6175/6174

6175/6174, the neonewtisma or neonewt comma, 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.

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¢
Names	neonewt comma, 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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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

The names neonewtisma and neonewt comma were named by Xenllium in 2023. The rank-three temperament which tempers out 2080/2079, 2401/2400 and 4096/4095 (lif temperament, 41&130&140) can be extended to the 2.3.5.7.11.13.19 subgroup by tempering out 1216/1215, 1729/1728, 2926/2925, 3136/3135 or 6175/6174, and the rank-two 2.3.5.7.11.13.19 subgroup 41&270 temperament (neonewt) also supports it.

See also

• List of superparticular intervals