Archytas–chromatic equivalence continuum: Difference between revisions
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| Line 13: | Line 13: | ||
! Ratio | ! Ratio | ||
! Monzo | ! Monzo | ||
|- | |||
| -2 | |||
| [[Dicot]] | |||
| [[54/49]] | |||
| {{monzo| 1 3 0 -2 }} | |||
|- | |||
| -1 | |||
| [[Armodue]] | |||
| [[243/224]] | |||
| {{monzo| -5 5 0 -1 }} | |||
|- | |- | ||
| 0 | | 0 | ||
| Line 25: | Line 35: | ||
|- | |- | ||
| 2 | | 2 | ||
| | | [[Mohajira]] | ||
| [[8680203/8388608]] | | [[8680203/8388608]] | ||
| {{monzo| -23 11 0 2 }} | | {{monzo| -23 11 0 2 }} | ||
|- | |- | ||
| 3 | | 3 | ||
| | | (29 & 36) | ||
| [[546852789/536870912]] | | [[546852789/536870912]] | ||
| {{monzo| -29 13 0 3 }} | | {{monzo| -29 13 0 3 }} | ||
|- | |- | ||
| 4 | | 4 | ||
| | | [[Sesquiquartififths]] | ||
| [[34451725707/34359738368]] | | [[34451725707/34359738368]] | ||
| {{monzo| -35 15 0 4 }} | | {{monzo| -35 15 0 4 }} | ||
|- | |- | ||
| 4{{frac|1|6}} | | 4{{frac|1|6}} | ||
| | | (1848 & 3431) | ||
| <abbr title="105343182492594861947326056299830127783078740498060829800981944087/105312291668557186697918027683670432318895095400549111254310977536">[very long]</abbr> | | <abbr title="105343182492594861947326056299830127783078740498060829800981944087/105312291668557186697918027683670432318895095400549111254310977536">[very long]</abbr> | ||
| {{monzo| -216 92 0 25 }} | | {{monzo| -216 92 0 25 }} | ||
| Line 52: | Line 62: | ||
| [[Archytas clan#Archy|Archy]] | | [[Archytas clan#Archy|Archy]] | ||
| [[64/63]] | | [[64/63]] | ||
| {{monzo| 6 -2 -1 }} | | {{monzo| 6 -2 0 -1 }} | ||
|} | |} | ||
[[Category:Equivalence continua]] | [[Category:Equivalence continua]] | ||
Revision as of 10:55, 12 April 2025
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The Archytas–chromatic equivalence continuum, or septimal–chromatic equivalence continuum, is a continuum of 7-limit temperaments which equate a number of Archytas commas (64/63) with the Pythagorean apotome (2187/2048).
All temperaments in the continuum satisfy (64/63)n ~ 2187/2048. Varying n results in different temperaments listed in the table below. It converges to archy as n approaches infinity. The just value of n is 4.169771, and temperaments near this tend to be the most accurate ones.
| n | Temperament | Comma | |
|---|---|---|---|
| Ratio | Monzo | ||
| -2 | Dicot | 54/49 | [1 3 0 -2⟩ |
| -1 | Armodue | 243/224 | [-5 5 0 -1⟩ |
| 0 | Whitewood | 2187/2048 | [-11 7⟩ |
| 1 | Flattone | 137781/131072 | [-17 9 0 1⟩ |
| 2 | Mohajira | 8680203/8388608 | [-23 11 0 2⟩ |
| 3 | (29 & 36) | 546852789/536870912 | [-29 13 0 3⟩ |
| 4 | Sesquiquartififths | 34451725707/34359738368 | [-35 15 0 4⟩ |
| 41⁄6 | (1848 & 3431) | [very long] | [-216 92 0 25⟩ |
| … | … | … | |
| ∞ | Archy | 64/63 | [6 -2 0 -1⟩ |