Escapade comma: Difference between revisions

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| Monzo = 32 -7 -9

| Name = escapade comma

| Color name = ~~ssp~~94, sasa-tritrigu 4th

| Color name = ssg94, sasa-tritrigu 4th

| Comma = yes

}}

The '''escapade comma''' (~~[[monzo]]:~~ {{monzo| 32 -7 -9 }}) is a [[comma]] with a size of 9.492 [[cent]]s. It is the difference between nine [[5/4|just major thirds]] and seven [[4/3|just perfect fourths]], that is, ~~<math>\left~~(~~\frac{~~4}{3~~}\right~~)^{7~~}\left~~(~~\frac{~~4~~}{5}\right~~)^{9}</~~math~~>. This can also be written as ~~<math>\frac{~~5}{3~~}\left~~(~~\frac{~~15~~}{16}\right~~)^{8}</~~math~~>, that is, the difference between a stack of eight [[16/15|classic diatonic semitones]] and a [[5/3|classic major sixth]].

The '''escapade comma''' ({{monzo|legend=1| 32 -7 -9 }}) is a [[small comma|small]] [[5-limit]] [[comma]] with a size of 9.492 [[cent]]s. It is the difference between nine [[5/4|just major thirds]] and seven [[4/3|just perfect fourths]], that is, (4/3)7/(5/4)9. This can also be written as (5/3)/(16/15)8, that is, the difference between a stack of eight [[16/15|classic diatonic semitones]] and a [[5/3|classic major sixth]]. In terms of commas, it is equal to two [[128/125|lesser dieses]] minus three [[81/80|syntonic commas]] and one [[15625/15552|kleisma]], that is, (128/125)2/((15625/15552)(81/80)3).

It is ~~also~~ equal to two [[128/125|lesser dieses]] minus three [[81/80|syntonic commas]] and one [[15625/15552|kleisma]].

== Temperaments ==

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== Etymology ==

The escapade comma seems to have been named by [[Paul Erlich]] in 2002, referring to the fact that this comma "escaped" a 5-limit comma search by [[Carl Lumma]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>.

~~== See also ==~~

* [[Small comma]]

== Notes ==

[[Category:Escapade]]

[[Category:Commas named following events]]

@@ Line 3: / Line 3: @@
 | Monzo = 32 -7 -9
 | Name = escapade comma
-| Color name = ssp<sup>9</sup>4, sasa-tritrigu 4th
+| Color name = ssg<sup>9</sup>4, sasa-tritrigu 4th
 | Comma = yes
 }}
-The '''escapade comma''' ([[monzo]]: {{monzo| 32 -7 -9 }}) is a [[comma]] with a size of 9.492 [[cent]]s. It is the difference between nine [[5/4|just major thirds]] and seven [[4/3|just perfect fourths]], that is, <math>\left(\frac{4}{3}\right)^{7}\left(\frac{4}{5}\right)^{9}</math>. This can also be written as <math>\frac{5}{3}\left(\frac{15}{16}\right)^{8}</math>, that is, the difference between a stack of eight [[16/15|classic diatonic semitones]] and a [[5/3|classic major sixth]].
+The '''escapade comma''' ({{monzo|legend=1| 32 -7 -9 }}) is a [[small comma|small]] [[5-limit]] [[comma]] with a size of 9.492 [[cent]]s. It is the difference between nine [[5/4|just major thirds]] and seven [[4/3|just perfect fourths]], that is, (4/3)<sup>7</sup>/(5/4)<sup>9</sup>. This can also be written as (5/3)/(16/15)<sup>8</sup>, that is, the difference between a stack of eight [[16/15|classic diatonic semitones]] and a [[5/3|classic major sixth]]. In terms of commas, it is equal to two [[128/125|lesser dieses]] minus three [[81/80|syntonic commas]] and one [[15625/15552|kleisma]], that is, (128/125)<sup>2</sup>/((15625/15552)(81/80)<sup>3</sup>).
-It is also equal to two [[128/125|lesser dieses]] minus three [[81/80|syntonic commas]] and one [[15625/15552|kleisma]].
 == Temperaments ==
@@ Line 15: / Line 13: @@
 == Etymology ==
 The escapade comma seems to have been named by [[Paul Erlich]] in 2002, referring to the fact that this comma "escaped" a 5-limit comma search by [[Carl Lumma]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html#5113 Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']</ref>.
-== See also ==
-* [[Small comma]]
 == Notes ==
 [[Category:Escapade]]
+[[Category:Commas named following events]]