Akjaysma
Ratio | 140737488355328/140710042265625 |
Factorization | 2^{47} × 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 |
Tenney height (log_{2} nd) | 93.9997 |
Weil height (log_{2} max(n, d)) | 94 |
Wilson height (sopfr (nd)) | 199 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~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
Optimal ET sequence: 140, 224, 301, 441, 665, 742, 966, 1106, 1407, 1547, 1848, 2289, 2513, 2954, 3395, 4802
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]}.