3L 3s - Revision history

Overthink: /* Scale tree */ Used template

2025-12-28T05:10:41Z

Scale tree: Used template

@@ Line 22: / Line 22: @@
 ==Scale tree==
-{{todo|inline=1|complete table|text=Convert manually-generated scale tree table to MOS tuning spectrum without losing information from the existing table}}
+{{MOS tuning spectrum
-{| class="wikitable center-all"
+| 9/7 = [[Oodako]]
-! colspan="6" rowspan="2" |Generator
+| 8/5 = [[Triforce]]
-! colspan="2" |Cents
+| 13/8 = Unnamed golden tuning
-! rowspan="2" |L
+| 7/3 = [[Deflated]] (optimal around here)
-! rowspan="2" |s
+| 13/5 = Unnamed golden tuning
-! rowspan="2" |L/s
+| 11/4 = [[August]]
-! rowspan="2" | Comments
+| 3/1 = [[Trug]] (optimal around here)
-|-
+| 10/3 = [[Augene]]
-! Chroma-positive
+| 4/1 = [[Inflated]]
-! Chroma-negative
+| 6/1 = [[Hemiug]]↓, [[hemiaug]]↓
-|-
+}}
 [[Category:Triwood| ]]
 [[Category:6-tone scales]]
   <!-- main article -->

BudjarnLambeth at 00:19, 28 December 2025

2025-12-28T00:19:02Z

← Older revision		Revision as of 00:19, 28 December 2025
Line 22:		Line 22:

	==Scale tree==		==Scale tree==
	{{todo\|inline=1\|complete table\|Convert manually-generated scale tree table to MOS tuning spectrum without losing information from the existing table}}		{{todo\|inline=1\|complete table\|text=Convert manually-generated scale tree table to MOS tuning spectrum without losing information from the existing table}}
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	! colspan="6" rowspan="2" \|Generator		! colspan="6" rowspan="2" \|Generator

Lucius Chiaraviglio: Apparently I have to be more specific in the ToDo

2025-08-01T22:27:12Z

Apparently I have to be more specific in the ToDo

← Older revision		Revision as of 22:27, 1 August 2025
Line 22:		Line 22:

	==Scale tree==		==Scale tree==
	{{todo\|inline=1\|complete table\|Convert manually-generated scale tree table to MOS tuning spectrum}}		{{todo\|inline=1\|complete table\|Convert manually-generated scale tree table to MOS tuning spectrum without losing information from the existing table}}
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	! colspan="6" rowspan="2" \|Generator		! colspan="6" rowspan="2" \|Generator

FloraC: Undo revision 205774 by MisterShafXen (talk). ???

2025-08-01T16:28:32Z

Undo revision 205774 by MisterShafXen (talk). ???

@@ Line 22: / Line 22: @@
 ==Scale tree==
-{{MOS tuning spectrum}}
+{{todo|inline=1|complete table|Convert manually-generated scale tree table to MOS tuning spectrum}}
 [[Category:Triwood| ]]
 [[Category:6-tone scales]]
   <!-- main article -->

MisterShafXen at 15:30, 1 August 2025

2025-08-01T15:30:54Z

@@ Line 22: / Line 22: @@
 ==Scale tree==
-{{todo|inline=1|complete table|Convert manually-generated scale tree table to MOS tuning spectrum}}
+{{MOS tuning spectrum}}
 [[Category:Triwood| ]]
 [[Category:6-tone scales]]
   <!-- main article -->

Lucius Chiaraviglio: /* Scale tree */ Add {{ToDo:Convert manually-generated table to MOS tuning spectrum template}}

2025-08-01T15:28:20Z

Scale tree: Add {{ToDo:Convert manually-generated table to MOS tuning spectrum template}}

← Older revision		Revision as of 15:28, 1 August 2025
Line 22:		Line 22:

	==Scale tree==		==Scale tree==
			{{todo\|inline=1\|complete table\|Convert manually-generated scale tree table to MOS tuning spectrum}}
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	! colspan="6" rowspan="2" \|Generator		! colspan="6" rowspan="2" \|Generator

BudjarnLambeth: == Intervals == {{MOS intervals}}

2024-12-15T23:58:24Z

== Intervals == {{MOS intervals}}

← Older revision		Revision as of 23:58, 15 December 2024
Line 10:		Line 10:

	{{MOS intro}}		{{MOS intro}}
	In addition to the true MOS (LsLsLs or sLsLsL), there are also near-MOS patterns of LLsLss and LLssLs, which are only proper if the generator is larger than 1\9.
			In addition to the true MOS (LsLsLs or sLsLsL), there are also near-MOS patterns of LLsLss and LLssLs, which are only proper if the generator is larger than [[9edo\|1\9]].

