Aberrismic theory - Revision history

Inthar at 02:17, 10 December 2025

2025-12-10T02:17:35Z

← Older revision		Revision as of 02:17, 10 December 2025
Line 76:		Line 76:
	\| 143/80<br/>21/11<br/>280/143		\| 143/80<br/>21/11<br/>280/143
	\|}		\|}

	~~== Code ==~~
	~~<syntaxhighlight lang="python">~~
	~~</syntaxhighlight>~~

	== See also ==		== See also ==

Inthar at 02:16, 10 December 2025

2025-12-10T02:16:53Z

← Older revision		Revision as of 02:16, 10 December 2025
Line 84:		Line 84:
	* [[Pseudo-MOS scale]]: A related but different concept of [[CompactStar]]		* [[Pseudo-MOS scale]]: A related but different concept of [[CompactStar]]

	~~== External links ==~~
	* [https://discord.gg/Ea68TymwDU Aberrismic DR Dual server]
	[[Category:Terms]]		[[Category:Terms]]
	[[Category:Aberrismic theory\| ]]<!--Main article-->		[[Category:Aberrismic theory\| ]]<!--Main article-->

Inthar at 15:15, 30 November 2025

2025-11-30T15:15:37Z

← Older revision		Revision as of 15:15, 30 November 2025
Line 1:		Line 1:
	[[groundfault]]'s '''aberrismic theory''' is a xen theoretical paradigm using '''aberrismas''', a type of scale step which can be added to a scale pattern to turn it into a scale of one rank higher. The aberrisma is a new category of melodic steps that are smaller than the steps in the original scale, which prototypically are categorical "seconds" such as whole tones and semitones. The typical range for an aberrisma is 20 to 55 [[cents]]; groundfault holds the optimal melodic size for an aberrisma to be approximately 40 cents. Examples of ternary patterns that can be made by adding aberrismas to the 5L2s diatonic MOS are:		[[groundfault]]'s '''aberrismic theory''' is a xen theoretical paradigm using '''aberrismas''', a type of scale step which can be added to a scale pattern to turn it into a scale of one rank higher. The aberrisma is a new category of melodic steps that are smaller than the steps in the original scale, which prototypically are categorical "seconds" such as whole tones and semitones. The typical range for an aberrisma is 25 to 55 [[cents]]; groundfault holds the optimal melodic size for an aberrisma to be approximately 40 cents. Examples of ternary patterns that can be made by adding aberrismas to the 5L2s diatonic MOS are:
	* [[pinedye]] (5L2m1s or 1s)		* [[pinedye]] (5L2m1s or 1s)
	* [[diasem]] (5L2m2s or 2s)		* [[diasem]] (5L2m2s or 2s)

Inthar: /* See also */

2025-11-24T12:17:05Z

Inthar at 23:39, 4 January 2025

2025-01-04T23:39:12Z

← Older revision		Revision as of 23:39, 4 January 2025
Line 3:		Line 3:
	* [[diasem]] (5L2m2s or 2s)		* [[diasem]] (5L2m2s or 2s)
	* [[blackdye]] (5L2m3s or 3s)		* [[blackdye]] (5L2m3s or 3s)
	* [[~~diamech~~]] (5L2m4s or 4s)		* [[diaslen]] (5L2m4s or 4s)
	* [[diachrome]] (5L2m5s or 5s)		* [[diachrome]] (5L2m5s or 5s)
	{{User:Inthar/Template:Notation}}		{{User:Inthar/Template:Notation}}

Inthar: /* See also */

2025-01-04T22:00:40Z

Abnormality: got rid of the inaccurate idiosyncratic tag

2024-12-12T23:02:20Z

got rid of the inaccurate idiosyncratic tag

← Older revision		Revision as of 23:02, 12 December 2024
Line 1:		Line 1:
	[[groundfault]]'s '''aberrismic theory''' is a xen theoretical paradigm using '''aberrismas'''~~{{idiosyncratic}}~~, a type of scale step which can be added to a scale pattern to turn it into a scale of one rank higher. The aberrisma is a new category of melodic steps that are smaller than the steps in the original scale, which prototypically are categorical "seconds" such as whole tones and semitones. The typical range for an aberrisma is 20 to 55 [[cents]]; groundfault holds the optimal melodic size for an aberrisma to be approximately 40 cents. Examples of ternary patterns that can be made by adding aberrismas to the 5L2s diatonic MOS are:		[[groundfault]]'s '''aberrismic theory''' is a xen theoretical paradigm using '''aberrismas''', a type of scale step which can be added to a scale pattern to turn it into a scale of one rank higher. The aberrisma is a new category of melodic steps that are smaller than the steps in the original scale, which prototypically are categorical "seconds" such as whole tones and semitones. The typical range for an aberrisma is 20 to 55 [[cents]]; groundfault holds the optimal melodic size for an aberrisma to be approximately 40 cents. Examples of ternary patterns that can be made by adding aberrismas to the 5L2s diatonic MOS are:
	* [[pinedye]] (5L2m1s or 1s)		* [[pinedye]] (5L2m1s or 1s)
	* [[diasem]] (5L2m2s or 2s)		* [[diasem]] (5L2m2s or 2s)

