6175/6174
| 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 | 0.28038449¢ |
| Names | neonewt comma, neonewtisma |
| Color name | 19o3or3yy-2, nothotriru-ayoyo negative 2nd, Nothotriru-ayoyo comma |
| FJS name | [math]\text{m}{-2}^{5,5,13,19}_{7,7,7}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 25.1842 |
| Weil height (log2 max(n, d)) | 25.1844 |
| Wilson height (sopfr(nd)) | 71 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.19983 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
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.
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:
* 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.