45/44

Interval information

Ratio	45/44
Factorization	2-2 × 32 × 5 × 11-1
Monzo	[-2 2 1 0 -1⟩
Size in cents	38.90577¢
Name	undecimal 1/5-tone
Color name	1uy1, luyo comma
FJS name	[math]\displaystyle{ \text{A1}^{5}_{11} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	10.9513
Weil height (log2 max(n, d))	10.9837
Wilson height (sopfr(nd))	26
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45/44, ~38.906 cents, the undecimal 1/5-tone, is the interval between 11/9 and 5/4, and also between 11/10 and 9/8. 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.

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.

Ocean's cake

See also

• 88/45 – its octave complement
• 22/15 – its fifth complement
• Gallery of just intervals
• List of superparticular intervals
• Medium commas