Tetrahanson - Revision history

Lériendil: Text replacement - "(unchanged-interval)" to "(unchanged interval)"

2025-06-21T06:59:25Z

Text replacement - "(unchanged-interval)" to "(unchanged interval)"

← Older revision		Revision as of 06:59, 21 June 2025
Line 182:		Line 182:
	\|-		\|-
	! ET<br />generator		! ET<br />generator
	! [[Eigenmonzo\|Eigenmonzo<br />(unchanged-interval)]]		! [[Eigenmonzo\|Eigenmonzo<br />(unchanged interval)]]
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments

FloraC: Collect non-octave temperaments in one category

2025-04-29T09:28:14Z

Collect non-octave temperaments in one category

← Older revision		Revision as of 09:28, 29 April 2025
Line 284:		Line 284:
	[[Category:Tetrahanson\| ]] <!-- main article -->		[[Category:Tetrahanson\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:~~Subgroup~~ temperaments]]		[[Category:Non-octave temperaments]]
	~~[[Category:Nonoctave~~]]

FloraC: - parent category

2025-04-28T14:46:27Z

- parent category

← Older revision		Revision as of 14:46, 28 April 2025
Line 282:		Line 282:
	\|}		\|}

	[[Category:~~Temperaments~~]]		[[Category:Tetrahanson\| ]] <!-- main article -->
			[[Category:Rank-2 temperaments]]
			[[Category:Subgroup temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
	~~[[Category:Rank-2 temperaments]]~~

Lériendil at 00:06, 20 April 2025

2025-04-20T00:06:01Z

← Older revision		Revision as of 00:06, 20 April 2025
Line 284:		Line 284:
	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Nonoctave]]		[[Category:Nonoctave]]
			[[Category:Rank-2 temperaments]]

ArrowHead294: Replace {{scale link}} with {{mos scalesig}}

2025-03-08T00:36:14Z

Replace {{scale link}} with {{mos scalesig}}

← Older revision		Revision as of 00:36, 8 March 2025
Line 157:		Line 157:
	<nowiki />* In 3.5.11.13-subgroup 13-throdd-limit minimax tuning		<nowiki />* In 3.5.11.13-subgroup 13-throdd-limit minimax tuning

	* [https://scaleworkshop.plainsound.org/scale/KXnc-_xfK] – 15-note scale ({{sl\|9L 6s}}, sLsLLsLsLLsLsLL)		* [https://scaleworkshop.plainsound.org/scale/KXnc-_xfK] – 15-note scale ({{mos scalesig\|9L 6s<3/1>\|link=1}}, sLsLLsLsLLsLsLL)
	* 2\3edt-equivalent [[Muddle]]s:		* 2\3edt-equivalent [[Muddle]]s:
	** sLsLLsLsLL parent with 2112121 target gives LsmLmLm minor? heptatonic		** sLsLLsLsLL parent with 2112121 target gives LsmLmLm minor? heptatonic

Dummy index: /* {{nowrap|b39 & b15}} */ 3\2-equivalent scales

2025-03-03T14:44:08Z

{{nowrap|b39 & b15}}: 3\2-equivalent scales

← Older revision		Revision as of 14:44, 3 March 2025
Line 158:		Line 158:

	* [https://scaleworkshop.plainsound.org/scale/KXnc-_xfK] – 15-note scale ({{sl\|9L 6s}}, sLsLLsLsLLsLsLL)		* [https://scaleworkshop.plainsound.org/scale/KXnc-_xfK] – 15-note scale ({{sl\|9L 6s}}, sLsLLsLsLLsLsLL)
			* 2\3edt-equivalent [[Muddle]]s:
			** sLsLLsLsLL parent with 2112121 target gives LsmLmLm minor? heptatonic
			** sLLsLsLLsL parent with 2112121 target gives LmsLmLm major? heptatonic

	{\| class="wikitable"		{\| class="wikitable"

