Collection of EDO impressions: Difference between revisions

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: '''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.

: '''Deja Igliashon:''' if this EDO got as much attention as [[31edo]], the world would be a better place. For many EDOs, getting into the particulars of how they [[temper]] extended [[JI]] is kind of unnecessary to really appreciate them, but 27edo is just so disgustingly ELEGANT in how it tempers that it makes it SO MUCH EASIER to navigate extended JI than darn near anything that can approach it in [[accuracy]]. First, consider the [[unison vector]] 64/63: just like {{EDOs|5, 10, 15, 20, 22, and 25edo}} (and I guess 12d?), tempering this out makes it so you can divide [[7/4]] into two equal parts that are each equal to [[4/3]], so even a short [[chain of fifths]] just automagically incorporates a bunch of ratios of 7. Then you've got [[128/125]], aka the Augmented comma, aka the diesis or something, which makes it so three approximate [[5/4]]s span exactly one octave--if you simply follow a chain of 5/4s, you literally can't get lost in the tuning! So far so good but also [[15edo]] can do both of these as well, so what else do we have? How about the holy trinity of 144/143, 169/168, and 196/195, the vanishing of which make it so [[12/11]]=[[13/12]]=[[14/13]]=[[15/14]]? This is the trinity that really gives 9edo its mojo, and in 27edo we have three parallel closed circles of [[9edo]], offset from one another by 1 and 2 steps of 27edo (respectively). Why is this cool? Because if you have a root note on one chain of 9edo, you have a [[5/4]] above it on the same chain, and then you have [[11/8]], [[3/2]], [[13/8]], [[7/4]], and [[15/8]] on the next chain of 9edo that's 1\27 higher. So you can just arpeggiate a bunch of [[harmonic]]s using motion by a single uniform step size, and if you keep moving by that same step size, instead of getting lost or circulating through ALL THE NOTES OF THE TUNING, you end up back at familiar territory after just a few off-kilter notes. Basically 27edo just makes it really easy not to get lost in [[15-odd-limit]] JI, because you have can find your way between harmonics with simple motions on small closed circles. Just AMAZING!

: '''Fumica:''' The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 [[subgroup]] with the sole exception of harmonic 15 tuned way too sharp, for I prefer a flat tuning of 15 or at least no sharper than 12edo's to improve its stability as a consonant major seventh. Other than that it's pretty good. B-tier.

: '''Fumica:''' The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 [[subgroup]] with the sole exception of harmonic 15 tuned way too sharp, for I prefer a flat tuning of 15 or at least no sharper than 12edo's to improve its stability as a consonant major seventh. Other than that it's pretty good. Octave compression gives better intonation. A-tier.

== [[28edo]] ==

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: '''Nicolai:''' 17EDO, but now there's a good third.

: '''Yourmusic Productions:''' Even better for [[5-limit]] music than [[31edo]], with it's gorgeous thirds, actually defined different sizes of whole tone and still sour harmonic 7, yet even more underused. Definitely deserves more attention. Maybe a half-[[kite guitar]], with full frets up to the perfect 4th or 5th, then [[17edo]] above that point, with adjacent strings tuned so the full range of higher notes can still be played would make it feasible.

: '''Fumica:''' This is to 17edo what [[24edo]] is to [[12edo]]. While 17edo is often good enough, this offers some more sophisticated solutions such as [[tetracot]]. Even the [[harmonic]]s 7 and 11, commonly cited as poor in this edo, are convincing enough to me, since when I worked with [[modus]] I never ~~felt~~ the ~~out-of-tune~~ intonation at all, unlike with [[porcupine]]. A-tier.

: '''Fumica:''' This is to 17edo what [[24edo]] is to [[12edo]]. While 17edo is often good enough, this offers some more sophisticated solutions such as [[tetracot]]. Even the [[harmonic]]s 7 and 11, commonly cited as poor in this edo, are convincing enough to me, since when I worked with [[modus]] I never had a problem with the intonation at all, unlike with [[porcupine]]. The sound is better than the structure. B-tier.

