Godzilla extensions - Revision history

FloraC: Complete interval table

2026-05-23T07:50:01Z

Complete interval table

← Older revision		Revision as of 07:50, 23 May 2026
Line 26:		Line 26:
	\| 0		\| 0
	\| 0.0		\| 0.0
	\| 1/1		\| '''1/1'''
	\|		\|
	\|		\|
Line 34:		Line 34:
	\| 1		\| 1
	\| 948.0		\| 948.0
	\| 7/4, 12/7, 26/15		\| '''7/4''', 12/7, 26/15
	\| 22/13		\| 22/13
	\|		\|
Line 42:		Line 42:
	\| 2		\| 2
	\| 696.0		\| 696.0
	\| 3/2		\| '''3/2'''
	\| 22/15		\| 22/15
	\| 16/11		\| '''16/11'''
	\|		\|
	\|		\|
Line 58:		Line 58:
	\| 4		\| 4
	\| 192.0		\| 192.0
	\| 9/8, 10/9		\| '''9/8''', 10/9
	\| 11/10		\| 11/10
	\| 12/11		\| 12/11
Line 86:		Line 86:
	\|		\|
	\| 22/15		\| 22/15
	\| 16/11		\| '''16/11'''
	\|-		\|-
	\| 8		\| 8
Line 114:		Line 114:
	\| 11		\| 11
	\| 828.0		\| 828.0
	\| 13/8		\| '''13/8'''
	\| 11/7		\| 11/7
	\|		\|
Line 123:		Line 123:
	\| 576.0		\| 576.0
	\| 25/18		\| 25/18
	\| 11/8		\| '''11/8'''
	\| 15/11		\| 15/11
	\|		\|
Line 130:		Line 130:
	\| 13		\| 13
	\| 324.0		\| 324.0
	\|		\| 39/32
	\|		\|
	\| 13/11		\| 13/11
Line 138:		Line 138:
	\| 14		\| 14
	\| 72.1		\| 72.1
	\| 25/24		\| 25/24, 50/49
	\|		\|
	\|		\|
Line 162:		Line 162:
	\| 17		\| 17
	\| 516.1		\| 516.1
			\| 65/49, 75/56
	\|		\|
	\|		\|
	\|		\| '''11/8'''
	\| 11/8
	\| 15/11		\| 15/11
	\|-		\|-
	\| 18		\| 18
	\| 264.1		\| 264.1
			\| 65/56, 75/64
			\|
			\|
			\|
			\| 13/11
			\|-
			\| 19
			\| 12.1
			\| 169/168, 225/224, 195/196
	\|		\|
	\|		\|
	\|		\|
	\|		\|
	~~\| 13/11~~
	\|}		\|}
	<nowiki/>* In 2.3.5.7.13-subgroup [[CWE tuning]]		<nowiki/>* In 2.3.5.7.13-subgroup [[CWE tuning]], octave reduced

	[[Category:Godzilla]]		[[Category:Godzilla]]
	[[Category:Temperament extensions]]		[[Category:Temperament extensions]]
	~~[[Category:Rank-2 temperaments]]~~

FloraC: All these extensions have the same mapping for 13

2026-05-23T07:38:59Z

All these extensions have the same mapping for 13

← Older revision		Revision as of 07:38, 23 May 2026
Line 1:		Line 1:
	{{Breadcrumb\|Semaphore and godzilla}}		{{Breadcrumb\|Semaphore and godzilla}}

	[[Godzilla]] has various competing [[extension]]s ~~to the~~ [[~~11-limit~~\|~~11-~~]] ~~and~~ [[~~13-limit~~]]. The following temperaments are discussed in this article:		[[Godzilla]] has various competing [[extension]]s for [[prime interval\|prime]] [[11/1\|11]]. The following temperaments are discussed in this article:

	* '''Tridecimal godzilla''' ({{nowrap\| 14cf & 19 }}) – tempering out 45/44, 49/48, 78/77, and 81/80;		* '''Tridecimal godzilla''' ({{nowrap\| 14cf & 19 }}) – tempering out 45/44, 49/48, 78/77, and 81/80;
	* '''Semafour''' ({{nowrap\| 14cf & 19e }}) – tempering out 33/32, 49/48, 55/54, and 91/90;		* '''Semafour''' ({{nowrap\| 14cf & 19e }}) – tempering out 33/32, 49/48, 55/54, and 91/90;
Line 8:		Line 7:
	* '''Baragon''' ({{nowrap\| 19 & 24 }}) – tempering out 49/48, 56/55, 81/80, and 91/90.		* '''Baragon''' ({{nowrap\| 19 & 24 }}) – tempering out 49/48, 56/55, 81/80, and 91/90.

	~~The most important of these is tridecimal~~ godzilla~~, where primes~~ 11 ~~and 13 are mapped~~ such that 10/9 and 11/10 are tempered together and that 7/6, 8/7~~, 13/11, and 15/13 are tempered together~~. Semafour ~~takes the same mapping of 13 as godzilla, but~~ swaps in a less complex and less accurate mapping for 11, so that 4/3 and 11/8 are tempered together. Similarly, varan ~~takes the same mapping of 13 as godzilla, but swaps in a more complex mapping for 11, so that~~ 6/5 and 13/11 ~~are tempered together~~. Finally, baragon swaps in a less complex mapping for prime 11, so that 7/5 and 11/8 are tempered together.		Tridecimal godzilla maps prime 11 such that [[10/9]] and [[11/10]] are tempered together and that [[13/11]] is tempered together with [[7/6]]~[[15/13]]~[[8/7]] semifourth cluster. Semafour swaps in a less complex and less accurate mapping for 11, so that [[4/3]] and [[11/8]] are tempered together. Similarly, varan tempers together 6/5 and 13/11. Finally, baragon swaps in a less complex mapping for prime 11, so that [[7/5]] and 11/8 are tempered together.

