User:FloraC/Fumica's edo impressions: Difference between revisions

Line 79:

|-

! B-tier

| 39, 43, 53, 72

| 39, 43, 53, 72, 77

|-

! C-tier

| 48, 50, 51, 60, 68, 70

| 48, 50, 51, 60, 65, 68, 70, 73

|-

! D-tier

| 44, 45, 55, 56, 63, 74

| 44, 45, 55, 56, 63, 74, 75

|-

! F-tier

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=== Comma-size ===

The sense of uniqueness of each edo begins to diminish in this range. As the steps get smaller, more and more intervals start to be reasonably approximated, and the edos feel more and more like free pitch. For one thing, starting from here, all edos have at least one diatonic scale (35edo being the last nondiatonic edo). For this reason I'm only ~~listing~~ those which have a good fifth (relative error < 1/3)~~. For the rest, expect~~

The sense of uniqueness of each edo begins to diminish in this range. As the steps get smaller, more and more intervals start to be reasonably approximated, and the edos feel more and more like free pitch. For one thing, starting from here, all edos have at least one diatonic scale (35edo being the last nondiatonic edo). For this reason I'm only discussing those which have a good fifth (relative error < 1/3).

~~: ''n''-edo – Potentially useful as every other step of 2''n''-edo. D-tier~~.

* 39 – 1/5-comma quasisuper, most notable for tuning the minor second to 28/27 (with the 39d val) which I feel is where the tension peaks for voice leading. Such an overlooked system despite being similar to 27edo in many ways. B-tier.

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

* 63 – Similar to 56edo, nothing notable about it. D-tier.

* 65 – As every other step of 130edo, this edo is excellent in the 2.3.5.11.19.23-subgroup, but the contrast between that and the poor approximations to 7 and 13 is fatal. Still, it allows a dual-7 dual-13 approach, not very satisfying at this level but better than nothing. C-tier.

…

* 67 – A disastrous meantone tuning. F-tier.

* 68 – While this edo contains 17edo and if we compare it with 51edo, it clearly hits more harmonic targets, it should be noted that linearly dividing the steps into four is a weaker move than into two or three, as quarter-step offsets don't tend to create new categories, unlike third- or half-step offsets. This is especially true of this edo, as 34edo hits lots of harmonic targets already. Another obvious flaw is the awkward situation with prime 11. C-tier.

* 70 – ~~This~~ edo's structure allows lots of niche uses. Unfortunately none of them is interesting enough to make me stay very long ~~here~~. C-tier.

* 70 – As every other step of 140edo, this edo's structure allows lots of niche uses. Unfortunately none of them is interesting enough to make me stay very long. C-tier.

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

* 73 – A strange sharp-tending hemicommatic system that seems to allow some niche uses. C-tier.

…

* 74 – A good meantone tuning. Not much else to offer. D-tier.

* 75 – A good tetracot tuning. Otherwise there's nothing notable. D-tier.

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

* 79 – A disastrous non-meantone tuning. F-tier.

…

== Hemicomma-size ==

Starting from here, it'd be better to adopt a more systematic approach, for which I'm planning an essay about the 2.3.5.7.11.13.19-subgroup JI and temperaments.

* 79 – A disastrous non-meantone tuning. F-~~tier~~.

@@ Line 79: / Line 79: @@
 |-
 ! B-tier
-| 39, 43, 53, 72
+| 39, 43, 53, 72, 77
 |-
 ! C-tier
-| 48, 50, 51, 60, 68, 70
+| 48, 50, 51, 60, 65, 68, 70, 73
 |-
 ! D-tier
-| 44, 45, 55, 56, 63, 74
+| 44, 45, 55, 56, 63, 74, 75
 |-
 ! F-tier
@@ Line 92: / Line 92: @@
 === Comma-size ===
-The sense of uniqueness of each edo begins to diminish in this range. As the steps get smaller, more and more intervals start to be reasonably approximated, and the edos feel more and more like free pitch. For one thing, starting from here, all edos have at least one diatonic scale (35edo being the last nondiatonic edo). For this reason I'm only listing those which have a good fifth (relative error < 1/3). For the rest, expect
+The sense of uniqueness of each edo begins to diminish in this range. As the steps get smaller, more and more intervals start to be reasonably approximated, and the edos feel more and more like free pitch. For one thing, starting from here, all edos have at least one diatonic scale (35edo being the last nondiatonic edo). For this reason I'm only discussing those which have a good fifth (relative error < 1/3).
-: ''n''-edo – Potentially useful as every other step of 2''n''-edo. D-tier.
 * 39 – 1/5-comma quasisuper, most notable for tuning the minor second to 28/27 (with the 39d val) which I feel is where the tension peaks for voice leading. Such an overlooked system despite being similar to 27edo in many ways. B-tier.
@@ Line 112: / Line 110: @@
 * 62 – The ultimate 23-limit meantone tuning. It re-tunes harmonics 13, 17, 19, and 23 for 31edo. I find these additions to 31edo's 11-limit very favorable. A-tier.
 * 63 – Similar to 56edo, nothing notable about it. D-tier.
+* 65 – As every other step of 130edo, this edo is excellent in the 2.3.5.11.19.23-subgroup, but the contrast between that and the poor approximations to 7 and 13 is fatal. Still, it allows a dual-7 dual-13 approach, not very satisfying at this level but better than nothing. C-tier.
-…
 * 67 – A disastrous meantone tuning. F-tier.
 * 68 – While this edo contains 17edo and if we compare it with 51edo, it clearly hits more harmonic targets, it should be noted that linearly dividing the steps into four is a weaker move than into two or three, as quarter-step offsets don't tend to create new categories, unlike third- or half-step offsets. This is especially true of this edo, as 34edo hits lots of harmonic targets already. Another obvious flaw is the awkward situation with prime 11. C-tier.
-* 70 – This edo's structure allows lots of niche uses. Unfortunately none of them is interesting enough to make me stay very long here. C-tier.
+* 70 – As every other step of 140edo, this edo's structure allows lots of niche uses. Unfortunately none of them is interesting enough to make me stay very long. C-tier.
 * 72 – The last essential comma-level edo. Has the same problem with 60edo. Even tho it approximates JI way better and thus qualifies for an essential comma-level edo, most of its structural features have been provided by 41- and 58edo. B-tier.
+* 73 – A strange sharp-tending hemicommatic system that seems to allow some niche uses. C-tier.
-…
 * 74 – A good meantone tuning. Not much else to offer. D-tier.
+* 75 – A good tetracot tuning. Otherwise there's nothing notable. D-tier.
+* 77 – This edo is very sophisticated and hard to evaluate. It's an ideal tuning for the valentine temperament, obviously. It also seems to be capable of somewhat approximating the full 23-limit. Overall, the structure is a tight fit, with lots of quirks, but that's not too troublesome – they may as well be turned into advantages in the right circumstances. B-tier.
+* 79 – A disastrous non-meantone tuning. F-tier.
-…
+== Hemicomma-size ==
+Starting from here, it'd be better to adopt a more systematic approach, for which I'm planning an essay about the 2.3.5.7.11.13.19-subgroup JI and temperaments.
-* 79 – A disastrous non-meantone tuning. F-tier.