441/440
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| Ratio | 441/440 |
| Factorization | 2-3 × 32 × 5-1 × 72 × 11-1 |
| Monzo | [-3 2 -1 2 -1⟩ |
| Size in cents | 3.9301584¢ |
| Name | werckisma |
| Color name | Luzozogu |
| FJS name | [math]\text{m2}^{7,7}_{5,11}[/math] |
| Special properties | square superparticular, reduced |
| Tenney height (log2 n⋅d) | 17.566 |
| Weil height (max(n, d)) | 441 |
| Benedetti height (n⋅d) | 194040 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.46438 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.
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 also
- Werckismic chords
- Rank-4 temperament #Werckismic (441/440)
- Werckismic temperaments, a collection of rank-3 temperaments where it is tempered out
- Small comma
- List of superparticular intervals