Gothic comma
| Ratio | 134217728/129140163 |
| Factorization | 227 × 3-17 |
| Monzo | [27 -17⟩ |
| Size in cents | 66.764985¢ |
| Names | gothic comma, 17-comma, Pythagorean gothma, Pythagorean double-diminished third |
| Color name | ssw3, sasawa 3rd, Wa-17 comma |
| FJS name | [math]\text{dd3}[/math] |
| Special properties | reduced, reduced subharmonic |
| Tenney height (log2 nd) | 53.9444 |
| Weil height (log2 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 gothic comma, otherwise known as the 17-comma or Pythagorean gothma (monzo: [27 -17⟩, ratio: 134217728/129140163), is a 3-limit interval of 66.765 ¢. It is the amount by which seventeen perfect fifths fall short of ten octaves, or 210/(3/2)17. If used as an interval in its own right, it is the Pythagorean double-diminished third.
Temperaments
Tempering out this comma in the 5-limit leads to the gothic temperament. For edos up to 152 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.
Additionally, by coincidence, the term "gothic" fits into the naming scheme of the comptonesque temperament collection, representing Vector's project Not!Earth in which the Goths are a major culture group.
The second term Pythagorean gothma is part of a series of step names in the Pythagorean diatonic scale, where gothma (adjective: gothmic) refers to the double diminished 2-step, i.e. |3s - L|.