Procyon comma: Difference between revisions
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The '''procyon comma''', 823543/820125, is a [[small comma|small]] no-twos [[7-limit]] [[comma]] with a size | The '''procyon comma''', 823543/820125, is a [[small comma|small]] no-twos [[7-limit]] [[comma]] with a size very close to exactly 7.2 [[cent]]s. It is the difference between four [[9/7|septimal supermajor thirds (9/7)]] and three [[7/5|small septimal tritones (7/5)]], that is, (7/5)<sup>3</sup>/(9/7)<sup>4</sup>. This can also be written as (9/5)/(49/45)<sup>8</sup>, that is, the difference between a stack of seven [[49/45]] neutral seconds and a [[9/5]] minor seventh; it is part of a series of [[Don Page comma]]s between adjacent [[delta-N ratio|odd-particular]]s, following the [[3125/3087|gariboh comma (3125/3087)]]. It is additionally the difference between two [[245/243|sensamagic commas (245/243)]] and a gariboh comma. | ||
== Temperaments == | == Temperaments == | ||
The [[procyon]] temperament in the [[3.5.7 subgroup]] tempers out this comma, giving it its name. It can also be tempered out in the 2.7/5.9/5 subgroup. | The [[procyon]] temperament in the [[3.5.7 subgroup]] tempers out this comma, giving it its name. It can also be tempered out in the 2.7/5.9/5 subgroup. | ||
[[Category:Commas named for other reasons]] | |||
Latest revision as of 06:51, 17 January 2025
| Interval information |
The procyon comma, 823543/820125, is a small no-twos 7-limit comma with a size very close to exactly 7.2 cents. It is the difference between four septimal supermajor thirds (9/7) and three small septimal tritones (7/5), that is, (7/5)3/(9/7)4. This can also be written as (9/5)/(49/45)8, that is, the difference between a stack of seven 49/45 neutral seconds and a 9/5 minor seventh; it is part of a series of Don Page commas between adjacent odd-particulars, following the gariboh comma (3125/3087). It is additionally the difference between two sensamagic commas (245/243) and a gariboh comma.
Temperaments
The procyon temperament in the 3.5.7 subgroup tempers out this comma, giving it its name. It can also be tempered out in the 2.7/5.9/5 subgroup.