Fractional 3-limit notation: Difference between revisions

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EDOs in parentheses (6), (8), (13), and (18) have fifths that are so wide they are usually notated as subsets of larger EDOs with good fifths. [59]-EDO is in square brackets because it is green not gold on the periodic table, and so it should have a JI-based notation. However, its fifth is very close to the bad-fifth threshold and its 1-step symbol is only ~~justified~~ by the apotome-fraction notation, so its notation is a hybrid.

EDOs in parentheses (6), (8), (13), and (18) have fifths that are so wide they are usually notated as subsets of larger EDOs with good fifths. [59]-EDO is in square brackets because it is green not gold on the periodic table, and so it should have a JI-based notation. However, its fifth is very close to the bad-fifth threshold and its 1-step symbol is best justified<ref>In just intonation, {{sagittal| )| }} doesn't notate any common ratio that would make it valid as 1\59. It does however notate the uncommon ratio 55/49 = 5·11/7² by representing, as a secondary comma, 441/440 which tempers to 1\59 if only prime 3 is tempered or using the 59d map (second-best approximation of prime 7). Thanks to Roee Sinai for this JI-based justification. 55/49 ranks 87th in popularity among 2,3-free equivalence classes of ratios, according to [[N2D3P9#Table_of_top_100_.282.2C3-equivalent.29_pitch_ratio_classes_by_N2D3P9|N2D3P9]].</ref> by the apotome-fraction notation, so its notation is a hybrid.

To obtain the Evo notations, replace the multishaft symbols above with their Evo equivalents from the previous table.

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To obtain the Evo notations, delete the multishaft symbols. There are no equivalent combinations with conventional sharps or flats, as limmas are conventionally notated as the intervals B-C and E-F. The multishaft symbols are not required, even in Revo notation; they merely allow for alternative spellings there. In theory, sharps and flats ''could'' be used with the notations for 33, 40, and 47 because the sharp is one step for them, while it is zero or negative for the other rose EDOs and Sagittal never uses symbols for commas that have been tempered out or tempered negative. But Sagittal recommends not using sharps or flats, conventional or sagittal, with ''any'' limma-fraction notation.

== References ==

[[Category:Notation]]

[[Category:Sagittal notation]]

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-EDOs in parentheses (6), (8), (13), and (18) have fifths that are so wide they are usually notated as subsets of larger EDOs with good fifths. [59]-EDO is in square brackets because it is green not gold on the periodic table, and so it should have a JI-based notation. However, its fifth is very close to the bad-fifth threshold and its 1-step symbol is only justified by the apotome-fraction notation, so its notation is a hybrid.
+EDOs in parentheses (6), (8), (13), and (18) have fifths that are so wide they are usually notated as subsets of larger EDOs with good fifths. [59]-EDO is in square brackets because it is green not gold on the periodic table, and so it should have a JI-based notation. However, its fifth is very close to the bad-fifth threshold and its 1-step symbol is best justified<ref>In just intonation, {{sagittal| )| }} doesn't notate any common ratio that would make it valid as 1\59. It does however notate the uncommon ratio 55/49 = 5·11/7² by representing, as a secondary comma, 441/440 which tempers to 1\59 if only prime 3 is tempered or using the 59d map (second-best approximation of prime 7). Thanks to Roee Sinai for this JI-based justification. 55/49 ranks 87th in popularity among 2,3-free equivalence classes of ratios, according to [[N2D3P9#Table_of_top_100_.282.2C3-equivalent.29_pitch_ratio_classes_by_N2D3P9|N2D3P9]].</ref> by the apotome-fraction notation, so its notation is a hybrid.
 To obtain the Evo notations, replace the multishaft symbols above with their Evo equivalents from the previous table.
@@ Line 136: / Line 136: @@
 To obtain the Evo notations, delete the multishaft symbols. There are no equivalent combinations with conventional sharps or flats, as limmas are conventionally notated as the intervals B-C and E-F. The multishaft symbols are not required, even in Revo notation; they merely allow for alternative spellings there. In theory, sharps and flats ''could'' be used with the notations for 33, 40, and 47 because the sharp is one step for them, while it is zero or negative for the other rose EDOs and Sagittal never uses symbols for commas that have been tempered out or tempered negative. But Sagittal recommends not using sharps or flats, conventional or sagittal, with ''any'' limma-fraction notation.
+== References ==
 [[Category:Notation]]
 [[Category:Sagittal notation]]