Gothic comma: Difference between revisions

(23 intermediate revisions by 11 users not shown)

Line 1:

134217728/129140163 = |~~27 -17>~~, ~~called~~ the 17-comma, is an interval of 66.765 ~~cents,~~ is the amount by which seventeen ~~fifths~~ fall short of ten ~~octaves~~, or 2^10/(3/2)^17. ~~For EDOs up to 150~~ the 17-~~comma is tempered out if and only if 17 divides it, for example [[17edo|17edo]], [[34edo|34edo]] or [[68edo|68edo]]~~.

{{Infobox Interval

| Ratio = 134217728/129140163

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

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

| Comma = yes

}}

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'''.

~~See~~: [[~~Comma|~~comma]], [[~~Gallery_of_Just_Intervals~~|Gallery of ~~Just Intervals~~]] [[Category:~~comma~~]]

== Temperaments ==

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 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'' (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: @@
-134217728/129140163 = |27 -17&gt;, called the 17-comma, is an interval of 66.765 cents, is the amount by which seventeen fifths fall short of ten octaves, or 2^10/(3/2)^17. For EDOs up to 150 the 17-comma is tempered out if and only if 17 divides it, for example [[17edo|17edo]], [[34edo|34edo]] or [[68edo|68edo]].
+{{Infobox Interval
+| Ratio = 134217728/129140163
+| Name = gothic comma, 17-comma, Pythagorean gothma, Pythagorean double-diminished third
+| Color name = ssw3, sasawa 3rd,<br>17wM, sewama
+| Comma = yes
+}}
+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'''.
-See: [[Comma|comma]], [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:comma]]
+== Temperaments ==
+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 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'' (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]]