Monkey - Revision history

FloraC: Text replacement - "Category:Hemifamity temperaments" to "Category:Aberschismic temperaments"

2026-06-06T12:39:46Z

Text replacement - "Category:Hemifamity temperaments" to "Category:Aberschismic temperaments"

← Older revision		Revision as of 12:39, 6 June 2026
Line 349:		Line 349:
	[[Category:Tetracot family]]		[[Category:Tetracot family]]
	[[Category:Keemic temperaments]]		[[Category:Keemic temperaments]]
	[[Category:~~Hemifamity~~ temperaments]]		[[Category:Aberschismic temperaments]]

FloraC: + more edo tunings in the spectrum

2026-04-30T10:21:11Z

+ more edo tunings in the spectrum

← Older revision		Revision as of 10:21, 30 April 2026
Line 23:		Line 23:
	In the following tables, odd harmonics 1–13 and their inverses are in '''bold'''.		In the following tables, odd harmonics 1–13 and their inverses are in '''bold'''.

	{\| class="wikitable ~~right~~-1 right-2"		{\| class="wikitable center-1 right-2"
	\|-		\|-
	! #		! #
Line 201:		Line 201:
	\| 11/10		\| 11/10
	\| 165.004		\| 165.004
			\|
			\|-
			\| 1\7
			\|
			\| 171.429
	\|		\|
	\|-		\|-
Line 312:		Line 317:
	\| 176.905		\| 176.905
	\|		\|
			\|-
			\| 4\27
			\|
			\| 177.778
			\| 27de val
	\|-		\|-
	\|		\|
Line 322:		Line 332:
	\| 179.736		\| 179.736
	\|		\|
			\|-
			\| 3\20
			\|
			\| 180.000
			\| 20cdde val
	\|-		\|-
	\|		\|

FloraC: Fix a copypasting error +1

2026-04-15T11:39:12Z

Fix a copypasting error +1

← Older revision		Revision as of 11:39, 15 April 2026
Line 14:		Line 14:
	The '''monkey''' [[regular temperament\|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (20000/19683), and is naturally a full [[13-limit]] temperament.		The '''monkey''' [[regular temperament\|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (20000/19683), and is naturally a full [[13-limit]] temperament.

	In addition to the tetracot comma, monkey tempers out [[875/864]], making it a [[keemic temperaments\|keemic temperament]]. It also tempers out [[5120/5103]], making it a [[hemifamity temperaments\|hemifamity temperament]], so the [[septimal comma]] is equated with the [[syntonic comma]]. At 7 generator steps, this [[diesis (interval region)\|diesis-sized]] interval also represents [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], and [[121/120]] in the [[2.3.5.7.13 subgroup\|2.3.5.7.13-subgroup]] version of tetracot, and divides the [[chromatic semitone]] in four. The same interval is now used to bridge septimal intervals with Pythagorean intervals alike.		In addition to the tetracot comma, monkey tempers out [[875/864]], making it a [[keemic temperaments\|keemic temperament]]. It also tempers out [[5120/5103]], making it a [[hemifamity temperaments\|hemifamity temperament]], so the [[septimal comma]] is equated with the [[syntonic comma]]. At 7 generator steps, this [[diesis (interval region)\|diesis-sized]] interval also represents [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], and [[121/120]] in the [[2.3.5.11.13 subgroup\|2.3.5.11.13-subgroup]] version of tetracot, and divides the [[chromatic semitone]] in four. The same interval is now used to bridge septimal intervals with Pythagorean intervals alike.

	Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at -12 generator steps.		Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at -12 generator steps.

FloraC: Fix a copypasting error

2026-04-15T11:07:42Z

Fix a copypasting error

← Older revision		Revision as of 11:07, 15 April 2026
Line 12:		Line 12:
	\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 12.8 \| Complexity 2 = 34		\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 12.8 \| Complexity 2 = 34
	}}		}}
	The '''monkey''' [[regular temperament\|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (~~15625~~/~~15552~~), and is naturally a full [[13-limit]] temperament.		The '''monkey''' [[regular temperament\|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (20000/19683), and is naturally a full [[13-limit]] temperament.

