8192/8019

Interval information

Ratio	8192/8019
Factorization	213 × 3-6 × 11-1
Monzo	[13 -6 0 0 -1⟩
Size in cents	36.95205¢
Name	Alpharabian inframinor second dimifondisma
Color name	s1u2, salu 2nd, Salu comma
FJS name	[math]\text{m2}_{11}[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	25.9692
Weil height (log2 max(n, d))	26
Wilson height (sopfr(nd))	55
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.51548 bits
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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 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).

See also

• 8019/4096 – its octave complement
• Gallery of just intervals