Trisected - Revision history

Overthink: /* Tuning spectrum */ + minimax tunings

2026-03-22T18:31:43Z

Tuning spectrum: + minimax tunings

← Older revision		Revision as of 18:31, 22 March 2026
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	\| [[7/6]]		\| [[7/6]]
	\| 633.282		\| 633.282
	\|		\| 7-odd-limit minimax
	\|-		\|-
	\| [[36edo\|19\36]]		\| [[36edo\|19\36]]
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	\| [[9/7]]		\| [[9/7]]
	\| 633.583		\| 633.583
	\|		\| 9-odd-limit minimax
	\|-		\|-
	\|		\|
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	\| [[13/7]]		\| [[13/7]]
	\| 633.962		\| 633.962
	\|		\| 13- and 15-odd-limit minimax
	\|-		\|-
	\|		\|

Overthink: /* Target tunings */ + minimax tunings

2026-03-22T18:30:45Z

Target tunings: + minimax tunings

@@ Line 164: / Line 164: @@
 === Target tunings ===
-{{Todo|inline=1|complete section}}
+{| class="wikitable center-all mw-collapsible mw-collapsed"
 === Tuning spectrum ===

Overthink: /* Tunings */ + tuning spectrum

2026-03-22T18:15:23Z

Tunings: + tuning spectrum

Show changes

Overthink: remove {{Clear}} (TOC now shows)

2026-03-20T16:37:53Z

remove {{Clear}} (TOC now shows)

← Older revision		Revision as of 16:37, 20 March 2026
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	For technical data, see [[Augmented family #Trisected]].		For technical data, see [[Augmented family #Trisected]].

	~~{{Clear}}<!-- remove when no longer needed -->~~
	== Intervals ==		== Intervals ==
	In the following table, odd harmonics 1–21 are in '''bold'''.		In the following table, odd harmonics 1–21 are in '''bold'''.

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

2026-03-20T16:37:26Z

Tunings: + norm-based tunings

@@ Line 114: / Line 114: @@
 == Tunings ==
-{{Todo|complete section|inline=1}}
+=== Norm-based tunings ===
 [[Category:Trisected| ]] <!-- main article -->
 [[Category:Rank-2 temperaments]]

Overthink: Add subgroup restriction

2026-03-20T15:57:12Z

Add subgroup restriction

← Older revision		Revision as of 15:57, 20 March 2026
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	In the [[11-limit]], the [[4/3\|perfect fourth]] is split into three ~[[11/10]]'s, thus tempering out [[4000/3993]]. Additionally, the 1/3-octave period represents [[14/11]], tempering out [[56/55]] and [[176/175]]. The [[13-limit]] extension equates the ~10/7 with [[13/9]], tempering out [[91/90]] and [[2197/2187]].		In the [[11-limit]], the [[4/3\|perfect fourth]] is split into three ~[[11/10]]'s, thus tempering out [[4000/3993]]. Additionally, the 1/3-octave period represents [[14/11]], tempering out [[56/55]] and [[176/175]]. The [[13-limit]] extension equates the ~10/7 with [[13/9]], tempering out [[91/90]] and [[2197/2187]].

			The 2.3.7.11/5 subgroup [[restriction]], known as [[trisect]], removes the individual mappings for 5 and 11 while still tempering out 1029/1024 and 4000/3993, and is much more accurate.

	For technical data, see [[Augmented family #Trisected]].		For technical data, see [[Augmented family #Trisected]].

Overthink: /* Intervals */ add interval table

2026-03-19T23:42:10Z

Intervals: add interval table

@@ Line 21: / Line 21: @@
 {{Clear}}<!-- remove when no longer needed -->
 == Intervals ==
-{{Todo|complete section|inline=1}}
+In the following table, odd harmonics 1–21 are in '''bold'''.
 == Tunings ==

Overthink: expand description

2026-03-19T19:41:03Z

expand description

← Older revision		Revision as of 19:41, 19 March 2026
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	\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 17.5 \| Complexity 2 = 36		\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 17.5 \| Complexity 2 = 36
	}}		}}
	'''Trisected''' is the [[rank-2 temperament]] tempering out [[128/125]], [[1029/1000]], and [[1029/1024]] in the [[7-limit]], making it a member of the [[augmented family]], [[keegic temperaments]], and [[gamelismic clan]].		'''Trisected''' is the [[rank-2 temperament]] tempering out [[128/125]], [[1029/1000]], and [[1029/1024]] in the [[7-limit]], making it a member of the [[augmented family]], [[keegic temperaments]], and [[gamelismic clan]]. Since it tempers out 128/125, the [[2/1\|octave]] is split into 3 ~[[5/4]]'s, each tuned to 400{{C}} if the octave is pure. Since it tempers out 1029/1024, the [[3/2\|perfect fifth]] is split into three intervals of ~[[8/7]].Since it tempers out [[1029/1000]], the [[3/1\|tritave]] is split into three intervals of [[10/7]]. This means that every [[Pythagorean tuning\|Pythagorean]] interval is split into three equal parts.

