User:Lhearne: Difference between revisions

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These pages provide supplementary material to the PhD thesis:

Chapter 4 - [[the 16 most stable triads of 22edo]]

* Chapter 4 - [[the 16 most stable triads of 22edo]]

* Chapter 5 - [[User:Lhearne/Analysis22-7|Exemplar scales for the space of all possible 7-note scales of 22-TET]]

Chapter 5 - [[User:Lhearne/Analysis22-7|Exemplar scales for the space of all possible 7-note scales of 22-TET]]

Some other work:

[https://www.dropbox.com/scl/fi/avkjwf3q5qqldp06brf26/Roman-numeral-and-neo-Riemannian-analyses.pdf?rlkey=9zbr9a4mbr80wfy9mpmy3emix&dl=0 Roman numeral and neo-Riemannian analyses of Blackwood's ''Suite for Guitar in 15-note Equal Tuning'']

* [https://www.dropbox.com/scl/fi/avkjwf3q5qqldp06brf26/Roman-numeral-and-neo-Riemannian-analyses.pdf?rlkey=9zbr9a4mbr80wfy9mpmy3emix&dl=0 Roman numeral and neo-Riemannian analyses of Blackwood's ''Suite for Guitar in 15-note Equal Tuning'']

* [[Pinetone]]

[[~~The~~ Pinetone ~~System~~]]

* Marvel Double Harmonic and Hexatonic System (to be written up)

* [[Extended-diatonic interval names]]

Marvel Double Harmonic and Hexatonic System (to be written up)

* [[FKH Extended-diatonic Interval Names|FKH Extended-diatonic interval names]]

* [[SKULO interval names]] (successor to FKH Extended-diatonic interval names): Sub-chroma accidentals as deviations from Pythagorean diatonic intervals: S/s, Super/sub, septimal, [[64/63]]; K/k, Komma-Wide/komma-narrow, klassisch, [[81/80]]; U/u, Über/unter, undecimal, [[33/32]]; L\l, Large\little, [[896/891]]; O/o, On/off, Oceanic, [[45/44]]. Great for [[10edo]], [[15edo]], [[17edo]] and [[22edo]], where U=K=1 and S=0; [[24edo]] and [[31edo]], where U=S=1, and K=0; [[41edo]], [[46edo]], and [[53edo]], where U=2 and S=K=1; [[72edo]], where U=3, S=O=2, and K=L=1; and [[118edo]], where U=5, O=4, S=3, K=2, and L=1. SKULO notation to follow.

[[Extended-diatonic interval names]]

* [[Prima]] - an interval size measure for [[11-limit]] [[comma]] arithmetic: one step of [[12276edo]]; 1 prima represents a [[parimo]]; 20 prima to a [[schisma]], 220 prima to [[81/80]], and 240 prima to the [[Pythagorean comma]]; exactly 1023 prima to 1\[[12edo]], 558 prima to 1\[[22edo]], 396 prima to 1\[[31edo]], 170.5 prima to a [[morion]], and 10.23 prima to a [[cent]].

* [[Rank-3 scale]]

[[~~SHEFKHED~~ interval names]]

* [[SN scale|Step-nested (SN) scales]] - generalization of [[MOS scales]] to n-dimensional [[regular temperaments]] (as ''n''-SN scales), where [[MOS scales]] are 2-SN scales. SN scales are symmetric, and can be uniquely definied by a step signature, i.e., 2L 1M 4s, and a mapping.

* [[Gallery of 3-SN scales]]

[[SKULO interval names]] (successor to ~~SHEFKHED~~ interval names): Sub-chroma accidentals as deviations from Pythagorean diatonic intervals: S/s, Super/sub, septimal, [[64/63]]; K/k, Komma-Wide/komma-narrow, klassisch, [[81/80]]; U/u, Über/unter, undecimal, [[33/32]]; L\l, Large\little, [[896/891]]; O/o, On/off, Oceanic, [[45/44]]. Great for [[10edo]], [[15edo]], [[17edo]] and [[22edo]], where U=K=1 and S=0; [[24edo]] and [[31edo]], where U=S=1, and K=0; [[41edo]], [[46edo]], and [[53edo]], where U=2 and S=K=1; [[72edo]], where U=3, S=O=2, and K=L=1; and [[118edo]], where U=5, O=4, S=3, K=2, and L=1. SKULO notation to follow.

* [[ABACABA JI scales]]

* [[ABACABADABACABA JI scales]]

[[Prima]] - an interval size measure for [[11-limit]] [[comma]] arithmetic: one step of [[12276edo]]; 1 prima represents a [[parimo]]; 20 prima to a [[schisma]], 220 prima to [[81/80]], and 240 prima to the [[Pythagorean comma]]; exactly 1023 prima to 1\[[12edo]], 558 prima to 1\[[22edo]], 396 prima to 1\[[31edo]], 170.5 prima to a [[morion]], and 10.23 prima to a [[cent]].

* [[Gallery of omnitetrachordal scales#Scales with 3 step sizes]]

* [[Dipentatonic scales#Just dipentatonic scales]]

[[Rank-3 scale]]

* [[Magic Tetrachords]]

[[SN scale|Step-nested (SN) scales]] - generalization of [[MOS scales]] to n-dimensional [[regular temperaments]] (as ''n''-SN scales), where [[MOS scales]] are 2-SN scales. SN scales are symmetric, and can be uniquely definied by a step signature, i.e., 2L 1M 4s, and a mapping.

