Tetracot extensions - Revision history

FloraC: Split page

2026-04-16T15:01:49Z

Split page

FloraC: + todo

2026-01-19T09:05:04Z

+ todo

← Older revision		Revision as of 09:05, 19 January 2026
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	\|}		\|}

			{{Todo\|split page\|comment=split to monkey, bunya, modus, and wollemia, as each of them is a temperament in its own rigth. }}
	[[Category:Temperament extensions]]		[[Category:Temperament extensions]]
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]

Overthink: add cat.

2026-01-19T00:28:19Z

add cat.

← Older revision		Revision as of 00:28, 19 January 2026
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	[[Category:Wollemia]]		[[Category:Wollemia]]
	[[Category:Tetracot family]]		[[Category:Tetracot family]]
			[[Category:Pages with mostly numerical content]]

FloraC: Temp rename followup

2025-10-12T11:17:01Z

Temp rename followup

← Older revision		Revision as of 11:17, 12 October 2025
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	{{Breadcrumb\|Tetracot}}		{{Breadcrumb\|Tetracot}}

	[[Tetracot]] has multiple competing [[extension]]s to the [[7-limit]]. The simplest 2.3.5.11 [[subgroup]] [[comma]]s of tetracot are [[100/99\|ptolemisma (100/99)]] and [[243/242\|rastma (243/242)]], and it can be viewed as the merge of the two corresponding [[rank-3 temperament]]s. 100/99 is particularly tricky as it can suggest tempering out either [[225/224]] (leading to [[apollo]]) or [[385/384]] (leading to [[~~supermagic~~]]), resulting in distinct extensions of tetracot:		[[Tetracot]] has multiple competing [[extension]]s to the [[7-limit]]. The simplest 2.3.5.11 [[subgroup]] [[comma]]s of tetracot are [[100/99\|ptolemisma (100/99)]] and [[243/242\|rastma (243/242)]], and it can be viewed as the merge of the two corresponding [[rank-3 temperament]]s. 100/99 is particularly tricky as it can suggest tempering out either [[225/224]] (leading to [[apollo]]) or [[385/384]] (leading to [[keemic]]), resulting in distinct extensions of tetracot:
	* '''Monkey''' (34 &~~amp;~~ 41) – tempering out 100/99, 243/242, 385/384		* '''Monkey''' (34 & 41) – tempering out 100/99, 243/242, 385/384
	* '''Bunya''' (34d &~~amp;~~ 41) – tempering out 100/99, 225/224, 243/242		* '''Bunya''' (34d & 41) – tempering out 100/99, 225/224, 243/242

	The two unite in [[41edo\|41et]], where both 225/224 and 385/384 are tempered out.		The two unite in [[41edo\|41et]], where both 225/224 and 385/384 are tempered out.

	In addition, there are two simpler entries:		In addition, there are two simpler entries:
	* '''Modus''' (27e &~~amp;~~ 34d) – tempering out 64/63, 100/99, 243/242		* '''Modus''' (27e & 34d) – tempering out 64/63, 100/99, 243/242
	* '''Wollemia''' (27e &~~amp;~~ 34) – tempering out 56/55, 100/99, 243/242		* '''Wollemia''' (27e & 34) – tempering out 56/55, 100/99, 243/242

	The two unite in [[27edo\|27et]], where both 56/55 and 64/63 are tempered out.		The two unite in [[27edo\|27et]], where both 56/55 and 64/63 are tempered out.

FloraC: FloraC moved page Tetracot/Extensions to Tetracot extensions over a redirect without leaving a redirect: Reversion for creating broken redirects with no clear gain

2025-08-06T12:06:36Z

FloraC moved page Tetracot/Extensions to Tetracot extensions over a redirect without leaving a redirect: Reversion for creating broken redirects with no clear gain

← Older revision	Revision as of 12:06, 6 August 2025
(No difference)

ArrowHead294: ArrowHead294 moved page Tetracot extensions to Tetracot/Extensions: Change to subpage format

2025-05-30T00:27:20Z

ArrowHead294 moved page Tetracot extensions to Tetracot/Extensions: Change to subpage format

← Older revision	Revision as of 00:27, 30 May 2025
(No difference)

