Counterquectisma

From Xenharmonic Wiki
Revision as of 15:15, 12 June 2023 by Eliora (talk | contribs) (Created page with "{{Infobox Interval |Monzo = -500 314 1 |Name = counterquectisma, deltapion comma, |Color name = Quintritrilayo comma |Comma = yes }} '''Counterquectisma''', alternately '''del...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
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, alternately 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.

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.