Chain-of-fifths notation: Difference between revisions

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The '''circle-of-fifths notation''' is suitable to open up the variety of tones of a selection of [[edo]]s and [[regular temperament]]s of fifth generator. The principle is based on one of the intervals taking over the role of the fifth of the traditional classical notation system (in [[12edo]] or the [[meantone]] tuning). The classical notation system uses seven root notes and accidentals (<span style="font-size:larger">♯, ♭</span> and their multiples) to sharpen and flatten these root notes by the same amount (which is an octave-reduced stack of 7 fifths).

The '''circle-of-fifths notation''' (aka '''extended Pythagorean notation''') is suitable to open up the variety of tones of a selection of [[edo]]s and [[regular temperament]]s of fifth generator. The principle is based on one of the intervals taking over the role of the fifth of the traditional classical notation system (in [[12edo]] or the [[meantone]] tuning). The classical notation system uses seven root notes and accidentals (<span style="font-size:larger">♯, ♭</span> and their multiples) to sharpen and flatten these root notes by the same amount (which is an octave-reduced stack of 7 fifths).

Edos that are best supported by this system are those whose fifth does not deviate too much from the pure fifth [[3/2]] (702{{cent}}) and that can be represented by only one ring of fifths. [[24edo]], as a counter-example to this, contains two rings. If we as well demand that whole tones (2 × P5 - P8), diatonic semitones (3 × P8 - 5 × P5), and chromatic semitones (shifts caused by one accidental, 7 × P5 - 4 × P8), use a positive number of steps, we exclude all edos below 12 and also {{EDOs| 13, 16, 18, and 23 }}. They make more sense notated as subsets. For example, 13edo can be notated as a subset of [[26edo]].

The '''neutral circle-of-fifths notation''' uses an extended accidental set including '''demisharps''' and '''demiflats'''. It works for any tuning system generated by a neutral third. The [[mohaha]] temperament and its typical edo tunings ([[17edo]], 24edo, [[31edo]], [[38edo]], [[45edo]]) are well represented by this system.

The '''neutral circle-of-fifths notation''' (aka '''quartertone notation''') uses an extended accidental set including '''demisharps''' and '''demiflats'''. It works for any tuning system generated by a neutral third. The [[mohaha]] temperament and its typical edo tunings ([[17edo]], 24edo, [[31edo]], [[38edo]], [[45edo]]) are well represented by this system.

== Edos up to 100 ==

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-The '''circle-of-fifths notation''' is suitable to open up the variety of tones of a selection of [[edo]]s and [[regular temperament]]s of fifth generator. The principle is based on one of the intervals taking over the role of the fifth of the traditional classical notation system (in [[12edo]] or the [[meantone]] tuning). The classical notation system uses seven root notes and accidentals (<span style="font-size:larger">♯, ♭</span> and their multiples) to sharpen and flatten these root notes by the same amount (which is an octave-reduced stack of 7 fifths).
+The '''circle-of-fifths notation''' (aka '''extended Pythagorean notation''') is suitable to open up the variety of tones of a selection of [[edo]]s and [[regular temperament]]s of fifth generator. The principle is based on one of the intervals taking over the role of the fifth of the traditional classical notation system (in [[12edo]] or the [[meantone]] tuning). The classical notation system uses seven root notes and accidentals (<span style="font-size:larger">♯, ♭</span> and their multiples) to sharpen and flatten these root notes by the same amount (which is an octave-reduced stack of 7 fifths).
 Edos that are best supported by this system are those whose fifth does not deviate too much from the pure fifth [[3/2]] (702{{cent}}) and that can be represented by only one ring of fifths. [[24edo]], as a counter-example to this, contains two rings. If we as well demand that whole tones (2 × P5 - P8), diatonic semitones (3 × P8 - 5 × P5), and chromatic semitones (shifts caused by one accidental, 7 × P5 - 4 × P8), use a positive number of steps, we exclude all edos below 12 and also {{EDOs| 13, 16, 18, and 23 }}. They make more sense notated as subsets. For example, 13edo can be notated as a subset of [[26edo]].
-The '''neutral circle-of-fifths notation''' uses an extended accidental set including '''demisharps''' and '''demiflats'''. It works for any tuning system generated by a neutral third. The [[mohaha]] temperament and its typical edo tunings ([[17edo]], 24edo, [[31edo]], [[38edo]], [[45edo]]) are well represented by this system.
+The '''neutral circle-of-fifths notation''' (aka '''quartertone notation''') uses an extended accidental set including '''demisharps''' and '''demiflats'''. It works for any tuning system generated by a neutral third. The [[mohaha]] temperament and its typical edo tunings ([[17edo]], 24edo, [[31edo]], [[38edo]], [[45edo]]) are well represented by this system.
 == Edos up to 100 ==