44edo: Difference between revisions

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44edo is a double of [[22edo]], to which it adds the ratios of 13, 19, and 23. While not the most accurate 2.3.5.7.11 tuning, 22edo is certainly a relatively compact one, and it's natural to extend it this way. The most practically useful of these additions is easily the [[13/1|13th harmonic]] with its neutral intervals, but the 17th, 19th, and 23rd are not to be dismissed.

It is on the [[optimal ET sequence]] for 7-, 11- and 13-limit [[nautilus]] temperament, for 11-limit [[spell]] temperament, and for 13-limit [[cantrip] temperament. In the [[13-limit]] it supplies the optimal [[patent val]] for [[vigin]] temperament.

It is on the [[optimal ET sequence]] for 7-, 11- and 13-limit [[nautilus]] temperament, for 11-limit [[spell]] temperament, and for 13-limit [[cantrip]] temperament. In the [[13-limit]] it supplies the optimal [[patent val]] for [[vigin]] temperament.

The [[k*N_subgroups|2*44]] subgroup of 44edo is 2.9.5.21.11.13.17.19.23, on which 44 tempers out the same commas as the [[patent val]] for [[88edo]].

The [[k*N_subgroups|2*44]] subgroup of 44edo is 2.9.5.21.11.13.17.19.23, on which 44 tempers out the same commas as the patent val for [[88edo]].

=== Harmonics ===

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! Degrees

! Cents

! colspan="3" | [[Ups and ~~Downs Notation~~]]

! colspan="3" | [[Ups and downs notation]]

|-

| 0

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| 190.91

| 9/8

| [[Spell]]/[[~~Cantrip~~]]

| [[Spell]]/[[cantrip]]

|-

| 1

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== Scales ==

* Evacuated planet{{idiosyncratic}} (approximated from [[66afdo|66]][[afdo]]): 5 13 8 12 6

* Approximations of [[gamelan]] scales:

** 5-tone pelog: 4 6 15 4 15

@@ Line 4: / Line 4: @@
 edo is a double of [[22edo]], to which it adds the ratios of 13, 19, and 23. While not the most accurate 2.3.5.7.11 tuning, 22edo is certainly a relatively compact one, and it's natural to extend it this way. The most practically useful of these additions is easily the [[13/1|13th harmonic]] with its neutral intervals, but the 17th, 19th, and 23rd are not to be dismissed.
-It is on the [[optimal ET sequence]] for 7-, 11- and 13-limit [[nautilus]] temperament, for 11-limit [[spell]] temperament, and for 13-limit [[cantrip] temperament. In the [[13-limit]] it supplies the optimal [[patent val]] for [[vigin]] temperament.
+It is on the [[optimal ET sequence]] for 7-, 11- and 13-limit [[nautilus]] temperament, for 11-limit [[spell]] temperament, and for 13-limit [[cantrip]] temperament. In the [[13-limit]] it supplies the optimal [[patent val]] for [[vigin]] temperament.
-The [[k*N_subgroups|2*44]] subgroup of 44edo is 2.9.5.21.11.13.17.19.23, on which 44 tempers out the same commas as the [[patent val]] for [[88edo]].
+The [[k*N_subgroups|2*44]] subgroup of 44edo is 2.9.5.21.11.13.17.19.23, on which 44 tempers out the same commas as the patent val for [[88edo]].
 === Harmonics ===
@@ Line 22: / Line 22: @@
 ! Degrees
 ! Cents
-! colspan="3" | [[Ups and Downs Notation]]
+! colspan="3" | [[Ups and downs notation]]
 |-
 | 0
@@ Line 371: / Line 371: @@
 | 190.91
 | 9/8
-| [[Spell]]/[[Cantrip]]
+| [[Spell]]/[[cantrip]]
 |-
 | 1
@@ Line 412: / Line 412: @@
 == Scales ==
+* Evacuated planet{{idiosyncratic}} (approximated from [[66afdo|66]][[afdo]]): 5 13 8 12 6
 * Approximations of [[gamelan]] scales:
 ** 5-tone pelog: 4 6 15 4 15