10edo - Revision history

MisterShafXen: Fixed typo

2026-03-12T18:04:31Z

Fixed typo

← Older revision		Revision as of 18:04, 12 March 2026
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	== Theory ==		== Theory ==
	10edo contains all the intervals of [[5edo]], but also adds another copy of it separated by 120 [[cent]]s. The new intervals have sizes of 120{{c}}, 360{{c}}, 600{{c}}, 840{{c}}, and 1080{{c}}. The 120{{c}} interval can be treated a small neutral second or large minor 2nd, and its inversion a large neutral seventh or small major 7th, with the 120{{c}} and 1080{{c}} intervals being close (about 0.6{{c}} off) to [[15/14]] and [[28/15]] respectively. The 360{{c}} interval is a large neutral third, being about 0.5{{c}} sharp of [[16/13]], with its inversion being equally close to [[13/8]]. Finally, the 600{{c}} ~~interva~~ is the tritone that appears in every even-numbered edo, including [[12edo]].		10edo contains all the intervals of [[5edo]], but also adds another copy of it separated by 120 [[cent]]s. The new intervals have sizes of 120{{c}}, 360{{c}}, 600{{c}}, 840{{c}}, and 1080{{c}}. The 120{{c}} interval can be treated a small neutral second or large minor 2nd, and its inversion a large neutral seventh or small major 7th, with the 120{{c}} and 1080{{c}} intervals being close (about 0.6{{c}} off) to [[15/14]] and [[28/15]] respectively. The 360{{c}} interval is a large neutral third, being about 0.5{{c}} sharp of [[16/13]], with its inversion being equally close to [[13/8]]. Finally, the 600{{c}} interval is the tritone that appears in every even-numbered edo, including [[12edo]].

	Taking the the 360{{c}} large neutral third as a [[generator]] produces a heptatonic [[MOS scale\|moment of symmetry scale]] with step sizes {{nowrap\|2 1 1 2 1 2 1}} (pattern [[3L 4s]], or "mosh"), which is the most [[Diatonic scale\|diatonic]]-like scale in 10edo excluding the 5edo [[collapsed]] diatonic scale, and can be seen as a [[neutralized]] diatonic scale.		Taking the the 360{{c}} large neutral third as a [[generator]] produces a heptatonic [[MOS scale\|moment of symmetry scale]] with step sizes {{nowrap\|2 1 1 2 1 2 1}} (pattern [[3L 4s]], or "mosh"), which is the most [[Diatonic scale\|diatonic]]-like scale in 10edo excluding the 5edo [[collapsed]] diatonic scale, and can be seen as a [[neutralized]] diatonic scale.

Squib: /* Theory */

2026-02-13T15:43:21Z

Theory

← Older revision		Revision as of 15:43, 13 February 2026
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	Since the neutral third is very close to 16/13, 10edo is usable as a 2.3.5.7.13 temperament, which includes 5edo's representation of 2.3.7; however, it is not without high damage. For one, all of [[9/7]], [[13/10]], [[21/16]], and [[4/3]] are equated to a flat fourth (or an extremely sharp supermajor third), tempering out [[28/27]], [[40/39]], [[49/48]], [[64/63]], [[91/90]], and [[105/104]]. Also, 5-limit major and minor thirds are equated as mentioned before (tempering out 25/24), and the third is also equated to 16/13, tempering out 40/39 and [[65/64]]. Additionally, 5-limit augmented and diminished intervals are equated with nearby septimal intervals (tempering out [[225/224]]), and since 3/2 is tuned sharp and 5/4 is tuned flat, the syntonic comma is exaggerated to a full step, or 120{{c}}. More accurately, it can be seen as a 2.7.13.15 temperament, restricting the 3.5 subgroup to powers of 15.		Since the neutral third is very close to 16/13, 10edo is usable as a 2.3.5.7.13 temperament, which includes 5edo's representation of 2.3.7; however, it is not without high damage. For one, all of [[9/7]], [[13/10]], [[21/16]], and [[4/3]] are equated to a flat fourth (or an extremely sharp supermajor third), tempering out [[28/27]], [[40/39]], [[49/48]], [[64/63]], [[91/90]], and [[105/104]]. Also, 5-limit major and minor thirds are equated as mentioned before (tempering out 25/24), and the third is also equated to 16/13, tempering out 40/39 and [[65/64]]. Additionally, 5-limit augmented and diminished intervals are equated with nearby septimal intervals (tempering out [[225/224]]), and since 3/2 is tuned sharp and 5/4 is tuned flat, the syntonic comma is exaggerated to a full step, or 120{{c}}. More accurately, it can be seen as a 2.7.13.15 temperament, restricting the 3.5 subgroup to powers of 15.

