Vermeil comma: Difference between revisions
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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. | 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|88EDO]], with 1 EDOstep = '''13.6364 ¢''' . | It is best approximated by [[88edo|88EDO]], with 1 EDOstep = '''13.6364 ¢''' .{{Infobox Interval | ||
{{Infobox Interval | |||
| Monzo = [—136; -34; 0; 68⟩ | | Monzo = [—136; -34; 0; 68⟩ | ||
| Cents = 13.6916104773216 | | Cents = 13.6916104773216 | ||
| Line 11: | Line 8: | ||
| Calc = 2/(49/48)^34 | | Calc = 2/(49/48)^34 | ||
}} | }} | ||
=== 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 [[Kite's color notation|color notation]], its name would be: “ascending quinla-sequadzo 28th“ | In [[Kite's color notation|color notation]], its name would be: “ascending quinla-sequadzo 28th“ | ||
Revision as of 21:31, 7 March 2026
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 |
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“