8192/8019: Difference between revisions

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'''8192/8019''', the '''Alpharabian inframinor second''', is the basic inframinor second in the 2.3.11 [[subgroup]]. It differs from [[4096/3993]], the Alpharabian paralimma, by [[243/242]]~~, it differs~~ from [[45/44]], the undecimal 1/5-tone, by the [[schisma]], and~~, it also differs~~ from [[64/63]], ~~the~~ Archytas comma, by [[896/891]]. ~~As suggested by its name, it~~ is reached by subtracting a [[33/32]] quartertone from [[256/243]]. ~~Conspicuously~~, ~~this interval~~ is almost exactly one third of a [[16/15]] diatonic semitone- a stack of three falling short of it by the [[triagnoshenisma]].

'''8192/8019''', the '''Alpharabian inframinor second''', is the basic inframinor second in the [[2.3.11 subgroup]]. It differs from [[4096/3993]], the Alpharabian paralimma, by [[243/242]]; from [[45/44]], the undecimal 1/5-tone or cake comma, by the [[schisma]] 38⋅5/215; from [[128/125]], the lesser diesis, by [[8019/8000]]; and from [[64/63]], Archytas' comma, by [[896/891]]. It is reached by subtracting a [[33/32]] quartertone from [[256/243]], the pythagorean limma. Interestingly, 8192/8019 is almost exactly one third of a [[16/15]] diatonic semitone — a stack of three falling short of it by the [[triagnoshenisma]] (113/5 schismina).

When treated as a comma to be ~~tempered, and thus~~ tempered out, for instance, in undecimal superpyth temperament, the result is the obliteration of any distinction between the diatonic intervals of [[Pythagorean tuning]] and nearby paradiatonic intervals~~- most~~ notably, ~~it obliterates the distinction between~~ 16/11 and 729/512, ~~and this, combined with the fact that this interval is an inframinor second when not tempered, leads to~~ the comma name '''dimifondisma'''~~, with "~~dimi~~" from "diminished", "~~f~~" from "fifth" and "~~ond~~" from "~~second".

When treated as a comma to be tempered out (for instance, in undecimal superpyth temperament), the result is the obliteration of any distinction between the diatonic intervals of [[Pythagorean tuning]] and nearby [[Alpharabian_tuning|paradiatonic]] intervals. Most notably, [[16/11]] and [[729/512]] are equated, inspiring the comma name '''dimifondisma''' from ''diminished'' + ''f&zwnj;ifth'' + ''second'' (as the interval is an inframinor second before tempering).

== See also ==

* [[8019/4096]] – its [[octave complement]]

* [[Gallery of just intervals]]

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-'''8192/8019''', the '''Alpharabian inframinor second''', is the basic inframinor second in the 2.3.11 [[subgroup]].  It differs from [[4096/3993]], the Alpharabian paralimma, by [[243/242]], it differs from [[45/44]], the undecimal 1/5-tone, by the [[schisma]], and, it also differs from [[64/63]], the Archytas comma, by [[896/891]]. As suggested by its name, it is reached by subtracting a [[33/32]] quartertone from [[256/243]]. Conspicuously, this interval is almost exactly one third of a [[16/15]] diatonic semitone- a stack of three falling short of it by the [[triagnoshenisma]].
+'''8192/8019''', the '''Alpharabian inframinor second''', is the basic inframinor second in the [[2.3.11 subgroup]]. It differs from [[4096/3993]], the Alpharabian paralimma, by [[243/242]]; from [[45/44]], the undecimal 1/5-tone or cake comma, by the [[schisma]] 3<sup>8</sup>⋅5/2<sup>15</sup>; from [[128/125]], the lesser diesis, by [[8019/8000]]; and from [[64/63]], Archytas' comma, by [[896/891]]. It is reached by subtracting a [[33/32]] quartertone from [[256/243]], the pythagorean limma. Interestingly, 8192/8019 is almost exactly one third of a [[16/15]] diatonic semitone &mdash; a stack of three falling short of it by the [[triagnoshenisma]] (11<sup>3</sup>/5 schismina).
-When treated as a comma to be tempered, and thus tempered out, for instance, in undecimal superpyth temperament, the result is the obliteration of any distinction between the diatonic intervals of [[Pythagorean tuning]] and nearby paradiatonic intervals- most notably, it obliterates the distinction between 16/11 and 729/512, and this, combined with the fact that this interval is an inframinor second when not tempered, leads to the comma name '''dimifondisma''', with "dimi" from "diminished", "f" from "fifth" and "ond" from "second".
+When treated as a comma to be tempered out (for instance, in undecimal superpyth temperament), the result is the obliteration of any distinction between the diatonic intervals of [[Pythagorean tuning]] and nearby [[Alpharabian_tuning|paradiatonic]] intervals. Most notably, [[16/11]] and [[729/512]] are equated, inspiring the comma name '''dimifondisma''' from ''<u>dimi</u>nished'' + ''<u>f</u>&zwnj;ifth'' + ''sec<u>ond</u>'' (as the interval is an inframinor second before tempering).
 == See also ==
 * [[8019/4096]] – its [[octave complement]]
 * [[Gallery of just intervals]]