User:Dave Keenan/sandbox: Difference between revisions

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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 fractional 3-limit notations ==

The Sagittal system uses fractional 3-limit notations only for EDOs with bad fifths, defined as fifths with errors of more than 10.5 cents from just. EDOs with good fifths have JI-based notations.

=== Bad-fifths apotome-fraction notation ===

This notation is used for EDOs with fifths of 712.5 cents or more. These are the gold EDOs on the [https://sagittal.org/#periodic-table Periodic Table], although it is recommended that EDOs with extremely wide fifths, 6, 8, 13 and 18 are notated as subsets of 12, 24, 26 and 36 respectively.

=== Bad-fifths limma-fraction notation ===

This notation is used for EDOs with fifths of 791.5 cents or less. These are the rose EDOs on the [https://sagittal.org/#periodic-table Periodic Table], although it is recommended that 11-EDO, which has an extremely narrow fifth, is notated as a subset of 22.

[[Category:Notation]]

[[Category:Sagittal notation]]

@@ Line 8: / Line 8: @@
 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 fractional 3-limit notations ==
+The Sagittal system uses fractional 3-limit notations only for EDOs with bad fifths, defined as fifths with errors of more than 10.5 cents from just. EDOs with good fifths have JI-based notations.
 === Bad-fifths apotome-fraction notation ===
+This notation is used for EDOs with fifths of 712.5 cents or more. These are the gold EDOs on the [https://sagittal.org/#periodic-table Periodic Table], although it is recommended that EDOs with extremely wide fifths, 6, 8, 13 and 18 are notated as subsets of 12, 24, 26 and 36 respectively.
 === Bad-fifths limma-fraction notation ===
+This notation is used for EDOs with fifths of 791.5 cents or less. These are the rose EDOs on the [https://sagittal.org/#periodic-table Periodic Table], although it is recommended that 11-EDO, which has an extremely narrow fifth, is notated as a subset of 22.
 [[Category:Notation]]
 [[Category:Sagittal notation]]