Tetracot (temperament): Difference between revisions
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== Extensions == | == Extensions == | ||
Tetracot has a number of strong extensions, but most of them are problematic in some way. | Tetracot has a number of strong extensions, but most of them are problematic in some way. This is because the Tetracot generator is, optimally, approximately 31/28 --- not easily interpretable as LCJI. | ||
* Prime 13 can be added by equating (10/9)^2 (the neutral third) with 16/13. | * Prime 13 can be added by equating (10/9)^2 (the neutral third) with 16/13. | ||
* Prime 11 is often added by equating (10/9)^2 with 11/9, but this is questionable because it produces either a very sharp 11/8 or a flat 5/4. | * Prime 11 is often added by equating (10/9)^2 with 11/9, but this is questionable because it produces either a very sharp 11/8 or a flat 5/4. | ||
Revision as of 21:03, 28 February 2026
Tetracot is a 2.3.5 temperament that splits 3/2 into four flattened 10/9's. Its 5-limit edo join is 27 & 34.
Extensions
Tetracot has a number of strong extensions, but most of them are problematic in some way. This is because the Tetracot generator is, optimally, approximately 31/28 --- not easily interpretable as LCJI.
- Prime 13 can be added by equating (10/9)^2 (the neutral third) with 16/13.
- Prime 11 is often added by equating (10/9)^2 with 11/9, but this is questionable because it produces either a very sharp 11/8 or a flat 5/4.
- There isn't a canonical way to add prime 7; there are no less than 4 strong extensions to 2.3.5.7: Bunya (34d & 41), Monkey (34 & 41), Modus (27e & 34d), and Wollemia (27e & 34). The weak extension Octacot (27 & 41) splits the Tetracot generator into two semitones representing 21/20, thus equating three Octacot generators with 7/6.
