3136/3135

Interval information

Ratio	3136/3135
Factorization	26 × 3-1 × 5-1 × 72 × 11-1 × 19-1
Monzo	[6 -1 -1 2 -1 0 0 -1⟩
Size in cents	0.5521397¢
Names	neomirkwai comma, neomirkwaisma
Color name	19u1uzzg2, nuluzozogu 2nd, Nuluzozogu comma
FJS name	[math]\text{m2}^{7,7}_{5,11,19}[/math]
Special properties	square superparticular, reduced
Tenney height (log2 nd)	23.229
Weil height (log2 max(n, d))	23.2294
Wilson height (sopfr(nd))	64
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20106 bits
Comma size	unnoticeable
S-expressions	S56, S96 × S97 × S98
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3136/3135, the neomirkwaisma or neomirkwai comma, is a 19-limit (also 2.3.5.7.11.19 subgroup) superparticular comma of about 0.55 cents. It is the amount by which a stack consisting of 11/8, 15/14 and 19/14 falls short of an octave.

Commatic relations

This comma is the difference between the following superparticular pairs:

• 56/55 and 57/56 *
• 96/95 and 99/98 *
• 196/195 and 209/208
• 210/209 and 225/224 *
• 343/342 and 385/384 *
• 441/440 and 513/512 *
• 476/475 and 561/560
• 1540/1539 and 3025/3024 *
• 2058/2057 and 5985/5984
• 2080/2079 and 6175/6174
• 2376/2375 and 9801/9800 *
• 2401/2400 and 10241/10240 *
• 2432/2431 and 10830/10829
• 2926/2925 and 43681/43680

It factors into the following superparticular pairs:

• 5929/5928 and 6656/6655
• 5776/5775 and 6860/6859 *
• 4200/4199 and 12376/12375
• 4096/4095 and 13377/13376
• 3250/3249 and 89376/89375

* relation within the 2.3.5.7.11.19 subgroup

Temperaments

By tempering it out is defined the neomirkwaismic temperament, which enables the neomirkwaismic chords.

Etymology

The names neomirkwaisma and neomirkwai comma were named by Xenllium in 2023. The indra temperament (31&41&80, an 11-limit extension of the mirkwai temperament) can be extended to the 2.3.5.7.11.19 subgroup by tempering out 400/399, 1540/1539, 2304/2299 or 3136/3135.

See also

• Unnoticeable comma
• List of superparticular intervals