12L 12s - Revision history

Overthink: /* Intervals */ grammar; change some writing

2026-05-29T04:29:23Z

Intervals: grammar; change some writing

← Older revision		Revision as of 04:29, 29 May 2026
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	=== Intervals ===		=== Intervals ===
	While 12L 12s can be treated as a 24-form system due to the scale containing 24 notes, it can also sense as two rings of 12edo that differ by a small step. For example, in compton, the small step represents the [[81/80]] comma, ~~which can be used to achieve~~ accurate 5-limit ~~harmony~~. In catler, the small step represents [[64/63]] and [[36/35]], and inflecting a 12edo minor seventh down by this step gives a more accurate ~[[7/4]], while 5-limit ~~intervals~~ are represented as in 12edo.		While 12L 12s can be treated as a 24-form system due to the scale containing 24 notes, it can also make sense as two rings of 12edo that differ by a small step. For example, in compton, the small step represents the [[81/80]] comma, and inflecting 12edo intervals by this step produces more accurate approximations of 5-limit intervals. In catler, the small step represents [[64/63]] and [[36/35]], and inflecting a 12edo minor seventh down by this step gives a more accurate ~7/4, with other ratios involving harmonic 7 also improved, while intervals within the 5-limit are represented as in 12edo.
	{{MOS intervals}}		{{MOS intervals}}

Overthink: /* Scale tree */ more optimal tunings (7-limit catler and 5-limit compton, since higher limits are less accessible within 12L 12s)

2026-05-29T04:25:49Z

Scale tree: more optimal tunings (7-limit catler and 5-limit compton, since higher limits are less accessible within 12L 12s)

← Older revision		Revision as of 04:25, 29 May 2026
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	{{MOS tuning spectrum		{{MOS tuning spectrum
	\| 3/2 = [[Duodecim]]		\| 3/2 = [[Duodecim]]
	\| 3/1 = [[Catler]]		\| 5/2 = [[Catler]]
	\| 5/1 = [[Compton]]		\| 6/1 = [[Compton]]
	}}		}}

Overthink: /* Scale tree */ description

2026-05-29T04:23:42Z

Scale tree: description

← Older revision		Revision as of 04:23, 29 May 2026
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	== Scale tree ==		== Scale tree ==
			Softer tunings of 12L 12s are closer to an unequal derivative of [[24edo]], while harder tunings are closer to two rings of 12edo a comma step apart.
	{{MOS tuning spectrum		{{MOS tuning spectrum
	\| 3/2 = [[Duodecim]]		\| 3/2 = [[Duodecim]]

Overthink: /* Scale properties */ Remove section which doesn't apply well to 12L 12s (also the table is too wide). Description for intervals

2026-05-29T04:21:40Z

Scale properties: Remove section which doesn't apply well to 12L 12s (also the table is too wide). Description for intervals

← Older revision		Revision as of 04:21, 29 May 2026
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	=== Intervals ===		=== Intervals ===
			While 12L 12s can be treated as a 24-form system due to the scale containing 24 notes, it can also sense as two rings of 12edo that differ by a small step. For example, in compton, the small step represents the [[81/80]] comma, which can be used to achieve accurate 5-limit harmony. In catler, the small step represents [[64/63]] and [[36/35]], and inflecting a 12edo minor seventh down by this step gives a more accurate ~[[7/4]], while 5-limit intervals are represented as in 12edo.
	{{MOS intervals}}		{{MOS intervals}}

	~~=== Generator chain ===~~
	~~{{MOS genchain}}~~

	=== Modes ===		=== Modes ===
	Since 12L 12s has only one large step and one small step per period, there are only two modes, which can be called major and minor. In compton, catler, and duodecim, the major mode favors otonalities above the root, while the minor mode favors utonalities above the root. This is because [[5/4]], [[7/4]], and [[11/8]] are all closer to the 12edo step above it than the step below it.		Since 12L 12s has only one large step and one small step per period, there are only two modes, which can be called the major and minor modes. In compton, catler, and duodecim, the major mode favors otonalities above the root, while the minor mode favors utonalities above the root. This is because [[5/4]], [[7/4]], and [[11/8]] are all closer to the 12edo step above it than the step below it.
	{{MOS mode degrees}}		{{MOS mode degrees}}

Overthink: /* Modes */ add description

2026-05-29T04:11:36Z

Modes: add description

← Older revision		Revision as of 04:11, 29 May 2026
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	=== Modes ===		=== Modes ===
			Since 12L 12s has only one large step and one small step per period, there are only two modes, which can be called major and minor. In compton, catler, and duodecim, the major mode favors otonalities above the root, while the minor mode favors utonalities above the root. This is because [[5/4]], [[7/4]], and [[11/8]] are all closer to the 12edo step above it than the step below it.
	{{MOS mode degrees}}		{{MOS mode degrees}}

Overthink: prime limits; explanation

2026-05-24T19:14:00Z

prime limits; explanation

← Older revision		Revision as of 19:14, 24 May 2026
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	{{MOS intro}}		{{MOS intro}}

