Ben Johnston's notation: Difference between revisions

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Composer '''[[Ben Johnston]]'s notation''' is a staff notation system for [[just intonation~~]]. Johnston used it up to the [[31-limit~~]].

Composer '''[[Ben Johnston]]'s notation''' is a staff notation system for [[just intonation]].

The base notes (white keys on the piano) are selected so that the chord F A C E G B D consists of three stacked 4:5:6 chords, i.e. F A C, C E G, and G B D are just major triads. Then the following symbols are used for inflections, all of which denote [[superparticular]] ratios or their reciprocals:

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~~When both a 7 and a flat symbol are present,~~ Johnston combines ~~them into a flat symbol~~ with ~~a line extending~~ from ~~the upper left. This is not to be confused with a flat symbol and a minus sign~~.

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.

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 {{Wikipedia| Ben Johnston (composer) #Staff notation}}
-Composer '''[[Ben Johnston]]'s notation''' is a staff notation system for [[just intonation]]. Johnston used it up to the [[31-limit]].
+Composer '''[[Ben Johnston]]'s notation''' is a staff notation system for [[just intonation]].
 The base notes (white keys on the piano) are selected so that the chord F A C E G B D consists of three stacked 4:5:6 chords, i.e. F A C, C E G, and G B D are just major triads. Then the following symbols are used for inflections, all of which denote [[superparticular]] ratios or their reciprocals:
@@ Line 31: / Line 31: @@
 |}
-When both a 7 and a flat symbol are present, Johnston combines them into a flat symbol with a line extending from the upper left. This is not to be confused with a flat symbol and a minus sign.
+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.