• Jon I'm not an "atonalist" and I'm definitely not an expert on any of this but I will say this. You have asked a simple question about a complex subject and there is some controversy involved. 

    Some background. Schoenberg hated the term atonal and Leonard Bernstein questioned whether it was even possible to write atonally with the tempered 12 note system that we use. I personally agree with him, atonality doesn't exist in 12 tone music; there is always a tonal center. Without a tonal center you have "white noise" where all sound frequencies are equally present. 

    But if it was possible to actually write atonally with the 12 tone system then the sharp/flat system which has been developed for tonal music would be irrelevant and you could use whatever accidental you want. 

    To learn the proper use of sharps and flats you should study music theory as applied to the "common practice period".

  • Just a guess: when he established the tone row, he used a flat or sharp or natural before each note. Then whenever that pitch appears in the music he just repeats whatever was in the tone row. So in the first measure, we see a G#, so we would mostly expect that pitch would normally appear that way (and not Ab). He might violate the rule here and there for the sake of clarity. In m3, we see a Bb. But in m4, we see an A#, which makes sense as it is part of an ascending line, where you normally expect to see pitches expressed with sharps and not flats.

  • Possibly just an affectation... you don't show enough to work out whether it's down to the shape of the row. But I know Dorico has a setting for "Second Viennese School" in which every note is given an "aacidental"

    In my text book "Bluff Your Way in Music" by Gammond, "accidental" is defined as "a wrong note played on purpose."

  • Thanks for the answers so far.  My knowledge of music theory is imperfect, but I'm trying to improve it, and I've gotten as far as understanding (if I'm right) that accidentals are sometimes used to make the notes appear to conform to a diatonic scale, where only the letter notes in the scale should be used, or where certain types of chords require certain letter notes to be recognizable in notation, and that this sometimes results in for instance notes in a sharp key being marked flat instead of sharp.   But those considerations apply to tonal pieces.  So I was wondering why a composer wouldn't just use all sharps or all flats notating an atonal piece, where these considerations don't apply.  If I've got all this totally wrong, please don't hesitate to say so.

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