	By treating 360{{c}} as 11/9, we arrive at 11/8 = 600{{c}} (tempering out [[144/143]]), which allows 10edo to be treated as a full [[13-limit]] temperament. However, it is more accurate as a no-11 system.		By treating 360{{c}} as 11/9, we arrive at 11/8 = 600{{c}} (tempering out [[144/143]] and [[243/242]]), which allows 10edo to be treated as a full [[13-limit]] temperament. However, it is more accurate as a no-11 system.

	10edo is a [[zeta peak edo]], due to its relatively decent tunings of the harmonics 2, 3, 5, 7, 13, and 17. 10edo is also the smallest edo that maintains [[minimal consistent EDOs\|25% or lower relative error]] on all of the first eight harmonics of the [[harmonic series]].		10edo is a [[zeta peak edo]], due to its relatively decent tunings of the harmonics 2, 3, 5, 7, 13, and 17. 10edo is also the smallest edo that maintains [[minimal consistent EDOs\|25% or lower relative error]] on all of the first eight harmonics of the [[harmonic series]].

Overthink: Add references section

2026-02-13T01:51:43Z

Add references section

← Older revision		Revision as of 01:51, 13 February 2026
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	{{Main\| 10edo/Music }}		{{Main\| 10edo/Music }}
	{{Catrel\|10edo tracks}}		{{Catrel\|10edo tracks}}

			== References ==
			<references/>

	[[Category:10-tone scales]]		[[Category:10-tone scales]]

Overthink: /* Rank-2 temperaments */ these can be tuned much better in other systems

2026-02-13T01:50:54Z

Rank-2 temperaments: these can be tuned much better in other systems

← Older revision		Revision as of 01:50, 13 February 2026
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	\| 1		\| 1
	\| 3\10		\| 3\10
	\| [[Dicot]] / [[beatles]] / [[neutral]]		\| [[Dicot]] / [[beatles]] (out-of-tune) / [[neutral]] (out-of-tune)
	\|-		\|-
	\| 2		\| 2

Overthink: /* Theory */ Add archetype paragraph; overall rewrite

2026-02-13T01:49:07Z

Theory: Add archetype paragraph; overall rewrite

← Older revision		Revision as of 01:49, 13 February 2026
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	== Theory ==		== Theory ==
	10edo ~~can be thought of as two circles~~ of [[5edo]] separated by 120 ~~cents~~. ~~It adds to 5edo~~ a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th)~~; an excellent approximation~~ of [[13/8]] ~~and~~ its inversion [[16/13]]~~; and~~ the ~~familiar~~ 600~~-cent~~ tritone that appears in every even-numbered edo.		10edo contains all the intervals of [[5edo]], but also adds another copy of it separated by 120 [[cent]]s. The new intervals have sizes of 120{{c}}, 360{{c}}, 600{{c}}, 840{{c}}, and 1080{{c}}. The 120{{c}} interval can be treated a small neutral second or large minor 2nd, and its inversion a large neutral seventh or small major 7th, with the 120{{c}} and 1080{{c}} intervals being close (about 0.6{{c}} off) to [[15/14]] and [[28/15]] respectively. The 360{{c}} interval is a large neutral third, being about 0.5{{c}} sharp of [[16/13]], with its inversion being equally close to [[13/8]]. Finally, the 600{{c}} interva is the tritone that appears in every even-numbered edo, including [[12edo]].

