Archytas–chromatic equivalence continuum: Difference between revisions
Jump to navigation
Jump to search
ArrowHead294 (talk | contribs) mNo edit summary |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| Line 40: | Line 40: | ||
| 4{{frac|1|6}} | | 4{{frac|1|6}} | ||
| | | | ||
| <abbr title="105343182492594861947326056299830127783078740498060829800981944087/105312291668557186697918027683670432318895095400549111254310977536 | | <abbr title="105343182492594861947326056299830127783078740498060829800981944087/105312291668557186697918027683670432318895095400549111254310977536">[very long]</abbr> | ||
| {{monzo| -216 92 0 25 }} | | {{monzo| -216 92 0 25 }} | ||
|- | |- | ||
Revision as of 13:25, 31 December 2024
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 | ||
| 0 | Whitewood | 2187/2048 | [-11 7⟩ |
| 1 | 137781/131072 | [-17 9 0 1⟩ | |
| 2 | 8680203/8388608 | [-23 11 0 2⟩ | |
| 3 | 546852789/536870912 | [-29 13 0 3⟩ | |
| 4 | 34451725707/34359738368 | [-35 15 0 4⟩ | |
| 41⁄6 | [very long] | [-216 92 0 25⟩ | |
| … | … | … | |
| ∞ | Archy | 64/63 | [6 -2 -1⟩ |