Inthar at 05:50, 3 December 2024

2024-12-03T05:50:30Z

← Older revision		Revision as of 05:50, 3 December 2024
Line 1:		Line 1:
	[[groundfault]]'s '''aberrismic theory''' is a xen theoretical paradigm using '''aberrismas'''{{idiosyncratic}}, a type of scale step which can be added to a scale pattern to turn it into a scale of one rank higher. The aberrisma is a new category of melodic steps that are smaller than the steps in the original scale, which prototypically are categorical "seconds" such as whole tones and semitones. The typical range for an aberrisma is 20 to 60 [[cents]]; groundfault holds the optimal melodic size for an aberrisma to be approximately 40 cents. Examples of ternary patterns that can be made by adding aberrismas to the 5L2s diatonic MOS are:		[[groundfault]]'s '''aberrismic theory''' is a xen theoretical paradigm using '''aberrismas'''{{idiosyncratic}}, a type of scale step which can be added to a scale pattern to turn it into a scale of one rank higher. The aberrisma is a new category of melodic steps that are smaller than the steps in the original scale, which prototypically are categorical "seconds" such as whole tones and semitones. The typical range for an aberrisma is 20 to 55 [[cents]]; groundfault holds the optimal melodic size for an aberrisma to be approximately 40 cents. Examples of ternary patterns that can be made by adding aberrismas to the 5L2s diatonic MOS are:
	* [[pinedye]] (5L2m1s or 1s)		* [[pinedye]] (5L2m1s or 1s)
	* [[diasem]] (5L2m2s or 2s)		* [[diasem]] (5L2m2s or 2s)

BudjarnLambeth: Add link to orphan page

2024-10-20T07:37:06Z

Add link to orphan page

← Older revision		Revision as of 07:37, 20 October 2024
Line 80:		Line 80:
	<syntaxhighlight lang="python">		<syntaxhighlight lang="python">
	</syntaxhighlight>		</syntaxhighlight>

			== See also ==
			* [[Pseudo-MOS scale]]: A related but different concept of [[CompactStar]]

	[[Category:Terms]]		[[Category:Terms]]
	[[Category:Aberrismic theory\|*]]<!--Main article-->		[[Category:Aberrismic theory\|*]]<!--Main article-->

ArrowHead294 at 18:00, 20 August 2024

2024-08-20T18:00:47Z

← Older revision		Revision as of 18:00, 20 August 2024
Line 8:		Line 8:

	== Edos with quasi-diatonic aberrismic scales ==		== Edos with quasi-diatonic aberrismic scales ==
	All edos 20 and above have an aberrismic scale of the form 5L2mks. If ''n'' = 5''p'' + 2''q'' where ''p'' > ''q'' > 1 (''n''-edo is a diatonic edo with step ratio ''p'':''q''), then (''n'' + ''k'')edo has a 5L2m''k''s scale with step ratio ''p'':''q'':1 for 1 ≤ ''k'' < ''q'', and (''n'' + ''rk'')edo has a 5L2m''k''s scale with step ratio ''p'':''q'':''r'' if 1 ≤ ''r'' ≤ ''rk'' < ''q''.		All edos 20 and above have an aberrismic scale of the form 5L2mks. If {{nowrap\|''n'' {{=}} 5''p'' + 2''q''}} where {{nowrap\|''p'' > ''q'' > 1}} (''n''-edo is a diatonic edo with step ratio ''p'':''q''), then ({{nowrap\|''n'' + ''k''}})edo has a 5L2m''k''s scale with step ratio ''p'':''q'':1 for {{nowrap\|1 ≤ ''k'' < ''q''}}, and ({{nowrap\|''n'' + ''rk''}})edo has a 5L2m''k''s scale with step ratio ''p'':''q'':''r'' if {{nowrap\|1 ≤ ''r'' ≤ ''rk'' < ''q''}}.