	In addition to the tetracot comma, monkey tempers out [[875/864]], making it a [[keemic temperaments\|keemic temperament]]. It also tempers out [[5120/5103]], making it a [[hemifamity temperaments\|hemifamity temperament]], so the [[septimal comma]] is equated with the [[syntonic comma]]. At 7 generator steps, this [[diesis (interval region)\|diesis-sized]] interval also represents [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], and [[121/120]] in the [[2.3.5.7.13 subgroup\|2.3.5.7.13-subgroup]] version of tetracot, and divides the [[chromatic semitone]] in four. The same interval is now used to bridge septimal intervals with Pythagorean intervals alike.		In addition to the tetracot comma, monkey tempers out [[875/864]], making it a [[keemic temperaments\|keemic temperament]]. It also tempers out [[5120/5103]], making it a [[hemifamity temperaments\|hemifamity temperament]], so the [[septimal comma]] is equated with the [[syntonic comma]]. At 7 generator steps, this [[diesis (interval region)\|diesis-sized]] interval also represents [[40/39]], [[45/44]], [[55/54]], [[65/64]], [[66/65]], and [[121/120]] in the [[2.3.5.7.13 subgroup\|2.3.5.7.13-subgroup]] version of tetracot, and divides the [[chromatic semitone]] in four. The same interval is now used to bridge septimal intervals with Pythagorean intervals alike.

FloraC: /* Tunings */ + norm-based tunings

2026-04-15T10:59:40Z

Tunings: + norm-based tunings

@@ Line 144: / Line 144: @@
 == Tunings ==
 === Tuning spectrum ===
 {| class="wikitable center-all left-4"

