45/44
Ratio | 45/44 |
Factorization | 2^{-2} × 3^{2} × 5 × 11^{-1} |
Monzo | [-2 2 1 0 -1⟩ |
Size in cents | 38.905773¢ |
Names | undecimal 1/5-tone, cake comma |
Color name | 1uy1, luyo 1sn, Luyo comma |
FJS name | [math]\text{A1}^{5}_{11}[/math] |
Special properties | superparticular, reduced |
Tenney height (log_{2} nd) | 10.9513 |
Weil height (log_{2} max(n, d)) | 10.9837 |
Wilson height (sopfr (nd)) | 26 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.5186 bits |
Comma size | medium |
S-expression | S9 × S10 |
[sound info] | |
open this interval in xen-calc |
45/44, ~38.906 cents, the undecimal 1/5-tone, is the interval between 11/9 and 5/4, between 11/10 and 9/8, and between 22/15 and 3/2. It is tempered out by the patent vals for 12, 19, and 26 equal. When one uses 45/44 as an interval in its own right, it has properties akin to a sort of chroma, and it differs from 8192/8019, the Alpharabian inframinor second, by the schisma.
45/44 is also known as the "cake" comma, from when Ocean Stegosaurus Tardigrade was baking a cake and misread flour and sugar measurements on his scale, leading to the inclusion of 11/9 times the amount suggested in his recipe. To compensate, he writes "I increased all the other ingredients by a neutral third, except the eggs, which I increased by a major third because I couldn't be bothered to measure out eight ninths of an egg." We see here the equating of 11/9 with 5/4, leading to the tempering out of 45/44. The cake turned out fine but slightly burnt on the top.