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- 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]].

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- 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]].

[[File:Frameshift Cadence.mp3|thumb|Sample modulatory cadence in [[159edo]] which exploits this comma.]]

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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- 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]].
+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- 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]].
 [[File:Frameshift Cadence.mp3|thumb|Sample modulatory cadence in [[159edo]] which exploits this comma.]]