45/44: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = undecimal 1/5-tone, cake comma

~~| Ratio = 45/44~~

| Color name = 1uy1, luyo 1sn,<br>Luyo comma

~~| Monzo = -2 2 1 0 -1~~

~~| Cents = 38.90577~~

| Name = undecimal 1/5-tone

| Color name = 1uy1, luyo ~~comma~~

~~| FJS name = A1~~<~~sup>5</sup><sub>11</sub~~>

| Sound = Ji-45-44-csound-foscil-220hz.mp3

| Comma = yes

}}

'''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~~.

'''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]].

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~~.

== 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]].

== Temperaments ==

[[File:Oceania's cake.jpg|thumb|Ocean's cake]]

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 [[Catalog of rank-4 temperaments #Cake (45/44)|cake temperament]], [[support]]ed by the [[patent val]]s for [[12edo|12-]], [[19edo|19-]], and [[26edo|26-tone equal temperament]].

== 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 ==

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* [[Gallery of just intervals]]

* [[List of superparticular intervals]]

* [[Medium ~~commas~~]]

* [[Medium comma]]

[[Category:~~11-limit~~]]

[[Category:Cake]]

[[Category:~~Interval]]~~

[[Category:Commas named following events]]

~~[[Category:Ratio]]~~

~~[[Category:Comma]]~~

~~[[Category:Medium comma]]~~

~~[[Category:Superparticular]]~~

~~[[Category:Listen~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = undecimal 1/5-tone, cake comma
-| Ratio = 45/44
+| Color name = 1uy1, luyo 1sn,<br>Luyo comma
-| Monzo = -2 2 1 0 -1
-| Cents = 38.90577
-| Name = undecimal 1/5-tone
-| Color name = 1uy1, luyo comma
-| FJS name = A1<sup>5</sup><sub>11</sub>
 | Sound = Ji-45-44-csound-foscil-220hz.mp3
+| Comma = yes
 }}
-'''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.
+'''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]].
-/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.
+== Approximation ==
+/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]].
+== Temperaments ==
 [[File:Oceania's cake.jpg|thumb|Ocean's cake]]
+/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 [[Catalog of rank-4 temperaments #Cake (45/44)|cake temperament]], [[support]]ed by the [[patent val]]s for [[12edo|12-]], [[19edo|19-]], and [[26edo|26-tone equal temperament]].
+== 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 ==
@@ Line 21: / Line 27: @@
 * [[Gallery of just intervals]]
 * [[List of superparticular intervals]]
-* [[Medium commas]]
+* [[Medium comma]]
-[[Category:11-limit]]
+[[Category:Cake]]
-[[Category:Interval]]
+[[Category:Commas named following events]]
-[[Category:Ratio]]
-[[Category:Comma]]
-[[Category:Medium comma]]
-[[Category:Superparticular]]
-[[Category:Listen]]