5985/5984
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Ratio | 5985/5984 |
Factorization | 2^{-5} × 3^{2} × 5 × 7 × 11^{-1} × 17^{-1} × 19 |
Monzo | [-5 2 1 1 -1 0 -1 1⟩ |
Size in cents | 0.28928633¢ |
Names | neogrendel comma, neogrendelisma |
Color name | 19o17u1uzy1, Nosuluzoyo 1sn, Nosuluzoyo comma |
FJS name | [math]\text{A1}^{5,7,19}_{11,17}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 25.094 |
Weil height (log_{2} max(n, d)) | 25.0943 |
Wilson height (sopfr (nd)) | 75 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.19988 bits |
Comma size | unnoticeable |
S-expression | S133 × S134 × S135 |
open this interval in xen-calc |
5985/5984, the neogrendelisma or neogrendel comma, is a 19-limit superparticular comma of about 0.29 cents. It is the amount by which a stack consisting of 17/14 and 22/19 falls short of 45/32. By tempering it out is defined the neogrendelismic temperament, which enables the neogrendelismic chords.
Commatic relations
This comma identifies itself as the difference between the following superparticular pairs:
- 133/132 and 136/135
- 171/170 and 176/175
- 273/272 and 286/285
- 375/374 and 400/399
- 441/440 and 476/475
- 513/512 and 561/560
- 969/968 and 1156/1155
- 1089/1088 and 1331/1330
- 1225/1224 and 1540/1539
- 1701/1700 and 2376/2375
- 1729/1728 and 2431/2430
- 2058/2057 and 3136/3135
- 2432/2431 and 4096/4095
- 4200/4199 and 14080/14079
- 4225/4224 and 14365/14364
- 4914/4913 and 27456/27455
- 5776/5775 and 165376/165375
- 5832/5831 and 228096/228095
- 5929/5928 and 633556/633555
It factors into the following superparticular pairs:
- 10830/10829 and 13377/13376
- 10241/10240 and 14400/14399
- 6175/6174 and 194481/194480
Etymology
The names neogrendelisma and neogrendel comma were named by Xenllium in 2023. They refer to the grendel temperament, which tempers out 256/255, 375/374, 400/399, 540/539 and 836/833 in the 2.3.5.7.11.17.19 subgroup.