4459/4455

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
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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-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

Tristanic

This is the main temperament that tempers out 4459/4455 in the no-twos 13-limit.

Subgroup: 3.5.7.11.13

Comma list: 4459/4455

Mapping:
⟨1 0 0 0 4]
⟨0 1 0 0 1]
⟨0 0 1 0 -3]
⟨0 0 0 1 1]

Optimal tuning (CWE): 3, ~5 = 2786.289, ~7 = 3368.412, ~11 = 4151.331

Badness (Sintel): 0.089