Vermeil comma: Difference between revisions

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== Overview ==
{{Infobox interval
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.
| Monzo = -137 -34 0 68
 
| Name = vermeil comma
It is best approximated by [[88edo|88EDO]], with 1 EDOstep = '''13.6364 ¢''' .{{Infobox Interval
| FJS name = -
| Monzo = [—136; -34; 0; 68⟩
| Color name = quinla-sequadzo 28th
| Cents = 13.6916104773216
| Calc = (49/48)^34/2
| Name = Vermeil Comma
| Calc = 2/(49/48)^34
}}
}}
The '''vermeil comma''', or systematically '''34-49/48-comma''' ({{monzo|legend=1| -136 -34 0 68 }}), is a [[small comma|small]] [[7-limit]]  [[comma]] of about 13.7 [[cent]]s. It is the amount by which a stack of thirty-four [[49/48]]'s exceeds an [[2/1|octave]], 2/(49/48)<sup>34</sup>.


=== Approximating it with non-octave EDOs: ===
== Approximation ==
The optimal EDO for approximating the Vermeil Comma would be calculated as follows:
This interval's size equals one step of 87.649…edo, so it is best approximated by [[88edo]], with 1\88 = 13.6364 cents.
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
== Etymology ==
This comma was named by [[User:Perry.k|Perry.k]] in 2026.  


== Other Names ==
[[Category:Vermeil]]
In [[Kite's color notation|color notation]], its name would be: “ascending quinla-sequadzo 28th“
[[Category:Commas with unknown etymology]]

Revision as of 08:28, 8 March 2026

Interval information
Factorization 2-137 × 3-34 × 768
Monzo [-137 -34 0 68⟩
Size in cents 13.69161¢
Name vermeil comma
Color name quinla-sequadzo 28th
FJS name [math]\displaystyle{ - }[/math]
Special properties reduced
Tenney norm (log2 nd) 381.789
Weil norm (log2 max(n, d)) 381.8
Wilson norm (sopfr(nd)) 852
Open this interval in xen-calc

The vermeil comma, or systematically 34-49/48-comma (monzo: [-136 -34 0 68⟩), is a small 7-limit comma of about 13.7 cents. It is the amount by which a stack of thirty-four 49/48's exceeds an octave, 2/(49/48)34.

Approximation

This interval's size equals one step of 87.649…edo, so it is best approximated by 88edo, with 1\88 = 13.6364 cents.

Etymology

This comma was named by Perry.k in 2026.

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