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]], 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. It is very 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]].

'''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 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]]

==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| (|( }}.

== See also ==

* [[88/45]] – its [[octave complement]]

* [[22/15]] – its [[fifth complement]]

* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

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-'''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.  It is very 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]].
+'''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.
 /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.
+/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]]
-==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| (|( }}.
 == See also ==
-* [[88/45]] – its [[octave complement]]
+* [[88/45]] &ndash; its [[octave complement]]
-* [[22/15]] – its [[fifth complement]]
+* [[22/15]] &ndash; its [[fifth complement]]
 * [[Gallery of just intervals]]
 * [[List of superparticular intervals]]