FloraC: Complete tuning spectrum

2026-04-15T10:55:27Z

Complete tuning spectrum

← Older revision		Revision as of 10:55, 15 April 2026
Line 35:		Line 35:
	\| 1		\| 1
	\| 175.6		\| 175.6
	\| 11/10~~, 10/9~~		\| 10/9, 11/10
	\|-		\|-
	\| 2		\| 2
Line 145:		Line 145:
	== Tunings ==		== Tunings ==
	=== Tuning spectrum ===		=== Tuning spectrum ===
	{\| class="wikitable center-all left-3"		{\| class="wikitable center-all left-4"
	\|-		\|-
	! [[Eigenmonzo\|Eigenmonzo<br>(unchanged-interval)]]		! Edo<br>generator
			! [[Eigenmonzo\|Eigenmonzo<br>(unchanged-interval)]]*
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments
	\|-		\|-
			\|
	\| 11/10		\| 11/10
	\| 165.004		\| 165.004
	\|		\|
	\|-		\|-
			\|
	\| 11/9		\| 11/9
	\| 173.704		\| 173.704
	\|		\|
	\|-		\|-
	\| 14/13		\|
			\| 13/7
	\| 174.746		\| 174.746
	\|		\|
	\|-		\|-
	\| 12/11		\|
			\| 11/6
	\| 174.894		\| 174.894
	\|		\|
	\|-		\|-
			\| 7\48
			\|
			\| 175.000
			\| Lower bound of 7-, 9-, 11-, and 13-odd-limit diamond monotone
			\|-
			\|
	\| 11/8		\| 11/8
	\| 175.132		\| 175.132
	\|		\|
	\|-		\|-
	\| 14/11		\|
			\| 11/7
	\| 175.300		\| 175.300
	\| 11-odd-limit minimax		\| 11-odd-limit minimax
	\|-		\|-
	\| 8/7		\|
			\| 7/4
	\| 175.412		\| 175.412
	\|		\|
	\|-		\|-
			\|
	\| 7/6		\| 7/6
	\| 175.428		\| 175.428
	\|		\|
	\|-		\|-
			\|
	\| 9/7		\| 9/7
	\| 175.438		\| 175.438
	\|		\|
	\|-		\|-
	\| 4/3		\|
			\| 3/2
	\| 175.489		\| 175.489
	\|		\|
	\|-		\|-
			\| 6\41
			\|
			\| 175.610
			\| 15-odd-limit diamond monotone (singleton)
			\|-
			\|
	\| 15/14		\| 15/14
	\| 175.694		\| 175.694
	\|		\|
	\|-		\|-
			\|
	\| 7/5		\| 7/5
	\| 175.729		\| 175.729
	\| 7, 9, 13 and 15-odd-limit minimax		\| 7-, 9-, 13- and 15-odd-limit minimax
	\|-		\|-
			\|
	\| 13/11		\| 13/11
	\| 175.899		\| 175.899
	\|		\|
	\|-		\|-
	\| 16/15		\|
			\| 15/8
	\| 176.021		\| 176.021
	\|		\|
	\|-		\|-
			\|
	\| 5/4		\| 5/4
	\| 176.257		\| 176.257
	\| 5-odd-limit minimax		\| 5-odd-limit minimax
	\|-		\|-
	\| 18/13		\|
			\| 13/9
	\| 176.338		\| 176.338
	\|		\|
	\|-		\|-
			\| 5\34
			\|
			\| 176.471
			\| Upper bound of 7-, 9-, 11-, and 13-odd-limit diamond monotone
			\|-
			\|
	\| 15/13		\| 15/13
	\| 176.516		\| 176.516
	\|		\|
	\|-		\|-
	\| 6/5		\|
			\| 5/3
	\| 176.872		\| 176.872
	\|		\|
	\|-		\|-
			\|
	\| 13/10		\| 13/10
	\| 176.890		\| 176.890
	\|		\|
	\|-		\|-
			\|
	\| 13/12		\| 13/12
	\| 176.905		\| 176.905
	\|		\|
	\|-		\|-
			\|
	\| 15/11		\| 15/11
	\| 178.984		\| 178.984
	\|		\|
	\|-		\|-
	\| 16/13		\|
			\| 13/8
	\| 179.736		\| 179.736
	\|		\|
	\|-		\|-
	\| 10/9		\|
			\| 9/5
	\| 182.404		\| 182.404
	\|		\|
	\|}		\|}
			<nowiki/>* Besides the octave

	[[Category:Monkey\| ]] <!-- main article -->		[[Category:Monkey\| ]] <!-- main article -->

