User:2^67-1/Sandbox: Difference between revisions
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| 0 || 0 || [[Blackwood]] || [[256/243]] || {{monzo| 8 -5 0 0 }} | | 0 || 0 || [[Blackwood]] || [[256/243]] || {{monzo| 8 -5 0 0 }} | ||
|- | |- | ||
| 0 || 1 || | | 0 || 1 || [[Archytas]] (squared) || [[4096/3969]] || {{monzo| 12 -4 0 -2 }} | ||
|- | |- | ||
| 0 || 2 || | | 0 || 2 || [[Buzzard]] || [[65536/64827]] || {{monzo| 16 -3 0 -4 }} | ||
|- | |- | ||
| 0 || 3 || | | 0 || 3 || [[Slendric]] (squared) || [[1058841/1048576]] || {{monzo| -20 2 0 6 }} | ||
|- | |- | ||
| 0 || ∞ || [[Semaphore]] || [[49/48]] || {{monzo| -4 -1 0 2 }} | | 0 || ∞ || [[Semaphore]] || [[49/48]] || {{monzo| -4 -1 0 2 }} | ||
Revision as of 23:11, 25 July 2024
Testing
The blackwood-dicot-semaphore equivalence continuum is a continuum of 7-limit rank-3 temperaments describing the set of all 7-limit rank-3 temperaments supported by 10edo. Any rank-2 temperament supported by 10edo can thus be represented by a line between two points in this continuum.
All temperaments in the continuum satisfy (25/24)p(49/48)q ~ 256/243, equating a stack of dicot commas (25/24) and semaphore commas (49/48) with the blackwood comma (256/243).
The blackwood comma is the characteristic 3-limit comma tempered out in 10edo.
| p | q | Temperament | Comma | |
|---|---|---|---|---|
| Ratio | Monzo | |||
| 0 | 0 | Blackwood | 256/243 | [8 -5 0 0⟩ |
| 0 | 1 | Archytas (squared) | 4096/3969 | [12 -4 0 -2⟩ |
| 0 | 2 | Buzzard | 65536/64827 | [16 -3 0 -4⟩ |
| 0 | 3 | Slendric (squared) | 1058841/1048576 | [-20 2 0 6⟩ |
| 0 | ∞ | Semaphore | 49/48 | [-4 -1 0 2⟩ |
| 1 | 0 | Srutal | 2048/2025 | [11 -4 -2 0⟩ |
| 1 | 1 | Mirwomo | 33075/32768 | [15 -3 -2 -2⟩ |
| 1 | ∞ | Jubilic | 50/49 | [1 0 2 -2⟩ |
| 2 | 0 | Negri | 16875/16384 | [-14 3 4 0⟩ |
| ∞ | 0 | Dicot | 25/24 | [-3 -1 2 0⟩ |
| ∞ | 1 | Jubilic | 50/49 | [1 0 2 -2⟩ |
| ∞ | 2 | Breedsmic | 2401/2400 | [-5 -1 -2 4⟩ |