Frameshift comma: Difference between revisions

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


== Frameshift progression ==
* 4 [[Apotome|apotomes]] and [[1331/1024]]
* The [[243/242|rastma]] and the [[pythrabian comma]]
* The [[gamelisma]] and 3 [[Symbiotic comma|symbiotic commas]]


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.
== 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).


[[File:Frameshift Cadence.mp3|thumb|Sample of the Frameshift progression as it appears 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.
 
== 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.[[File:Frameshift Cadence.mp3|thumb|Frameshift progression sample in [[159edo]].]]


[[File:Frameshift Cadence Score.png|thumb|Score for the above sample of the Frameshift progression in 159edo.]]
[[File:Frameshift Cadence Score.png|thumb|Score for the above sample of the Frameshift progression in 159edo.]]
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== See also ==
== See also ==
* [[Unnoticeable comma]]
* [[Unnoticeable comma]]
* [[Frameshift microtemperaments]]


[[Category:Alpharabian]]
[[Category:Alpharabian]]

Revision as of 11:47, 9 April 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

Tempering out this comma results in theframeshift 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

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