Tetracot comma: Difference between revisions

(11 intermediate revisions by 8 users not shown)

Line 1:

20000/19683, ~~the~~ tetracot [[~~Comma|comma~~]] or minimal diesis, is ~~an interval~~ of 27.660 ~~cents~~ which is the amount by which four [[10/9|minor whole tones]] exceed a fifth; that is, (10/9)^4/(3/2). Tempering it out leads to [[~~Tetracot_family|~~tetracot ~~temperament~~]].

{{Infobox Interval

[[Category:~~comma~~]]

| Ratio = 20000/19683

[[Category:~~tetracot~~]]

| Name = tetracot comma, minimal diesis

| Color name = sy<sup>4</sup>1, Saquadyo comma

| Comma = yes

}}

The '''tetracot comma''' ({{monzo|legend=1| 5 -9 4 }}, [[ratio]]: 20000/19683), or '''minimal diesis''', is a [[small comma|small]] [[5-limit]] [[comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9|minor whole tones]] exceed a [[3/2|fifth]]; that is, (10/9)<sup>4</sup>/(3/2). It can also be expressed as the octave-reduced difference between four [[5/4|just major thirds]] and nine just perfect fifths, which directly follows from its monzo. Another characterization is the interval between four [[81/80|syntonic commas]] and a [[2187/2048|Pythagorean apotome]], making the corresponding temperament a member of the [[syntonic–chromatic equivalence continuum]]. Since an apotome minus two syntonic commas is a [[25/24|classical chroma]], the comma can be expressed as the difference between an apotome and a stack of two classical chromas, or between a classical chroma and a stack of two syntonic commas.

== Temperaments ==

Tempering out this comma leads to the [[tetracot family]] of temperaments.

[[Category:Tetracot]]

[[Category:Commas named for how they divide the fifth]]

@@ Line 1: / Line 1: @@
-/19683, the tetracot [[Comma|comma]] or minimal diesis, is an interval of 27.660 cents which is the amount by which four [[10/9|minor whole tones]] exceed a fifth; that is, (10/9)^4/(3/2). Tempering it out leads to [[Tetracot_family|tetracot temperament]].
+{{Infobox Interval
-[[Category:comma]]
+| Ratio = 20000/19683
-[[Category:tetracot]]
+| Name = tetracot comma, minimal diesis
+| Color name = sy<sup>4</sup>1, Saquadyo comma
+| Comma = yes
+}}
+The '''tetracot comma''' ({{monzo|legend=1| 5 -9 4 }}, [[ratio]]: 20000/19683), or '''minimal diesis''', is a [[small comma|small]] [[5-limit]] [[comma]] of 27.660 [[cent]]s which is the amount by which four [[10/9|minor whole tones]] exceed a [[3/2|fifth]]; that is, (10/9)<sup>4</sup>/(3/2). It can also be expressed as the octave-reduced difference between four [[5/4|just major thirds]] and nine just perfect fifths, which directly follows from its monzo. Another characterization is the interval between four [[81/80|syntonic commas]] and a [[2187/2048|Pythagorean apotome]], making the corresponding temperament a member of the [[syntonic&ndash;chromatic equivalence continuum]]. Since an apotome minus two syntonic commas is a [[25/24|classical chroma]], the comma can be expressed as the difference between an apotome and a stack of two classical chromas, or between a classical chroma and a stack of two syntonic commas.
+== Temperaments ==
+Tempering out this comma leads to the [[tetracot family]] of temperaments.
+[[Category:Tetracot]]
+[[Category:Commas named for how they divide the fifth]]