4459/4455: Difference between revisions

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

Revision as of 20:34, 28 September 2025

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. 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 edos including 9, 12, 22, 27, 41, 72, 130, 190, 198, 270, and 311.

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

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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]]<nowiki/>s [[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]]. 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}}.
 == Etymology ==