Aberrisma - Revision history

Vector at 02:31, 7 June 2026

2026-06-07T02:31:14Z

← Older revision		Revision as of 02:31, 7 June 2026
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	An '''aberrisma''' is an interval between roughly 20 and 55 cents representing some comma as an additional smaller type of melodic step (that is, a [[diesis]]). The aberrisma is used as one of the parameters in constructing an aberrismic scale, a type of ternary scale. For example, blackdye is a 10-note aberrismic superset of the 7-note nicetone, but with a more distinctive set of three step sizes and added opportunities to avoid pythagorean and wolf intervals.		An '''aberrisma''' is an interval between roughly 20 and 55 cents representing some comma as an additional smaller type of melodic step (that is, a [[diesis]]). The aberrisma is used as one of the parameters in constructing an aberrismic scale, a type of ternary scale. For example, blackdye is a 10-note aberrismic superset of the 7-note nicetone, but with a more distinctive set of three step sizes and added opportunities to avoid pythagorean and wolf intervals.

			Aberrismas may also appear in MOS scales, such as garibaldi[17].

	'''Aberrismic theory''' is the subset of microtonal theory pioneered by [[User:Ground\|Ground]] and [[User:Inthar\|Inthar]] that deals with aberrismas.		'''Aberrismic theory''' is the subset of microtonal theory pioneered by [[User:Ground\|Ground]] and [[User:Inthar\|Inthar]] that deals with aberrismas.

Inthar: /* External links */

2026-06-06T22:56:03Z

External links

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	== External links ==		== External links ==
	* [https://turbofishcrow.github.io/~~ternary Ternary~~: aberrismic-focused ternary scale analysis]		* [https://turbofishcrow.github.io/tern Tern: aberrismic-focused ternary scale analysis]
	{{cat\|		{{cat\|
	Terms		Terms

Overthink: /* Example: The emergence of blackdye */ capitalize temperament name

2026-05-25T23:50:58Z

Example: The emergence of blackdye: capitalize temperament name

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	The Zarlino diatonic is chiral - there are two different, equally valid second degrees of the Ionian mode. Both are useful, as the sharp one forms a perfect fifth with the fifth degree but a wolf fifth with the sixth degree, and the flat one forms a perfect fifth with the sixth degree but a wolf fifth with the fifth degree.		The Zarlino diatonic is chiral - there are two different, equally valid second degrees of the Ionian mode. Both are useful, as the sharp one forms a perfect fifth with the fifth degree but a wolf fifth with the sixth degree, and the flat one forms a perfect fifth with the sixth degree but a wolf fifth with the fifth degree.
	[[File:Blackdye.png\|thumb\|510x510px\|The construction of blackdye from Zarlino diatonic]]		[[File:Blackdye.png\|thumb\|510x510px\|The construction of blackdye from Zarlino diatonic]]
	One way to make it achiral is to temper out 81/80, the difference between these two steps, resulting in [[~~meantone~~]] diatonic; intuitively this requires flattening the fifth and sharpening the sixth somewhat. However, an alternative way, if you wish to observe 81/80 or to use just intonation, is to include both varieties of whole tone over the unison, treating 81/80 as a melodic step between them. This can be thought of as dividing up a 9/8 into a 10/9 and an 81/80. It is then reasonable to extend this action to all instances of 9/8 in the scale (as, for instance, the Didymic diatonic has 27/16 as opposed to 5/3). The result is a 10-note ternary scale called '''blackdye'''.		One way to make it achiral is to temper out 81/80, the difference between these two steps, resulting in [[Meantone]] diatonic; intuitively this requires flattening the fifth and sharpening the sixth somewhat. However, an alternative way, if you wish to observe 81/80 or to use just intonation, is to include both varieties of whole tone over the unison, treating 81/80 as a melodic step between them. This can be thought of as dividing up a 9/8 into a 10/9 and an 81/80. It is then reasonable to extend this action to all instances of 9/8 in the scale (as, for instance, the Didymic diatonic has 27/16 as opposed to 5/3). The result is a 10-note ternary scale called '''blackdye'''.

