24ed7 - Revision history

BudjarnLambeth at 23:51, 22 December 2024

2024-12-22T23:51:19Z

← Older revision		Revision as of 23:51, 22 December 2024
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	== Intervals ==		== Intervals ==
	{\| class="wikitable mw-collapsible"		{\| class="wikitable mw-collapsible"
			\|+ Intervals of 24ed7
	\|-		\|-
	! \| degree		! \| degree

BudjarnLambeth: stub OR Todo:expand • add table or make collapsible if needed • add harmonics if missing • improve linking if needed • add subheadings if needed

2024-12-22T23:50:58Z

stub OR Todo:expand • add table or make collapsible if needed • add harmonics if missing • improve linking if needed • add subheadings if needed

← Older revision		Revision as of 23:50, 22 December 2024
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	'''[[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]].		'''[[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"
	\|-		\|-
	! \| degree		! \| degree
Line 134:		Line 135:
	\| \| [[7/4\|harmonic seventh]] plus two octaves		\| \| [[7/4\|harmonic seventh]] plus two octaves
	\|}		\|}

			== Harmonics ==
			{{Harmonics in equal\|24\|7\|1}}
			{{Harmonics in equal\|24\|7\|1\|collapsed=1\|start=12}}

	== Music ==		== Music ==
	; [[Ambient Esoterica]]		; [[Ambient Esoterica]]
	* [https://www.youtube.com/watch?v=qVB1UFLMO4U ''SQRT(7):1 \| Irrational Octave Microtones''] (2023)		* [https://www.youtube.com/watch?v=qVB1UFLMO4U ''SQRT(7):1 \| Irrational Octave Microtones''] (2023)

FloraC: Music moved from "12ed-sqrt(7)"

2024-02-05T17:12:53Z

Music moved from "12ed-sqrt(7)"

← Older revision		Revision as of 17:12, 5 February 2024
Line 135:		Line 135:
	\|}		\|}

	[[~~Category:Ed7~~]]		== Music ==
	[~~[Category~~:~~Edonoi]~~]		; [[Ambient Esoterica]]
			* [https://www.youtube.com/watch?v=qVB1UFLMO4U ''SQRT(7):1 \| Irrational Octave Microtones''] (2023)

Plumtree: Infobox ET added

2022-10-05T20:30:32Z

Infobox ET added

← Older revision		Revision as of 20:30, 5 October 2022
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			{{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]].		'''[[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]].

Xenllium at 02:02, 6 January 2019

2019-01-06T02:02:10Z

← Older revision		Revision as of 02:02, 6 January 2019
Line 1:		Line 1:
	'''[[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~~; 253/252, 345/343, 352/351, 391/390, 442/441, and 460/459 in the 2.3.5.7.11.13.17.23 subgroup~~. The step size is about 140.3677 cents, corresponding to 8.5490 [[edo]].		'''[[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"		{\| class="wikitable"
Line 25:		Line 25:
	\| \| 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]]
	\| \|		\| \|
	\|-		\|-
Line 95:		Line 95:
	\| \| 17		\| \| 17
	\| \| 2386.2517		\| \| 2386.2517
	\| \| 119/30, ~~250~~/63		\| \| 119/30, 143/36
	\| \|		\| \|
	\|-		\|-
	\| \| 18		\| \| 18
	\| \| 2526.6194		\| \| 2526.6194
	\| \| 56/13		\| \| [[14/13\|56/13]]
	\| \|		\| \|
	\|-		\|-

Xenllium at 00:54, 6 January 2019

2019-01-06T00:54:35Z

← Older revision		Revision as of 00:54, 6 January 2019
Line 1:		Line 1:
	'''[[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]].		'''[[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; 253/252, 345/343, 352/351, 391/390, 442/441, and 460/459 in the 2.3.5.7.11.13.17.23 subgroup. The step size is about 140.3677 cents, corresponding to 8.5490 [[edo]].

	{\| class="wikitable"		{\| class="wikitable"
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	\| \| 18		\| \| 18
	\| \| 2526.6194		\| \| 2526.6194
	\| \| ~~30/7, 77/18,~~ 56/13		\| \| 56/13
	\| \|		\| \|
	\|-		\|-
Line 133:		Line 133:
	\| \| [[7/4\|harmonic seventh]] plus two octaves		\| \| [[7/4\|harmonic seventh]] plus two octaves
	\|}		\|}

	~~==24ed7 as a generator==~~
	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.

	[[Category:Ed7]]		[[Category:Ed7]]
	[[Category:Edonoi]]		[[Category:Edonoi]]

Xenllium: Created page with "'''Division of the 7th harmonic into 24 equal parts''' (24ed7) is related to the quanic temperament, which is a cluster temperament wit..."

2019-01-06T00:36:27Z

Created page with "'''Division of the 7th harmonic into 24 equal parts''' (24ed7) is related to the quanic temperament, which is a cluster temperament wit..."

New page

'''[[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]].

{| class="wikitable"
|-
! | degree
! | cents value
! | corresponding <br>JI intervals
! | comments
|-
| | 0
| | 0.0000
| | '''exact [[1/1]]'''
| |
|-
| | 1
| | 140.3677
| | [[13/12]], 25/23
| |
|-
| | 2
| | 280.7355
| | [[20/17]]
| |
|-
| | 3
| | 421.1032
| | [[14/11]], 23/18, [[32/25]]
| |
|-
| | 4
| | 561.4710
| | [[18/13]]
| |
|-
| | 5
| | 701.8387
| | [[3/2]]
| |
|-
| | 6
| | 842.2065
| | [[13/8]], 80/49
| |
|-
| | 7
| | 982.5742
| | [[30/17]]
| |
|-
| | 8
| | 1122.9420
| | [[21/11]]
| |
|-
| | 9
| | 1263.3097
| | [[28/27|56/27]], [[27/26|27/13]]
| |
|-
| | 10
| | 1403.6775
| | [[9/4]]
| |
|-
| | 11
| | 1544.0452
| | 56/23, 39/16, [[11/9|22/9]], 120/49
| |
|-
| | 12
| | 1684.4130
| |
| |
|-
| | 13
| | 1824.7807
| | 63/22, 112/39, 23/8
| |
|-
| | 14
| | 1965.1484
| | [[14/9|28/9]]
| |
|-
| | 15
| | 2105.5162
| | [[27/16|27/8]]
| |
|-
| | 16
| | 2245.8839
| | [[11/3]]
| |
|-
| | 17
| | 2386.2517
| | 119/30, 250/63
| |
|-
| | 18
| | 2526.6194
| | 30/7, 77/18, 56/13
| |
|-
| | 19
| | 2666.9872
| | [[14/3]]
| |
|-
| | 20
| | 2807.3549
| | 91/18
| |
|-
| | 21
| | 2947.7227
| | [[11/2]]
| |
|-
| | 22
| | 3088.0904
| | 119/20
| |
|-
| | 23
| | 3228.4582
| | 84/13
| |
|-
| | 24
| | 3368.8259
| | '''exact [[7/1]]'''
| | [[7/4|harmonic seventh]] plus two octaves
|}

==24ed7 as a generator==
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.

[[Category:Ed7]]
[[Category:Edonoi]]