4459/4455: Difference between revisions
Cleanup. + categories |
Update data |
||
| Line 4: | Line 4: | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''4459/4455''', the '''tristanisma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] no-twos [[comma]] measuring roughly a [[cent]] and a half. It is the difference between the [[odd-particular]]s [[245/243]] and [[275/273]], and between [[91/90]] and [[99/98]]. It factors into the [[superparticular ratio]] pairs ([[2080/2079]])⋅([[2401/2400]]) or ([[1001/1000]])⋅([[9801/9800]]). | '''4459/4455''', the '''tristanisma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] no-twos [[comma]] measuring roughly a [[cent]] and a half. It is the difference between the [[odd-particular]]s [[245/243]] and [[275/273]], and between [[91/90]] and [[99/98]]. It factors into the [[superparticular ratio]] pairs ([[2080/2079]])⋅([[2401/2400]]) or ([[1001/1000]])⋅([[9801/9800]]). | ||
== Temperaments == | == Temperaments == | ||
[[Tempering out]] this comma in the full 13-limit leads to the rank-5 '''tristanismic''' temperament, or in the 3.5.7.11.13 subgroup, the '''tristanic''' temperament. | [[Tempering out]] this comma in the full 13-limit leads to the rank-5 '''tristanismic''' temperament, or in the 3.5.7.11.13 subgroup, the '''tristanic''' temperament. | ||
=== Tristanic === | |||
[[Subgroup]]: 3.5.7.11.13 | |||
[[Comma list]]: 4459/4455 | |||
{{Mapping|legend=2| 1 0 0 0 4 | 0 1 0 0 1 | 0 0 1 0 -3 | 0 0 0 1 1 }} | |||
: mapping generators: ~3, ~5, ~7, ~11 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~3 = 1902.0648{{c}}, ~5/3 = 884.3078{{c}}, ~7/3 = 1466.5027{{c}}, ~11/9 = 347.3191{{c}} | |||
* [[CWE]]: ~3 = 1901.9550{{c}}, ~5/3 = 884.3336{{c}}, ~7/3 = 1466.4567{{c}}, ~11/9 = 347.4207{{c}} | |||
[[Optimal ET sequence]]: [[13edt|b13]], [[17edt|b17]], [[22edt|b22]], [[26edt|b26]], [[36edt|b36]], [[39edt|b39]], [[92edt|b92]], [[114edt|b114]], [[131edt|b131]], [[170edt|b170]], [[245edt|b245]], [[284edt|b284]], [[415edt|b415]], [[428edt|b428]], [[559edt|b559]], [[598edt|b598]], [[712edt|b712]], [[843edt|b843]], [[882edt|b882]], [[1725edt|b1725]], [[4332edt|b4332ddf]] | |||
[[Badness]] (Sintel): 0.0885 | |||
=== Tristanismic === | === Tristanismic === | ||
| Line 28: | Line 43: | ||
| ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]] | | ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]] | ||
|} | |} | ||
: mapping generators: ~2, ~3, ~5, ~7, ~11 | |||
[[Optimal tuning]] | [[Optimal tuning]]s: | ||
* [[WE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0648{{c}}, ~5/4 = 386.3726{{c}}, ~7/4 = 968.5675{{c}}, ~11/8 = 551.4487{{c}} | |||
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0648{{c}}, ~5/4 = 386.3726{{c}}, ~7/4 = 968.5675{{c}}, ~11/8 = 551.4487{{c}} | |||
{{Optimal ET sequence|legend=1| | {{Optimal ET sequence|legend=1| 17c, 19e, 22, 31f, 41, 58, 72, 118, 121, 130, 190, 198, 270, 581, 711, 981, 1171, 1441, 1752, 2022, 2463d, 2733d }} | ||
[[Badness]] (Sintel): 0.963 | [[Badness]] (Sintel): 0.963 | ||
== Etymology == | == Etymology == | ||