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 | '''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). | ||
When treated as a comma to be | 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). | ||
== See also == | == See also == | ||
* [[8019/4096]] – its [[octave complement]] | * [[8019/4096]] – its [[octave complement]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
Revision as of 20:38, 23 November 2024
| Interval information |
dimifondisma
reduced subharmonic
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 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).