86/85

Interval information

Ratio	86/85
Subgroup monzo	2.5.17.43 [1 -1 -1 1⟩
Size in cents	20.24858¢
Names	43-limit 10th-tone, greater quadragesimotertial 10th-tone
Color name	43o17ug1, fothosugu 1sn
FJS name	[math]\displaystyle{ \text{P1}^{43}_{5,17} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	12.8357
Weil height (log2 max(n, d))	12.8525
Wilson height (sopfr(nd))	67
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~3.79204 bits
Comma size	small
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86/85 is a 43-limit (2.5.17.43 subgroup) comma of about 20.25 cents. Mister Shaf suggests the name 43-limit 10th-tone for this interval, as it is 0.25 cents or so from the step of 60edo.

Temperaments

Tempering out this comma in the full 43-limit results in a rank-11 temperament.

Tempering out this comma in the 2.5.17.43 subgroup results in a rank-3 temperament.

2.5.17.43 Fothosugu (3&9&13n)

Subgroup: 2.5.17.43

Mapping: [⟨1 0 0 -1] ⟨0 1 0 1] ⟨0 0 1 1]]

TE Tuning: ~2 = 1199.615, ~5 = 2788.391, ~17 = 4911.394

EDOs: 3, 9, 13n, 22

See also

• 87/86 – lesser quadragesimotertial 10th-tone