4459/4455: Difference between revisions
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'''4459/4455''', the '''tristanisma''', is [[13-limit]] no-twos [[unnoticeable comma]] measuring roughly a [[cent]] and a half. It is the difference between the [[Odd-particular|odd-particulars]] [[245/243]] and [[275/273]]. It factors into the superparticular ratio pairs ([[2080/2079]])([[2401/2400]]) or ([[1001/1000]])([[9801/9800]]) | '''4459/4455''', the '''tristanisma''', is [[13-limit]] no-twos [[unnoticeable comma]] measuring roughly a [[cent]] and a half. It is the difference between the [[Odd-particular|odd-particulars]] [[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]]). | ||
== Etymology == | == Etymology == | ||
This comma was named by [[User:Tristanbay|Tristan Bay]] in early May 2024 after himself. | This comma was named by [[User:Tristanbay|Tristan Bay]] in early May 2024 after himself. | ||
== Temperaments == | |||
=== Tristanismic === | |||
Tempering out 4459/4455 in the full 13-limit leads to this rank-5 temperament. | |||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Comma list]]: 4459/4455 | |||
[[Mapping]]:<br> | |||
{{val| 1 0 0 0 0 0 }}<br> | |||
{{val| 0 1 0 0 0 4 }}<br> | |||
{{val| 0 0 1 0 0 1 }}<br> | |||
{{val| 0 0 0 1 0 -3 }}<br> | |||
{{val| 0 0 0 0 1 1 }} | |||
[[Optimal tuning]] ([[CWE]]): 2, ~3 = 1902.065, ~5 = 2786.373, ~7 = 3368.568, ~11 = 4151.449 | |||
{{Optimal ET sequence|legend=1| 8d, 9, 12, 14cf, 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 | |||
[[Category:Tristanismic]] | [[Category:Tristanismic]] | ||
Revision as of 08:05, 7 November 2025
| Interval information |
tholutrizo-agu comma
4459/4455, the tristanisma, is 13-limit no-twos unnoticeable comma measuring roughly a cent and a half. It is the difference between the odd-particulars 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).
Etymology
This comma was named by Tristan Bay in early May 2024 after himself.
Temperaments
Tristanismic
Tempering out 4459/4455 in the full 13-limit leads to this rank-5 temperament.
Subgroup: 2.3.5.7.11.13
Comma list: 4459/4455
Mapping:
⟨1 0 0 0 0 0]
⟨0 1 0 0 0 4]
⟨0 0 1 0 0 1]
⟨0 0 0 1 0 -3]
⟨0 0 0 0 1 1]
Optimal tuning (CWE): 2, ~3 = 1902.065, ~5 = 2786.373, ~7 = 3368.568, ~11 = 4151.449
Optimal ET sequence: 8d, 9, 12, 14cf, 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