Gothic comma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 134217728/129140163 | | Ratio = 134217728/129140163 | ||
| Name = 17-comma, gothic comma, Pythagorean gothma | | Name = 17-comma, gothic comma, Pythagorean gothma, Pythagorean double-diminished third | ||
| 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 | The '''17-comma''', otherwise known as the '''gothic comma''' or '''Pythagorean gothma''' ({{monzo|legend=1| 27 -17 }}, [[ratio]]: 134217728/129140163), is a [[3-limit]] interval of 66.765{{cent}}. It is the amount by which seventeen [[perfect fifth]]s fall short of ten [[octave]]s, or 2<sup>10</sup>/(3/2)<sup>17</sup>. If used as an interval in its own right, it is the '''Pythagorean double-diminished third'''. | ||
== Temperaments == | == Temperaments == | ||
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# 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 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, i.e. |3s - L|. | The second term ''Pythagorean gothma'' is part of a series of step names in the [[Pythagorean tuning|Pythagorean]] [[diatonic scale]], where ''gothma'' (adjective: ''gothmic'') refers to the double diminished 2-step, i.e. |3s - L|. | ||
== See also == | == See also == | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[Medium comma]] | * [[Medium comma]] | ||
Revision as of 10:33, 25 July 2024
| Interval information |
gothic comma,
Pythagorean gothma,
Pythagorean double-diminished third
Wa-17 comma
reduced subharmonic
The 17-comma, otherwise known as the gothic 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.
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|.