	Taking the the 360{{c}} large neutral third as a [[generator]] produces a heptatonic [[MOS scale\|moment of symmetry scale]] ~~of the form~~ {{nowrap\|1 2 1 2 1 2 1}} ([[3L 4s]], or "mosh"), which is the most [[Diatonic scale\|diatonic]]-like scale in 10edo excluding the 5edo ~~degenerate~~ diatonic scale, and can be seen as a neutralized diatonic scale.		Taking the the 360{{c}} large neutral third as a [[generator]] produces a heptatonic [[MOS scale\|moment of symmetry scale]] with step sizes {{nowrap\|2 1 1 2 1 2 1}} (pattern [[3L 4s]], or "mosh"), which is the most [[Diatonic scale\|diatonic]]-like scale in 10edo excluding the 5edo [[collapsed]] diatonic scale, and can be seen as a [[neutralized]] diatonic scale.

	It shares [[5edo]]'s approximation quality in the 2.3.7 subgroup (though the detuned fifth could be seen as a bigger problem with the more fine division of steps), ~~but expands on its~~ accuracy in the full 7-limit, by including a better approximation of 5/4 at 360 ~~cents~~, resulting in the better tuning of various intervals including 5, such as [[16/15]] and [[7/5]]. However, [[6/5]] is ~~very poorly approximated~~, ~~over 40 cents~~ sharp, ~~due to to the errors on 3~~/2 and ~~5/4 compounding. In fact, it is mapped to the exact same interval as 5/4, which results~~ in the [[dicot]] exotemperament. So, if one wishes to represent JI with 10edo, it is best to use 5 carefully or not at all.		It shares [[5edo]]'s approximation quality in the [[2.3.7 subgroup]], though the detuned fifth could be seen as a bigger problem with the more fine division of steps. Compared to 5edo, 10edo attains more accuracy in the full [[7-limit]], by including a better approximation of [[5/4]] at 360{{c}}, resulting in the better tuning of various intervals including 5, such as [[16/15]] and [[7/5]]. However, the approximation to 5/4 is still over 25{{c}} flat, and this interval is also equated with [[6/5]] (which is even more inaccurate, at 44{{c}} sharp), tempering out [[25/24]] and resulting in the [[dicot]] exotemperament. Thus, if one wishes to represent JI with 10edo, it is best to use prime [[5/1\|5]] carefully or not at all.

	~~This third also serves~~ as ~~an extremely accurate approximation of~~ [[16/13]], ~~making 10edo usable as~~ a ~~2.3.5~~.7~~.13 temperament, in which, alongside 5edo's temperaments in 2.3.~~7~~, septimal supermajor intervals are equated with tridecimal ultramajor intervals (tempering out~~ [[~~105~~/~~104~~]]), and 5~~-limit~~ major and minor ~~thirds are equated~~ as ~~mentioned before (tempering~~ out [[25/24]]). ~~Additionally, 5~~-~~limit augmented and diminished intervals are equated with nearby septimal intervals (tempering~~ out [[~~225/224~~]]), and ~~from this it can be seen that the syntonic comma is mapped to 120 cents~~. ~~More accurately~~, ~~it can be seen as a 2~~.7.13.~~15 temperament, restricting the 3~~.~~5 subgroup to powers of 15~~.		Even if 10edo isn't directly used to represent JI, it could still serve as a structural archetype for the 7-limit. The fact that 25/24 is tempered out means that the 5-limit major triad [[4:5:6]] and minor triad [[10:12:15\|1/(6:5:4)]] are mapped to the same number of scale steps in the 10-form, a feature shared with [[7edo]] and the [[heptatonic]] system used in western music. 10edo additionally sends [[49/48]] to the unison, meaning the 7-limit triad [[4:6:7]] and its inverse [[14:21:24\|1/(12:8:7)]] are the same number of scale steps in a decatonic system as well, and therefore also the [[4:5:6:7]] major and [[70:84:105:120\|1/(12:10:8:7)]] minor tetrads as well. Tempering out 25/24 and 49/48 leads to the [[decimal]] exotemperament (which is named after 10edo). A more accurate temperament based off of the 10-form that doesn't temper out 25/24 or 49/48 is [[pajara]], which shares many desireable properties with diatonic<ref>Erlich, Paul. "Tuning, Tonality and 22-Tone Temperament." Xenharmonicon 17, 1998. [http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf http://sethares.engr.wisc.edu/paperspdf/Erlich-22.pdf]</ref>.

