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'''[[Ed7|Division of the 7th harmonic]] into 24 equal parts''' (24ed7) is related to the [[Hemifamity temperaments|quanic temperament]], which is a [[cluster temperament]] with nine clusters of notes in an octave. The step size is about 140.3677 cents, corresponding to 8.5490 [[edo]].
{{Infobox ET}}
'''[[Ed7|Division of the 7th harmonic]] into 24 equal parts''' (24ed7) is related to the [[Hemifamity temperaments|quanic temperament]], which tempers out 352/351, 540/539, 729/728, and 1331/1323 in the 13-limit; 352/351, 442/441, 540/539, 561/560, and 715/714 in the 17-limit. The step size is about 140.3677 cents, corresponding to 8.5490 [[edo]].


{| class="wikitable"
== Intervals ==
{| class="wikitable mw-collapsible"
|+ Intervals of 24ed7
|-
|-
! | degree
! | degree
Line 25: Line 28:
| | 3
| | 3
| | 421.1032
| | 421.1032
| | [[14/11]], 23/18, [[32/25]]
| | [[14/11]], 65/51, 51/40, 23/18, [[32/25]]
| |  
| |  
|-
|-
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| | 12
| | 12
| | 1684.4130
| | 1684.4130
| |  
| | 119/45, 45/17
| |  
| |  
|-
|-
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| | 15
| | 15
| | 2105.5162
| | 2105.5162
| | [[27/16|27/8]]
| | 91/27, [[27/16|27/8]]
| |  
| |  
|-
|-
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| | 17
| | 17
| | 2386.2517
| | 2386.2517
| | 119/30, 250/63
| | 119/30, 143/36
| |  
| |  
|-
|-
| | 18
| | 18
| | 2526.6194
| | 2526.6194
| | 30/7, 77/18, 56/13
| | [[14/13|56/13]]
| |  
| |  
|-
|-
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|}
|}


==24ed7 as a generator==
== Harmonics ==
24ed7 can also be thought of as a [[generator]] of the quanic temperament, which tempers out 352/351, 540/539, 729/728, and 1331/1323 in the 13-limit; 352/351, 442/441, 540/539, 561/560, and 715/714 in the 17-limit; 253/252, 345/343, 352/351, 391/390, 442/441, and 460/459 in the 2.3.5.7.11.13.17.23 subgroup.
{{Harmonics in equal|24|7|1}}
{{Harmonics in equal|24|7|1|collapsed=1|start=12}}


[[Category:Ed7]]
== Music ==
[[Category:Edonoi]]
; [[Ambient Esoterica]]
* [https://www.youtube.com/watch?v=qVB1UFLMO4U ''SQRT(7):1 | Irrational Octave Microtones''] (2023)
Retrieved from "https://en.xen.wiki/w/24ed7"