== [[35edo]] ==

@@ Line 336: / Line 336: @@
 : '''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.
 : '''Deja Igliashon:''' if this EDO got as much attention as [[31edo]], the world would be a better place. For many EDOs, getting into the particulars of how they [[temper]] extended [[JI]] is kind of unnecessary to really appreciate them, but 27edo is just so disgustingly ELEGANT in how it tempers that it makes it SO MUCH EASIER to navigate extended JI than darn near anything that can approach it in [[accuracy]]. First, consider the [[unison vector]] 64/63: just like {{EDOs|5, 10, 15, 20, 22, and 25edo}} (and I guess 12d?), tempering this out makes it so you can divide [[7/4]] into two equal parts that are each equal to [[4/3]], so even a short [[chain of fifths]] just automagically incorporates a bunch of ratios of 7. Then you've got [[128/125]], aka the Augmented comma, aka the diesis or something, which makes it so three approximate [[5/4]]s span exactly one octave--if you simply follow a chain of 5/4s, you literally can't get lost in the tuning! So far so good but also [[15edo]] can do both of these as well, so what else do we have? How about the holy trinity of 144/143, 169/168, and 196/195, the vanishing of which make it so [[12/11]]=[[13/12]]=[[14/13]]=[[15/14]]? This is the trinity that really gives 9edo its mojo, and in 27edo we have three parallel closed circles of [[9edo]], offset from one another by 1 and 2 steps of 27edo (respectively). Why is this cool? Because if you have a root note on one chain of 9edo, you have a [[5/4]] above it on the same chain, and then you have [[11/8]], [[3/2]], [[13/8]], [[7/4]], and [[15/8]] on the next chain of 9edo that's 1\27 higher. So you can just arpeggiate a bunch of [[harmonic]]s using motion by a single uniform step size, and if you keep moving by that same step size, instead of getting lost or circulating through ALL THE NOTES OF THE TUNING, you end up back at familiar territory after just a few off-kilter notes. Basically 27edo just makes it really easy not to get lost in [[15-odd-limit]] JI, because you have can find your way between harmonics with simple motions on small closed circles. Just AMAZING!
-: '''Fumica:''' The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 [[subgroup]] with the sole exception of harmonic 15 tuned way too sharp, for I prefer a flat tuning of 15 or at least no sharper than 12edo's to improve its stability as a consonant major seventh. Other than that it's pretty good. B-tier.
+: '''Fumica:''' The cyberpunk edo. Good sharp-tending tuning profile in the 2.3.5.7.13 [[subgroup]] with the sole exception of harmonic 15 tuned way too sharp, for I prefer a flat tuning of 15 or at least no sharper than 12edo's to improve its stability as a consonant major seventh. Other than that it's pretty good. Octave compression gives better intonation. A-tier.
 == [[28edo]] ==
@@ Line 381: / Line 381: @@
 : '''Nicolai:''' 17EDO, but now there's a good third.
 : '''Yourmusic Productions:''' Even better for [[5-limit]] music than [[31edo]], with it's gorgeous thirds, actually defined different sizes of whole tone and still sour harmonic 7, yet even more underused. Definitely deserves more attention. Maybe a half-[[kite guitar]], with full frets up to the perfect 4th or 5th, then [[17edo]] above that point, with adjacent strings tuned so the full range of higher notes can still be played would make it feasible.
-: '''Fumica:''' This is to 17edo what [[24edo]] is to [[12edo]]. While 17edo is often good enough, this offers some more sophisticated solutions such as [[tetracot]]. Even the [[harmonic]]s 7 and 11, commonly cited as poor in this edo, are convincing enough to me, since when I worked with [[modus]] I never felt the out-of-tune intonation at all, unlike with [[porcupine]]. A-tier.
+: '''Fumica:''' This is to 17edo what [[24edo]] is to [[12edo]]. While 17edo is often good enough, this offers some more sophisticated solutions such as [[tetracot]]. Even the [[harmonic]]s 7 and 11, commonly cited as poor in this edo, are convincing enough to me, since when I worked with [[modus]] I never had a problem with the intonation at all, unlike with [[porcupine]]. The sound is better than the structure. B-tier.
 == [[35edo]] ==