Generator sequence: Difference between revisions
m Add missing CS size 6 to Rhombi. →JI scales obtained from guided generator sequences |
m →Related concepts: Added conjectures regarding ternary scales with 3-interval WFGSes |
||
| Line 43: | Line 43: | ||
* A Slendric detemper, GS(8/7, 147/128, 8/7): 5, 6, 11, 16, 21, 26, 31, 36, 41, 77 | * A Slendric detemper, GS(8/7, 147/128, 8/7): 5, 6, 11, 16, 21, 26, 31, 36, 41, 77 | ||
== Ternary scales and WFGS == | |||
If a ternary [[billiard scale]] has a WFGS, the WFGS must use either two or three distinct generators, since ternary billiard scales are MV3 or MV4 and the closing generator is excluded from the generator sequence. | If a ternary [[billiard scale]] has a WFGS, the WFGS must use either two or three distinct generators, since ternary billiard scales are MV3 or MV4 and the closing generator is excluded from the generator sequence. | ||
=== MOS substitution | === Conjectures === | ||
'''Conjecture:''' There are only finitely many ternary scales with a 3-interval WFGS. | |||
'''Conjecture:''' There exist no ternary scale with more than 14 notes that has a 3-interval WFGS. | |||
== MOS substitution == | |||
[[MOS substitution]] is a procedure that yields ternary scales with binary generator sequences. | [[MOS substitution]] is a procedure that yields ternary scales with binary generator sequences. | ||
== Multi-GS == | |||
To extend the GS construction to a multiple-period MOS that splits the 2/1 into p > 1 periods, we can take a MOS-sized CS generated with a WFGS, and take offset copies of this scale by a detempered version of p-edo. This is what Inthar calls a ''multi-(WF)GS''. | To extend the GS construction to a multiple-period MOS that splits the 2/1 into p > 1 periods, we can take a MOS-sized CS generated with a WFGS, and take offset copies of this scale by a detempered version of p-edo. This is what Inthar calls a ''multi-(WF)GS''. | ||