Ben Johnston's notation: Difference between revisions

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Johnston combines the symbols 7 <span style="display: inline-block; transform: rotate(180deg)">7</span> ↑ ↓ with ♯ ♭ if symbols from both categories are present.

A circle of just fifths is given by ... D♭-- A♭- E♭- B♭- F C G D A+ E+ B+ F♯++ ..., with a plus or minus added for every loop around the ends of the core F A C E G B D sequence. The odd harmonic series up to 31 starting on C is given by C G E B♭7 D F↑ A♭13 B C♯17 E♭19 F+7 ~~F♯23~~ G♯ A+ B♭29 B31.

A circle of just fifths is given by ... D♭-- A♭- E♭- B♭- F C G D A+ E+ B+ F♯++ ..., with a plus or minus added for every loop around the ends of the core F A C E G B D sequence. The odd harmonic series up to 31 starting on C is given by C G E B♭7 D F↑ A♭13 B C♯17 E♭19 F+7 F♯+23 G♯ A+ B♭29 B31.

Johnston's notation sacrifices some mathematical purity compared to [[Helmholtz-Ellis notation]], as it is based on 4:5:6 chords rather than [[Pythagorean tuning]]. This comes at the possible advantage of fewer inflection markers needed for music that emphasizes the 5-limit.

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 Johnston combines the symbols 7 <span style="display: inline-block; transform: rotate(180deg)">7</span> ↑ ↓ with ♯ ♭ if symbols from both categories are present.
-A circle of just fifths is given by ... D♭-- A♭- E♭- B♭- F C G D A+ E+ B+ F♯++ ..., with a plus or minus added for every loop around the ends of the core F A C E G B D sequence. The odd harmonic series up to 31 starting on C is given by C G E B♭7 D F↑ A♭13 B C♯17 E♭19 F+7 F♯23 G♯ A+ B♭29 B31.
+A circle of just fifths is given by ... D♭-- A♭- E♭- B♭- F C G D A+ E+ B+ F♯++ ..., with a plus or minus added for every loop around the ends of the core F A C E G B D sequence. The odd harmonic series up to 31 starting on C is given by C G E B♭7 D F↑ A♭13 B C♯17 E♭19 F+7 F♯+23 G♯ A+ B♭29 B31.
 Johnston's notation sacrifices some mathematical purity compared to [[Helmholtz-Ellis notation]], as it is based on 4:5:6 chords rather than [[Pythagorean tuning]]. This comes at the possible advantage of fewer inflection markers needed for music that emphasizes the 5-limit.