User:BudjarnLambeth/272ed23: Difference between revisions

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{{ED intro}}.

272ed23 is primarily intended to be used as [[60edo]] but with slightly [[Octave shrinking|compressed]] octaves.

== Theory ==

Compared to pure-[[octave]]s 60edo, ~~272ed3~~ features a relatively large improvement to [[7/1]] and [[11/1]], at the cost of moderate worsening of [[2/1]], [[3/1]] and [[5/1]].

Compared to pure-[[octave]]s 60edo, 272ed23 features a relatively large improvement to [[7/1]] and [[11/1]], at the cost of moderate worsening of [[2/1]], [[3/1]] and [[5/1]].

It also causes the [[val]]s to flip for [[5/1]], [[7/1]], [[13/1]] and [[17/1]].

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=== Prime harmonics ===

In the [[47-limit]], 272ed3 has less than 40% relative error on primes 2, 3, 5, 7, 11, 17, 23, 29, 31, 37, 41, 43 and 47.

In the [[47-limit]], 272ed3 has less than 40% [[relative error]] on primes 2, 3, 5, 7, 11, 17, 23, 29, 31, 37, 41, 43 and 47.

This makes it a solid tuning for the entire no-13, no-19 47-limit.

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==== 60edo for comparison ====

In the [[47-limit]], 60edo has less than 40% relative error on primes 2, 3, 5, 13, 17, 19, 31, 47.

In the 47-limit, 60edo has less than 40% relative error on primes 2, 3, 5, 13, 17, 19, 31, 47.

This makes it a solid tuning for the no-7, no-11 [[19-limit]] (or [[dual-n|dual]]-7, dual-11).

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! 7

! 139.70

| ~~12/11~~

|

| 25/23, 51/47

| 13/12, 38/35

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! 11

! 219.53

| 8/7

| 8/7 (patent)

| 17/15, 42/37

|

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! 12

! 239.48

| 8/7

| 8/7 (catnip)

| 23/20, 31/27, 54/47, 85/74

| 15/13

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-{{Infobox ET}}
+{{Editable user page}}
-{{ED intro}}.
+{{Infobox ET|debug=1}}
+{{ED intro}}
 ed23 is primarily intended to be used as [[60edo]] but with slightly [[Octave shrinking|compressed]] octaves.
 == Theory ==
-Compared to pure-[[octave]]s 60edo, 272ed3 features a relatively large improvement to [[7/1]] and [[11/1]], at the cost of moderate worsening of [[2/1]], [[3/1]] and [[5/1]].
+Compared to pure-[[octave]]s 60edo, 272ed23 features a relatively large improvement to [[7/1]] and [[11/1]], at the cost of moderate worsening of [[2/1]], [[3/1]] and [[5/1]].
 It also causes the [[val]]s to flip for [[5/1]], [[7/1]], [[13/1]] and [[17/1]].
@@ Line 16: / Line 17: @@
 === Prime harmonics ===
-In the [[47-limit]], 272ed3 has less than 40% relative error on primes 2, 3, 5, 7, 11, 17, 23, 29, 31, 37, 41, 43 and 47.
+In the [[47-limit]], 272ed3 has less than 40% [[relative error]] on primes 2, 3, 5, 7, 11, 17, 23, 29, 31, 37, 41, 43 and 47.
 This makes it a solid tuning for the entire no-13, no-19 47-limit.
@@ Line 25: / Line 26: @@
 ==== 60edo for comparison ====
-In the [[47-limit]], 60edo has less than 40% relative error on primes 2, 3, 5, 13, 17, 19, 31, 47.
+In the 47-limit, 60edo has less than 40% relative error on primes 2, 3, 5, 13, 17, 19, 31, 47.
 This makes it a solid tuning for the no-7, no-11 [[19-limit]] (or [[dual-n|dual]]-7, dual-11).
@@ Line 97: / Line 98: @@
 ! 7
 ! 139.70
-| 12/11
+|
 | 25/23, 51/47
 | 13/12, 38/35
@@ Line 121: / Line 122: @@
 ! 11
 ! 219.53
-| 8/7
+| 8/7 (patent)
 | 17/15, 42/37
 |
@@ Line 127: / Line 128: @@
 ! 12
 ! 239.48
-| 8/7
+| 8/7 (catnip)
 | 23/20, 31/27, 54/47, 85/74
 | 15/13