Frameshift comma: Difference between revisions

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The '''frameshift comma''' is an [[unnoticeable comma|unnoticeable]] [[11-limit]] (2.3.11) comma. It is the difference between:
* Four [[Pythagorean apotome]]s and [[1331/1024]];
* The [[243/242|rastma]] and the [[pythrabian comma]];
* The [[gamelisma]] and three [[symbiotic comma]]s.


The '''frameshift comma''' is an [[unnoticeable comma|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 [[cent]]s.  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 [[apotome]]s. 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.  Naturally, tempering out this comma results in some form of [[frameshift microtemperaments|frameshift microtemperament]], and such temperaments are known to be associated with higher-accuracy systems.
== Temperaments ==
 
[[File:Frameshift Cadence.mp3|thumb|Frameshift progression sample in [[159edo]].]]
== Frameshift progression ==
[[File:Frameshift Cadence Score.png|thumb|Score for the above sample of the Frameshift progression in 159edo.]]
 
The name of the frameshift comma is even more appropriate in light of the fact that when one tempers out this comma, one can move stepwise to 11/8 though a series of four motions by the apotome and one motion by [[128/121]]- all rather typical-sounding semitone-based motions- with this gesture forming the basis of what has since been dubbed the '''frameshift progression'''- a cadence which shifts a listener's perception of pitch relations such that a modulation to 11/8 sounds in tune.


[[File:Frameshift Cadence.mp3|thumb|Sample of the Frameshift progression as it appears 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).


[[File:Frameshift Cadence Score.png|thumb|Score for the above sample of the Frameshift progression in 159edo.]]
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.


== See also ==
== Etymology ==
* [[Unnoticeable comma]]
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.


[[Category:Alpharabian]]
[[Category:Alpharabian]]
[[Category:Pythrabian]]
[[Category:Pythrabian]]
[[Category:Frameshift]]
[[Category:Frameshift]]
[[Category:Chord progressions]]
[[Category:Commas named for their regular temperament properties]]
[[Category:Commas named for their regular temperament properties]]
[[Category:Chord progressions]]

Latest revision as of 07:48, 17 September 2026

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
Open this interval in xen-calc

The frameshift comma is an unnoticeable 11-limit (2.3.11) comma. It is the difference between:

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.

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