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
FJS name	[math]\displaystyle{ \text{dddd}{-3}_{11,11,11} }[/math]
Special properties	reduced
Tenney height (log2 nd)	88.7572
Weil height (log2 max(n, d))	88.7579
Wilson height (sopfr(nd))	185
Open this interval in xen-calc

The Frameshift comma is an unnoticeable 11-limit comma- specifically of the 2.3.11 subgroup- with a complicated ratio of 22876792454961/22866405883904, and a size of roughly 0.79 cents. It is the interval separating the Rastma from the Pythrabian comma as well as the amount by which an octave-reduced stack of three 11/8 intervals falls short of a stack of four apotomes. Since both the Rastmic and Pythrabian temperaments are ways of conceptualizing how the 11-prime relates to the 3-prime within the 2.3.11 subgroup, that means that these two distinct frameworks for viewing the 11-prime relative to the 3-prime become linked when 22876792454961/22866405883904 is tempered out- hence the name "Frameshift" comma- a name which is even more appropriate in light of the fact that when one tempers out this comma, one can effectively modulate to 11/8 though a series of five, rather typical-sounding semitone-based motions- thus shifting a listener's perception of pitch relations such that the modulation sounds in tune. Naturally, tempering out this comma results in some form of Frameshift microtemperament.

Sample modulatory cadence in 159edo which exploits this comma.

Score for the above sample modulatory cadence in 159edo.

See also

• Unnoticeable comma