User:Lhearne: Difference between revisions
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SKULO notation and 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]]. Particularly native to [[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 and 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]]. Particularly native to [[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. | ||
Prima - an interval size measure for [[11-limit]] [[comma]] arithmetic: one step of [[12276edo]]; represents [[ | Prima - an interval size measure for [[11-limit]] [[comma]] arithmetic: one step of [[12276edo]]; 1 prima represents a [[parimo comma]]; 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]]. | ||
Step-nested Scales (SNS) - generalization of [[MOS scales]] to n-dimensional [[regular temperaments]] (as n-SNS), where [[MOS scales]] are 2-SNS. SNS are symmetric. | Step-nested Scales (SNS) - generalization of [[MOS scales]] to n-dimensional [[regular temperaments]] (as n-SNS), where [[MOS scales]] are 2-SNS. SNS are symmetric. | ||
[[Magic Tetrachords]] | [[Magic Tetrachords]] | ||
Revision as of 16:32, 16 April 2021
Hello, my name's Lillian Hearne. Welcome to my Xenwiki page. This is where I'll link all of my research :)
My thesis PhD thesis The Cognition of Stability in Microtonal Scales, focuses on 22edo.
These pages provide supplementary material to the 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:
Extended-diatonic interval names
SKULO notation and 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. Particularly native to 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.
Prima - an interval size measure for 11-limit comma arithmetic: one step of 12276edo; 1 prima represents a parimo comma; 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.
Step-nested Scales (SNS) - generalization of MOS scales to n-dimensional regular temperaments (as n-SNS), where MOS scales are 2-SNS. SNS are symmetric.