Mathematical theory - Revision history

Inthar: /* Lattices and scale shapes */

2025-12-06T16:07:58Z

Lattices and scale shapes

← Older revision		Revision as of 16:07, 6 December 2025
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	* [[7-limit symmetrical lattices]]		* [[7-limit symmetrical lattices]]
	* [[Comma-based lattices]]		* [[Comma-based lattices]]
			=== Combinatorics on words ===
			* [[Ternary scale theorems]]

	== More pages ==		== More pages ==

Dummy index: /* Regular temperaments */ add link to Temperament merging

2025-10-01T13:06:54Z

Regular temperaments: add link to Temperament merging

← Older revision		Revision as of 13:06, 1 October 2025
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	* [[Dual list]]		* [[Dual list]]
	* [[Mathematical theory of saturation]]		* [[Mathematical theory of saturation]]
			* [[Temperament merging]]
	* [[Temperament addition]]		* [[Temperament addition]]

FloraC: Cleanup

2025-09-03T13:35:34Z

Cleanup

← Older revision		Revision as of 13:35, 3 September 2025
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	* [[Height]]		* [[Height]]
	* [[Benedetti height]]		* [[Benedetti height]]
	* [[Tenney ~~height~~]]		* [[Tenney norm]]
	* [[Kees ~~height~~]]		* [[Kees seminorm]]
	* [[Wilson ~~height~~]]		* [[Wilson norm]]
	* [[Weil norm, Tenney–Weil norm, and TWp interval and tuning space\|Weil ~~height~~ and Tenney–Weil ~~height~~]]		* [[Weil norm, Tenney–Weil norm, and TWp interval and tuning space\|Weil norm and Tenney–Weil norm]]

	=== Chords ===		=== Chords ===
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	* [[Chord matrices]]		* [[Chord matrices]]
	* [[Permutation product set]]		* [[Permutation product set]]
	* [[Tablet]]s		* [[Tablet]]

	=== Musical information theory ===		=== Musical information theory ===
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	=== Interval classification ===		=== Interval classification ===
	* [[Delta-N ratio]]		* [[Delta-N ratio\|Delta-''N'' ratio]]
	* [[Non radical intervals with musical significance]]		* [[Non radical intervals with musical significance]]
	* [[Abc, high quality commas, and epimericity\|''abc'', high quality commas, and epimericity]]		* [[Abc, high quality commas, and epimericity\|''abc'', high quality commas, and epimericity]]
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	* [[Mathematical theory of regular temperaments]]		* [[Mathematical theory of regular temperaments]]
	* [[Monzos and interval space]]		* [[Monzos and interval space]]
	** [[~~Fractional monzos~~]]		** [[Radical interval]]
	* [[Vals and tuning space]]		* [[Vals and tuning space]]
	* [[Temperament mapping ~~matrices~~]]		* [[Temperament mapping matrix]]
	* [[Dual list]]		* [[Dual list]]
	* [[Mathematical theory of saturation]]		* [[Mathematical theory of saturation]]
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	=== Subgroup temperaments ===		=== Subgroup temperaments ===
	* [[Subgroup temperament families, relationships, and genes]]		* [[Subgroup temperament families, relationships, and genes]]
	* [[~~Smonzos and svals\|~~Subgroup monzos ~~("smonzos")~~ and ~~subgroup~~ vals ~~("svals")~~]]		* [[Subgroup monzos and vals]]
	* [[~~Tmonzos and tvals\|~~Tempered monzos ~~("tmonzos")~~ and ~~tempered~~ vals ~~("tvals")~~]]		* [[Tempered monzos and vals]]
	* [[Subgroup basis ~~matrices~~]]		* [[Subgroup basis matrix]]
	* [[Meet and join]]		* [[Meet and join]]
	* [[k*N subgroups]]		* [[k*N subgroups]]

	=== [[Exterior algebra]] ~~===~~		=== Exterior algebra ===
			* [[Exterior algebra]]
	* [[Dave Keenan & Douglas Blumeyer's guide to EA for RTT]]		* [[Dave Keenan & Douglas Blumeyer's guide to EA for RTT]]
	* [[~~Wedgies and multivals~~]]		* [[Wedgie]] and [[Plücker coordinates]]
	* [[Plücker coordinates]]
	* [[Recoverability]]		* [[Recoverability]]
	* [[~~The~~ dual]]		* [[Hodge dual]]
	* [[Interior product]]		* [[Interior product]]

