User:Dave Keenan/sandbox: Difference between revisions
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On 24-Sep-2016 in the Facebook Group: Microtonal Music and Tuning Theory, [[Cryptic Ruse]] 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. | On 24-Sep-2016 in the Facebook Group: Microtonal Music and Tuning Theory, [[Cryptic Ruse]] 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 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. | 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 ideas, they were 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. | Although Cryptic Ruse later abandoned these ideas, they were 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. | ||