Lériendil at 00:05, 20 April 2025

2025-04-20T00:05:23Z

← Older revision		Revision as of 00:05, 20 April 2025
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			{{Breadcrumb\|Tetracot}}

	[[Tetracot]] has multiple competing [[extension]]s to the [[7-limit]]. The simplest 2.3.5.11 [[subgroup]] [[comma]]s of tetracot are [[100/99\|ptolemisma (100/99)]] and [[243/242\|rastma (243/242)]], and it can be viewed as the merge of the two corresponding [[rank-3 temperament]]s. 100/99 is particularly tricky as it can suggest tempering out either [[225/224]] (leading to [[apollo]]) or [[385/384]] (leading to [[supermagic]]), resulting in distinct extensions of tetracot:		[[Tetracot]] has multiple competing [[extension]]s to the [[7-limit]]. The simplest 2.3.5.11 [[subgroup]] [[comma]]s of tetracot are [[100/99\|ptolemisma (100/99)]] and [[243/242\|rastma (243/242)]], and it can be viewed as the merge of the two corresponding [[rank-3 temperament]]s. 100/99 is particularly tricky as it can suggest tempering out either [[225/224]] (leading to [[apollo]]) or [[385/384]] (leading to [[supermagic]]), resulting in distinct extensions of tetracot:
	* '''Monkey''' (34 & 41) – tempering out 100/99, 243/242, 385/384		* '''Monkey''' (34 & 41) – tempering out 100/99, 243/242, 385/384
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	\|}		\|}

	[[Category:~~Temperaments~~]]		[[Category:Temperament extensions]]
			[[Category:Rank-2 temperaments]]
	[[Category:Tetracot]]		[[Category:Tetracot]]
	[[Category:Monkey]]		[[Category:Monkey]]

FloraC: Created page with "Tetracot has multiple competing extensions to the 7-limit. The simplest 2.3.5.11 subgroup commas of tetracot are ptolemisma (100/99) and 243/2..."

2023-12-31T03:09:21Z

Created page with "Tetracot has multiple competing extensions to the 7-limit. The simplest 2.3.5.11 subgroup commas of tetracot are ptolemisma (100/99) and 243/2..."

New page

[[Tetracot]] has multiple competing [[extension]]s to the [[7-limit]]. The simplest 2.3.5.11 [[subgroup]] [[comma]]s of tetracot are [[100/99|ptolemisma (100/99)]] and [[243/242|rastma (243/242)]], and it can be viewed as the merge of the two corresponding [[rank-3 temperament]]s. 100/99 is particularly tricky as it can suggest tempering out either [[225/224]] (leading to [[apollo]]) or [[385/384]] (leading to [[supermagic]]), resulting in distinct extensions of tetracot:
* '''Monkey''' (34 & 41) – tempering out 100/99, 243/242, 385/384
* '''Bunya''' (34d & 41) – tempering out 100/99, 225/224, 243/242

The two unite in [[41edo|41et]], where both 225/224 and 385/384 are tempered out.

In addition, there are two simpler entries:
* '''Modus''' (27e & 34d) – tempering out 64/63, 100/99, 243/242
* '''Wollemia''' (27e & 34) – tempering out 56/55, 100/99, 243/242

The two unite in [[27edo|27et]], where both 56/55 and 64/63 are tempered out.

Another possible path, which is a weak extension, is to temper out [[441/440]], [[540/539]], or [[2401/2400]], leading to [[octacot]], discussed separately.

