Cthon5m: Difference between revisions
No edit summary |
|||
| (29 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
'''Cthon5m''' (in [[aberrismic theory|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 == | == 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 | 13/12 | ||
| Line 20: | Line 22: | ||
2/1 | 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 ==== | |||
Kleismic (properly [[Cata]]) tempering corresponds to using Island tempering and then letting L = 2m. This makes Kleismic-tempered cthon5m a subset of a permutation (mmmmmsmmmsmmmmsmmms) of the Kleismic[19] MOS. | |||
== External links == | == External links == | ||
* [https://sw3.lumipakkanen.com/scale/ | * [https://sw3.lumipakkanen.com/scale/Udm0Ix3Kl 34edo (4:2:1) tuning] | ||
* [https://sw3.lumipakkanen.com/scale/ | * [https://sw3.lumipakkanen.com/scale/UdmzxDxtu 53edo (6:3:2) tuning] | ||
* [https://sw3.lumipakkanen.com/scale/ | * [https://sw3.lumipakkanen.com/scale/Udmr6q8k8 58edo (7:3:2) tuning] | ||
* [https://sw3.lumipakkanen.com/scale/UdmMBly3k 87edo (10:5:3) tuning] | |||
[[Category:Aberrismic theory]] | [[Category:Aberrismic theory]] | ||
[[Category:Rank-3 scales]] | [[Category:Rank-3 scales]] | ||
Latest revision as of 21:44, 5 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
Kleismic (properly Cata) tempering corresponds to using Island tempering and then letting L = 2m. This makes Kleismic-tempered cthon5m a subset of a permutation (mmmmmsmmmsmmmmsmmms) of the Kleismic[19] MOS.