	Out of all ''[[Rothenberg propriety\|proper]]'' six-note MOS scales, this augmented scale probably has the lowest harmonic entropy{{Clarify}}.		Out of all ''[[Rothenberg propriety\|proper]]'' six-note MOS scales, this augmented scale probably has the lowest harmonic entropy{{Clarify}}.

			== Intervals ==
			{{MOS intervals}}

	== Modes==		== Modes==

Nick Vuci: /* Modes */ added MOS mode degrees template

2024-07-24T23:09:36Z

Modes: added MOS mode degrees template

← Older revision		Revision as of 23:09, 24 July 2024
Line 15:		Line 15:

	== Modes==		== Modes==
	{{MOS ~~modes~~}}		{{MOS mode degrees}}

	==Scale tree==		==Scale tree==
	{\| class="wikitable center-all"		{\| class="wikitable center-all"

Ganaram inukshuk: spaces

2024-03-01T01:01:59Z

spaces

← Older revision		Revision as of 01:01, 1 March 2024
Line 13:		Line 13:

	Out of all ''[[Rothenberg propriety\|proper]]'' six-note MOS scales, this augmented scale probably has the lowest harmonic entropy{{Clarify}}.		Out of all ''[[Rothenberg propriety\|proper]]'' six-note MOS scales, this augmented scale probably has the lowest harmonic entropy{{Clarify}}.


	== Modes==		== Modes==
	{{MOS modes}}		{{MOS modes}}


	==Scale tree==		==Scale tree==
	{\| class="wikitable center-all"		{\| class="wikitable center-all"

Ganaram inukshuk: Reworded intro

2024-02-17T10:09:56Z

Reworded intro

← Older revision		Revision as of 10:09, 17 February 2024
Line 10:		Line 10:

	{{MOS intro}}		{{MOS intro}}
	~~The~~ true MOS is LsLsLs ~~but interesting~~ near-~~MOSs include~~ LLsLss and LLssLs~~. The MOS is always proper but the other forms~~ are only proper if the generator is larger than 1\9 ~~of an octave (so not augmented)~~.		In addition to the true MOS (LsLsLs or sLsLsL), there are also near-MOS patterns of LLsLss and LLssLs, which are only proper if the generator is larger than 1\9.

	Out of all ''[[Rothenberg propriety\|proper]]'' six-note MOS scales, this augmented scale probably has the lowest harmonic entropy.		Out of all ''[[Rothenberg propriety\|proper]]'' six-note MOS scales, this augmented scale probably has the lowest harmonic entropy{{Clarify}}.