== Interval chain ==
=== Monkey ===
{| class="wikitable right-1 right-2"
|-
! #
! Cents<nowiki>*</nowiki>
! Approximate Ratios
|-
| 0
| 0.00
| 1/1
|-
| 1
| 175.62
| 11/10, 10/9
|-
| 2
| 351.24
| 11/9, '''16/13'''
|-
| 3
| 526.87
| 15/11
|-
| 4
| 702.49
| '''3/2'''
|-
| 5
| 878.11
| 5/3
|-
| 6
| 1053.73
| 11/6, 24/13
|-
| 7
| 29.36
| 55/54, 45/44, 40/39
|-
| 8
| 204.98
| 9/8
|-
| 9
| 380.60
| '''5/4'''
|-
| 10
| 556.22
| '''11/8''', 18/13
|-
| 11
| 731.85
| 20/13
|-
| 12
| 907.47
| 22/13
|-
| 13
| 1083.09
| 13/7, 15/8
|-
| 14
| 58.71
| 33/32, 27/26, 25/24
|-
| 15
| 234.34
| '''8/7''', 15/13
|-
| 16
| 409.96
|
|-
| 17
| 585.58
| 45/32
|-
| 18
| 761.20
|
|-
| 19
| 936.83
| 12/7
|-
| 20
| 1112.45
|
|-
| 21
| 88.07
|
|-
| 22
| 263.69
|
|-
| 23
| 439.31
| 9/7
|-
| 24
| 614.94
| 10/7
|-
| 25
| 790.56
| 11/7
|-
| 26
| 966.18
|
|-
| 27
| 1141.80
| 27/14
|-
| 28
| 117.43
| 15/14
|}
: <nowiki>*</nowiki> in 13-limit POTE tuning

=== Bunya ===
{| class="wikitable right-1 right-2"
|-
! #
! Cents<nowiki>*</nowiki>
! Approximate Ratios
|-
| 0
| 0.00
| 1/1
|-
| 1
| 175.89
| 11/10, 10/9
|-
| 2
| 351.77
| 11/9, '''16/13'''
|-
| 3
| 527.66
| 15/11
|-
| 4
| 703.54
| '''3/2'''
|-
| 5
| 879.43
| 5/3
|-
| 6
| 1055.31
| 11/6, 24/13
|-
| 7
| 31.20
| 56/55, 55/54, 45/44, 40/39
|-
| 8
| 207.09
| 9/8
|-
| 9
| 382.97
| 5/4
|-
| 10
| 558.86
| '''11/8''', 18/13
|-
| 11
| 734.74
| 20/13
|-
| 12
| 910.63
| 22/13
|-
| 13
| 1086.52
| 28/15, 15/8
|-
| 14
| 62.40
| 33/32, 28/27, 27/26, 25/24
|-
| 15
| 238.29
| 15/13
|-
| 16
| 414.17
| 14/11
|-
| 17
| 590.06
| 7/5
|-
| 18
| 765.94
| 14/9
|-
| 19
| 941.83
|
|-
| 20
| 1117.72
| 21/11
|-
| 21
| 93.60
| 21/20
|-
| 22
| 269.49
| 7/6
|-
| 23
| 445.37
|
|-
| 24
| 621.26
|
|-
| 25
| 797.15
|
|-
| 26
| 973.03
| '''7/4'''
|-
| 27
| 1148.92
| 35/18
|-
| 28
| 124.80
| 14/13
|}
: <nowiki>*</nowiki> in 13-limit POTE tuning

=== Modus ===
{| class="wikitable right-1 right-2"
|-
! #
! Cents<nowiki>*</nowiki>
! Approximate Ratios
|-
| 0
| 0.00
| 1/1
|-
| 1
| 176.95
| 11/10, 10/9
|-
| 2
| 353.91
| 11/9, '''16/13'''
|-
| 3
| 530.86
| 15/11
|-
| 4
| 707.81
| '''3/2'''
|-
| 5
| 884.77
| 5/3
|-
| 6
| 1061.72
| 11/6, 24/13, 13/7
|-
| 7
| 38.67
| 55/54, 45/44, 40/39, 36/35
|-
| 8
| 215.63
| 9/8, '''8/7'''
|-
| 9
| 392.58
| '''5/4'''
|-
| 10
| 569.53
| '''11/8''', 18/13
|-
| 11
| 746.49
| 20/13
|-
| 12
| 923.44
| 22/13, 12/7
|-
| 13
| 1100.39
| 15/8, 40/21
|-
| 14
| 77.35
| 27/26, 25/24, 22/21
|-
| 15
| 254.30
| 15/13
|-
| 16
| 431.25
| 9/7
|-
| 17
| 608.20
| 10/7
|-
| 18
| 785.16
| 11/7
|-
| 19
| 962.11
|
|-
| 20
| 1139.06
| 27/14
|-
| 21
| 116.02
| 15/14
|}
: <nowiki>*</nowiki> in 13-limit POTE tuning