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	* [[Tenney–Euclidean temperament measures]]		* [[Tenney–Euclidean temperament measures]]
	* [[Tenney–Euclidean metrics]]		* [[Tenney–Euclidean metrics]]
	* [[Generalized Tenney norms and Tp interval space]]		* [[Generalized Tenney norms and Tp interval space\|Generalized Tenney norms and T<sub>''p''</sub> interval space]]
	* [[Generalized Tenney dual norms and Tp tuning space]]		* [[Generalized Tenney dual norms and Tp tuning space\|Generalized Tenney dual norms and T<sub>''p''</sub> tuning space]]
	* [[Weil norm, Tenney–Weil norm, and TWp interval and tuning space]]		* [[Weil norm, Tenney–Weil norm, and TWp interval and tuning space\|Weil norm, Tenney–Weil norm, and TW<sub>''p''</sub> interval and tuning space]]
	* [[Tp tuning]]		* [[Tp tuning\|T<sub>''p''</sub> tuning]]
	* [[Constrained tuning]]		* [[Constrained tuning]]
	* [[Logarithmic approximants]]		* [[Logarithmic approximants]]

	=== Temperament classification ===		=== Temperament classification ===
	* [[Rank-2 temperament]]s (include linear temperaments)		* [[Rank-2 temperament]] (include linear temperaments)
	* [[Rank-3 temperament]]s (include planar temperaments)		* [[Rank-3 temperament]] (include planar temperaments)
	(''Rank-1 temperaments are [[equal-step tuning]]s''.)		(''Rank-1 temperaments are [[equal-step tuning]]s''.)
	* [[Temperament families and clans]]		* [[Temperament families and clans]]
	* [[Cluster temperament]]s		* [[Cluster temperament]]
	* [[Associated temperament]]s		* [[Associated temperament]]
	* [[Microtemperament]]s		* [[Microtemperament]] and [[exotemperament]]
	* [[~~Exotemperament~~]]s		* [[Trivial temperament]]
	* [[Trivial temperament]]s
	* [[Sane and insane temperaments]]		* [[Sane and insane temperaments]]

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	=== MOS scales ===		=== MOS scales ===
	* [[Periodic scale]]		* [[Periodic scale]]
	* [[MOS ~~scales~~]]		* [[MOS scale]]
	* [[Mathematics of MOS]]		* [[Mathematics of MOS]]
	* [[MODMOS ~~scales~~]]		* [[MODMOS scale]]
	* [[Modal UDP Notation]]		* [[Modal UDP Notation]]
	* [[Graph-theoretic properties of scales]]		* [[Graph-theoretic properties of scales]]
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	* [[Projection pair]]		* [[Projection pair]]
	* [[Modulatory space]]		* [[Modulatory space]]
	* [[~~Transversal~~]]		* [[Detempering]]
	* [[~~Transversal generators~~]]		* [[Generator preimage]]
	* [[Fokker ~~blocks]]~~		* [[Fokker block]]
	* [[Weak Fokker blocks]]		* [[Minkowski block]]
	* [[Minkowski ~~blocks~~]]
	* [[Minkowski reduced bases for Fokker groups of certain vals]]		* [[Minkowski reduced bases for Fokker groups of certain vals]]
	* [[~~The Seven Limit Symmetrical Lattices~~]]		* [[7-limit symmetrical lattices]]
	* [[Comma-based lattices]]		* [[Comma-based lattices]]
	* [[Distinct EDO Scales]]

	== More pages ==		== More pages ==
	* [[:Category:Theory]]		* [[:Category: Theory]]
	* [[:Category:Math]]		* [[:Category: Math]]

	[[Category:Math]]		[[Category:Math]]
	[[Category:Theory]]		[[Category:Theory]]

	~~{{todo\|review\|comment=ensure the list items are under the correct subheading, and in the right order (most foundational first, most advanced last)}}~~

FloraC: - "list of factorizations". That's hardly mathematical theory!

2025-06-30T13:17:27Z

- "list of factorizations". That's hardly mathematical theory!

← Older revision		Revision as of 13:17, 30 June 2025
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	* [[Abc, high quality commas, and epimericity\|''abc'', high quality commas, and epimericity]]		* [[Abc, high quality commas, and epimericity\|''abc'', high quality commas, and epimericity]]
	* [[Don Page comma]]		* [[Don Page comma]]

	~~=== Lists of factorizations ===~~
	* [[List of 3-limit factorizations]]
	* [[List of 5-limit factorizations]]
	* [[List of 7-limit factorizations]]
	* [[List of 11-limit factorizations]]
	* [[List of 13-limit factorizations]]

	== Regular temperaments ==		== Regular temperaments ==

BudjarnLambeth: /* Lattices and scale shapes */ add link to orphaned page

2025-06-06T01:04:46Z

Lattices and scale shapes: add link to orphaned page

← Older revision		Revision as of 01:04, 6 June 2025
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	* [[The Seven Limit Symmetrical Lattices]]		* [[The Seven Limit Symmetrical Lattices]]
	* [[Comma-based lattices]]		* [[Comma-based lattices]]
			* [[Distinct EDO Scales]]

	== More pages ==		== More pages ==

FloraC: Move portal to talk page

2025-04-10T18:35:05Z

Move portal to talk page

← Older revision		Revision as of 18:35, 10 April 2025
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	{{interwiki		{{interwiki
			\| en = Mathematical theory
	\| de =		\| de =
	~~\| en = General Theory~~
	\| es = Teoría Profunda		\| es = Teoría Profunda
	\| ja =		\| ja =
	}}		}}
	~~{{Portal}}~~
	Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters.		Tuning theory can become heavily mathematical, and here are links to some of the pages which wade into deeper waters.

