Akjaysma

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]\displaystyle{ \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 nd)	93.9997
Weil height (log2 max(n, d))	94
Wilson height (sopfr(nd))	199
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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

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: Template:Val list

See also

• Unnoticeable comma