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]]; 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 — a stack of three falling short of it by the [[triagnoshenisma]] (11<sup>3</sup>/5 schismina). | '''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 — 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 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>‌ifth'' + ''sec<u>ond</u>'' (as the interval is an inframinor second before tempering). | 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>‌ifth'' + ''sec<u>ond</u>'' (as the interval is an inframinor second before tempering). | ||
Revision as of 16:51, 8 May 2025
| Interval information |
dimifondisma
reduced subharmonic
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, 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 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, 16/11 and 729/512 are equated, inspiring the comma name dimifondisma from diminished + fifth + second (as the interval is an inframinor second before tempering).