4L 4s (3/1-equivalent) - Revision history

BudjarnLambeth: /* Temperament interpretations */

2026-08-22T12:32:49Z

Temperament interpretations

← Older revision		Revision as of 12:32, 22 August 2026
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	Potentially useful temperaments include:		Potentially useful temperaments include:
	==== 3.5.7 subgroup ====		==== 3.5.7 subgroup ====
	* b32 & b52 (EDTs: [[32edt]], [[52edt]], [[84edt]], [[116edt]], [[136edt]])		* b32 & b52 (EDTs: [[32edt]], [[52edt]], [[84edt]], [[116edt]], [[136edt]]) (Unison vector: [-2, 5, -3⟩ or [[3125/3087]])

	==== 3.5.7.11 subgroup ====		==== 3.5.7.11 subgroup ====

BudjarnLambeth: /* 3.5.7 subgroup */

2026-08-22T11:47:43Z

3.5.7 subgroup

← Older revision		Revision as of 11:47, 22 August 2026
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	==== 3.5.7 subgroup ====		==== 3.5.7 subgroup ====
	* b32 & b52 (EDTs: [[32edt]], [[52edt]], [[84edt]], [[116edt]], [[136edt]])		* b32 & b52 (EDTs: [[32edt]], [[52edt]], [[84edt]], [[116edt]], [[136edt]])

			==== 3.5.7.11 subgroup ====
			* b32 & b84 (EDTs: [[32edt]], [[84edt]], [[116edt]])

			==== 3.5.7.11.13 subgroup ====
			* b32 & b84 (EDTs: [[32edt]], [[84edt]], [[116edt]])

			==== 3.5.7.17.19 subgroup ====
			* b52 & 84 (EDTs: [[52edt]], [[84edt]], [[136edt]])

	== Intervals ==		== Intervals ==

BudjarnLambeth: /* 3.5.7 subgroup */

2026-08-22T11:41:53Z

3.5.7 subgroup

← Older revision		Revision as of 11:41, 22 August 2026
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	Potentially useful temperaments include:		Potentially useful temperaments include:
	==== 3.5.7 subgroup ====		==== 3.5.7 subgroup ====
	* b52 ~~& b84~~ (EDTs: [[52edt]], [[84edt]], [[136edt]])		* b32 & b52 (EDTs: [[32edt]], [[52edt]], [[84edt]], [[116edt]], [[136edt]])

	== Intervals ==		== Intervals ==

BudjarnLambeth: /* 3.5.7 subgroup */

2026-08-22T11:38:48Z

3.5.7 subgroup

← Older revision		Revision as of 11:38, 22 August 2026
Line 15:		Line 15:
	Potentially useful temperaments include:		Potentially useful temperaments include:
	==== 3.5.7 subgroup ====		==== 3.5.7 subgroup ====
	* b52 & b84 (EDTs: [[52edt, 84edt, 136edt]])		* b52 & b84 (EDTs: [[52edt]], [[84edt]], [[136edt]])

	== Intervals ==		== Intervals ==

BudjarnLambeth: /* 3.5.7 subgroup */

2026-08-22T11:38:09Z

3.5.7 subgroup

← Older revision		Revision as of 11:38, 22 August 2026
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	Potentially useful temperaments include:		Potentially useful temperaments include:
	==== 3.5.7 subgroup ====		==== 3.5.7 subgroup ====
	* b8 & ~~b19; [8, -3, -2⟩;~~ (~~6561~~:~~6125)~~		* b52 & b84 (EDTs: [[52edt, 84edt, 136edt]])
	* b8d & b19; [12, ~~-13~~, ~~4⟩; (1275989841:1220703125~~)

	== Intervals ==		== Intervals ==

BudjarnLambeth: Created page with "{{Infobox MOS}} {{MOS intro}} This is a relatively unexplored MOS. All its neighbouring MOS sizes have seen some degree of exploration, but 4L 4s<3/1> hasn't yet. Its scale shape is highly reminiscent of the familiar diminished scale from octave-bssed music theory (4L 4s). In addition to the true mos form, LsLsLsLs, there are four near-mos forms – LLsLsLss, LLsLssLs, LLssLLss, and LLssLsLs – in which the period and its multiples are the only intervals with m..."

2026-08-22T11:32:15Z

Created page with "{{Infobox MOS}} {{MOS intro}} This is a relatively unexplored MOS. All its neighbouring MOS sizes have seen some degree of exploration, but 4L 4s<3/1> hasn't yet. Its scale shape is highly reminiscent of the familiar diminished scale from octave-bssed music theory (4L 4s). In addition to the true mos form, LsLsLsLs, there are four near-mos forms – LLsLsLss, LLsLssLs, LLssLLss, and LLssLsLs – in which the period and its multiples are the only intervals with m..."

New page

{{Infobox MOS}}
{{MOS intro}}

This is a relatively unexplored MOS. All its neighbouring MOS sizes have seen some degree of exploration, but 4L 4s<3/1> hasn't yet.

Its scale shape is highly reminiscent of the familiar diminished scale from octave-bssed music theory ([[4L 4s]]).

In addition to the true mos form, LsLsLsLs, there are four near-mos forms – LLsLsLss, LLsLssLs, LLssLLss, and LLssLsLs – in which the period and its multiples are the only intervals with more than two varieties. The near-mos forms are only proper if the dark generator is larger than 1\[[12edt]] (158.5{{c}}).

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

=== Temperament interpretations ===
Potentially useful temperaments include:
==== 3.5.7 subgroup ====
* b8 & b19; [8, -3, -2⟩; (6561:6125)
* b8d & b19; [12, -13, 4⟩; (1275989841:1220703125)

== Intervals ==
{{MOS intervals}}

=== Scale degrees ===
{{MOS mode degrees}}

== Scale tree ==
{{MOS tuning spectrum}}

{{todo|expand|inline=1}}