FloraC: Complete interval table

2026-04-15T10:38:44Z

Complete interval table

← Older revision		Revision as of 10:38, 15 April 2026
Line 30:		Line 30:
	\|-		\|-
	\| 0		\| 0
	\| 0.00		\| 0.0
	\| '''1/1'''		\| '''1/1'''
	\|-		\|-
	\| 1		\| 1
	\| 175.62		\| 175.6
	\| 11/10, 10/9		\| 11/10, 10/9
	\|-		\|-
	\| 2		\| 2
	\| 351.24		\| 351.2
	\| 11/9, '''16/13'''		\| 11/9, '''16/13'''
	\|-		\|-
	\| 3		\| 3
	\| 526.87		\| 526.9
	\| 15/11		\| 15/11
	\|-		\|-
	\| 4		\| 4
	\| 702.49		\| 702.5
	\| '''3/2'''		\| '''3/2'''
	\|-		\|-
	\| 5		\| 5
	\| 878.11		\| 878.1
	\| 5/3		\| 5/3
	\|-		\|-
	\| 6		\| 6
	\| 1053.73		\| 1053.7
	\| 11/6, 24/13		\| 11/6, 24/13
	\|-		\|-
	\| 7		\| 7
	\| 29.36		\| 29.4
	\| 55/54, 45/44, 40/39		\| 40/39, 45/44, 55/54, 64/63
	\|-		\|-
	\| 8		\| 8
	\| ~~204~~.98		\| 205.0
	\| 9/8		\| '''9/8'''
	\|-		\|-
	\| 9		\| 9
	\| 380.60		\| 380.6
	\| '''5/4'''		\| '''5/4'''
	\|-		\|-
	\| 10		\| 10
	\| 556.22		\| 556.2
	\| '''11/8''', 18/13		\| '''11/8''', 18/13
	\|-		\|-
	\| 11		\| 11
	\| 731.85		\| 731.8
	\| 20/13		\| 20/13, 32/21
	\|-		\|-
	\| 12		\| 12
	\| 907.47		\| 907.5
	\| 22/13		\| 22/13
	\|-		\|-
	\| 13		\| 13
	\| 1083.09		\| 1083.1
	\| 13/7, 15/8		\| 13/7, 15/8
	\|-		\|-
	\| 14		\| 14
	\| 58.71		\| 58.7
	\| 33/32, 27/26, 25/24		\| 25/24, 27/26, 33/32, 36/35
	\|-		\|-
	\| 15		\| 15
	\| 234.34		\| 234.3
	\| '''8/7''', 15/13		\| '''8/7''', 15/13
	\|-		\|-
	\| 16		\| 16
	\| 409.96		\| 409.9
	\|		\| 33/26
	\|-		\|-
	\| 17		\| 17
	\| 585.58		\| 585.6
	\| 45/32		\| 45/32, 88/63
	\|-		\|-
	\| 18		\| 18
	\| 761.20		\| 761.2
	\|		\| 25/16, 54/35
	\|-		\|-
	\| 19		\| 19
	\| 936.83		\| 936.8
	\| 12/7		\| 12/7
	\|-		\|-
	\| 20		\| 20
	\| 1112.45		\| 1112.4
	\|		\| 40/21
	\|-		\|-
	\| 21		\| 21
	\| 88.07		\| 88.1
	\|		\| 22/21
	\|-		\|-
	\| 22		\| 22
	\| 263.69		\| 263.7
	\|		\| 75/64, 81/70
	\|-		\|-
	\| 23		\| 23
	\| 439.31		\| 439.3
	\| 9/7		\| 9/7
	\|-		\|-
	\| 24		\| 24
	\| 614.94		\| 614.9
	\| 10/7		\| 10/7
	\|-		\|-
	\| 25		\| 25
	\| 790.56		\| 790.5
	\| 11/7		\| 11/7
	\|-		\|-
	\| 26		\| 26
	\| 966.18		\| 966.2
	\|		\| 225/128, 243/140, 256/147
	\|-		\|-
	\| 27		\| 27
	\| 1141.80		\| 1141.8
	\| 27/14		\| 27/14
	\|-
	~~\| 28~~
	~~\| 117.43~~
	~~\| 15/14~~
	\|}		\|}
	<nowiki/>* in 13-limit ~~POTE~~ tuning		<nowiki/>* In 13-limit CWE tuning, octave reduced

	== Tunings ==		== Tunings ==

FloraC: Birth

2026-04-15T10:28:02Z

Birth

Show changes

FloraC at 13:51, 23 November 2025

2025-11-23T13:51:10Z

← Older revision		Revision as of 13:51, 23 November 2025
Line 1:		Line 1:
	#redirect [[Tetracot family #Monkey]]		#redirect [[Tetracot family #Monkey]]

	[[Category:~~Temperaments~~]]		[[Category:Rank-2 temperaments]]
	[[Category:Tetracot family]]		[[Category:Tetracot family]]
			[[Category:Keemic temperaments]]
			[[Category:Hemifamity temperaments]]

Xenwolf: replace {{IoT}} by plain categorization

2022-03-01T19:29:30Z

replace {{IoT}} by plain categorization

← Older revision		Revision as of 19:29, 1 March 2022
Line 1:		Line 1:
	#redirect [[Tetracot family #Monkey]]		#redirect [[Tetracot family #Monkey]]

			[[Category:Temperaments]]
	[[Category:Tetracot family]]		[[Category:Tetracot family]]
	~~{{IoT}}~~