User:Dave Keenan/sandbox: Difference between revisions

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== History ==

[[Chain-of-fifths_notation#Accidentals|Stein-Zimmermann notation]] can be viewed as a very simple apotome-fraction notation, only ~~capable of notating~~ half-apotomes.

[[Chain-of-fifths_notation#Accidentals|Stein-Zimmermann notation]] can be viewed as a very simple apotome-fraction notation, notating only half-apotomes.

On 24-Sep-2016 in the Facebook Group: Microtonal Music and Tuning Theory, [[Cryptic Ruse|Cryptic Ruse (aka Jason Yerger)]] introduced [https://www.facebook.com/groups/497105067092502/permalink/840445019425170/ |a combination of apotome-fraction and limma-fraction notations] to cover all EDOs up to 72. This may have been the first proposal of a limma fraction notation.

On 24-Sep-2016 in the Facebook Group: Microtonal Music and Tuning Theory, [[Cryptic Ruse|Cryptic Ruse (aka Jason Yerger)]] introduced the idea of using [https://www.facebook.com/groups/497105067092502/permalink/840445019425170/ |a combination of apotome-fraction and limma-fraction notations] to cover all EDOs up to 72. This may have been the first proposal of a limma fraction notation.

When the EDO has fifths so ~~wide~~ that the ~~limma~~ becomes very small or negative (e.g. 32-EDO), ~~an apotome~~-fraction notation must be used. When the EDO has fifths so ~~narrow~~ that the ~~apotome~~ becomes very small or negative (e.g. 33-EDO), ~~limma~~-fraction ~~notations~~ must be used.

When the EDO has fifths so narrow that the apotome becomes very small or negative (e.g. 33-EDO), a limma-fraction notation must be used. When the EDO has fifths so wide that the limma becomes very small or negative (e.g. 32-EDO), an apotome-fraction notation must be used.

Although Cryptic Ruse later abandoned these notations, the ~~principle~~ was adopted by George Secor and Dave Keenan ~~for~~ the notation of EDOs with bad fifths~~, where~~ a bad fifth ~~is defined~~ as one with an error of more than 10 cents ~~(check this)~~.

Although Cryptic Ruse later abandoned these notations, the idea was adopted by George Secor and Dave Keenan to simplify the notation of EDOs with bad fifths in the Sagittal notation system. Sagittal defines a bad fifth as one with an error of more than 10.5 cents from just.

== Apotome-fraction notations ==

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 == History ==
-[[Chain-of-fifths_notation#Accidentals|Stein-Zimmermann notation]] can be viewed as a very simple apotome-fraction notation, only capable of notating half-apotomes.
+[[Chain-of-fifths_notation#Accidentals|Stein-Zimmermann notation]] can be viewed as a very simple apotome-fraction notation, notating only half-apotomes.
-On 24-Sep-2016 in the Facebook Group: Microtonal Music and Tuning Theory, [[Cryptic Ruse|Cryptic Ruse (aka Jason Yerger)]] introduced [https://www.facebook.com/groups/497105067092502/permalink/840445019425170/ |a combination of apotome-fraction and limma-fraction notations] to cover all EDOs up to 72. This may have been the first proposal of a limma fraction notation.
+On 24-Sep-2016 in the Facebook Group: Microtonal Music and Tuning Theory, [[Cryptic Ruse|Cryptic Ruse (aka Jason Yerger)]] introduced the idea of using [https://www.facebook.com/groups/497105067092502/permalink/840445019425170/ |a combination of apotome-fraction and limma-fraction notations] to cover all EDOs up to 72. This may have been the first proposal of a limma fraction notation.
-When the EDO has fifths so wide that the limma becomes very small or negative (e.g. 32-EDO), an apotome-fraction notation must be used. When the EDO has fifths so narrow that the apotome becomes very small or negative (e.g. 33-EDO), limma-fraction notations must be used.
+When the EDO has fifths so narrow that the apotome becomes very small or negative (e.g. 33-EDO), a limma-fraction notation must be used. When the EDO has fifths so wide that the limma becomes very small or negative (e.g. 32-EDO), an apotome-fraction notation must be used.
-Although Cryptic Ruse later abandoned these notations, the principle was adopted by George Secor and Dave Keenan for the notation of EDOs with bad fifths, where a bad fifth is defined as one with an error of more than 10 cents (check this).
+Although Cryptic Ruse later abandoned these notations, the idea was adopted by George Secor and Dave Keenan to simplify the notation of EDOs with bad fifths in the Sagittal notation system. Sagittal defines a bad fifth as one with an error of more than 10.5 cents from just.
 == Apotome-fraction notations ==