441/440

From Xenharmonic Wiki
Revision as of 07:38, 24 December 2020 by Aura (talk | contribs) (re-added the approach mentioned in the original version of this article as an additional approach option and rewrote the last sentence)
Jump to navigation Jump to search
Interval information
Ratio 441/440
Factorization 2-3 × 32 × 5-1 × 72 × 11-1
Monzo [-3 2 -1 2 -1
Size in cents 3.930158¢
Name werckisma
Color name Luzozogu
FJS name [math]\displaystyle{ \text{m2}^{7,7}_{5,11} }[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 17.566
Weil height (log2 max(n, d)) 17.5693
Wilson height (sopfr(nd)) 42
Open this interval in xen-calc

441/440, also known as Werckmeister's undecimal septenarian schisma, or more simply, the werckisma, is a small superparticular 11-limit comma with a size of roughly 3.93 cents. It is the difference between 21/20 and 22/21, as well as the difference between a stack of two 21/16 septimal subfourths and a single 55/32 supermajor sixth. Among other things, tempering it out splits 11/10 into two even halves and makes werckismic chords possible.

See also