the fifth is so flat, so it really is pretty difficult to listen to if you're not using a timbre that is literally out of tune. Plus, there are other edos that support [[Mavila]] with much better fifths. Overall, while the tuning isn't very versatile, the sounds it makes are utterly phantasmagoric, and I highly recommend you try this temperament in a harmonic context.

== Semitonal ==

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placeholder

== ~~Commatonal~~ ==

== Supra-syntonic ==

=== [[40edo]] ===

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placeholder

== Sub-syntonic ==

=== [[56edo]] ===

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placeholder

__NOTOC__

__NOEDITSECTION__

@@ Line 1: / Line 1: @@
+{{DISPLAYTITLE:Ebooone's EDO Impressions}}
 [[File:EDO Tier List.png|alt=A tier list of EDOs. S Tier - 12, 34, 31, 53, 72, 50, 22, 17, 15, 26, 19. A Tier - 27, 10, 46, 21, 20, 7, 16, 41, 55. B Tier - 18, 24, 36, 48, 65, 58, 25, 63, 13, 11, 56, 29, 23, 9, 5, 8. C Tier - 40, 43, 28, 14, 70, 68, 57, 37, 30, 60, 54, 49, 47, 44, 38, 67, 59, 35, 6. F Tier - 52, 62, 66, 71, 64, 39, 51, 61, 32, 39, 42, 45, 33.|thumb|Ebooone's tier list of EDOs 5-72, available at https://tiermaker.com/list/personal/numbers-0-100-15569788/3966935.]]
-I, at least currently, work strictly in [[EDO|edos]]. I don't tend to go any higher than 72edo in my own works, so here are my impressions of all the edos from 5 to 72.
+I, at least currently, work strictly in [[EDO|'''edos''']]. I don't tend to go any higher than '''72edo''' in my own works, so here are my impressions of all the positive integer edos up to 72.
-Additionally, I will be referencing the tier list I made (see above).
+Additionally, I will be referencing the '''tier list''' I made (see above). Of course, this tier list is subject to change in the future, as are all of the impressions on this page.
-''Yes, this page currently has no impressions. I will be back shortly.''
+''EDOs I haven't gotten to yet are marked with "placeholder."''
 == Categorization ==
 I have split these edos into categories based on step size:
+* 1-4edo — '''Trivial''' (subset of 12edo)
 * 5-9edo — '''Macrotonal''' (133.33-240¢)
@@ Line 14: / Line 16: @@
 * 20-29edo — '''Large Diesitonal''' (41.38-60¢)
 * 30-39edo — '''Small Diesitonal''' (30.77-40¢)
-* 40-72edo — '''Commatonal''' (16.67-30¢)
+* 40-55edo — '''Supra-syntonic''' (21.82-30¢)
+* 56-72edo — '''Sub-syntonic''' (16.67-21.43¢)
 ''These terms are not standard in any way. I just made them up.''
+== Trivial ==
+=== [[1edo]] ===
+''Tier: '''N/A'''''
+Honestly, can this one even be called an edo? I mean, "equal divisions of the octave" implies that the octave is divided. Anyway, this edo is pretty lame because the whole point of using different temperaments is to access certain melodic and harmonic properties, and this edo doesn't allow any of that. The only way to make this edo musical is through rhythm, dynamics, form, etc... stuff that isn't related to tuning.
+=== [[2edo]] ===
+''Tier: '''N/A'''''
+This edo is literally just a tritone. And, in this case, it isn't really that great of a tritone. It's the 600¢ hemioctave tritone, the only one with no octave complement, so the melodic and harmonic capabilities of this tritone in isolation are pretty bare. That being said, this is the smallest edo with any dissonance, so that's a bonus.
+=== [[3edo]] ===
+''Tier: '''N/A'''''
+This edo is just an augmented triad, but specifically one that closes the octave and, as such, cannot be inverted. This means that, once again, the melodic and harmonic capabilities of this edo are pretty limited. Nothing much else to say.
+=== [[4edo]] ===
+''Tier: '''N/A'''''
+This edo is just straight up a better version of 2edo. It's a diminished tetrad, but specifically one that closes the octave and, as such, cannot be inverted. It's so metal it has 2 tritones.
 == Macrotonal ==
@@ Line 23: / Line 48: @@
 ''Tier: '''B-'''''
-placeholder