[[Gallery of 3-SN scales]]

[[ABACABA JI scales]]

[[Gallery of omnitetrachordal scales#Scales with 3 step sizes]]

[[Dipentatonic scales#Just dipentatonic scales]]

[[Magic Tetrachords]]

[[Category:User en-N]]

@@ Line 5: / Line 5: @@
 These pages provide supplementary material to the PhD thesis:
-Chapter 4 - [[the 16 most stable triads of 22edo]]
+* Chapter 4 - [[the 16 most stable triads of 22edo]]
+* Chapter 5 - [[User:Lhearne/Analysis22-7|Exemplar scales for the space of all possible 7-note scales of 22-TET]]
-Chapter 5 - [[User:Lhearne/Analysis22-7|Exemplar scales for the space of all possible 7-note scales of 22-TET]]
 Some other work:
-[https://www.dropbox.com/scl/fi/avkjwf3q5qqldp06brf26/Roman-numeral-and-neo-Riemannian-analyses.pdf?rlkey=9zbr9a4mbr80wfy9mpmy3emix&dl=0 Roman numeral and neo-Riemannian analyses of Blackwood's ''Suite for Guitar in 15-note Equal Tuning'']
+* [https://www.dropbox.com/scl/fi/avkjwf3q5qqldp06brf26/Roman-numeral-and-neo-Riemannian-analyses.pdf?rlkey=9zbr9a4mbr80wfy9mpmy3emix&dl=0 Roman numeral and neo-Riemannian analyses of Blackwood's ''Suite for Guitar in 15-note Equal Tuning'']
+* [[Pinetone]]
-[[The Pinetone System]]
+* Marvel Double Harmonic and Hexatonic System (to be written up)
+* [[Extended-diatonic interval names]]
-Marvel Double Harmonic and Hexatonic System (to be written up)
+* [[FKH Extended-diatonic Interval Names|FKH Extended-diatonic interval names]]
+* [[SKULO interval names]] (successor to FKH Extended-diatonic interval names): Sub-chroma accidentals as deviations from Pythagorean diatonic intervals: S/s, Super/sub, septimal, [[64/63]]; K/k, Komma-Wide/komma-narrow, klassisch, [[81/80]]; U/u, Über/unter, undecimal, [[33/32]]; L\l, Large\little, [[896/891]]; O/o, On/off, Oceanic, [[45/44]]. Great for [[10edo]], [[15edo]], [[17edo]] and [[22edo]], where U=K=1 and S=0; [[24edo]] and [[31edo]], where U=S=1, and K=0; [[41edo]], [[46edo]], and [[53edo]], where U=2 and S=K=1; [[72edo]], where U=3, S=O=2, and K=L=1; and [[118edo]], where U=5, O=4, S=3, K=2, and L=1. SKULO notation to follow.
-[[Extended-diatonic interval names]]
+* [[Prima]] - an interval size measure for [[11-limit]] [[comma]] arithmetic: one step of [[12276edo]]; 1 prima represents a [[parimo]]; 20 prima to a [[schisma]], 220 prima to [[81/80]], and 240 prima to the [[Pythagorean comma]]; exactly 1023 prima to 1\[[12edo]], 558 prima to 1\[[22edo]], 396 prima to 1\[[31edo]], 170.5 prima to a [[morion]], and 10.23 prima to a [[cent]].
+* [[Rank-3 scale]]
-[[SHEFKHED interval names]]
+* [[SN scale|Step-nested (SN) scales]] - generalization of [[MOS scales]] to n-dimensional [[regular temperaments]] (as ''n''-SN scales), where [[MOS scales]] are 2-SN scales. SN scales are symmetric, and can be uniquely definied by a step signature, i.e., 2L 1M 4s, and a mapping.
+* [[Gallery of 3-SN scales]]
-[[SKULO interval names]] (successor to SHEFKHED interval names): Sub-chroma accidentals as deviations from Pythagorean diatonic intervals: S/s, Super/sub, septimal, [[64/63]]; K/k, Komma-Wide/komma-narrow, klassisch, [[81/80]]; U/u, Über/unter, undecimal, [[33/32]]; L\l, Large\little, [[896/891]]; O/o, On/off, Oceanic, [[45/44]]. Great for [[10edo]], [[15edo]], [[17edo]] and [[22edo]], where U=K=1 and S=0; [[24edo]] and [[31edo]], where U=S=1, and K=0; [[41edo]], [[46edo]], and [[53edo]], where U=2 and S=K=1; [[72edo]], where U=3, S=O=2, and K=L=1; and [[118edo]], where U=5, O=4, S=3, K=2, and L=1. SKULO notation to follow.
+* [[ABACABA JI scales]]
+* [[ABACABADABACABA JI scales]]
-[[Prima]] - an interval size measure for [[11-limit]] [[comma]] arithmetic: one step of [[12276edo]]; 1 prima represents a [[parimo]]; 20 prima to a [[schisma]], 220 prima to [[81/80]], and 240 prima to the [[Pythagorean comma]]; exactly 1023 prima to 1\[[12edo]], 558 prima to 1\[[22edo]], 396 prima to 1\[[31edo]], 170.5 prima to a [[morion]], and 10.23 prima to a [[cent]].
+* [[Gallery of omnitetrachordal scales#Scales with 3 step sizes]]
+* [[Dipentatonic scales#Just dipentatonic scales]]
-[[Rank-3 scale]]
+* [[Magic Tetrachords]]
-[[SN scale|Step-nested (SN) scales]] - generalization of [[MOS scales]] to n-dimensional [[regular temperaments]] (as ''n''-SN scales), where [[MOS scales]] are 2-SN scales. SN scales are symmetric, and can be uniquely definied by a step signature, i.e., 2L 1M 4s, and a mapping.
-[[Gallery of 3-SN scales]]
-[[ABACABA JI scales]]
-[[Gallery of omnitetrachordal scales#Scales with 3 step sizes]]
-[[Dipentatonic scales#Just dipentatonic scales]]
-[[Magic Tetrachords]]
 [[Category:User en-N]]