45/44
| Interval information |
cake comma
Luyo comma
reduced
[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.
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 2 | 0\2 | 0.00 | -38.91 | -6.48 |
| 3 | 0\3 | 0.00 | -38.91 | -9.73 |
| 28 | 1\28 | 42.86 | +3.95 | +9.22 |
| 29 | 1\29 | 41.38 | +2.47 | +5.98 |
| 30 | 1\30 | 40.00 | +1.09 | +2.74 |
| 31 | 1\31 | 38.71 | -0.20 | -0.51 |
| 32 | 1\32 | 37.50 | -1.41 | -3.75 |
| 33 | 1\33 | 36.36 | -2.54 | -6.99 |
| 59 | 2\59 | 40.68 | +1.77 | +8.71 |
| 60 | 2\60 | 40.00 | +1.09 | +5.47 |
| 61 | 2\61 | 39.34 | +0.44 | +2.23 |
| 62 | 2\62 | 38.71 | -0.20 | -1.01 |
| 63 | 2\63 | 38.10 | -0.81 | -4.26 |
| 64 | 2\64 | 37.50 | -1.41 | -7.50 |
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 .