Cthon5m: Difference between revisions
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Here L = ~13/12, m = ~26/25~27/26, and s = 40/39. | Here L = ~13/12, m = ~26/25~27/26, and s = 40/39. | ||
(Hence Cthon5m admits an Island (2.3.5.13[ [[676/675]] ] temperament) interpretation | (Hence Cthon5m admits an Island (2.3.5.13[ [[676/675]] ] temperament) interpretation.) | ||
As a 2.3.5.13 subgroup scale, cthon5m is comparable to the MOS Kleismic[15] in size, but it's "fifthier" than Kleismic[15] and has one fewer note: | As a 2.3.5.13 subgroup scale, cthon5m is comparable to the MOS Kleismic[15] in size, but it's "fifthier" than Kleismic[15] and has one fewer note: | ||
* Kleismic[15] has 9 3/2's whereas cthon5m has 10 3/2's. | * Kleismic[15] has 9 3/2's whereas cthon5m has 10 3/2's. | ||
* 3/2 chains in Kleismic[15] only have at most 3 notes whereas cthon5m interpreted in Kleismic has 3/2 chains with 3 and 4 notes. | * 3/2 chains in Kleismic[15] only have at most 3 notes whereas cthon5m interpreted in Kleismic has 3/2 chains with 3 and 4 notes. | ||
Kleismic temperring corresponds to letting L = 2m. This makes cthon5m a subset of a 19-note binary non-MOS scale mmmmmsmmmsmmmmsmmms. | |||
== External links == | == External links == | ||
Revision as of 15:31, 4 March 2025
Cthon5m (in aberrismic systematic naming) is the even-regular 5L5m4s scale pattern LmLsmLsmLmsLms, so named because it is generated by a generator of the semiquartal MOS and the m step is the offset in its generator-offset structure.
Cthon5m is comprised of two interleaved nicetone/Zarlino scales of opposite chirality. In the JI preimage below these are 5-limit Zarlino scales.
Temperaments
2.3.5.13 Island (2.3.5.13[34&53&58])
Cthon5m has the following 2.3.5.13 interpretation in the 34edo (4:2:1), 53edo (6:3:2), and 58edo (7:3:2) tunings:
13/12 9/8 39/32 5/4 13/10 45/32 13/9 3/2 13/8 27/16 26/15 15/8 39/20 2/1
Here L = ~13/12, m = ~26/25~27/26, and s = 40/39.
(Hence Cthon5m admits an Island (2.3.5.13[ 676/675 ] temperament) interpretation.)
As a 2.3.5.13 subgroup scale, cthon5m is comparable to the MOS Kleismic[15] in size, but it's "fifthier" than Kleismic[15] and has one fewer note:
- Kleismic[15] has 9 3/2's whereas cthon5m has 10 3/2's.
- 3/2 chains in Kleismic[15] only have at most 3 notes whereas cthon5m interpreted in Kleismic has 3/2 chains with 3 and 4 notes.
Kleismic temperring corresponds to letting L = 2m. This makes cthon5m a subset of a 19-note binary non-MOS scale mmmmmsmmmsmmmmsmmms.