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]]. 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).

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).

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 '''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).
+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).