441/440
Ratio | 441/440 |
Factorization | 2^{-3} × 3^{2} × 5^{-1} × 7^{2} × 11^{-1} |
Monzo | [-3 2 -1 2 -1⟩ |
Size in cents | 3.9301584¢ |
Name | werckisma |
Color name | 1uzzg2, luzozogu 2nd, Luzozogu comma |
FJS name | [math]\text{m2}^{7,7}_{5,11}[/math] |
Special properties | square superparticular, reduced |
Tenney height (log_{2} nd) | 17.566 |
Weil height (log_{2} max(n, d)) | 17.5693 |
Wilson height (sopfr (nd)) | 42 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.34196 bits |
Comma size | small |
S-expression | S21 |
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, and between 80/63 ( = (10/9)(8/7)) and 14/11, as well as the amount by which a stack of two 21/16 septimal subfourths exceeds a single 55/32 supermajor sixth. It also arises as the following comma differences: (49/48)/(55/54), (56/55)(64/63), (81/80)/(99/98), (126/125)/(176/175), and (243/242)/(540/539).
Temperaments
Tempering it out splits 11/10 into two even halves, equates 21/16 with 55/42 to create some interesting-sounding triads, and makes werckismic chords possible. See Rank-4 temperament #Werckismic (441/440) for some technical data. See Werckismic temperaments for a collection of rank-3 temperaments where it is tempered out.