Vermeil comma

Overview

The Vermeil comma (Monzo: [—136; -34; 0; 68⟩), is an interval of 13.691 cents which is the amount by which thirty-four 49/48’s exceed an octave, (2/(49/48)^34). It is a 7-limit small comma.

It is best approximated by 88EDO, with 1 EDOstep = 13.6364 ¢ .

Interval information

Monzo	[[—136; -34; 0; 68⟩⟩
Size in cents	13.69161¢
Name	Vermeil Comma
Special properties	reduced
Open this interval in xen-calc

Approximating it with non-octave EDOs:

The optimal EDO for approximating the Vermeil Comma would be calculated as follows:

N = 1200/13.691

N ≈ 87.649 EDO

However, if we actually wanted to get the closest non-decimal tuning system for approximating the Vermeil Comma, we would need to find the correlated EDn (Equal division of the nth harmonic), with an integer as the number of divisions.

That is,

139ED3.002, which when rounded, gives us 139ED3. 

Number of cents in a tritave: 1200 * log2​(3) = 1200 * 1.5849625007 ≈ 1901.955 cents

Number cents per step in 139ED3: 1901.955/139 ≈ 13.68313 cents

Other Names

In color notation, its name would be: “ascending quinla-sequadzo 28th“