Procyon comma

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]\text{5d5}^{7,7,7,7,7,7,7}_{5,5,5}[/math]
Special properties	reduced
Tenney height (log2 nd)	39.297
Weil height (log2 max(n, d))	39.303
Wilson height (sopfr(nd))	88
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.67047 bits
Comma size	small
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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.