Gothic comma: Difference between revisions

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{{Infobox Interval

| Ratio = 134217728/129140163

| Name = 17-comma, ~~gothic comma~~, Pythagorean ~~gothma~~

| Name = gothic comma, 17-comma, Pythagorean gothma, Pythagorean double-diminished third

| Color name = ssw3, sasawa 3rd, ~~Wa-17 comma~~

| Color name = ssw3, sasawa 3rd, 17wM, sewama

| 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 [[perfect fifth]]s fall short of ten [[octave]]s, or 210/(3/2)17.

The '''gothic comma''', otherwise known as the '''17-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 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]].

Tempering out this comma in the 5-limit leads to the [[gothic]] temperament. For edos up to [[136edo|136]], 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 [[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 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 ==

* [[Gallery of just intervals]]

* [[Medium comma]]

[[Category:Commas named for other reasons]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Ratio = 134217728/129140163
-| Name = 17-comma, gothic comma, Pythagorean gothma
+| Name = gothic comma, 17-comma, Pythagorean gothma, Pythagorean double-diminished third
-| Color name = ssw3, sasawa 3rd,<br>Wa-17 comma
+| Color name = ssw3, sasawa 3rd,<br>17wM, sewama
 | 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 [[perfect fifth]]s fall short of ten [[octave]]s, or 2<sup>10</sup>/(3/2)<sup>17</sup>.
+The '''gothic comma''', otherwise known as the '''17-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 ==
-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]].
+Tempering out this comma in the 5-limit leads to the [[gothic]] temperament. For edos up to [[136edo|136]], 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 [[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.
+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 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 ==
 * [[Gallery of just intervals]]
 * [[Medium comma]]
+[[Category:Commas named for other reasons]]