	== The "why" of aberrismic theory ==		== The "why" of aberrismic theory ==

Inthar: /* Compositional examples */

2026-04-23T02:16:34Z

Compositional examples

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	* The Art of It makes almost exclusive use of 31edo diasem: [[File:A New Dusk-02 The Art of It.mp3]]		* The Art of It makes almost exclusive use of 31edo diasem: [[File:A New Dusk-02 The Art of It.mp3]]
			* A fugue using aberrismic scales: [[File:Inthar - Fugue in 32edo and 33edo.mp3]]
	* A 34edo blackdye fugue exposition: [[File:Blackdye-fugue-expo.mp3]]		* A 34edo blackdye fugue exposition: [[File:Blackdye-fugue-expo.mp3]]

Inthar: /* List of aberrismic scales */

2026-04-16T23:37:59Z

List of aberrismic scales

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	* {{Adv\|"GS(...)[n]" is [[generator sequence]] notation.}}		* {{Adv\|"GS(...)[n]" is [[generator sequence]] notation.}}
	* {{adv\|"subst ax(bycz)" denotes [[MOS substitution]].}}		* {{adv\|"subst ax(bycz)" denotes [[MOS substitution]].}}
	* {{adv\|"Almost" a cross-set means that one or two notes ~~are~~ missing from the full cross-set and one note may have been added. Exact cross-sets are italicized.}}		* {{adv\|"Almost" a cross-set means that one or two notes may be missing from the full cross-set and one note may have been added. Exact cross-sets are italicized.}}
	* {{adv\|Under "Patterns", "C" is [[achiral]], and "R" and "L" denote two [[chiral]]ities of a chiral pair.}}		* {{adv\|Under "Patterns", "C" is [[achiral]], and "R" and "L" denote two [[chiral]]ities of a chiral pair.}}
	=== Quasi-diatonic aberrismic scales ===		=== Quasi-diatonic aberrismic scales ===

Inthar: /* List of aberrismic scales */

2026-04-16T12:36:35Z

List of aberrismic scales

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	== List of aberrismic scales ==		== List of aberrismic scales ==
	* {{Adv\|"GS(...)[n]" is [[generator sequence]] notation.}}		* {{Adv\|"GS(...)[n]" is [[generator sequence]] notation.}}
	* {{Adv\|The word "by" denotes the [[cross-set]].}}
	* {{adv\|"subst ax(bycz)" denotes [[MOS substitution]].}}		* {{adv\|"subst ax(bycz)" denotes [[MOS substitution]].}}
	* {{adv\|"Almost" a cross-set means that one or two notes are missing from the full cross-set and one note may have been added. Exact cross-sets are italicized.}}		* {{adv\|"Almost" a cross-set means that one or two notes are missing from the full cross-set and one note may have been added. Exact cross-sets are italicized.}}

Inthar: /* Other aberrismic scales */

2026-04-16T09:00:12Z

Other aberrismic scales

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	!\|Pattern(s)		!\|Pattern(s)
	!\|Possible JI/[[erac]] interp.		!\|Possible JI/[[erac]] interp.
	!\|{{adv\|Almost a [[cross-set]] of<br/>(interpreted)}}		!\|{{adv\|Almost a [[cross-set]] of...<br/>(interpreted)}}
	!\|Notes		!\|Notes
	\|-		\|-

Inthar: /* Quasi-diatonic aberrismic scales */

2026-04-16T08:34:04Z

Quasi-diatonic aberrismic scales

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	\|\|LsLsLsmsLsLsms		\|\|LsLsLsmsLsLsms
	\|\|5120/5103-tempered 2.3.5.7<br/>[L, m, s] = [10/9, 28/27, 81/80]		\|\|5120/5103-tempered 2.3.5.7<br/>[L, m, s] = [10/9, 28/27, 81/80]
	\|\|{{adv\|''GS(3/2)[7] by 81/80''}}		\|\|{{adv\|''GS(3/2)[7] and 81/80''}}
	\|\|Two interleaved diatonics		\|\|Two interleaved diatonics
	\|}		\|}

Inthar: /* Other aberrismic scales */

2026-04-16T08:21:03Z

Other aberrismic scales

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	\|\|LmLsLsLmLsLsLs		\|\|LmLsLsLmLsLsLs
	\|\|2.x<3.5.7.11.13[37edo] (4:2:1)		\|\|2.x<3.5.7.11.13[37edo] (4:2:1)
	\|\|{{adv\|GS(<<3/2)[7] by 14/13}}		\|\|{{adv\|''GS(<<3/2)[7] and 14/13''}}
	\|\|An interleaving of two antidiatonic scales.		\|\|An interleaving of two antidiatonic scales.
	\|-		\|-

