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 best justified<ref>In just intonation, {{sagittal| )| }} doesn't notate any ~~simple~~ ratio that would make it valid as 1\59. It does however notate the ~~complex~~ ratio 55/49 = (5·11/7²) by representing ~~the~~ 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.</ref> 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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-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 simple ratio that would make it valid as 1\59. It does however notate the complex ratio 55/49 = (5·11/7²) by representing the 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.</ref> 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.