=== Wollemia ===
{| class="wikitable right-1 right-2"
|-
! #
! Cents<nowiki>*</nowiki>
! Approximate Ratios
|-
| 0
| 0.00
| 1/1
|-
| 1
| 177.23
| 11/10, 10/9
|-
| 2
| 354.46
| 11/9, '''16/13'''
|-
| 3
| 531.69
| 15/11
|-
| 4
| 708.92
| '''3/2'''
|-
| 5
| 886.16
| 5/3
|-
| 6
| 1063.39
| 11/6, 24/13, 28/15
|-
| 7
| 40.62
| 55/54, 45/44, 40/39
|-
| 8
| 217.85
| 9/8
|-
| 9
| 395.08
| '''5/4''', 14/11
|-
| 10
| 572.31
| '''11/8''', 18/13, 7/5
|-
| 11
| 749.54
| 20/13, 14/9
|-
| 12
| 926.77
| 22/13
|-
| 13
| 1104.01
| 15/8
|-
| 14
| 81.24
| 27/26, 25/24
|-
| 15
| 258.47
| 15/13, 7/6
|-
| 16
| 435.70
|
|-
| 17
| 612.93
|
|-
| 18
| 790.16
|
|-
| 19
| 967.39
| '''7/4'''
|-
| 20
| 1144.62
|
|-
| 21
| 121.86
| 14/13
|}
: <nowiki>*</nowiki> in 13-limit POTE tuning

== Tuning spectra ==
=== Monkey ===
Gencom: [2 10/9; 100/99 105/104 144/143 243/242]

Gencom mapping: [{{val|1 1 1 5 2 4}}, {{val|0 4 9 -15 10 -2}}]

{| class="wikitable center-all"
|-
! [[Eigenmonzo|Eigenmonzo (Unchanged-interval)]]
! Generator (¢)
! Comments
|-
| | 11/10
| | 165.004
| |
|-
| | 11/9
| | 173.704
| |
|-
| | 14/13
| | 174.746
| |
|-
| | 12/11
| | 174.894
| |
|-
| | 11/8
| | 175.132
| |
|-
| | 14/11
| | 175.300
| | 11-odd-limit minimax
|-
| | 8/7
| | 175.412
| |
|-
| | 7/6
| | 175.428
| |
|-
| | 9/7
| | 175.438
| |
|-
| | 4/3
| | 175.489
| |
|-
| | 15/14
| | 175.694
| |
|-
| | 7/5
| | 175.729
| | 7, 9, 13 and 15-odd-limit minimax
|-
| | 13/11
| | 175.899
| |
|-
| | 16/15
| | 176.021
| |
|-
| | 5/4
| | 176.257
| | 5-odd-limit minimax
|-
| | 18/13
| | 176.338
| |
|-
| | 15/13
| | 176.516
| |
|-
| | 6/5
| | 176.872
| |
|-
| | 13/10
| | 176.890
| |
|-
| | 13/12
| | 176.905
| |
|-
| | 15/11
| | 178.984
| |
|-
| | 16/13
| | 179.736
| |
|-
| | 10/9
| | 182.404
| |
|}

=== Bunya ===
Gencom: [2 10/9; 100/99 144/143 225/224 243/242]

Gencom mapping: [{{val|1 1 1 -1 2 4}}, {{val|0 4 9 26 10 -2}}]

{| class="wikitable center-all"
|-
! [[Eigenmonzo|Eigenmonzo (Unchanged-interval)]]
! Generator (¢)
! Comments
|-
| | 11/10
| | 165.004
| |
|-
| | 11/9
| | 173.704
| |
|-
| | 12/11
| | 174.894
| |
|-
| | 11/8
| | 175.132
| |
|-
| | 15/14
| | 175.427
| |
|-
| | 7/5
| | 175.442
| | 11-odd-limit minimax
|-
| | 4/3
| | 175.489
| |
|-
| | 8/7
| | 175.724
| |
|-
| | 7/6
| | 175.767
| | 7-odd-limit minimax
|-
| | 9/7
| | 175.829
| | 9-odd-limit minimax
|-
| | 13/11
| | 175.899
| | 13 and 15-odd-limit minimax
|-
| | 14/13
| | 176.011
| |
|-
| | 16/15
| | 176.021
| |
|-
| | 14/11
| | 176.094
| |
|-
| | 5/4
| | 176.257
| | 5-odd-limit minimax
|-
| | 18/13
| | 176.338
| |
|-
| | 15/13
| | 176.516
| |
|-
| | 6/5
| | 176.872
| |
|-
| | 13/10
| | 176.890
| |
|-
| | 13/12
| | 176.905
| |
|-
| | 15/11
| | 178.984
| |
|-
| | 16/13
| | 179.736
| |
|-
| | 10/9
| | 182.404
| |
|}

