8192/8019
| Interval information |
dimifondisma
reduced subharmonic
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])
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).
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 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).