ArrowHead294 at 12:24, 31 March 2025

2025-03-31T12:24:59Z

← Older revision		Revision as of 12:24, 31 March 2025
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	=== Subgroup temperaments ===		=== Subgroup temperaments ===
	* [[Subgroup ~~Temperament Families~~, ~~Relationships~~, and ~~Genes~~]]		* [[Subgroup temperament families, relationships, and genes]]
	* [[Smonzos and svals\|Subgroup monzos ("smonzos") and subgroup vals ("svals")]]		* [[Smonzos and svals\|Subgroup monzos ("smonzos") and subgroup vals ("svals")]]
	* [[Tmonzos and tvals\|Tempered monzos ("tmonzos") and tempered vals ("tvals")]]		* [[Tmonzos and tvals\|Tempered monzos ("tmonzos") and tempered vals ("tvals")]]

Sintel: /* Exterior algebra */ Remove note, add links and plucker coords

2025-03-27T13:01:14Z

Exterior algebra: Remove note, add links and plucker coords

← Older revision		Revision as of 13:01, 27 March 2025
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	* [[k*N subgroups]]		* [[k*N subgroups]]

	=== Exterior algebra ===		=== [[Exterior algebra]] ===
	* [[Dave Keenan & Douglas Blumeyer's guide to EA for RTT]]		* [[Dave Keenan & Douglas Blumeyer's guide to EA for RTT]]
	** ''Mike's note: Douglas and Dave, having their own interpretation of RTT, sometimes use different terminology than the rest of the stuff here, but this page still has some very good insights and is a worthwhile read.''
	* [[Wedgies and multivals]]		* [[Wedgies and multivals]]
			* [[Plücker coordinates]]
	* [[Recoverability]]		* [[Recoverability]]
	* [[The dual]]		* [[The dual]]

ArrowHead294 at 13:43, 24 February 2025

2025-02-24T13:43:04Z

← Older revision		Revision as of 13:43, 24 February 2025
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	* [[TOP tuning]]		* [[TOP tuning]]
	* [[BOP tuning]]		* [[BOP tuning]]
	* [[~~Tenney-Euclidean~~ tuning]]		* [[Tenney–Euclidean tuning]]
	* [[~~Tenney-Euclidean~~ temperament measures]]		* [[Tenney–Euclidean temperament measures]]
	* [[~~Tenney-Euclidean~~ metrics]]		* [[Tenney–Euclidean metrics]]
	* [[Generalized Tenney norms and Tp interval space]]		* [[Generalized Tenney norms and Tp interval space]]
	* [[Generalized Tenney dual norms and Tp tuning space]]		* [[Generalized Tenney dual norms and Tp tuning space]]
	* [[Weil norm, ~~Tenney-Weil~~ norm, and TWp interval and tuning space]]		* [[Weil norm, Tenney–Weil norm, and TWp interval and tuning space]]
	* [[Tp tuning]]		* [[Tp tuning]]
	* [[Constrained tuning]]		* [[Constrained tuning]]
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	== More pages ==		== More pages ==
	* [[:~~Category:Theory\|~~Category:Theory]]		* [[:Category:Theory]]
	* [[:~~Category:Math\|~~Category:Math]]		* [[:Category:Math]]

	[[Category:Math]]		[[Category:Math]]

ArrowHead294 at 13:41, 24 February 2025

2025-02-24T13:41:36Z

← Older revision		Revision as of 13:41, 24 February 2025
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	* [[Kees height]]		* [[Kees height]]
	* [[Wilson height]]		* [[Wilson height]]
	* [[Weil height and ~~Tenney-Weil~~ height]]		* [[Weil norm, Tenney–Weil norm, and TWp interval and tuning space\|Weil height and Tenney–Weil height]]

	=== Chords ===		=== Chords ===
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	=== Musical information theory ===		=== Musical information theory ===
	* [[Categorical ~~Entropy~~, ~~Mutual Information~~, and ~~Channel Capacity~~]]		* [[Categorical entropy, mutual information, and channel capacity]]
	* [[Harmonic entropy]]		* [[Harmonic entropy]]
	* [[The Riemann zeta function and tuning]]		* [[The Riemann zeta function and tuning]]