User:Dave Keenan/sandbox: Difference between revisions
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A '''fractional-3-limit notation''' is a kind of musical notation built on a [[chain-of-fifths notation]], which is used for notating [[EDOs]] when the EDO has no obvious mapping from just intonation, while preserving the notation of subsets. Fractional-3-limit notations may be contrasted with two other kinds of chain-of-fifths notation for EDOs: ''JI-based notations'', like "good fifths" [[Sagittal|Sagittal notations]], which assume specific JI mappings, and ''step-count notations'', like [[Ups and downs|Ups and Downs notations]], which do not preserve the notation of subsets. Fractional-3-limit notations | A '''fractional-3-limit notation''' is a kind of musical notation built on a [[chain-of-fifths notation]], which is used for notating [[EDOs]] or [[ETs]] when the EDO has no obvious mapping from just intonation, while preserving the notation of EDO subsets. Fractional-3-limit notations may be contrasted with two other kinds of chain-of-fifths notation for EDOs: ''JI-based notations'', like "good fifths" [[Sagittal|Sagittal notations]], which assume specific JI mappings, and ''step-count notations'', like [[Ups and downs|Ups and Downs notations]], which do not preserve the notation of EDO subsets. Fractional-3-limit notations assign symbols to fractions of some tempered 3-limit comma. In practice, this 3-limit comma is either the [[2187/2048|apotome]] (chromatic semitone) as represented by a sharp or flat, or the [[256/243|limma]] (diatonic semitone) as represented by the intervals B-C and E-F. | ||
== Apotome-fraction notations == | == Apotome-fraction notations == | ||
Revision as of 08:19, 18 October 2024
A fractional-3-limit notation is a kind of musical notation built on a chain-of-fifths notation, which is used for notating EDOs or ETs when the EDO has no obvious mapping from just intonation, while preserving the notation of EDO subsets. Fractional-3-limit notations may be contrasted with two other kinds of chain-of-fifths notation for EDOs: JI-based notations, like "good fifths" Sagittal notations, which assume specific JI mappings, and step-count notations, like Ups and Downs notations, which do not preserve the notation of EDO subsets. Fractional-3-limit notations assign symbols to fractions of some tempered 3-limit comma. In practice, this 3-limit comma is either the apotome (chromatic semitone) as represented by a sharp or flat, or the limma (diatonic semitone) as represented by the intervals B-C and E-F.