	== Modes ==		== Modes==
	{{MOS modes}}		{{MOS modes}}


	== Scale tree ==		==Scale tree==
	{\| class="wikitable center-all"		{\| class="wikitable center-all"
	! colspan="6" rowspan="2" \| Generator		! colspan="6" rowspan="2" \|Generator
	! colspan="2" \| Cents		! colspan="2" \|Cents
	! rowspan="2" \| L		! rowspan="2" \|L
	! rowspan="2" \| s		! rowspan="2" \|s
	! rowspan="2" \| L/s		! rowspan="2" \|L/s
	! rowspan="2" \| Comments		! rowspan="2" \| Comments
	\|-		\|-
Line 31:		Line 31:
	! Chroma-negative		! Chroma-negative
	\|-		\|-
	\| 1\6 \|\| \|\| \|\| \|\| \|\| \|\| 200.000 \|\| 200.000 \|\| 1 \|\| 1 \|\| 1.000 \|\|		\|1\6\|\| \|\| \|\| \|\| \|\| \|\|200.000\|\|200.000 \|\| 1\|\|1\|\|1.000\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 6\33 \|\| 218.182 \|\| 181.818 \|\| 6 \|\| 5 \|\| 1.200 \|\|		\| \|\| \|\| \|\| \|\| \|\|6\33\|\|218.182\|\| 181.818\|\|6\|\|5\|\|1.200\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| 5\27 \|\| \|\| 222.222 \|\| 177.778 \|\| 5 \|\| 4 \|\| 1.250 \|\|		\| \|\| \|\| \|\| \|\|5\27\|\| \|\|222.222\|\| 177.778\|\|5\|\|4\|\|1.250\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 9\48 \|\| 225.000 \|\| 175.000 \|\| 9 \|\| 7 \|\| 1.286 \|\| Oodako		\| \|\| \|\| \|\| \|\| \|\|9\48\|\|225.000\|\| 175.000\|\|9\|\|7\|\|1.286\|\|Oodako
	\|-		\|-
	\| \|\| \|\| \|\| 4\21 \|\| \|\| \|\| 228.571 \|\| 171.429 \|\| 4 \|\| 3 \|\| 1.333 \|\|		\| \|\| \|\| \|\|4\21\|\| \|\| \|\|228.571\|\| 171.429\|\|4\|\|3\|\|1.333\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 11\57 \|\| 231.579 \|\| 168.421 \|\| 11 \|\| 8 \|\| 1.375 \|\|		\| \|\| \|\| \|\| \|\| \|\|11\57\|\|231.579\|\|168.421 \|\| 11 \|\|8\|\|1.375\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| 7\36 \|\| \|\| 233.333 \|\| 166.667 \|\| 7 \|\| 5 \|\| 1.400 \|\|		\| \|\| \|\| \|\| \|\|7\36\|\| \|\|233.333\|\| 166.667\|\|7\|\|5\|\|1.400\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 10\51 \|\| 235.294 \|\| 164.706 \|\| 10 \|\| 7 \|\| 1.428 \|\|		\| \|\| \|\| \|\| \|\| \|\|10\51\|\|235.294\|\|164.706 \|\| 10 \|\|7\|\|1.428\|\|
	\|-		\|-
	\| \|\| \|\| 3\15 \|\| \|\| \|\| \|\| 240.000 \|\| 160.000 \|\| 3 \|\| 2 \|\| 1.500 \|\|		\| \|\| \|\|3\15 \|\| \|\| \|\| \|\|240.000\|\| 160.000\|\| 3\|\|2\|\|1.500\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 11\54 \|\| 244.444 \|\| 155.556 \|\| 11 \|\| 7 \|\| 1.571 \|\|		\| \|\| \|\| \|\| \|\| \|\|11\54\|\|244.444\|\|155.556 \|\| 11 \|\|7\|\|1.571\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| 8\39 \|\| \|\| 246.154 \|\| 153.846 \|\| 8 \|\| 5 \|\| 1.600 \|\| Triforce		\| \|\| \|\| \|\| \|\|8\39\|\| \|\|246.154\|\| 153.846\|\|8\|\|5\|\|1.600\|\|Triforce
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 13\63 \|\| 247.619 \|\| 152.381 \|\| 13 \|\| 8 \|\| 1.625 \|\| Unnamed golden tuning		\| \|\| \|\| \|\| \|\| \|\|13\63\|\|247.619\|\|152.381 \|\| 13 \|\|8\|\|1.625\|\| Unnamed golden tuning
	\|-		\|-
	\| \|\| \|\| \|\| 5\24 \|\| \|\| \|\| 250.000 \|\| 150.000 \|\| 5 \|\| 3 \|\| 1.667 \|\|		\| \|\| \|\| \|\|5\24\|\| \|\| \|\|250.000\|\| 150.000\|\|5\|\|3\|\|1.667\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 12\57 \|\| 252.632 \|\| 147.368 \|\| 12 \|\| 7 \|\| 1.714 \|\|		\| \|\| \|\| \|\| \|\| \|\|12\57\|\|252.632\|\|147.368 \|\| 12 \|\|7\|\|1.714\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| 7\33 \|\| \|\| 254.545 \|\| 145.455 \|\| 7 \|\| 4 \|\| 1.750 \|\|		\| \|\| \|\| \|\| \|\|7\33\|\| \|\|254.545\|\| 145.455\|\|7\|\|4\|\|1.750\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 9\42 \|\| 257.143 \|\| 142.857 \|\| 9 \|\| 5 \|\| 1.800 \|\|		\| \|\| \|\| \|\| \|\| \|\|9\42\|\|257.143\|\| 142.857\|\|9\|\|5\|\|1.800\|\|
