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. ~~ImWith~~ 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 ~~while~~ reducing the need for double sharps and double flats. The notes from C to D are C, D♭, C[[File:HeQu1.svg|28x28px]], D[[File:HeQd1.svg|28x28px]], C♯, and D, with some ascending intervals appearing to be descending on the staff.

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- and sesqui-sharps and flats, reducing the need for double sharps and double flats. The notes from C to D are C, D♭, C[[File:HeQu1.svg|28x28px]], D[[File:HeQd1.svg|28x28px]], C♯, and D, with some ascending intervals appearing to be descending on the staff.

Furthermore, the major third of a 4:5:6 chord must be notated as an augmented second, since (for example) C–E is a 9/7 supermajor thirds and the note located one major third above C is now D♯. Conversely, the minor third of a 10:12:15 chord must be notated as a diminished fourth, since ((for example) D–F is a 7/6 subminor third and the note located one minor third above D is now G♭. 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.

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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. ImWith 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 while reducing the need for double sharps and double flats. The notes from C to D are C, D♭, C[[File:HeQu1.svg|28x28px]], D[[File:HeQd1.svg|28x28px]], C♯, and D, with some ascending intervals appearing to be descending on the staff.
+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- and sesqui-sharps and flats, reducing the need for double sharps and double flats. The notes from C to D are C, D♭, C[[File:HeQu1.svg|28x28px]], D[[File:HeQd1.svg|28x28px]], C♯, and D, with some ascending intervals appearing to be descending on the staff.
 Furthermore, the major third of a 4:5:6 chord must be notated as an augmented second, since (for example) C–E is a 9/7 supermajor thirds and the note located one major third above C is now D♯. Conversely, the minor third of a 10:12:15 chord must be notated as a diminished fourth, since ((for example) D–F is a 7/6 subminor third and the note located one minor third above D is now G♭. 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.