=== Modus ===
Gencom: [2 10/9; 64/63 78/77 100/99 144/143]

Gencom mapping: [{{val|1 1 1 4 2 4}}, {{val|0 4 9 -8 10 -2}}]

{| class="wikitable center-all"
|-
! [[Eigenmonzo|Eigenmonzo (Unchanged-interval)]]
! Generator (¢)
! Comments
|-
| | 11/10
| | 165.004
| |
|-
| | 11/9
| | 173.704
| |
|-
| | 12/11
| | 174.894
| |
|-
| | 11/8
| | 175.132
| |
|-
| | 4/3
| | 175.489
| |
|-
| | 13/11
| | 175.899
| |
|-
| | 16/15
| | 176.021
| |
|-
| | 5/4
| | 176.257
| | 5-odd-limit minimax
|-
| | 18/13
| | 176.338
| |
|-
| | 15/13
| | 176.516
| |
|-
| | 14/11
| | 176.805
| | 11, 13 and 15-odd-limit minimax
|-
| | 6/5
| | 176.872
| |
|-
| | 13/10
| | 176.890
| |
|-
| | 13/12
| | 176.905
| |
|-
| | 15/14
| | 177.116
| |
|-
| | 9/7
| | 177.193
| | 9-odd-limit minimax
|-
| | 7/5
| | 177.499
| | 7-odd-limit minimax
|-
| | 7/6
| | 177.761
| |
|-
| | 14/13
| | 178.617
| |
|-
| | 8/7
| | 178.897
| |
|-
| | 15/11
| | 178.984
| |
|-
| | 16/13
| | 179.736
| |
|-
| | 10/9
| | 182.404
| |
|}

=== Wollemia ===
Gencom: [2 10/9; 56/55 91/90 100/99 243/242]

Gencom mapping: [{{val|1 1 1 0 2 4}}, {{val|0 4 9 19 10 -2}}]

{| class="wikitable center-all"
|-
! [[Eigenmonzo|Eigenmonzo (Unchanged-interval)]]
! Generator (¢)
! Comments
|-
| | 11/10
| | 165.004
| |
|-
| | 11/9
| | 173.704
| |
|-
| | 12/11
| | 174.894
| |
|-
| | 11/8
| | 175.132
| |
|-
| | 4/3
| | 175.489
| |
|-
| | 13/11
| | 175.899
| |
|-
| | 16/15
| | 176.021
| |
|-
| | 5/4
| | 176.257
| | 5-odd-limit minimax
|-
| | 18/13
| | 176.338
| |
|-
| | 15/13
| | 176.516
| |
|-
| | 6/5
| | 176.872
| |
|-
| | 13/10
| | 176.890
| |
|-
| | 13/12
| | 176.905
| |
|-
| | 8/7
| | 177.307
| | 7, 9, 11, 13 and 15-odd-limit minimax
|-
| | 14/13
| | 177.538
| |
|-
| | 7/6
| | 177.791
| |
|-
| | 7/5
| | 178.251
| |
|-
| | 9/7
| | 178.629
| |
|-
| | 15/11
| | 178.984
| |
|-
| | 14/11
| | 179.723
| |
|-
| | 16/13
| | 179.736
| |
|-
| | 15/14
| | 180.093
| |
|-
| | 10/9
| | 182.404
| |
|}

[[Category:Temperaments]]
[[Category:Tetracot]]
[[Category:Monkey]]
[[Category:Bunya]]
[[Category:Modus]]
[[Category:Wollemia]]
[[Category:Tetracot family]]