Nanisma
Factorization | 2^{109} × 3^{-67} × 7^{-1} |
Monzo | [109 -67 0 -1⟩ |
Size in cents | 0.18903555¢ |
Name | nanisma |
Color name | s^{10}r7, quinbisaru 7th |
FJS name | [math]\text{9d7}_{7}[/math] |
Special properties | reduced, reduced subharmonic |
Tenney height (log_{2} nd) | 218 |
Weil height (log_{2} max(n, d)) | 218 |
Wilson height (sopfr (nd)) | 426 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.19855 bits |
Comma size | unnoticeable |
open this interval in xen-calc |
Nanisma (monzo: [109 -67 0 -1⟩) is a no-five 7-limit unnoticeable comma measuring about 0.189 cents in size. It is the tiny interval between the pythagorean ratio [107 -67⟩ and the harmonic minor-7th of ratio 7/4.
The nanisma is considered as a 3=7 xenharmonic bridge. It also describes the difference between [108 -68⟩ (a stack of four 17-commas) and the septimal minor third of ratio 7/6, and also the difference between [-109 69⟩ and the wide septimal major third of ratio 9/7. It can also be thought of as the difference between Mercator's comma and the garischisma.
Temperaments
The nanisma is tempered out in such notable edos as 306, 612, 1277, 1583, 2860, 4137, 4802, 5414, 6079, 6691, 11493, 12105, and 12770, leading to the nanismic temperament, in which sixty-seven fifths make up a septimal whole tone 8/7 with octave reduction.
Nanismic
Subgroup: 2.3.5.7
Comma list: [109 -67 0 -1⟩
Mapping: [⟨1 0 0 109], ⟨0 1 0 -67], ⟨0 0 1 0]]
- sval mapping generators: ~2, ~3, ~5
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9578, ~5/4 = 386.3137
Optimal ET sequence: 53, 147d, 200, 253, 306c, 359, 412, 506d, 559, 612, 1277, 1889, 3525, 4137, 4190, 4802, 5414, 6079, 6691, 18184, 24875, 92809, 117684, 142559
Badness: 6.09 × 10^{-3}
Nanic
Subgroup: 2.3.7
Comma list: [109 -67 -1⟩
Sval mapping: [⟨1 0 109], ⟨0 1 -67]]
- sval mapping generators: ~2, ~3
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9578
Optimal ET sequence: 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733
Badness: 0.0138
Etymology
This comma was named by Margo Schulter in 2002^{[1]}.