	~~By treating 360{{c}}~~ as 11/9, ~~we arrive at 11~~/~~8 = 600{{c}}~~ (tempering out [[~~144~~/~~143~~]]), ~~which allows 10edo~~ to ~~be treated as a full~~ [[13-limit]] ~~temperament~~. ~~However~~, it ~~is more accurate to~~ the ~~no-11~~ subgroup.		Since the neutral third is very close to 16/13, 10edo is usable as a 2.3.5.7.13 temperament, which includes 5edo's representation of 2.3.7; however, it is not without high damage. For one, all of [[9/7]], [[13/10]], [[21/16]], and [[4/3]] are equated to a flat fourth (or an extremely sharp supermajor third), tempering out [[28/27]], [[40/39]], [[49/48]], [[64/63]], [[91/90]], and [[105/104]]. Also, 5-limit major and minor thirds are equated as mentioned before (tempering out 25/24), and the third is also equated to 16/13, tempering out 40/39 and [[65/64]]. Additionally, 5-limit augmented and diminished intervals are equated with nearby septimal intervals (tempering out [[225/224]]), and since 3/2 is tuned sharp and 5/4 is tuned flat, the syntonic comma is exaggerated to a full step, or 120{{c}}. More accurately, it can be seen as a 2.7.13.15 temperament, restricting the 3.5 subgroup to powers of 15.

	10edo is a [[zeta peak edo]], due to its decent ~~tuning~~ of the harmonics 2, 3, 5, 7, 13, and 17. 10edo is also the smallest edo that maintains [[minimal consistent EDOs\|25% or lower relative error]] on all of the first eight harmonics of the [[harmonic series]].		By treating 360{{c}} as 11/9, we arrive at 11/8 = 600{{c}} (tempering out [[144/143]]), which allows 10edo to be treated as a full [[13-limit]] temperament. However, it is more accurate as a no-11 system.

			10edo is a [[zeta peak edo]], due to its relatively decent tunings of the harmonics 2, 3, 5, 7, 13, and 17. 10edo is also the smallest edo that maintains [[minimal consistent EDOs\|25% or lower relative error]] on all of the first eight harmonics of the [[harmonic series]].

	Thanks to its sevenths, 10edo is an ideal tuning for its size for [[metallic harmony]].		Thanks to its sevenths, 10edo is an ideal tuning for its size for [[metallic harmony]].

BudjarnLambeth: Fix ref error

2025-10-15T09:19:56Z

Fix ref error

← Older revision		Revision as of 09:19, 15 October 2025
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	\| Island comma, parizeksma		\| Island comma, parizeksma
	\|}		\|}
			<references group="note"/>

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===

Lucius Chiaraviglio: Move notes to appear under the corresponding tables

2025-10-09T10:22:34Z

Move notes to appear under the corresponding tables

← Older revision		Revision as of 10:22, 9 October 2025
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	\| [[File:0-1200 octave.mp3\|frameless]]		\| [[File:0-1200 octave.mp3\|frameless]]
	\|}		\|}
			<references group="note" />

	== Notation ==		== Notation ==
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	{{Main\| 10edo/Music }}		{{Main\| 10edo/Music }}
	{{Catrel\|10edo tracks}}		{{Catrel\|10edo tracks}}

	~~== Notes ==~~
	~~<references group="note" />~~

	[[Category:10-tone scales]]		[[Category:10-tone scales]]

BudjarnLambeth: Temporary until full version is done

2025-09-16T08:21:27Z

Temporary until full version is done

← Older revision		Revision as of 08:21, 16 September 2025
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	\| [[Blackwood]]		\| [[Blackwood]]
	\|}		\|}

			== Octave stretch or compression ==
			If one wishes to use 10edo as a no-5s, 19-or-lower-limit tuning, then it benefits from [[octave shrinking]]. [[zpi\|26zpi]] and [[36ed12]] are compressed-octave versions of 10edo.

			If one wishes to use 10edo as a no-3s, 13-or-lower-limit tuning, then it benefits from [[octave stretching]]. [[ed7\|28ed7]] is a stretched version of 10edo.

	== Scales ==		== Scales ==

FloraC: /* Theory */ duh

2025-09-11T13:27:26Z

Theory: duh

← Older revision		Revision as of 13:27, 11 September 2025
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	10edo can be thought of as two circles of [[5edo]] separated by 120 cents. It adds to 5edo a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of [[13/8]] and its inversion [[16/13]]; and the familiar 600-cent tritone that appears in every even-numbered edo.		10edo can be thought of as two circles of [[5edo]] separated by 120 cents. It adds to 5edo a small neutral second (or large minor 2nd) and its inversion a large neutral seventh (or small major 7th); an excellent approximation of [[13/8]] and its inversion [[16/13]]; and the familiar 600-cent tritone that appears in every even-numbered edo.

