45/44: Difference between revisions

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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 [[12edo|12]], [[19edo|19]], and [[26edo|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''', ~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 [[12edo|12]], [[19edo|19]], and [[26edo|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.
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.

Revision as of 19:44, 31 March 2024

Interval information
Ratio 45/44
Factorization 2-2 × 32 × 5 × 11-1
Monzo [-2 2 1 0 -1
Size in cents 38.90577¢
Names undecimal 1/5-tone,
cake comma
Color name 1uy1, luyo 1sn,
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
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.

Ocean's cake

See also