Inthar: /* List of aberrismic scales */

2026-04-16T08:20:22Z

List of aberrismic scales

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	* {{Adv\|The word "by" denotes the [[cross-set]].}}		* {{Adv\|The word "by" denotes the [[cross-set]].}}
	* {{adv\|"subst ax(bycz)" denotes [[MOS substitution]].}}		* {{adv\|"subst ax(bycz)" denotes [[MOS substitution]].}}
	* {{adv\|~~≈ denotes~~ that one or two notes are missing from the full cross-set and one note may have been added.}}		* {{adv\|"Almost" a cross-set means that one or two notes are missing from the full cross-set and one note may have been added. Exact cross-sets are italicized.}}
	* {{adv\|Under "Patterns", "C" is [[achiral]], and "R" and "L" denote two [[chiral]]ities of a chiral pair.}}		* {{adv\|Under "Patterns", "C" is [[achiral]], and "R" and "L" denote two [[chiral]]ities of a chiral pair.}}
	=== Quasi-diatonic aberrismic scales ===		=== Quasi-diatonic aberrismic scales ===
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	!\|Pattern(s)		!\|Pattern(s)
	!\|Possible JI interp.		!\|Possible JI interp.
	!\|{{adv\|~~Generator~~-~~offset structure~~<br/>(interpreted)}}		!\|{{adv\|Almost a [[cross-set]] of...<br/>(interpreted)}}
	!\|Notes		!\|Notes
	\|-		\|-
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	\|\|1sC: LLsLLmLm<br/>1sR: LLmLLmLs<br/>1sL: LLmLLsLm		\|\|1sC: LLsLLmLm<br/>1sR: LLmLLmLs<br/>1sL: LLmLLsLm
	\|\|2.3.5<br/>[L, m, s] = [10/9, 27/25, 81/80]		\|\|2.3.5<br/>[L, m, s] = [10/9, 27/25, 81/80]
	\|\|{{adv\|≈ GS(3/2)[3] by GS(10/9)[3]}}		\|\|{{adv\|GS(3/2)[3] and GS(10/9)[3]}}
	\|\|1sC has 4 fifths and 1sR/1sL have 5		\|\|1sC has 4 fifths and 1sR/1sL have 5
	\|-		\|-
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	\|\|2sR: LmLsLmLsL<br/>2sL: LsLmLsLmL		\|\|2sR: LmLsLmLsL<br/>2sL: LsLmLsLmL
	\|\|2.3.7<br/>[L, m, s] = [9/8, 28/27, 64/63]		\|\|2.3.7<br/>[L, m, s] = [9/8, 28/27, 64/63]
	\|\|{{adv\|≈ GS(3/2)[5] by 7/6}}		\|\|{{adv\|GS(3/2)[5] and 7/6}}
	\|\|Aggregate generator is 4/3, thus has fifth arcs of 5 and 4 notes respectively.		\|\|Aggregate generator is 4/3, thus has fifth arcs of 5 and 4 notes respectively.
	''See also: [[Chthonic harmony#Diasem\|Diasem]]''		''See also: [[Chthonic harmony#Diasem\|Diasem]]''
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	\|\|sLmLsLmLsL		\|\|sLmLsLmLsL
	\|\|2.3.5<br/>[L, m, s] = [10/9, 16/15, 81/80]		\|\|2.3.5<br/>[L, m, s] = [10/9, 16/15, 81/80]
	\|\|{{adv\|GS(3/2)[5] by 10/9}}		\|\|{{adv\|''GS(3/2)[5] and 10/9''}}
	\|\|Two interleaved 3-limit pentatonics		\|\|Two interleaved 3-limit pentatonics
	''See also: [[10-form#Blackdye\|Blackdye]]''		''See also: [[10-form#Blackdye\|Blackdye]]''
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	\|\|4sC: LmLsLsLmLss<br/>4sR: LsLmLsLsLms<br/>4sL: LsLsLmLsLsm		\|\|4sC: LmLsLsLmLss<br/>4sR: LsLmLsLsLms<br/>4sL: LsLsLmLsLsm
	\|\|2.3.7<br/>[L, m, s] = [9/8, 49/48, 64/63]		\|\|2.3.7<br/>[L, m, s] = [9/8, 49/48, 64/63]
	\|\|{{adv\|≈ GS(3/2)[4] by GS(8/7)[3]}}		\|\|{{adv\|GS(3/2)[4] and GS(8/7)[3]}}