			In the [[11-limit]], the [[4/3\|perfect fourth]] is split into three ~[[11/10]]'s, thus tempering out [[4000/3993]]. Additionally, the 1/3-octave period represents [[14/11]], tempering out [[56/55]] and [[176/175]]. The [[13-limit]] extension equates the ~10/7 with [[13/9]], tempering out [[91/90]] and [[2197/2187]].

	For technical data, see [[Augmented family #Trisected]].		For technical data, see [[Augmented family #Trisected]].

FloraC: Complete infobox. Categorize

2026-03-19T09:57:04Z

Complete infobox. Categorize

← Older revision		Revision as of 09:57, 19 March 2026
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	\| Title = Trisected		\| Title = Trisected
	\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13		\| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
	\| Comma basis = [[128/125]], [[1029/~~1024~~]] (7-limit);<br>[[56/55]], [[128/125]], [[1029/1000]] (11-limit);<br>[[56/55]], [[91/90]], [[128/125]], [[1029/1000]] (13-limit)		\| Comma basis = [[128/125]], [[1029/1000]] (7-limit);<br>[[56/55]], [[128/125]], [[1029/1000]] (11-limit);<br>[[56/55]], [[91/90]], [[128/125]], [[1029/1000]] (13-limit)
	\| Edo join 1 = 15 \| Edo join 2 = 36		\| Edo join 1 = 15 \| Edo join 2 = 36
	\| Mapping = 3; 3 0 -1 -1 7		\| Mapping = 3; 3 0 -1 -1 7
	\| Generators = 8/7		\| Generators = 10/7
	\| Generators tuning = ~~235~~.0		\| Generators tuning = 635.0
	\| Optimization method = CWE		\| Optimization method = CWE
	\| MOS scales = [[6L 9s]], [[15L 6s]], [[15L 21s]]		\| MOS scales = [[6L 9s]], [[15L 6s]], [[15L 21s]]
	\| Pergen = (P8/3, P5/3)		\| Pergen = (P8/3, P5/3)
	\| Odd limit 1 = 9 \| Mistuning 1 = 16.1 \| Complexity 1 =		\| Odd limit 1 = 9 \| Mistuning 1 = 16.1 \| Complexity 1 = 36
	\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 17.5 \| Complexity 2 =		\| Odd limit 2 = 13-limit 21 \| Mistuning 2 = 17.5 \| Complexity 2 = 36
	}}		}}
	'''Trisected''' is the [[rank-2 temperament]] tempering out [[128/125]], [[1029/1000]], and [[1029/1024]] in the [[7-limit]], making it a member of the [[augmented family]], [[keegic temperaments]], and [[gamelismic clan]].		'''Trisected''' is the [[rank-2 temperament]] tempering out [[128/125]], [[1029/1000]], and [[1029/1024]] in the [[7-limit]], making it a member of the [[augmented family]], [[keegic temperaments]], and [[gamelismic clan]].
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	== Tunings ==		== Tunings ==
	{{Todo\|complete section~~\|categorize~~\|inline=1}}		{{Todo\|complete section\|inline=1}}

	{{Stub}}		{{Stub}}
			[[Category:Trisected\| ]] <!-- main article -->
			[[Category:Rank-2 temperaments]]
			[[Category:Augmented family]]
			[[Category:Gamelismic clan]]
			[[Category:Keegic temperaments]]

Overthink: + technical data link

2026-03-19T04:59:55Z

+ technical data link

← Older revision		Revision as of 04:59, 19 March 2026
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	}}		}}
	'''Trisected''' is the [[rank-2 temperament]] tempering out [[128/125]], [[1029/1000]], and [[1029/1024]] in the [[7-limit]], making it a member of the [[augmented family]], [[keegic temperaments]], and [[gamelismic clan]].		'''Trisected''' is the [[rank-2 temperament]] tempering out [[128/125]], [[1029/1000]], and [[1029/1024]] in the [[7-limit]], making it a member of the [[augmented family]], [[keegic temperaments]], and [[gamelismic clan]].

			For technical data, see [[Augmented family #Trisected]].

	{{Clear}}<!-- remove when no longer needed -->		{{Clear}}<!-- remove when no longer needed -->