+This is the first edo with a perfect fifth, but it's pretty sharp, coming in at 720¢ (18.04¢ sharp of [[3/2]]). This means 5edo works best in timbres with quick decay, like a marimba, so that the dissonance of the fifth is softened. Although, the sharp fifth when used melodically has quite a desirable "uplifting" quality to it that brings it out amidst the texture of the rest of the scale. This edo also features [[Interseptimal interval|interseptimal intervals]], giving melodies an "open" quality. It's a bit reminiscent of the minor pentatonic scale of 12edo, making it quite familiar to unaccustomed ears, but still with a tang of xen. Overall, this is a fun edo to work in, it's just that it suffers from the same problem that all very small edos have; there just aren't enough notes. It isn't a very versatile edo, so you usually have to rely on nontonal musical factors such as rhythm, dynamics, and form to create an interesting piece.
 === [[6edo]] ===
 ''Tier: '''C-'''''
-placeholder
+This is technically a trivial edo, but I'd say it's much more interesting than 1-4edo because it contains a whole tone (6edo being the familiar whole tone scale of 12edo). There are many pieces that make use of the whole tone scale, but very few that strictly exist in 6edo. [[wikipedia:Claude_Debussy|Claude Debussy]] is well known for his use of this scale. Overall, this is a very interesting color to use while working in 6n-edos, but a very limiting scale to use in isolation. The best 6edo pieces I could find are the prelude and invention from [[Aaron Andrew Hunt]]'s "[https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard The Equal Tempered Keyboard]," and honestly they are pretty interesting.
 === [[7edo]] ===
 ''Tier: '''A'''''
-placeholder
+This is the first edo with a perfect fifth and a third. The fifth is pretty flat, coming in at 685.71¢ (16.25¢ flat of 3/2), and the third is a supraminor third of 342.86¢. It's a bit reminiscent of the dorian scale of 12edo, but not really. The 2nd, 3rd, 6th, and 7th are all neutral, so this edo has a very distinct (and very xen) sound. It may seem quite limiting to only have one third, but honestly this is a very fun edo to work in. Quartal and quintal structures have a distinct "underwater" quality to them, which I really like. Overall, a very nice edo and one that is trivially easy to notate.
 === [[8edo]] ===
 ''Tier: '''B-'''''
-placeholder
+This edo does not have a perfect fifth, but it does have 2 flavors of thirds... kind of. Because 8 is divisible by 4, it contains the 300¢ minor third, but it also includes a 450¢ interval that could be used either as an ultramajor third or a very flat fourth. This dual purpose actually makes it a pretty interesting interval to work with harmonically. This edo also has a neutral second, but one that much more closely approximates [[12/11]] than 7edo, giving melodies a pretty distinct neutral sound. This edo actually works surprisingly well on organ, producing a very sinister, foreboding sound. Overall, a decent edo to work in but one that I don't find myself using often.
 === [[9edo]] ===
 ''Tier: '''B-'''''
-placeholder
+This edo, while I put it in low B tier, is actually a very fun edo. It is, what most people would say, the first edo with 2 flavors of thirds, featuring the familiar 400¢ major third because it's divisible by 3, but also a scarily close approximation of 7/6. In fact, this edo approximates many septimal intervals down to the decimal point, which is quite strange, but definitely contributes to the sound of this tuning. The fifth is heinously flat (over 30¢ flat of 3/2), but I've found that even this fifth can be softened via the use of a honky-tonk piano timbre. The distinct septimal resonance of the subminor third juxtaposed with the abhorrently flat fifth is an almost ineffable combination, but one that creates some of the most beautiful harmonies. The only reason I put this temperament so low is because the fifth is so flat, so it really is pretty difficult to listen to if you're not using a timbre that is literally out of tune. Plus, there are other edos that support [[Mavila]] with much better fifths. Overall, while the tuning isn't very versatile, the sounds it makes are utterly phantasmagoric, and I highly recommend you try this temperament in a harmonic context.
 == Semitonal ==
@@ Line 201: / Line 226: @@
 placeholder
-== Commatonal ==
+== Supra-syntonic ==
 === [[40edo]] ===
@@ Line 282: / Line 307: @@
 placeholder
+== Sub-syntonic ==
 === [[56edo]] ===
@@ Line 367: / Line 394: @@
 placeholder
+__NOTOC__
+__NOEDITSECTION__