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 norm (log2 nd)	93.9997
Weil norm (log2 max(n, d))	94
Wilson norm (sopfr(nd))	199
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The akjaysma (monzo: [47 -7 -7 -7⟩) is an unnoticeable 7-limit comma with a size of about 0.338 cents. It is the difference between a stack of seven 105/64's and five octaves.

Temperaments

Tempering out this comma leads to the akjaysmic temperament, which splits the octave into 7 equal parts and maps the 105th harmonic to 5\7. For edos N up to 37316, this comma is tempered out only if 7 divides N. Examples are 7edo, 77edo, 217edo, 224edo, 441edo and 665edo.

Akjaysmic can be further tempered to a number of rank-2 temperaments such as absurdity, brahmagupta, and neutron, all of which also temper out (128/105)/(39/32) = 4096/4095 in the 13-limit.

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 21 parts.

Etymology

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