	== Aberrismic theory and RTT ==		== Aberrismic theory and RTT ==
Line 17:		Line 17:
	Mathematically, this difference corresponds to choices of <math>\mathbb{Z}</math>-linear maps		Mathematically, this difference corresponds to choices of <math>\mathbb{Z}</math>-linear maps
	<math>\alpha : \mathbb{Z}^3\langle\mathbf{L}, \mathbf{m}, \mathbf{s}\rangle \to \mathrm{JI}( 2, p_1, ..., p_s )/\mathrm{ker}(T)</math> (here <math>T</math> is a temperament map defined on the 2.p<sub>1</sub>....p<sub>s</sub> subgroup), determined by differing choices of <math>\alpha(\mathbf{L}), \alpha(\mathbf{m}), \alpha(\mathbf{s})</math> and subject to the constraint that <math>a\alpha(\mathbf{L}) + b\alpha(\mathbf{m}) + c\alpha(\mathbf{s}) = T(2)</math> for the ternary scale ''a'''''L'''''b'''''m'''''c'''''s'''. Thus there are two choices involved in interpreting a given ternary scale, namely the choice of temperament and the choice of where to map the scale steps. The assignment of scale steps to tempered intervals is chosen to improve coverage of important LCJI intervals.		<math>\alpha : \mathbb{Z}^3\langle\mathbf{L}, \mathbf{m}, \mathbf{s}\rangle \to \mathrm{JI}( 2, p_1, ..., p_s )/\mathrm{ker}(T)</math> (here <math>T</math> is a temperament map defined on the 2.p<sub>1</sub>....p<sub>s</sub> subgroup), determined by differing choices of <math>\alpha(\mathbf{L}), \alpha(\mathbf{m}), \alpha(\mathbf{s})</math> and subject to the constraint that <math>a\alpha(\mathbf{L}) + b\alpha(\mathbf{m}) + c\alpha(\mathbf{s}) = T(2)</math> for the ternary scale ''a'''''L'''''b'''''m'''''c'''''s'''. Thus there are two choices involved in interpreting a given ternary scale, namely the choice of temperament and the choice of where to map the scale steps. The assignment of scale steps to tempered intervals is chosen to improve coverage of important LCJI intervals.
	=== Example: ~~blackdye~~ ===
			=== Example: Blackdye ===
	The following table shows two different temperament interpretations for the same aberrismic scale pattern blackdye (sLmLsLmLsL), under untempered 2.3.5 and Ultrapyth respectively.		The following table shows two different temperament interpretations for the same aberrismic scale pattern blackdye (sLmLsLmLsL), under untempered 2.3.5 and Ultrapyth respectively.
	* ''Untempered'' does not mean that the final tuning must be the JI tuning, but simply that there exists an exact JI tuning, or that the temperament before applying the tuning map has the same rank as the JI subgroup. This also implies that there is only one JI ratio for each interval under such interpretations, unlike in temperaments that temper out commas.		* ''Untempered'' does not mean that the final tuning must be the JI tuning, but simply that there exists an exact JI tuning, or that the temperament before applying the tuning map has the same rank as the JI subgroup. This also implies that there is only one JI ratio for each interval under such interpretations, unlike in temperaments that temper out commas.
	* [[Ultrapyth]], 2.3.5.7.11.13[32 & 37], is a diatonic temperament generated by a fifth even sharper than in Superpyth. [[37edo]] provides a nearly optimal tuning. Note that we chose to regard the 3-step 2L + s as a 14/11 rather than as a 5/4, lest the interpretation merely be an extension of the untempered 2.3.5 one. groundfault terms the tuning of blackdye that makes aberrisma-altered Pyth thirds 13/11 and 14/11 ''Flutterpyth blackdye'', since [[Flutterpyth]] temperament is restricted to (maximally) 2.3.7.11.13.19 and does not include 5-limit thirds.		* [[Ultrapyth]], 2.3.5.7.11.13[32 & 37], is a diatonic temperament generated by a fifth even sharper than in Superpyth. [[37edo]] provides a nearly optimal tuning. Note that we chose to regard the 3-step 2L + s as a 14/11 rather than as a 5/4, lest the interpretation merely be an extension of the untempered 2.3.5 one. groundfault terms the tuning of blackdye that makes aberrisma-altered Pyth thirds 13/11 and 14/11 ''Flutterpyth blackdye'', since [[Flutterpyth]] temperament is restricted to (maximally) 2.3.7.11.13.19 and does not include 5-limit thirds.

