29edo: Difference between revisions

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Edson is a 2.3.7/5.11/5.13/5 subgroup temperament, and 29edo represents the 2.3.11/5.13/5 subgroup to very high accuracy, and the 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the [[7:11:13|1-11/7-13/7 (7:11:13)]] chord, the [[The Archipelago|barbados]] triad [[10:13:15|1-13/10-3/2 (10:13:15)]], the minor barbados triad [[26:30:39|1-15/13-3/2 (26:30:39)]], the [[22:28:33|1-14/11-3/2 (22:28:33)]] triad, the [[22:26:33|1-13/11-3/2 (22:26:33)]] triad, and the [[petrmic triad]], a 13-limit [[Dyadic chord|essentially tempered dyadic chord]].

29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 ~~and~~ 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the [[k*N subgroups|3*29 subgroup]] 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the [[k*N subgroups|2*29 subgroup]] 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas.

29 tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195, 364/363, and 847/845 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the [[k*N subgroups|3*29 subgroup]] 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the [[k*N subgroups|2*29 subgroup]] 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas.

Due to 29edo's tone-efficient mapping of 2.3.7/5.11/5.13/5, it makes sense to collapse this subgroup to 29edo. One may then expand the subgroup to the full 13-limit, adding an independent generator to reach primes 5, 7, 11, and 13 in one generator. This is [[mystery]] temperament, which has very low [[badness]] despite so many periods per octave. The 58-note MOS gives scope for harmony, with 29 15-odd-limit otonal chords and 29 utonal chords.

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| 1

| 41.379

| [[33/32]], [[40/39]], [[45/44]], [[81/80]]

| [[33/32]], [[40/39]], [[45/44]],<br>[[81/80]], [[64/63]]

| negative diminished 2nd,<br>double diminished 3rd

| ^1, vm2

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| 28

| 1158.621

| [[64/33]], [[39/20]], [[88/45]] [[160/81]]

| [[64/33]], [[39/20]], [[88/45]],<br>[[160/81]], [[63/32]]

| diminished 9th,<br>double augmented 6th

| ^M7, v8

Line 1,052:

* [https://www.youtube.com/watch?v=ktk0VWbUbDg ''microtonal improvisation in 29edo''] (2023)

* [https://www.youtube.com/shorts/SH5IQOi33Oo ''29edo groove''] (2025)

* [https://www.youtube.com/shorts/PuaNvxX11II ''an idea in 29edo''] (2026)

; [[duckapus]]

@@ Line 31: / Line 31: @@
 Edson is a 2.3.7/5.11/5.13/5 subgroup temperament, and 29edo represents the 2.3.11/5.13/5 subgroup to very high accuracy, and the 2.3.7/5.11/5.13/5 to a lesser but still good accuracy, and so can be used with this subgroup, which is liberally supplied with chords such as the [[7:11:13|1-11/7-13/7 (7:11:13)]] chord, the [[The Archipelago|barbados]] triad [[10:13:15|1-13/10-3/2 (10:13:15)]], the minor barbados triad [[26:30:39|1-15/13-3/2 (26:30:39)]], the [[22:28:33|1-14/11-3/2 (22:28:33)]] triad, the [[22:26:33|1-13/11-3/2 (22:26:33)]] triad, and the [[petrmic triad]], a 13-limit [[Dyadic chord|essentially tempered dyadic chord]].
-tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195 and 364/363 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the [[k*N subgroups|3*29 subgroup]] 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the [[k*N subgroups|2*29 subgroup]] 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas.
+tempers out 352/351, 676/675 and 4000/3993 from the 2.3.11/5.13/5 subgroup, and in addition 196/195, 364/363, and 847/845 from the 2.3.7/5.11/5.13/5 subgroup, so we have various relationships from the tempering, such as the fact that the 1-13/11-3/2 chord and the 1-14/11-3/2 chord are inverses of each other, a major-minor pairing. A larger subgroup containing both of these subgroups is the [[k*N subgroups|3*29 subgroup]] 2.3.125.175.275.325; on this subgroup 29 tunes the same as 87, and the commas of 29 on this subgroup are the same as the 13-limit commas of 87. Still another subgroup of interest is the [[k*N subgroups|2*29 subgroup]] 2.3.25.35.55.65.85; on this subgroup 29 tunes the same as 58 and has the same 17-limit commas.
 Due to 29edo's tone-efficient mapping of 2.3.7/5.11/5.13/5, it makes sense to collapse this subgroup to 29edo. One may then expand the subgroup to the full 13-limit, adding an independent generator to reach primes 5, 7, 11, and 13 in one generator. This is [[mystery]] temperament, which has very low [[badness]] despite so many periods per octave. The 58-note MOS gives scope for harmony, with 29 15-odd-limit otonal chords and 29 utonal chords.
@@ Line 66: / Line 66: @@
 | 1
 | 41.379
-| [[33/32]],  [[40/39]],  [[45/44]], [[81/80]]
+| [[33/32]],  [[40/39]],  [[45/44]],<br>[[81/80]], [[64/63]]
 | negative diminished 2nd,<br>double diminished 3rd
 | ^1, vm2
@@ Line 363: / Line 363: @@
 | 28
 | 1158.621
-| [[64/33]], [[39/20]], [[88/45]] [[160/81]]
+| [[64/33]], [[39/20]], [[88/45]],<br>[[160/81]], [[63/32]]
 | diminished 9th,<br>double augmented 6th
 | ^M7, v8
@@ Line 1,052: / Line 1,052: @@
 * [https://www.youtube.com/watch?v=ktk0VWbUbDg ''microtonal improvisation in 29edo''] (2023)
 * [https://www.youtube.com/shorts/SH5IQOi33Oo ''29edo groove''] (2025)
+* [https://www.youtube.com/shorts/PuaNvxX11II ''an idea in 29edo''] (2026)
 ; [[duckapus]]