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
	Open this interval in xen-calc

4459/4455, the tristanisma, is an unnoticeable 13-limit no-twos 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).

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.

Tristanismic

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

Subgroup: 3.5.7.11.13

Comma list: 4459/4455

Subgroup-val 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 ¢

Optimal ET sequence: b9, b13, b17, b22, b26, b36, b39, b92, b114, b131, b170, b245, b284, b415, b428, b559, b598, b712, b843, b882, b1725, b4332ddf

Badness (Sintel): 0.089

Etymology

This comma was named by Tristan Bay in early May 2024 after himself.