Nanisma

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Factorization 2109 × 3-67 × 7-1
Monzo [109 -67 0 -1
Size in cents 0.18903555¢
Name nanisma
FJS name [math]\text{9d7}_{7}[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 n⋅d) 218
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.39765 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.

Temperament

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.

No-five nanismic (1277&2860)

Subgroup: 2.3.7

Comma list: [109 -67 -1

Sval mapping: [1 2 -25], 0 -1 67]]

Optimal tuning (POTE): ~3/2 = 701.9578

Optimal GPV sequence53, 200, 253, 306, 665, 971, 1277, 4137, 5414, 6691, 7968

See also