6175/6174
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Ratio | 6175/6174 |
Factorization | 2^{-1} × 3^{-2} × 5^{2} × 7^{-3} × 13 × 19 |
Monzo | [-1 -2 2 -3 0 1 0 1⟩ |
Size in cents | 0.28038449¢ |
Names | neonewt comma, neonewtisma |
Color name | 19o3or^{3}yy-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 (log_{2} nd) | 25.1842 |
Weil height (log_{2} 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 a 19-limit 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.
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.