Ben Johnston's notation: Difference between revisions

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'''Ben Johnston's notation''' is a staff notation system for [[just intonation]]. [[Ben Johnston]] ~~developed it~~ up to ~~the [[~~31~~-limit]],~~ employed in his String Quartet No. 9, although intervals exceeding the [[13-limit]] are encountered ~~mostly incidentally~~ in his music.

'''Ben Johnston's notation''' is a staff notation system for [[just intonation]] developed by composer [[Ben Johnston]], which supports prime harmonics up to and including 31. It is employed in his String Quartet No. 9, although intervals exceeding the [[13-limit]] are encountered only occasionally in his music.

The base notes (white keys on the piano) are selected so that the chord {{dash|F, A, C, E, G, B, D|s=hair|d=med}} consists of three stacked 4:5:6 chords, i.e. {{dash|F, A, C|s=hair|d=med}}, {{dash|C, E, G|s=hair|d=med}}, and {{dash|G, B, D|s=hair|d=med}} are just major triads. This in turn makes {{dash|C, D, E, F, G, A, B, C|s=hair|d=med}} a justly-intonated [[Zarlino|Ptolemy–Zarlino "intense" diatonic scale]]. Then the following accidentals are used for inflections, all of which denote [[superparticular ratio]]s or their reciprocals:

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 {{Wikipedia| Ben Johnston (composer) #Staff notation}}
-'''Ben Johnston's notation''' is a staff notation system for [[just intonation]]. [[Ben Johnston]] developed it up to the [[31-limit]], employed in his String Quartet No. 9, although intervals exceeding the [[13-limit]] are encountered mostly incidentally in his music.
+'''Ben Johnston's notation''' is a staff notation system for [[just intonation]] developed by composer [[Ben Johnston]], which supports prime harmonics up to and including 31. It is employed in his String Quartet No. 9, although intervals exceeding the [[13-limit]] are encountered only occasionally in his music.
 The base notes (white keys on the piano) are selected so that the chord {{dash|F, A, C, E, G, B, D|s=hair|d=med}} consists of three stacked 4:5:6 chords, i.e. {{dash|F, A, C|s=hair|d=med}}, {{dash|C, E, G|s=hair|d=med}}, and {{dash|G, B, D|s=hair|d=med}} are just major triads. This in turn makes {{dash|C, D, E, F, G, A, B, C|s=hair|d=med}} a justly-intonated [[Zarlino|Ptolemy&ndash;Zarlino "intense" diatonic scale]]. Then the following accidentals are used for inflections, all of which denote [[superparticular ratio]]s or their reciprocals: