Gammic comma: Difference between revisions
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The '''gammic comma''' ({{monzo|legend=1| -29 -11 20 }}) is a [[small comma|small]] [[5-limit]] [[comma]] with a size of 4.769 [[cent]]s. It is the difference between nine [[5/4|just major thirds]] and eleven [[6/5|just minor thirds]], that is, (5/4)<sup>9</sup>/(6/5)<sup>11</sup>. This can also be written as (3/2)/(25/24)<sup>10</sup>, that is, the difference between a stack of ten [[25/24|classic chromatic semitones]] and a [[5/3|classic major sixth]]; it is part of a series of [[Don Page comma]]s between adjacent [[superparticular]]s, following the [[escapade comma]], which follows the [[Pythagorean comma]]; and also the difference between the [[valentine comma]] and [[sycamore comma]]. | The '''gammic comma''' ({{monzo|legend=1| -29 -11 20 }}) is a [[small comma|small]] [[5-limit]] [[comma]] with a size of 4.769 [[cent]]s. It is the difference between nine [[5/4|just major thirds]] and eleven [[6/5|just minor thirds]], that is, (5/4)<sup>9</sup>/(6/5)<sup>11</sup>. This can also be written as (3/2)/(25/24)<sup>10</sup>, that is, the difference between a stack of ten [[25/24|classic chromatic semitones]] and a [[5/3|classic major sixth]]; it is part of a series of [[Don Page comma]]s between adjacent [[superparticular]]s, following the [[escapade comma]], which follows the [[Pythagorean comma]]; and also the difference between the [[valentine comma]] and [[sycamore comma]]. It is additionally the difference between a [[diaschisma]] and three [[kleisma]]s. | ||
== Temperaments == | == Temperaments == | ||
Revision as of 23:54, 10 December 2024
| Interval information |
The gammic comma (monzo: [-29 -11 20⟩) is a small 5-limit comma with a size of 4.769 cents. It is the difference between nine just major thirds and eleven just minor thirds, that is, (5/4)9/(6/5)11. This can also be written as (3/2)/(25/24)10, that is, the difference between a stack of ten classic chromatic semitones and a classic major sixth; it is part of a series of Don Page commas between adjacent superparticulars, following the escapade comma, which follows the Pythagorean comma; and also the difference between the valentine comma and sycamore comma. It is additionally the difference between a diaschisma and three kleismas.
Temperaments
Temperaments in the gammic family temper out this comma.
Etymology
The gammic comma is named after the Carlos Gamma scale, nearly identical to 20edf, which the gammic temperament generates.