45/44
| Interval information |
cake comma
Luyo comma
reduced
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
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.
Approximation
45/44 is extremely close to a single step of 31edo, and is represented consistently there as well. 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.
Temperaments
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.
This temperament is the cake temperament, supported by the patent vals for 12-, 19-, and 26-tone equal temperament.
Notation
Sagittal notation
In the Sagittal system, the downward version of this comma (possibly tempered) is represented by the sagittal and is called the 11/5 small diesis, or 11/5S for short, because the simplest interval it notates is 11/5 (equiv. 11/10), as for example in C–D . The upward version is called 5/11S or 11/5S up and is represented by .