Frameshift comma

Interval information

Ratio	22876792454961/22866405883904
Factorization	2-34 × 328 × 11-3
Monzo	[-34 28 0 0 -3⟩
Size in cents	0.7861971 ¢
Name	frameshift comma
Color name	Quadla-trilu comma
FJS name	[math]\displaystyle{ \text{dddd}{-3}_{11,11,11} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	88.7572
Weil norm (log2 max(n, d))	88.7579
Wilson norm (sopfr(nd))	185
Comma size	unnoticeable
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The frameshift comma is an unnoticeable 11-limit (2.3.11) comma. It is the difference between:

• Four Pythagorean apotomes and 1331/1024;
• The rastma and the pythrabian comma;
• The gamelisma and three symbiotic commas.

Temperaments

Frameshift progression sample in 159edo.

Score for the above sample of the Frameshift progression in 159edo.

Tempering out this comma results in the frameshift temperament in the 2.3.11. This allows reaching 11/8 by a stepwise motion consisting of four apotomes and one 128/121 with astoundingly small error. Aura dubs this the frameshift progression (see below).

It also splits the fifth into three 22528/19683's – an interval sharp of 8/7 by the symbiotic comma. Naturally, tempering it out results in a slendric extension. If both rastma and pythrabian comma are tempered out, this results in 41edo – a trivial tuning of frameshift.

Etymology

Discovered by Aura in 2021, it comes from the fact that both the rastmic and pythrabian temperaments are ways of conceptualizing how the 11-prime relates to the 3-prime, these two frameworks for viewing the 11-prime relative to the 3-prime become linked when this comma is tempered out – hence the name "frameshift" comma.