# Akjaysma

 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 $\text{ddd1}_{5,5,5,5,5,5,5,7,7,7,7,7,7,7}$ Special properties reduced Tenney height (log2 nd) 93.9997 Weil height (log2 max(n, d)) 94 Wilson height (sopfr (nd)) 199 Harmonic entropy(Shannon, $\sqrt{nd}$) ~1.20016 bits open this interval in xen-calc

The akjaysma is an unnoticeable 7-limit 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, akjaysma appears in temperaments whose period is a multiple of 7 (14, 21, 28, 35, etc.), however from a composer's standpoint it may not be the most prominent characterization of these temperaments due to a lot of inherent differences between multiples of 7edo. Tempering it out along with the landscape comma offers the aptly named 441 & 1407 akjayland temperament, that divides the octave into 7 x 3 = 21 parts.

### Akjaysmic

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

Optimal tuning (POTE): ~1157625/1048576 = 1\7, ~3/2 = 701.965, ~5/4 = 386.330

In higher limits, akjaysmic rank-3 temperament can be described as the 441 & 1848 & 2954 temperament, and it tempers out 184549376/184528125 and 199297406/199290375 in the 11-limit. See 7th-octave temperaments.

## Etymology

This comma was named by Aaron Krister Johnson in 2011 after himself[1].