Akjaysma

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Interval information
Ratio 140737488355328/140710042265625
Factorization 247 × 3-7 × 5-7 × 7-7
Monzo [47 -7 -7 -7
Size in cents 0.3376516¢
Names akjaysma,
5/7-octave comma
Color name Trisa-seprugu comma
FJS name [math]\text{ddd1}_{5,5,5,5,5,5,5,7,7,7,7,7,7,7}[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 n⋅d) 93.9997
Weil height (max(n, d)) 140737488355328
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.39798 bits
open this interval in xen-calc

The akjaysma is a 7-limit unnoticeable comma. It is the difference between a stack of seven 105/64's and five octaves; [47 -7 -7 -7 in monzo and 0.338 cents in size. For equal divisions N up to 37316, this comma is tempered out only if 7 divides N. Examples are 7edo, 77edo, 217edo, 224edo, 441edo and 665edo.

Temperaments

Tempering out the akjaysma splits the octave into 7 equal parts and maps 105th harmonic into 5\7. It leads to a number of regular temperaments including absurdity, brahmagupta, and neutron.

In addition, tempering it out offers aptly named 441 & 1407 akjayland temperament, where it is also tempered along with the landscape comma.

Akjaysmic rank-3 temperament can be described as the 441&1848&2954 temperament, which tempers out 184549376/184528125 and 199297406/199290375 in the 11-limit.

Akjaysmic (441&1848&2954)

Subgroup: 2.3.5.7

Comma list: [47 -7 -7 -7

Mapping: [7 0 0 47], 0 1 0 -1], 0 0 1 -1]]

Mapping generators: ~1157625/1048576, ~3, ~5

POTE generators: ~3/2 = 701.965, ~5/4 = 386.330

Optimal GPV sequence140, 224, 301, 441, 665, 742, 966, 1106, 1407, 1547, 1848, 2289, 2513, 2954, 3395, 4802

11-limit 441&1848&2954

Subgroup: 2.3.5.7.11

Comma list: 184549376/184528125, 199297406/199290375

Mapping: [7 0 0 47 -168], 0 1 0 -1 10], 0 0 1 -1 5]]

Mapping generators: ~29160/26411, ~3, ~5

POTE generators: ~3/2 = 701.968, ~5/4 = 386.332

Optimal GPV sequence: 301, 364, 441, 742, 805, 1043, 1106, 1407, 1547, 1848, 2289, 2653, 2954, 3395, 4501, 5243, 6349, 8197

See also