27edo: Difference between revisions

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The 27-note system can be notated using [[ups and downs notation]], in which case arrows or [[Helmholtz-Ellis notation|Helmholtz–Ellis]] accidentals can be used, or with a variation on quarter tone accidentals. With standard circle-of-fifths notation, a sharp raises a note by 4 steps, just one step beneath the following nominal (for example C to C♯ describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and the remaining places can then be filled in with half-sharps, half-flats, sesquisharps, and sesquiflats, reducing the need for double sharps and double flats.The notes from C to D are C, D♭, C{{demisharp2}}, D{{demiflat2}}, C♯, and D, with some ascending intervals appearing to be descending on the staff.

There are eight ~~sets of~~ enharmonic equivalences ~~without~~ microtonal accidentals:

There are eight enharmonic equivalences that do not involve microtonal accidentals:

* B♯ = F𝄫

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* B𝄪 = F♭

~~Furthermore~~, the 5/4 major third present in the 4:5:6 chord is technically an augmented second, since (for example) C–E is a 9/7 supermajor third and so the note located one major third above C must be notated as D♯ or E{{naturaldown}}. Conversely, the 6/5 minor third of a 10:12:15 chord is technically a diminished fourth, since (for example) D–F is a 7/6 subminor third and so the note located one minor third above D must be notated as either G♭ or F{{naturalup}}. The composer can decide for themselves which ~~addidional~~ accidental pair is ~~necessary~~ if they will need redundancy to remedy these problems, and to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.). Otherwise it is simple enough, and the same tendency for A♯ to be higher than B♭ is not only familiar, though here very exaggerated, to those working with the Pythagorean scale, but also to many classically trained violinists.

Another notational implication is that, being a Superpythagorean system, the 5/4 major third present in the 4:5:6 chord is technically an augmented second, since (for example) C–E is a 9/7 supermajor third and so the note located one major third above C must be notated as D♯ or E{{naturaldown}}. Conversely, the 6/5 minor third of a 10:12:15 chord is technically a diminished fourth, since (for example) D–F is a 7/6 subminor third and so the note located one minor third above D must be notated as either G♭ or F{{naturalup}}. The composer can decide for themselves which additional accidental pair is appropriate if they will need redundancy to remedy these problems, and to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.). Otherwise it is simple enough, and the same tendency for A♯ to be higher than B♭ is not only familiar, though here very exaggerated, to those working with the Pythagorean scale (see [[53edo]]), but also to many classically trained violinists.

== Intervals ==

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 The 27-note system can be notated using [[ups and downs notation]], in which case arrows or [[Helmholtz-Ellis notation|Helmholtz–Ellis]] accidentals can be used, or with a variation on quarter tone accidentals. With standard circle-of-fifths notation, a sharp raises a note by 4 steps, just one step beneath the following nominal (for example C to C♯ describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and the remaining places can then be filled in with half-sharps, half-flats, sesquisharps, and sesquiflats, reducing the need for double sharps and double flats.The notes from C to D are C, D♭, C{{demisharp2}}, D{{demiflat2}}, C♯, and D, with some ascending intervals appearing to be descending on the staff.
-There are eight sets of enharmonic equivalences without microtonal accidentals:
+There are eight enharmonic equivalences that do not involve microtonal accidentals:
 * B♯ = F𝄫
@@ Line 67: / Line 67: @@
 * B𝄪 = F♭
-Furthermore, the 5/4 major third present in the 4:5:6 chord is technically an augmented second, since (for example) C–E is a 9/7 supermajor third and so the note located one major third above C must be notated as D♯ or E{{naturaldown}}. Conversely, the 6/5 minor third of a 10:12:15 chord is technically a diminished fourth, since (for example) D–F is a 7/6 subminor third and so the note located one minor third above D must be notated as either G♭ or F{{naturalup}}. The composer can decide for themselves which addidional accidental pair is necessary if they will need redundancy to remedy these problems, and to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.). Otherwise it is simple enough, and the same tendency for A♯ to be higher than B♭ is not only familiar, though here very exaggerated, to those working with the Pythagorean scale, but also to many classically trained violinists.
+Another notational implication is that, being a Superpythagorean system, the 5/4 major third present in the 4:5:6 chord is technically an augmented second, since (for example) C–E is a 9/7 supermajor third and so the note located one major third above C must be notated as D♯ or E{{naturaldown}}. Conversely, the 6/5 minor third of a 10:12:15 chord is technically a diminished fourth, since (for example) D–F is a 7/6 subminor third and so the note located one minor third above D must be notated as either G♭ or F{{naturalup}}. The composer can decide for themselves which additional accidental pair is appropriate if they will need redundancy to remedy these problems, and to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.). Otherwise it is simple enough, and the same tendency for A♯ to be higher than B♭ is not only familiar, though here very exaggerated, to those working with the Pythagorean scale (see [[53edo]]), but also to many classically trained violinists.
 == Intervals ==