Gothic comma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 134217728/129140163 | | Ratio = 134217728/129140163 | ||
| Name = 17-comma, | | Name = 17-comma, gothic comma, Pythagorean gothma | ||
| Color name = ssw3, sasawa 3rd,<br>Wa-17 comma | | Color name = ssw3, sasawa 3rd,<br>Wa-17 comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
''' | The '''17-comma''', otherwise known as the '''gothic comma''' or '''Pythagorean gothma''' ({{monzo|legend=1| 27 -17 }}, [[ratio]]: 134217728/129140163), is an interval of 66.765{{cent}}. It is the amount by which seventeen [[fifth]]s fall short of ten [[octave]]s, or 2<sup>10</sup>/(3/2)<sup>17</sup>. | ||
== 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 : pytha<u>go</u>tonic :: mystery : pytha<u>mys</u>tonic. | |||
The second term ''Pythagorean gothma'', is part of a series of step names in the [[Pythagorean tuning|Pythagorean]] [[diatonic scale]], where ''gothma'' refers to the double diminished 2-step. | |||
== See also == | == See also == | ||
* [[Gallery of | * [[Gallery of just intervals]] | ||
* [[Medium commas]] | * [[Medium commas]] | ||
Revision as of 05:55, 13 June 2023
| Interval information |
gothic comma,
Pythagorean gothma
Wa-17 comma
reduced subharmonic
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 fifths fall short of ten octaves, or 210/(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.