	\|-		\|-
	\| \|\| 2\9 \|\| \|\| \|\| \|\| \|\| 266.667 \|\| 133.333 \|\| 2 \|\| 1 \|\| 2.000 \|\| Basic triwood		\| \|\|2\9 \|\| \|\| \|\| \|\| \|\|266.667\|\|133.333 \|\| 2\|\|1\|\|2.000\|\|Basic triwood
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 9\39 \|\| 276.923 \|\| 123.077 \|\| 9 \|\| 4 \|\| 2.250 \|\|		\| \|\| \|\| \|\| \|\| \|\| 9\39\|\|276.923\|\| 123.077\|\|9\|\|4\|\|2.250\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| 7\30 \|\| \|\| 280.000 \|\| 120.000 \|\| 7 \|\| 3 \|\| 2.333 \|\| Deflated (optimal around here)		\| \|\| \|\| \|\| \|\|7\30\|\| \|\|280.000\|\| 120.000\|\|7\|\|3\|\|2.333\|\|Deflated (optimal around here)
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 12\51 \|\| 282.353 \|\| 117.647 \|\| 12 \|\| 5 \|\| 2.400 \|\|		\| \|\| \|\| \|\| \|\| \|\|12\51\|\|282.353\|\|117.647 \|\| 12 \|\|5\|\|2.400\|\|
	\|-		\|-
	\| \|\| \|\| \|\| 5\21 \|\| \|\| \|\| 285.714 \|\| 114.286 \|\| 5 \|\| 2 \|\| 2.500 \|\|		\| \|\| \|\| \|\| 5\21\|\| \|\| \|\|285.714\|\| 114.286\|\|5\|\|2\|\|2.500\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 13\54 \|\| 288.889 \|\| 111.111 \|\| 13 \|\| 5 \|\| 2.600 \|\| Unnamed golden tuning		\| \|\| \|\| \|\| \|\| \|\|13\54\|\|288.889\|\|111.111 \|\| 13 \|\|5\|\|2.600\|\| Unnamed golden tuning
	\|-		\|-
	\| \|\| \|\| \|\| \|\| 8\33 \|\| \|\| 290.909 \|\| 109.091 \|\| 8 \|\| 3 \|\| 2.667 \|\|		\| \|\| \|\| \|\| \|\|8\33\|\| \|\|290.909\|\| 109.091\|\|8\|\|3\|\|2.667\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 11\45 \|\| 293.333 \|\| 106.667 \|\| 11 \|\| 4 \|\| 2.750 \|\| August		\| \|\| \|\| \|\| \|\| \|\|11\45\|\|293.333\|\|106.667 \|\| 11 \|\|4\|\|2.750\|\| August
	\|-		\|-
	\| \|\| \|\| 3\12 \|\| \|\| \|\| \|\| 300.000 \|\| 100.000 \|\| 3 \|\| 1 \|\| 3.000 \|\| Trug (optimal around here)		\| \|\| \|\|3\12\|\| \|\| \|\| \|\|300.000\|\| 100.000\|\| 3\|\|1\|\|3.000\|\|Trug (optimal around here)
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 10\39 \|\| 307.692 \|\| 92.308 \|\| 10 \|\| 3 \|\| 3.333 \|\| Augene		\| \|\| \|\| \|\| \|\| \|\|10\39\|\|307.692\|\|92.308\|\|10\|\|3\|\|3.333\|\|Augene
	\|-		\|-
	\| \|\| \|\| \|\| \|\| 7\27 \|\| \|\| 311.111 \|\| 88.889 \|\| 7 \|\| 2 \|\| 3.500 \|\|		\| \|\| \|\| \|\| \|\|7\27\|\| \|\|311.111\|\| 88.889\|\|7 \|\|2 \|\| 3.500\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 11\42 \|\| 314.286 \|\| 85.714 \|\| 11 \|\| 3 \|\| 3.667 \|\|		\| \|\| \|\| \|\| \|\| \|\|11\42\|\|314.286\|\|85.714\|\|11\|\|3\|\|3.667\|\|
	\|-		\|-
	\| \|\| \|\| \|\| 4\15 \|\| \|\| \|\| 320.000 \|\| 80.000 \|\| 4 \|\| 1 \|\| 4.000 \|\| Inflated		\| \|\| \|\| \|\|4\15 \|\| \|\| \|\|320.000\|\| 80.000\|\|4\|\|1 \|\| 4.000\|\|Inflated
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 9\33 \|\| 327.273 \|\| 72.727 \|\| 9 \|\| 2 \|\| 4.500 \|\|		\| \|\| \|\| \|\| \|\| \|\|9\33 \|\|327.273\|\| 72.727\|\|9 \|\| 2\|\| 4.500\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| 5\18 \|\| \|\| 333.333 \|\| 66.667 \|\| 5 \|\| 1 \|\| 5.000 \|\|		\| \|\| \|\| \|\| \|\|5\18\|\| \|\|333.333\|\| 66.667\|\|5 \|\|1 \|\| 5.000\|\|
	\|-		\|-
	\| \|\| \|\| \|\| \|\| \|\| 6\21 \|\| 342.857 \|\| 57.143 \|\| 6 \|\| 1 \|\| 6.000 \|\| Hemiug↓, hemiaug↓		\| \|\| \|\| \|\| \|\| \|\|6\21\|\|342.857\|\| 57.143\|\|6 \|\| 1\|\| 6.000\|\|Hemiug↓, hemiaug↓
	\|-		\|-
	\| 1\3 \|\| \|\| \|\| \|\| \|\| \|\| 400.000 \|\| 0.000 \|\| 1 \|\| 0 \|\| → inf \|\|		\|1\3 \|\| \|\| \|\| \|\| \|\| \|\|400.000\|\|0.000\|\|1 \|\| 0\|\|→ inf\|\|
	\|}		\|}