Dummy index: /* {{nowrap|b39 & b15}} */ +tetracatakleismic

2025-02-27T12:48:44Z

{{nowrap|b39 & b15}}: +tetracatakleismic

← Older revision		Revision as of 12:48, 27 February 2025
Line 75:		Line 75:

	=== {{nowrap\|b39 & b15}} ===		=== {{nowrap\|b39 & b15}} ===
	This is restriction of [[catalan]] extension. This can maintain the structure of the 3rd-octave period in 3.4.5, 3.5.11, and 3.5.13. Well, 3.4.5 and 3.5.13, which do not include 7 nor 11 in their basis, should simply be called tetrahanson (and no-twos cata, respectively).		This is restriction of [[catalan]] extension. This can maintain the structure of the 3rd-octave period in 3.4.5, 3.5.11, and 3.5.13. Well, 3.4.5 and 3.5.13, which do not include 7 nor 11 in their basis, should simply be called tetrahanson (and no-twos cata, respectively). Another point that must be noted is the tetracatakleismic on 3.4.5.14.

	{\| class="wikitable"		{\| class="wikitable"

ArrowHead294 at 14:40, 26 February 2025

2025-02-26T14:40:55Z

← Older revision		Revision as of 14:40, 26 February 2025
Line 5:		Line 5:
	== Interval chain ==		== Interval chain ==
	{\| class="wikitable"		{\| class="wikitable"
			\|-
	! Generators		! Generators
	! Cents (CTE)		! Cents (CTE)
	! Approximate ratios		! Approximate ratios
	\|-		\|-
	\| -7		\| −7
	\| 1019.413		\| 1019.413
	\| [[9/5]]		\| [[9/5]]
	\|-		\|-
	\| -6		\| −6
	\| 1902.354		\| 1902.354
	\| [[3/1]]		\| [[3/1]]
	\|-		\|-
	\| -5		\| −5
	\| 385.295		\| 385.295
	\| [[5/4]]		\| [[5/4]]
	\|-		\|-
	\| -4		\| −4
	\| 1268.236		\| 1268.236
	\| 25/12		\| 25/12
	\|-		\|-
	\| -3		\| −3
	\| 2151.177		\| 2151.177
	\| 125/36		\| 125/36
	\|-		\|-
	\| -2		\| −2
	\| 634.118		\| 634.118
	\| [[36/25]]		\| [[36/25]]
	\|-		\|-
	\| -1		\| −1
	\| 1517.059		\| 1517.059
	\| [[12/5]]		\| [[12/5]]
Line 73:		Line 74:
	In tritave-repeating tetrahanson (3.4.5 subgroup), 36/25 actually represents 1\3edt, which makes the 3rd-tritave period.		In tritave-repeating tetrahanson (3.4.5 subgroup), 36/25 actually represents 1\3edt, which makes the 3rd-tritave period.

	=== b39 & b15 ===		=== {{nowrap\|b39 & b15}} ===
	This is restriction of [[catalan]] extension. This can maintain the structure of the 3rd-octave period in 3.4.5, 3.5.11, and 3.5.13. Well, 3.4.5 and 3.5.13, which do not include 7 nor 11 in their basis, should simply be called tetrahanson (and no-twos cata, respectively).		This is restriction of [[catalan]] extension. This can maintain the structure of the 3rd-octave period in 3.4.5, 3.5.11, and 3.5.13. Well, 3.4.5 and 3.5.13, which do not include 7 nor 11 in their basis, should simply be called tetrahanson (and no-twos cata, respectively).

