User:Lhearne: Difference between revisions
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Hello, my name's Lillian Hearne. Welcome to my Xenwiki page | Hello, my name's Lillian Hearne (she/her). I'm a native English speaker. Welcome to my Xenwiki page! This is where I'll link all of my research :) | ||
My | My honours dissertation [https://www.dropbox.com/preview/Towards%20a%20new%20model%20for%20microtonal%20music.pdf Towards a new Model for microtonal music: The regular temperaments of 22edo], and my PhD thesis [https://www.dropbox.com/scl/fi/bwe3z98o4sfhw1fl22y4m/The-Cognition-of-Harmonic-Tonality-in-Microtonal-Scales-Lillian-M-Hearne.pdf?rlkey=665hh1iql4evczp0yieo1btmp&dl=0 The Cognition of Harmonic Tonality in Microtonal Scales], focus on [[22edo|22edo.]] | ||
These pages provide supplementary material to the thesis: | These pages provide supplementary material to the PhD thesis: | ||
* 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]] | |||
Some other work: | Some other work: | ||
[[Extended-diatonic interval names]] | * [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]] | |||
[[ | * Marvel Double Harmonic and Hexatonic System (to be written up) | ||
* [[Extended-diatonic interval names]] | |||
SKULO | * [[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. | |||
Prima | * [[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]] | |||
Step-nested Scales | * [[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]] | |||
* [[ABACABADABACABA JI scales]] | |||
* [[Gallery of omnitetrachordal scales#Scales with 3 step sizes]] | |||
* [[Dipentatonic scales#Just dipentatonic scales]] | |||
* [[Magic Tetrachords]] | |||
[[ | [[Category:User en-N]] | ||
Latest revision as of 09:39, 13 October 2024
Hello, my name's Lillian Hearne (she/her). I'm a native English speaker. Welcome to my Xenwiki page! This is where I'll link all of my research :)
My honours dissertation Towards a new Model for microtonal music: The regular temperaments of 22edo, and my PhD thesis The Cognition of Harmonic Tonality in Microtonal Scales, focus on 22edo.
These pages provide supplementary material to the PhD thesis:
- Chapter 4 - the 16 most stable triads of 22edo
- Chapter 5 - Exemplar scales for the space of all possible 7-note scales of 22-TET
Some other work:
- Roman numeral and neo-Riemannian analyses of Blackwood's Suite for Guitar in 15-note Equal Tuning
- Pinetone
- Marvel Double Harmonic and Hexatonic System (to be written up)
- 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.
- 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
- 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
- ABACABADABACABA JI scales
- Gallery of omnitetrachordal scales#Scales with 3 step sizes
- Dipentatonic scales#Just dipentatonic scales
- Magic Tetrachords