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:

• 4 apotomes and 1331/1024
• The rastma and the pythrabian comma
• The gamelisma and 3 symbiotic commas

Temperaments

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.

Frameshift progression sample in 159edo.

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

See also

• Unnoticeable comma
• Frameshift microtemperaments