	Taking the the 360{{c}} large neutral third as a [[generator]] produces a heptatonic [[MOS ~~scales~~\|moment of symmetry scale]] of the form {{nowrap\|1 2 1 2 1 2 1}} ([[3L 4s]], or "mosh"), which is the most [[Diatonic scale\|diatonic]]-like scale in 10edo excluding the 5edo degenerate diatonic scale, and can be seen as a neutralized diatonic scale.		Taking the the 360{{c}} large neutral third as a [[generator]] produces a heptatonic [[MOS scale\|moment of symmetry scale]] of the form {{nowrap\|1 2 1 2 1 2 1}} ([[3L 4s]], or "mosh"), which is the most [[Diatonic scale\|diatonic]]-like scale in 10edo excluding the 5edo degenerate diatonic scale, and can be seen as a neutralized diatonic scale.

	It shares [[5edo]]'s approximation quality in the 2.3.7 subgroup (though the detuned fifth could be seen as a bigger problem with the more fine division of steps), but expands on its accuracy in the full 7-limit, by including a better approximation of 5/4 at 360 cents, resulting in the better tuning of various intervals including 5, such as [[16/15]] and [[7/5]]. However, [[6/5]] is very poorly approximated, over 40 cents sharp, due to to the errors on 3/2 and 5/4 compounding. In fact, it is mapped to the exact same interval as 5/4, which results in the [[dicot]] exotemperament. So, if one wishes to represent JI with 10edo, it is best to use 5 carefully or not at all.		It shares [[5edo]]'s approximation quality in the 2.3.7 subgroup (though the detuned fifth could be seen as a bigger problem with the more fine division of steps), but expands on its accuracy in the full 7-limit, by including a better approximation of 5/4 at 360 cents, resulting in the better tuning of various intervals including 5, such as [[16/15]] and [[7/5]]. However, [[6/5]] is very poorly approximated, over 40 cents sharp, due to to the errors on 3/2 and 5/4 compounding. In fact, it is mapped to the exact same interval as 5/4, which results in the [[dicot]] exotemperament. So, if one wishes to represent JI with 10edo, it is best to use 5 carefully or not at all.
Line 17:		Line 17:
	This third also serves as an extremely accurate approximation of [[16/13]], making 10edo usable as a 2.3.5.7.13 temperament, in which, alongside 5edo's temperaments in 2.3.7, septimal supermajor intervals are equated with tridecimal ultramajor intervals (tempering out [[105/104]]), and 5-limit major and minor thirds are equated as mentioned before (tempering out [[25/24]]). Additionally, 5-limit augmented and diminished intervals are equated with nearby septimal intervals (tempering out [[225/224]]), and from this it can be seen that the syntonic comma is mapped to 120 cents. More accurately, it can be seen as a 2.7.13.15 temperament, restricting the 3.5 subgroup to powers of 15.		This third also serves as an extremely accurate approximation of [[16/13]], making 10edo usable as a 2.3.5.7.13 temperament, in which, alongside 5edo's temperaments in 2.3.7, septimal supermajor intervals are equated with tridecimal ultramajor intervals (tempering out [[105/104]]), and 5-limit major and minor thirds are equated as mentioned before (tempering out [[25/24]]). Additionally, 5-limit augmented and diminished intervals are equated with nearby septimal intervals (tempering out [[225/224]]), and from this it can be seen that the syntonic comma is mapped to 120 cents. More accurately, it can be seen as a 2.7.13.15 temperament, restricting the 3.5 subgroup to powers of 15.

	By treating ~~360c~~ as 11/9, we arrive at 11/8 = ~~600c~~ (tempering out [[144/143]]), which allows 10edo to be treated as a full [[13-limit]] temperament. However, it is more accurate to the no-11 subgroup.		By treating 360{{c}} as 11/9, we arrive at 11/8 = 600{{c}} (tempering out [[144/143]]), which allows 10edo to be treated as a full [[13-limit]] temperament. However, it is more accurate to the no-11 subgroup.

