1225/1224: Difference between revisions
Expand with some ways to pump it |
→Temperaments: + relation to the breed temperament |
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== Temperaments == | == Temperaments == | ||
[[Tempering out]] this comma in the 17-limit results in the rank-6 '''noellismic''' temperament, or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic''' temperament. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below. | [[Tempering out]] this comma in the 17-limit results in the rank-6 '''noellismic''' temperament, or in the 2.3.5.7.17 subgroup, the rank-4 '''noellic''' temperament. In either case [[18/17]] is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below. | ||
Since 1225/1224 factors as (2401/2400)⋅(2500/2499), it would make sense to temper them both out, so noellic can be further tempered to a simple extension of [[breed (temperament)|breed]] that adds prime 17, though it loses accuracy when compared to breed. | |||
=== Noellic === | === Noellic === | ||
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: mapping generators: ~2, ~3, ~5, ~7 | : mapping generators: ~2, ~3, ~5, ~7 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1200.0477{{c}}, ~3/2 = 701.9872{{c}}, ~5/4 = 386.0466{{c}}, ~7/4 = 968.4796{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9993{{c}}, ~5/4 = 386.0746{{c}}, ~7/4 = 968.4911{{c}} | |||
{{Optimal ET sequence|legend=1| | {{Optimal ET sequence|legend=1| 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d }} | ||
[[Badness]] (Sintel): 0.0985 | |||
=== Noellismic === | === Noellismic === | ||
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: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | : mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | ||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1200.0477{{c}}, ~3/2 = 701.9872{{c}}, ~5/4 = 386.0466{{c}}, ~7/4 = 968.4796{{c}}, ~11/8 = 551.1747{{c}}, ~13/8 = 840.3844{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9993{{c}}, ~5/4 = 386.0746{{c}}, ~7/4 = 968.4911{{c}}, ~11/8 = 551.2309{{c}}, ~13/8 = 840.4346{{c}} | |||
{{Optimal ET sequence|legend=1| 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d }} | |||
[[Badness]] (Sintel): 0.578 | |||
== Etymology == | == Etymology == | ||