	\|\|Fifth arcs with 4 notes, 4 notes, and 3 notes, with offset 8/7. Tempered to the slentonic {5L6s) MOS by [[Slendric]].<br/>{{adv\|Detempered Slendric[11] generator structure, aggregate generator is 3/2}}		\|\|Fifth arcs with 4 notes, 4 notes, and 3 notes, with offset 8/7. Tempered to the slentonic {5L6s) MOS by [[Slendric]].<br/>{{adv\|Detempered Slendric[11] generator structure, aggregate generator is 3/2}}
	\|-		\|-
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	\|\|5sC: LsLsLmsLsLsm {{adv\|{{nowrap\|(subst 2m(5L5s))}}}}<br/>5sR: LmsLsLsLmsLs<br/>5sL: LsLsLsmLsLsm		\|\|5sC: LsLsLmsLsLsm {{adv\|{{nowrap\|(subst 2m(5L5s))}}}}<br/>5sR: LmsLsLsLmsLs<br/>5sL: LsLsLsmLsLsm
	\|\|5120/5103-tempered 2.3.5.7<br/>[L, m, s] = [10/9, 256/243, 81/80]		\|\|5120/5103-tempered 2.3.5.7<br/>[L, m, s] = [10/9, 256/243, 81/80]
	\|\|{{adv\|5sC: GS(3/2)[6] by 40/27~~<br/>5sR and 5sL: superimposition of GS(3/2)[5] and GS(3/2)[7]~~}}		\|\|{{adv\|5sC: ''GS(3/2)[6] and 40/27''}}
	\|\|Fifth-generated but with a 6-step offset		\|\|Fifth-generated but with a 6-step offset
	\|-		\|-
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	\|\|LsLsLsmsLsLsms		\|\|LsLsLsmsLsLsms
	\|\|5120/5103-tempered 2.3.5.7<br/>[L, m, s] = [10/9, 28/27, 81/80]		\|\|5120/5103-tempered 2.3.5.7<br/>[L, m, s] = [10/9, 28/27, 81/80]
	\|\|{{adv\|GS(3/2)[7] by 81/80}}		\|\|{{adv\|''GS(3/2)[7] by 81/80''}}
	\|\|Two interleaved diatonics		\|\|Two interleaved diatonics
	\|}		\|}
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	!\|Pattern(s)		!\|Pattern(s)
	!\|Possible JI/[[erac]] interp.		!\|Possible JI/[[erac]] interp.
	!\|{{adv\|~~Generator~~-~~offset structure~~<br/>(interpreted)}}		!\|{{adv\|Almost a [[cross-set]] of<br/>(interpreted)}}
	!\|Notes		!\|Notes
	\|-		\|-
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	\|\|LmsLmsLsmLsmLsms		\|\|LmsLmsLsmLsmLsms
	\|\|2.3.5.7.11[41 & 46]<br/>[L, m, s] = [12/11, 33/32, 64/63]		\|\|2.3.5.7.11[41 & 46]<br/>[L, m, s] = [12/11, 33/32, 64/63]
	\|\|{{adv\|GS(8/7)[8] by 11/8}}		\|\|{{adv\|''GS(8/7)[8] and 11/8''}}
	\|\| Has two aberrisma sizes, s and m.		\|\| Has two aberrisma sizes, s and m.
	\|-		\|-
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	\|\|C: LLsmLsLms<br/>R: LmLsLmsLs<br/>L: LmLsLsmLs		\|\|C: LLsmLsLms<br/>R: LmLsLmsLs<br/>L: LmLsLsmLs
	\|\|2.5.7<br/>[L, m, s] = [28/25, 35/32, 50/49]		\|\|2.5.7<br/>[L, m, s] = [28/25, 35/32, 50/49]
	\|\|{{adv\|≈ GS(5/4)[3] by GS(7/5)[3] (exact for C)}}		\|\|{{adv\|GS(5/4)[3] and GS(7/5)[3] (exact for C)}}
	\|\|Didacus tempering makes L = m + s.		\|\|Didacus tempering makes L = m + s.
	\|-		\|-
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	\|\|LmsLmsmLsm		\|\|LmsLmsmLsm
	\|\|2.x<3.7.11.13[37edo] (5:4:2)		\|\|2.x<3.7.11.13[37edo] (5:4:2)
	\|\|{{adv\|GS(16/13)[5] by 11/8}}		\|\|{{adv\|''GS(16/13)[5] and 11/8''}}
	\|\|		\|\|
	\|-		\|-
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	\|\|C: LLmsLmLsm<br/>R: LmLmsLmLs<br/>L: LmLsLmLsm		\|\|C: LLmsLmLsm<br/>R: LmLmsLmLs<br/>L: LmLsLmLsm
	\|\|2.9.7.11.17[46edo] (8:4:1)		\|\|2.9.7.11.17[46edo] (8:4:1)
	\|\|{{adv\|≈ GS(17/14)[3] by GS(11/8)[3] (exact for C)}}		\|\|{{adv\|GS(17/14)[3] and GS(11/8)[3] (exact for C)}}
	\|\|		\|\|
	\|}		\|}

