833/832: Difference between revisions
→Commatic relations: Added product of ultraparticulars |
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== Temperaments == | == Temperaments == | ||
Tempering out this comma in the 17-limit results in the rank-6 '''horizmic temperament''', or in the 2.7.13.17 subgroup, the rank-3 '''horizon temperament'''. | Tempering out this comma in the 17-limit results in the rank-6 '''horizmic temperament''', or in the 2.7.13.17 subgroup, the rank-3 '''horizon temperament'''. | ||
=== Horizon === | |||
[[Subgroup]]: 2.7.13.17 | |||
[[Comma list]]: 833/832 | |||
{{Mapping|legend=2| 1 0 0 6 | 0 1 0 -2 | 0 0 1 1 }} | |||
: sval mapping generators: ~2, ~7, ~11 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1\1, ~7/4 = 968.2966, ~13/8 = 840.9875 | |||
* [[CWE]]: ~2 = 1\1, ~7/4 = 968.1967, ~13/8 = 840.5950 | |||
{{Optimal ET sequence|legend=1| 10, 21, 26, 36, 46, 47, 57, 93, 150, 207, 357, 704g, 854g, 911dg, 1061dg, 1268dg, 1418dgg }} | |||
=== Horizmic === | |||
[[Subgroup]]: 2.3.5.7.11.13.17 | |||
[[Comma list]]: 833/832 | |||
[[Mapping]]:<br> | |||
{| class="right-all" | |||
|- | |||
| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 6 || ], | |||
|- | |||
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 0 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || -2 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 1 || ]] | |||
|} | |||
: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1\1, ~3/2 = 701.9550, ~5/4 = 386.3137, ~7/4 = 968.2966, ~11/8 = 551.3179, ~13/8 = 840.9875 | |||
* [[CWE]]: ~2 = 1\1, ~3/2 = 701.8313, ~5/4 = 386.1324, ~7/4 = 968.1967, ~11/8 = 551.0479, ~13/8 = 840.5950 | |||
{{Optimal ET sequence|legend=1| 22f, 26, 31, 41, 46, 58, 72, 103, 130, 140, 171, 212g, 217, 243e, 289, 301, 311, 414, 460, 684g, 771, 1004dg, 1144degg, 1558cdegg, 1775ddgg }} | |||
== Etymology == | == Etymology == | ||