	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	! !! 3.4.5 !! 3.5.11 !! 3.5.13		! !! 3.4.5 !! 3.5.11 !! 3.5.13
	\|-		\|-
	\| CWE \|\| 883.071 \|\| 879.416 \|\| 883.808		\| CWE \|\| 883.071 \|\| 879.416 \|\| 883.808
Line 92:		Line 93:

	{\| class="wikitable center-1 right-2"		{\| class="wikitable center-1 right-2"
	\|+ Interval chain		\|+ style="font-size: 105%;" \| Interval chain
	\|-		\|-
	! rowspan="2" \| #		! rowspan="2" \| #
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	! Approximate ratios		! Approximate ratios
	\|-		\|-
	\| -1		\| −1
	\| 1656.6		\| 1656.6
	\| 125/48, [[13/5]]		\| 125/48, [[13/5]]
Line 159:		Line 160:

	{\| class="wikitable"		{\| class="wikitable"
	\|+ Chords		\|+ style="font-size: 105%;" \| Chords
	\|-		\|-
	! Mossteps !! Tonic and then every +2 mossteps		! Mossteps !! Tonic and then every +2 mossteps
Line 175:		Line 176:

	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	\|+ Tuning spectrum		\|+ style="font-size: 105%;" \| Tuning spectrum
	\|-		\|-
	! ET<br />generator		! ET<br />generator

Dummy index: /* Tetrahanson on tritave */

2025-02-20T15:24:53Z

Tetrahanson on tritave

← Older revision		Revision as of 15:24, 20 February 2025
Line 181:		Line 181:
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments
			\|-
			\|
			\| 11/4
			\| 875.659
			\|
	\|-		\|-
	\|		\|
Line 230:		Line 235:
	\| 36/13		\| 36/13
	\| 881.691		\| 881.691
			\|
			\|-
			\|
			\| 15/13
			\| 881.726
	\|		\|
	\|-		\|-

Dummy index: /* Tetrahanson on tritave */

2025-02-20T14:54:27Z

Tetrahanson on tritave

← Older revision		Revision as of 14:54, 20 February 2025
Line 108:		Line 108:
	\| -1		\| -1
	\| 1656.6		\| 1656.6
	\| [[13/5]]		\| 125/48, [[13/5]]
	\| 388.6		\| 388.6
	\| 5/4		\| 5/4
Line 120:		Line 120:
	\| 36/25, [[13/9]]		\| 36/25, [[13/9]]
	\| 1268.0		\| 1268.0
	\| 25/12, 27/13		\| 25/12, 27/13, 52/25
	\|-		\|-
	\| 1		\| 1
Line 126:		Line 126:
	\| [[125/108]], [[15/13]]		\| [[125/108]], [[15/13]]
	\| 879.3		\| 879.3
	\| 5/3		\| 5/3, [[33/20]]
	\| 1513.3		\| 1513.3
	\| 12/5		\| 12/5
Line 150:		Line 150:
	\| [[16/9]], [[44/25]]		\| [[16/9]], [[44/25]]
	\| 1615.4		\| 1615.4
	\| 64/25,33/13		\| 64/25, 33/13
	\| 347.4		\| 347.4
	\| [[100/81]], [[16/13]], [[11/9]]		\| [[100/81]], [[16/13]], [[11/9]]
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	\|-		\|-
	! Mossteps !! Tonic and then every +2 mossteps		! Mossteps !! Tonic and then every +2 mossteps
			\|-
			\| 0-3-6 \|\| 36:44:55 → 36:45:55 → 16:20:25 ↩↩
	\|-		\|-
	\| 0-3-7 \|\| 9:11:15 → 12:15:20 ↩↩ → 16:20:27		\| 0-3-7 \|\| 9:11:15 → 12:15:20 ↩↩ → 16:20:27
Line 193:		Line 195:
	\| 33/13		\| 33/13
	\| 878.675		\| 878.675
			\|
			\|-
			\|
			\| 144/125
			\| 878.954
	\|		\|
	\|-		\|-
Line 233:		Line 240:
	\| 16/13		\| 16/13
	\| 882.349		\| 882.349
			\|
			\|-
			\|
			\| 16/15
			\| 882.557
	\|		\|
	\|-		\|-
Line 243:		Line 255:
	\| 5/3		\| 5/3
	\| 884.359		\| 884.359
			\|
			\|-
			\|
			\| 125/108
			\| 887.061
	\|		\|
	\|-		\|-