	It is the 24-note mos scale of the [[compton]], [[catler]], and [[duodecim]] temperaments of the [[compton family]], which divide the octave into 12 parts. As such, this mos scale can be considered to be 2 rings of [[12edo]], and can be replicated with two 12edo instruments detuned from each other by a fixed amount. ~~Each~~ of these temperaments ~~maps~~ [[3/2]] to 7 steps of 12edo, tempering out the [[Pythagorean comma]]. Compton uses the [[3-limit]] of 12edo and adds an independent [[generator]] for [[5/4]]. Catler additionally maps 5/4 to 4\12, and ~~has~~ [[7/4]] as an independent generator. Duodecim is a low-accuracy temperament that further maps 7/4 to 10\12 and uses 11/8 as an independent generator.		It is the 24-note mos scale of the [[compton]], [[catler]], and [[duodecim]] temperaments of the [[compton family]], which divide the octave into 12 parts. As such, this mos scale can be considered to be 2 rings of [[12edo]], and can be replicated with two 12edo instruments detuned from each other by a fixed amount. All of these temperaments map [[3/2]] to 7 steps of 12edo, thus tempering out the [[Pythagorean comma]]. Compton uses the [[3-limit]] of 12edo, and adds an independent [[generator]] for [[5/4]] to improve the accuracy of [[5-limit]] harmony. Catler additionally maps 5/4 to 4\12, thus preserving the 5-limit of 12edo, and adds [[7/4]] as an independent generator. Duodecim is a low-accuracy temperament that further maps 7/4 to 10\12, thus keeping the full [[7-limit]] of 12edo, and uses [[11/8]] as an independent generator.

	Using the [[TAMNAMS extension]], it can be named '''dodecawood''', since it has 12 periods per octave, each with one large step and one small step.		Using the [[TAMNAMS extension]], it can be named '''dodecawood''', since it has 12 periods per octave, each with one large step and one small step.

Overthink: low accuracy

2026-05-24T19:10:50Z

low accuracy

← Older revision		Revision as of 19:10, 24 May 2026
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	{{MOS intro}}		{{MOS intro}}

	It is the 24-note mos scale of the [[compton]], [[catler]], and [[duodecim]] temperaments of the [[compton family]], which divide the octave into 12 parts. As such, this mos scale can be considered to be 2 rings of [[12edo]], and can be replicated with two 12edo instruments detuned from each other by a fixed amount. Each of these temperaments maps [[3/2]] to 7 steps of 12edo, tempering out the [[Pythagorean comma]]. Compton uses the [[3-limit]] of 12edo and adds an independent [[generator]] for [[5/4]]. Catler additionally maps 5/4 to 4\12, and has [[7/4]] as an independent generator. Duodecim further maps 7/4 to 10\12 and uses 11/8 as an independent generator.		It is the 24-note mos scale of the [[compton]], [[catler]], and [[duodecim]] temperaments of the [[compton family]], which divide the octave into 12 parts. As such, this mos scale can be considered to be 2 rings of [[12edo]], and can be replicated with two 12edo instruments detuned from each other by a fixed amount. Each of these temperaments maps [[3/2]] to 7 steps of 12edo, tempering out the [[Pythagorean comma]]. Compton uses the [[3-limit]] of 12edo and adds an independent [[generator]] for [[5/4]]. Catler additionally maps 5/4 to 4\12, and has [[7/4]] as an independent generator. Duodecim is a low-accuracy temperament that further maps 7/4 to 10\12 and uses 11/8 as an independent generator.

	Using the [[TAMNAMS extension]], it can be named '''dodecawood''', since it has 12 periods per octave, each with one large step and one small step.		Using the [[TAMNAMS extension]], it can be named '''dodecawood''', since it has 12 periods per octave, each with one large step and one small step.

Overthink: Create page

2026-05-24T19:09:44Z

Create page

New page

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

It is the 24-note mos scale of the [[compton]], [[catler]], and [[duodecim]] temperaments of the [[compton family]], which divide the octave into 12 parts. As such, this mos scale can be considered to be 2 rings of [[12edo]], and can be replicated with two 12edo instruments detuned from each other by a fixed amount. Each of these temperaments maps [[3/2]] to 7 steps of 12edo, tempering out the [[Pythagorean comma]]. Compton uses the [[3-limit]] of 12edo and adds an independent [[generator]] for [[5/4]]. Catler additionally maps 5/4 to 4\12, and has [[7/4]] as an independent generator. Duodecim further maps 7/4 to 10\12 and uses 11/8 as an independent generator.

Using the [[TAMNAMS extension]], it can be named '''dodecawood''', since it has 12 periods per octave, each with one large step and one small step.

== Scale properties ==
{{TAMNAMS use}}

=== Intervals ===
{{MOS intervals}}

=== Generator chain ===
{{MOS genchain}}

=== Modes ===
{{MOS mode degrees}}

== Scale tree ==
{{MOS tuning spectrum
| 3/2 = [[Duodecim]]
| 3/1 = [[Catler]]
| 5/1 = [[Compton]]
}}