Counterquectisma

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Interval information

Factorization

2^-500 × 3³¹⁴ × 5

Monzo

[-500 314 1⟩

Size in cents

0.1839856¢

Names

counterquectisma,
deltapion comma,

Color name

Quintritrilayo comma

FJS name

[math]\displaystyle{ \text{45d}{-31}^{5} }[/math]

Special properties

reduced,
reduced harmonic

Tenney height (log₂ nd)

1000

Weil height (log₂ max(n, d))

1000

Wilson height (sopfr(nd))

1947

Comma size

unnoticeable

Open this interval in xen-calc

Counterquectisma, alternatively known as the deltapion comma, is an unnoticeable 5-limit comma.

Temperaments

It is associated with systems which have a precise perfect fifth, such as 359edo and 665edo. Tempering it out in the 5-limit produces rank-2 counterquectismic temperament (→ Very high accuracy temperaments #Counterquectismic). Equal tempereaments tempering out this comma include 359, 665, 1024, 1689, 3684, 4349, 7368, 8033 among others.

Etymology

The comma was named by Eliora. First name derives from comma's monzo, number 500 being D in roman numerals, and phonetic alphabet for D is "delta", to which "pi" is added to signify 314, the decimal expansion of pi. The second name is by analogy with quectisma, meaning that both are the same commas that reach 5/4 from a different angle, with two mappings converging from opposite ends in 665edo.