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	* {{Adv\|"GS(...)[n]" is [[generator sequence]] notation.}}		* {{Adv\|"GS(...)[n]" is [[generator sequence]] notation.}}
	* {{adv\|"subst ax(bycz)" denotes [[MOS substitution]].}}		* {{adv\|"subst ax(bycz)" denotes [[MOS substitution]].}}
	* {{adv\|"Almost" a cross-set means that one or two notes ~~are~~ missing from the full cross-set and one note may have been added. Exact cross-sets are italicized.}}		* {{adv\|"Almost" a cross-set means that one or two notes may be missing from the full cross-set and one note may have been added. Exact cross-sets are italicized.}}
	* {{adv\|Under "Patterns", "C" is [[achiral]], and "R" and "L" denote two [[chiral]]ities of a chiral pair.}}		* {{adv\|Under "Patterns", "C" is [[achiral]], and "R" and "L" denote two [[chiral]]ities of a chiral pair.}}
	=== Quasi-diatonic aberrismic scales ===		=== Quasi-diatonic aberrismic scales ===

← Older revision		Revision as of 12:36, 16 April 2026
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	== List of aberrismic scales ==		== List of aberrismic scales ==
	* {{Adv\|"GS(...)[n]" is [[generator sequence]] notation.}}		* {{Adv\|"GS(...)[n]" is [[generator sequence]] notation.}}
	* {{Adv\|The word "by" denotes the [[cross-set]].}}
	* {{adv\|"subst ax(bycz)" denotes [[MOS substitution]].}}		* {{adv\|"subst ax(bycz)" denotes [[MOS substitution]].}}
	* {{adv\|"Almost" a cross-set means that one or two notes are missing from the full cross-set and one note may have been added. Exact cross-sets are italicized.}}		* {{adv\|"Almost" a cross-set means that one or two notes are missing from the full cross-set and one note may have been added. Exact cross-sets are italicized.}}

← Older revision		Revision as of 09:00, 16 April 2026
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	!\|Pattern(s)		!\|Pattern(s)
	!\|Possible JI/[[erac]] interp.		!\|Possible JI/[[erac]] interp.
	!\|{{adv\|Almost a [[cross-set]] of<br/>(interpreted)}}		!\|{{adv\|Almost a [[cross-set]] of...<br/>(interpreted)}}
	!\|Notes		!\|Notes
	\|-		\|-

← Older revision		Revision as of 08:34, 16 April 2026
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	\|\|LsLsLsmsLsLsms		\|\|LsLsLsmsLsLsms
	\|\|5120/5103-tempered 2.3.5.7<br/>[L, m, s] = [10/9, 28/27, 81/80]		\|\|5120/5103-tempered 2.3.5.7<br/>[L, m, s] = [10/9, 28/27, 81/80]
	\|\|{{adv\|''GS(3/2)[7] by 81/80''}}		\|\|{{adv\|''GS(3/2)[7] and 81/80''}}
	\|\|Two interleaved diatonics		\|\|Two interleaved diatonics
	\|}		\|}

← Older revision		Revision as of 08:21, 16 April 2026
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	\|\|LmLsLsLmLsLsLs		\|\|LmLsLsLmLsLsLs
	\|\|2.x<3.5.7.11.13[37edo] (4:2:1)		\|\|2.x<3.5.7.11.13[37edo] (4:2:1)
	\|\|{{adv\|GS(<<3/2)[7] by 14/13}}		\|\|{{adv\|''GS(<<3/2)[7] and 14/13''}}
	\|\|An interleaving of two antidiatonic scales.		\|\|An interleaving of two antidiatonic scales.
	\|-		\|-