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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 thesis 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:

The Porcutone System

Extended-diatonic interval names

SHEFKHED interval names

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.

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


Gallery of omnitetrachordal scales#Scales with 3 step sizes

Dipentatonic scales#Just dipentatonic scales

Magic Tetrachords