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 | 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 (5/4)]] and eleven [[6/5|just minor thirds (6/5)]], that is, (6/5)<sup>11</sup>/(5/4)<sup>9</sup>. This can also be written as (25/24)<sup>10</sup>/(3/2), that is, the difference between a stack of ten [[25/24|classic chromatic semitones]] and a [[3/2|perfect fifth]]; 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 three [[15625/15552|kleismas (15625/15552)]] and a [[diaschisma]] (2048/2025). | ||
== Temperaments == | == Temperaments == | ||
Latest revision as of 12:54, 14 January 2025
| 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 (5/4) and eleven just minor thirds (6/5), that is, (6/5)11/(5/4)9. This can also be written as (25/24)10/(3/2), that is, the difference between a stack of ten classic chromatic semitones and a perfect fifth; 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 three kleismas (15625/15552) and a diaschisma (2048/2025).
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.