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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]].  
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.
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
| 1
| 41.379
| 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
| negative diminished 2nd,<br>double diminished 3rd
| ^1, vm2
| ^1, vm2
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| 28
| 28
| 1158.621
| 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
| diminished 9th,<br>double augmented 6th
| ^M7, v8
| ^M7, v8
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29edo can be notated three different ways. Using only sharps and flats, the chromatic scale from C is:
29edo can be notated three different ways. Using only sharps and flats, the chromatic scale from C is:


{{dash|C, B♯, D♭, C♯, B𝄪/E𝄫, D, C𝄪/F𝄫, E♭, D♯, F♭, E, D𝄪/G𝄫, F, E♯, G♭, F♯, E𝄪/A𝄫, G, F𝄪, A♭, G♯, B𝄫, A, G𝄪/C𝄫, B♭, A♯, C♭, B, A𝄪/D𝄫, C|s=hair|d=long}}
{{dash|C, B♯, D♭, C♯, B𝄪/E𝄫, D, C𝄪/F𝄫, E♭, D♯, F♭, E, D𝄪/G𝄫, F, E♯, G♭, F♯, E𝄪/A𝄫, G, F𝄪, A♭, G♯, B𝄫, A, G𝄪/C𝄫, B♭, A♯, C♭, B, A𝄪/D𝄫, C|s=hair}}


Here, six pairs of enharmonic equivalents exist:
Here, six pairs of enharmonic equivalents exist:
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* C𝄪 = F𝄫
* C𝄪 = F𝄫


=== Ups and downs notation ===
=== Stein–Zimmermann–Gould notation ===
Since a sharp raises by three steps, 29edo is a good candidate for [[ups and downs notation]], similar to [[22edo]]. Spoken as up, downsharp, sharp, etc. Note that downsharp (v#) can be respelled as dup (^^).
Since a sharp raises by three steps, 29edo is a good candidate for [[Stein–Zimmermann–Gould notation]], using sharps and flats with arrows similar to [[22edo]]:
{{Ups and downs sharpness}}
{{Sharpness-sharp3-szg}}
 
Here, sharps and flats with arrows from [[Helmholtz–Ellis notation]] are used:
{{Sharpness-sharp3}}


Note that C♯ is enharmonic to D{{flatup}}, and D♭ is enharmonic to C{{sharpdown}}.
Note that C♯ is enharmonic to D{{flatup}}, and D♭ is enharmonic to C{{sharpdown}}.


If arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best spelled with double arrows.
If arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best spelled with double arrows.
=== Kite's ups and downs notation ===
29edo can also be notated with [[Kite's ups and downs notation|Kite's ups and downs]], spoken as up, downsharp, sharp, etc. Note that downsharp (v#) can be respelled as dup (^^).
{{Ups and downs sharpness}}


=== Sagittal notation ===
=== Sagittal notation ===
This notation uses the same sagittal sequence as EDOs [[15edo#Sagittal notation|15]] and [[22edo#Sagittal notation|22]].
This notation uses the same sagittal sequence as edos [[15edo #Sagittal notation|15]] and [[22edo #Sagittal notation|22]].


==== Evo flavor ====
==== Evo flavor ====
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* [https://www.youtube.com/shorts/lOaG5mgYMuM ''Concertina Ballerina''] (1983) – microtonal cover in 29edo by [[Bryan Deister]] (2026)
* [https://www.youtube.com/shorts/lOaG5mgYMuM ''Concertina Ballerina''] (1983) – microtonal cover in 29edo by [[Bryan Deister]] (2026)


; {{W|Toby Fox}} (via {{W|Deltarune}})
; {{W|Toby Fox}}
* [https://www.youtube.com/shorts/NYN8EBllJkE ''Deltarune Chapter 2 - A Cyber's World''] (2021) – microtonal cover in 29edo by [[Bryan Deister]] (2023)
* [https://www.youtube.com/shorts/NYN8EBllJkE ''A Cyber's World''] via ''{{W|Deltarune}} Chapter 2'' (2021) – microtonal cover in 29edo by [[Bryan Deister]] (2023)
* [https://www.youtube.com/watch?v=JOqnRPIOb5o ''Deltarune Chapter 2 - Dialtone''] (2021) – microtonal cover in 29edo by [[Bryan Deister]] (2024)
* [https://www.youtube.com/watch?v=JOqnRPIOb5o ''Dialtone''] via ''{{W|Deltarune}} Chapter 2'' (2021) – microtonal cover in 29edo by [[Bryan Deister]] (2024)


; {{W|Bart Howard}}
; {{W|Bart Howard}}
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* [https://www.youtube.com/watch?v=ktk0VWbUbDg ''microtonal improvisation in 29edo''] (2023)
* [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/SH5IQOi33Oo ''29edo groove''] (2025)
* [https://www.youtube.com/shorts/PuaNvxX11II ''an idea in 29edo''] (2026)


; [[duckapus]]
; [[duckapus]]
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