441/440

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	1uzzg2, luzozogu 2nd, Luzozogu comma
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
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.34196 bits
Comma size	small
S-expression	S21
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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.

See also

• List of superparticular intervals