Frameshift comma

Revision as of 16:10, 8 August 2021 by Aura (talk | contribs)

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.

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 norm (log2 nd) 88.7572
Weil norm (log2 max(n, d)) 88.7579
Wilson norm (sopfr(nd)) 185
Open this interval in xen-calc
Sample modulatory cadence in 159edo which exploits this comma.

See also