17-comma
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Ratio | 134217728/129140163 |
Factorization | 2^{27} × 3^{-17} |
Monzo | [27 -17⟩ |
Size in cents | 66.764985¢ |
Names | 17-comma, gothic comma, Pythagorean gothma |
Color name | ssw3, sasawa 3rd, Wa-17 comma |
FJS name | [math]\text{dd3}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 53.9444 |
Weil height (log_{2} max(n, d)) | 54 |
Wilson height (sopfr (nd)) | 105 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.36401 bits |
Comma size | medium |
open this interval in xen-calc |
The 17-comma, otherwise known as the gothic comma or Pythagorean gothma (monzo: [27 -17⟩, ratio: 134217728/129140163), is an interval of 66.765 ¢. It is the amount by which seventeen perfect fifths fall short of ten octaves, or 2^{10}/(3/2)^{17}.
Temperaments
Tempering out this comma in the 5-limit leads to the gothic temperament. For edos up to 150 the comma is tempered out if and only if 17 divides it, for example 17edo, 34edo or 68edo.
Terminology
The names were given by Flora Canou in 2023. The first term gothic comma draws two inspirations:
- the neogothic tuning available in 17edo, and
- the link of TAMNAMS Extension name and comma names by the analogy pair gothic : pythagotonic :: mystery : pythamystonic.
The second term Pythagorean gothma is part of a series of step names in the Pythagorean diatonic scale, where gothma refers to the double diminished 2-step, i.e. |3s - L|.