	{\| class="wikitable right-2 right-3 right-4 right-5"		{\| class="wikitable right-2 right-3 right-4 right-5"
	\|+ Blackdye intervals in two temperaments		\|+ style="font-size: 105%;" \| Blackdye intervals in two temperaments
	\|-		\|-
	! \| Interval class		! Interval class
	! Sizes		! Sizes
	! Untempered 2.3.5		! Untempered 2.3.5
	! 2.3.7.11.13 Flutterpyth (extended to 13-limit Ultrapyth)		! 2.3.7.11.13 Flutterpyth (extended to 13-limit Ultrapyth)
	\|-		\|-
	!\|[[TAMNAMS\|1-steps]]		! [[TAMNAMS\|1-steps]]
	\| s<br/>m<br/>L		\| s<br/>m<br/>L
	\| 81/80<br/>16/15<br/>10/9		\| 81/80<br/>16/15<br/>10/9
	\| 143/140<br/>22/21<br/>160/143		\| 143/140<br/>22/21<br/>160/143
	\|-		\|-
	!\|[[TAMNAMS\|2-steps]]		! [[TAMNAMS\|2-steps]]
	\| L + s<br/>L + m		\| L + s<br/>L + m
	\| 9/8<br/>32/27		\| 9/8<br/>32/27
	\| 8/7, 9/8<br/>7/6		\| 8/7, 9/8<br/>7/6
	\|-		\|-
	!\|[[TAMNAMS\|3-steps]]		! [[TAMNAMS\|3-steps]]
	\| L + 2s<br/>L + m + s<br/>2L + s<br/>2L + m		\| L + 2s<br/>L + m + s<br/>2L + s<br/>2L + m
	\| 729/640<br/>6/5<br/>5/4<br/>320/243		\| 729/640<br/>6/5<br/>5/4<br/>320/243
	\| 7/6<br/>13/11<br/>14/11<br/>13/10		\| 7/6<br/>13/11<br/>14/11<br/>13/10
	\|-		\|-
	!\|[[TAMNAMS\|4-steps]]		! [[TAMNAMS\|4-steps]]
	\| 2L + 2s<br/>2L + m + s		\| 2L + 2s<br/>2L + m + s
	\| 81/64<br/>4/3		\| 81/64<br/>4/3
	\| 13/10<br/>4/3		\| 13/10<br/>4/3
	\|-		\|-
	!\|[[TAMNAMS\|5-steps]]		! [[TAMNAMS\|5-steps]]
	\| 2L + m + 2s<br/>2L + 2m + s<br/>3L + 2s<br/>3L + m + s		\| 2L + m + 2s<br/>2L + 2m + s<br/>3L + 2s<br/>3L + m + s
	\| 27/20<br/>64/45<br/>45/32<br/>40/27		\| 27/20<br/>64/45<br/>45/32<br/>40/27
	\| 66/49<br/>11/8<br/>16/11<br/>49/33		\| 66/49<br/>11/8<br/>16/11<br/>49/33
	\|-		\|-
	!\|[[TAMNAMS\|6-steps]]		! [[TAMNAMS\|6-steps]]
	\| 3L + m + 2s<br/>3L + 2m + s		\| 3L + m + 2s<br/>3L + 2m + s
	\| 3/2<br/>128/81		\| 3/2<br/>128/81
	\| 3/2<br/>20/13		\| 3/2<br/>20/13
	\|-		\|-
	!\|[[TAMNAMS\|7-steps]]		! [[TAMNAMS\|7-steps]]
	\| 3L + m + 3s<br/>3L + 2m + 2s<br/>4L + m + 2s<br/>4L + 2m + s		\| 3L + m + 3s<br/>3L + 2m + 2s<br/>4L + m + 2s<br/>4L + 2m + s
	\| 243/160<br/>8/5<br/>5/3<br/>1280/729		\| 243/160<br/>8/5<br/>5/3<br/>1280/729
	\| 20/13<br/>11/7<br/>22/13<br/>12/7		\| 20/13<br/>11/7<br/>22/13<br/>12/7
	\|-		\|-
	!\|[[TAMNAMS\|8-steps]]		! [[TAMNAMS\|8-steps]]
	\| 4L + m + 3s<br/>4L + 2m + 2s		\| 4L + m + 3s<br/>4L + 2m + 2s
	\| 27/16<br/>16/9		\| 27/16<br/>16/9
	\| 12/7<br/>7/4, 16/9		\| 12/7<br/>7/4, 16/9
	\|-		\|-
	!\|[[TAMNAMS\|9-steps]]		! [[TAMNAMS\|9-steps]]
	\| 5L + 2m + s<br/>5L + m + 2s<br/>4L + 2m + 2s		\| 5L + 2m + s<br/>5L + m + 2s<br/>4L + 2m + 2s
	\| 9/5<br/>15/8<br/>160/81		\| 9/5<br/>15/8<br/>160/81

← Older revision		Revision as of 22:00, 4 January 2025
Line 85:		Line 85:

	[[Category:Terms]]		[[Category:Terms]]
	[[Category:Aberrismic theory\|*]]<!--Main article-->		[[Category:Aberrismic theory\| ]]<!--Main article-->

← Older revision		Revision as of 12:17, 24 November 2025
Line 84:		Line 84:
	* [[Pseudo-MOS scale]]: A related but different concept of [[CompactStar]]		* [[Pseudo-MOS scale]]: A related but different concept of [[CompactStar]]

			== External links ==
			* [https://discord.gg/Ea68TymwDU Aberrismic DR Dual server]
	[[Category:Terms]]		[[Category:Terms]]
	[[Category:Aberrismic theory\| ]]<!--Main article-->		[[Category:Aberrismic theory\| ]]<!--Main article-->