	== Interval chain ==		== Interval chain ==

Xenllium: Created page with "{{Breadcrumb|Semaphore and godzilla}} Godzilla has various competing extensions to the 11- and 13-limit. The following temperaments are discussed in this article: * '''Tridecimal godzilla''' ({{nowrap| 14cf & 19 }}) – tempering out 45/44, 49/48, 78/77, and 81/80; * '''Semafour''' ({{nowrap| 14cf & 19e }}) – tempering out 33/32, 49/48, 55/54, and 91/90; * '''Varan''' ({{nowrap| 19e & 24 }}) – tempering out 49/48, 66/65, 77/75, and 81/80;..."

2026-05-23T01:29:48Z

Created page with "{{Breadcrumb|Semaphore and godzilla}} Godzilla has various competing extensions to the 11- and 13-limit. The following temperaments are discussed in this article: * '''Tridecimal godzilla''' ({{nowrap| 14cf & 19 }}) – tempering out 45/44, 49/48, 78/77, and 81/80; * '''Semafour''' ({{nowrap| 14cf & 19e }}) – tempering out 33/32, 49/48, 55/54, and 91/90; * '''Varan''' ({{nowrap| 19e & 24 }}) – tempering out 49/48, 66/65, 77/75, and 81/80;..."

New page

{{Breadcrumb|Semaphore and godzilla}}

[[Godzilla]] has various competing [[extension]]s to the [[11-limit|11-]] and [[13-limit]]. The following temperaments are discussed in this article:

* '''Tridecimal godzilla''' ({{nowrap| 14cf & 19 }}) – tempering out 45/44, 49/48, 78/77, and 81/80;
* '''Semafour''' ({{nowrap| 14cf & 19e }}) – tempering out 33/32, 49/48, 55/54, and 91/90;
* '''Varan''' ({{nowrap| 19e & 24 }}) – tempering out 49/48, 66/65, 77/75, and 81/80;
* '''Baragon''' ({{nowrap| 19 & 24 }}) – tempering out 49/48, 56/55, 81/80, and 91/90.

The most important of these is tridecimal godzilla, where primes 11 and 13 are mapped such that 10/9 and 11/10 are tempered together and that 7/6, 8/7, 13/11, and 15/13 are tempered together. Semafour takes the same mapping of 13 as godzilla, but swaps in a less complex and less accurate mapping for 11, so that 4/3 and 11/8 are tempered together. Similarly, varan takes the same mapping of 13 as godzilla, but swaps in a more complex mapping for 11, so that 6/5 and 13/11 are tempered together. Finally, baragon swaps in a less complex mapping for prime 11, so that 7/5 and 11/8 are tempered together.

== Interval chain ==
{| class="wikitable center-1 right-2"
|-
! rowspan="3" | #
! rowspan="3" | Cents*
! colspan="5" | Approximate ratios
|-
! rowspan="2" | 2.3.5.7.13 subgroup
! colspan="4" | Full 13-limit extensions
|-
! Godzilla
! Semafour
! Varan
! Baragon
|-
| 0
| 0.0
| 1/1
|
|
|
|
|-
| 1
| 948.0
| 7/4, 12/7, 26/15
| 22/13
|
|
|
|-
| 2
| 696.0
| 3/2
| 22/15
| 16/11
|
|
|-
| 3
| 444.0
| 9/7, 13/10, 21/16
|
| 14/11
|
|
|-
| 4
| 192.0
| 9/8, 10/9
| 11/10
| 12/11
|
|
|-
| 5
| 1140.0
| 25/13, 27/14, 39/20, 40/21
|
|
|
|
|-
| 6
| 888.0
| 5/3
|
| 18/11
| 22/13
|
|-
| 7
| 636.0
| 10/7, 13/9
|
|
| 22/15
| 16/11
|-
| 8
| 384.0
| 5/4
| 11/9
|
|
| 14/11
|-
| 9
| 132.0
| 13/12, 15/14
|
|
| 11/10
| 12/11
|-
| 10
| 1080.0
| 13/7, 15/8
| 11/6
| 20/11
|
|
|-
| 11
| 828.0
| 13/8
| 11/7
|
|
| 18/11
|-
| 12
| 576.0
| 25/18
| 11/8
| 15/11
|
|
|-
| 13
| 324.0
|
|
| 13/11
| 11/9
|
|-
| 14
| 72.1
| 25/24
|
|
|
|
|-
| 15
| 1020.1
| 25/14
|
|
| 11/6
| 20/11
|-
| 16
| 768.1
| 25/16
|
|
| 11/7
|
|-
| 17
| 516.1
|
|
|
| 11/8
| 15/11
|-
| 18
| 264.1
|
|
|
|
| 13/11
|}
<nowiki/>* In 2.3.5.7.13-subgroup [[CWE tuning]]

[[Category:Godzilla]]
[[Category:Temperament extensions]]
[[Category:Rank-2 temperaments]]