45/44: Difference between revisions
Expansion. |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| Line 6: | Line 6: | ||
}} | }} | ||
'''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 | '''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]]-tone equal temperament. | ||
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. | ||
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]]. | |||
[[File:Oceania's cake.jpg|thumb|Ocean's cake]] | [[File:Oceania's cake.jpg|thumb|Ocean's cake]] | ||
==Sagittal notation== | == Sagittal notation == | ||
In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{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{{nbhsp}}{{sagittal | (!( }}. The upward version is called '''5/11S''' or '''11/5S up''' and is represented by {{sagittal| (|( }}. | In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{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{{nbhsp}}{{sagittal | (!( }}. The upward version is called '''5/11S''' or '''11/5S up''' and is represented by {{sagittal| (|( }}. | ||
== See also == | == See also == | ||
* [[88/45]] | * [[88/45]] – its [[octave complement]] | ||
* [[22/15]] | * [[22/15]] – its [[fifth complement]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
Revision as of 18:21, 12 November 2024
| 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. It is tempered out by the patent vals for 12, 19, and 26-tone equal temperament.
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 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.
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 .