Counterquectisma

This page presents a topic of primarily mathematical interest. While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

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 norm (log2 nd)	1000
Weil norm (log2 max(n, d))	1000
Wilson norm (sopfr(nd))	1947
Comma size	unnoticeable
Open this interval in xen-calc

The 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. Equal tempereaments tempering out this comma include 359, 665, 1024, 1689, 3684, 4349, 7368, 8033 among others.

Etymology

The comma was named by Eliora. The first 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. The second 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.