6175/6174

Interval information

Ratio	6175/6174
Factorization	2-1 × 3-2 × 52 × 7-3 × 13 × 19
Monzo	[-1 -2 2 -3 0 1 0 1⟩
Size in cents	0.2803845¢
Name	neonewtisma
Color name	19o3or3yy-2, nothotriru-ayoyo negative 2nd, Nothotriru-ayoyo comma
FJS name	[math]\displaystyle{ \text{m}{-2}^{5,5,13,19}_{7,7,7} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	25.1842
Weil norm (log2 max(n, d))	25.1844
Wilson norm (sopfr(nd))	71
Comma size	unnoticeable
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6175/6174, the neonewtisma, is an unnoticeable 19-limit (also 2.3.5.7.13.19-subgroup) superparticular comma of about 0.28 cents. It is the amount by which a stack consisting of 7/5, 9/5, 14/13 and 28/19 falls short of two octaves. By tempering it out is defined the neonewtismic temperament, which enables the neonewtismic chords.

Commatic relations

This comma is the difference between the following superparticular pairs:

• 190/189 and 196/195
• 325/324 and 343/342 *
• 442/441 and 476/475
• 1716/1715 and 2376/2375
• 1729/1728 and 2401/2400 *
• 2080/2079 and 3136/3135
• 2500/2499 and 4200/4199
• 3025/3024 and 5929/5928
• 3250/3249 and 6860/6859 *
• 4225/4224 and 13377/13376
• 5776/5775 and 89376/89375
• 5832/5831 and 104976/104975
• 5985/5984 and 194481/194480

It factors into the following superparticular pairs:

• 10830/10829 and 14365/14364

* relation within the 2.3.5.7.13.19 subgroup

Etymology

This comma was named by Xenllium in 2023, since it is one of the commas tempered out by the 2.3.5.7.11.13.19-subgroup version of newt, a.k.a. neonewt.

See also

• List of superparticular intervals