8192/8019: Difference between revisions

(6 intermediate revisions by 4 users not shown)

Line 1:

{{Infobox Interval

| Name = Alpharabian inframinor second dimifondisma

| Color name =

| Color name = s1u2, salu 2nd, Salu comma

}}

'''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]].

'''8192/8019''', the '''Alpharabian inframinor second''', is the basic inframinor second in the [[2.3.11 subgroup]]. When tuned justly or near-justly, it is among the smallest reasonable melodic intervals to use outside of ornamentation according to some microtonal composers- for example, [[User:Aura|Aura]]- as smaller intervals ostensibly tend to sound more like dirty variations on the same note when used in sequence. 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".

Among the more reasonably sized large EDOs that represent this interval and other intervals in its class- such as

[[1024/891]], [[4096/2673]] and [[512/297]]- with a pretty good level of accuracy include 159edo.

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]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Name = Alpharabian inframinor second <br>dimifondisma
-| Color name =
+| Color name = s1u2, salu 2nd, Salu comma
 }}
-'''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]].
+'''8192/8019''', the '''Alpharabian inframinor second''', is the basic inframinor second in the [[2.3.11 subgroup]].  When tuned justly or near-justly, it is among the smallest reasonable melodic intervals to use outside of ornamentation according to some microtonal composers- for example, [[User:Aura|Aura]]- as smaller intervals ostensibly tend to sound more like dirty variations on the same note when used in sequence.  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".
+Among the more reasonably sized large EDOs that represent this interval and other intervals in its class- such as
+[[1024/891]], [[4096/2673]] and [[512/297]]- with a pretty good level of accuracy include 159edo.
+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]]