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 of 7.200 [[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 [[gariboh comma|gariboh comma (3125/3087)]]. It is additionally the difference between two [[245/243|sensamagic commas (245/243)]] and a gariboh comma.
The '''procyon comma''', 823543/820125, is a [[small comma|small]] no-twos [[7-limit]] [[comma]] with a size of 7.200 [[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.

Revision as of 13:00, 14 January 2025

Interval information
Ratio 823543/820125
Factorization 3-8 × 5-3 × 77
Monzo [0 -8 -3 7
Size in cents 7.200197¢
Name procyon comma
FJS name [math]\displaystyle{ \text{5d5}^{7,7,7,7,7,7,7}_{5,5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 39.297
Weil norm (log2 max(n, d)) 39.303
Wilson norm (sopfr(nd)) 88
Comma size small
Open this interval in xen-calc

The procyon comma, 823543/820125, is a small no-twos 7-limit comma with a size of 7.200 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.