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]]). Tempering it out and adding the octave back in yields the rank-5 [[tristanismic]] temperament, which is supported by [[EDO|edos]] including {{EDOs | 9, 12, 22, 27, 41, 72, 130, 190, 198, 270, and 311}}.
'''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
Ratio 4459/4455
Factorization 3-4 × 5-1 × 73 × 11-1 × 13
Monzo [0 -4 -1 3 -1 1⟩
Size in cents 1.553721¢
Name tristanisma
Color name tholutrizo-agu 3rd, 3o1uz3g3,
tholutrizo-agu comma
FJS name [math]\displaystyle{ \text{dd3}^{7,7,7,13}_{5,11} }[/math]
Special properties reduced
Tenney norm (log2 nd) 24.2437
Weil norm (log2 max(n, d)) 24.245
Wilson norm (sopfr(nd)) 62
Comma size unnoticeable
Open this interval in xen-calc

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

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