	10edo is a [[~~The Riemann zeta function and tuning #Zeta edo lists\|~~zeta peak edo]], due to its decent tuning of the harmonics 2, 3, 5, 7, 13, and 17. 10edo is also the smallest edo that maintains [[minimal consistent EDOs\|25% or lower relative error]] on all of the first eight harmonics of the [[harmonic series]].		10edo is a [[zeta peak edo]], due to its decent tuning of the harmonics 2, 3, 5, 7, 13, and 17. 10edo is also the smallest edo that maintains [[minimal consistent EDOs\|25% or lower relative error]] on all of the first eight harmonics of the [[harmonic series]].

	Thanks to its sevenths, 10edo is an ideal tuning for its size for [[metallic harmony]].		Thanks to its sevenths, 10edo is an ideal tuning for its size for [[metallic harmony]].

FloraC: Septimal blackwood is now canon

2025-09-11T13:26:03Z

Septimal blackwood is now canon

← Older revision		Revision as of 13:26, 11 September 2025
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	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br />8ve stretch (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning error		! colspan="2" \| Tuning error
	\|-		\|-
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	\| 2.3.5		\| 2.3.5
	\| 25/24, 256/243		\| 25/24, 256/243
	\| {{~~mapping~~\| 10 16 23 }}		\| {{Mapping\| 10 16 23 }}
	\| -0.089		\| -0.089
	\| 9.27		\| 9.27
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	\| 2.3.5.7		\| 2.3.5.7
	\| 25/24, 28/27, 49/48		\| 25/24, 28/27, 49/48
	\| {{~~mapping~~\| 10 16 23 28 }}		\| {{Mapping\| 10 16 23 28 }}
	\| +0.718		\| +0.718
	\| 8.15		\| 8.15
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	\| 2.3.5.7.13		\| 2.3.5.7.13
	\| 25/24, 28/27, 40/39, 49/48		\| 25/24, 28/27, 40/39, 49/48
	\| {{~~mapping~~\| 10 16 23 28 37 }}		\| {{Mapping\| 10 16 23 28 37 }}
	\| +0.603		\| +0.603
	\| 7.30		\| 7.30
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	{\| class="commatable wikitable center-1 center-2 right-4 center-5"		{\| class="commatable wikitable center-1 center-2 right-4 center-5"
	\|-		\|-
	! [[Harmonic limit\|Prime<br />limit]]		! [[Harmonic limit\|Prime<br>limit]]
	! [[Ratio]]<ref group="note">{{rd}}</ref>		! [[Ratio]]<ref group="note">{{rd}}</ref>
	! [[Monzo]]		! [[Monzo]]
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	{\| class="wikitable center-1 center-2"		{\| class="wikitable center-1 center-2"
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator		! Generator
	! Temperament(s)		! Temperament(s)
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	\| 5		\| 5
	\| 1\10		\| 1\10
	\| [[Blackwood~~]] / [[blacksmith~~]]		\| [[Blackwood]]
	\|}		\|}

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	=== Other scales ===		=== Other scales ===
	* [[~~The~~ Pinetone ~~System~~#Pinetone pentatonic\|Pinetone major pentatonic]] (subset of Dicot[7]): 2 1 3 1 3		* [[Pinetone #Pinetone pentatonic\|Pinetone major pentatonic]] (subset of Dicot[7]): 2 1 3 1 3
	* [[~~The~~ Pinetone ~~System~~#Pinetone pentatonic\|Pinetone minor pentatonic]] (subset of Dicot[7]): 3 1 2 3 1		* [[Pinetone #Pinetone pentatonic\|Pinetone minor pentatonic]] (subset of Dicot[7]): 3 1 2 3 1
	* [[Marvel hexatonic\|Marvel augmented hexatonic]] (subset of Dicot[7]): 2 1 3 1 2 1		* [[Marvel hexatonic\|Marvel augmented hexatonic]] (subset of Dicot[7]): 2 1 3 1 2 1
	* Marvel double harmonic hexatonic (subset of Dicot[7]): 1 2 1 3 2 1, 1 2 3 1 2 1		* Marvel double harmonic hexatonic (subset of Dicot[7]): 1 2 1 3 2 1, 1 2 3 1 2 1