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So I have always composed my atonal music using natural signs after having showed a sharp of flat, recently I showed someone one of these compositions and they told me that I should not use them when composing atonal music because it is presumed that the notes are naturals when not shown with a sharp or flat. I have also heard people say the you shouldn't do it because it bring around the idea that they are "accidentals" which is contradictory to the idea of atonality in which all notes are given equal precedence. 

I'd love to hear what everyone has to say.

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"Unequivocal ambiguity is the hallmark of flexible bias."

I became . . . I don't know . . . I can't say. So I deleted my last post on the ambiguity issue. But I 'm not sure I should have done that.

To look to the future, examine the past.  Music writing as we know it began around 1200 AD. We don't know whatGreek music sounded like-only the emotions it invoked.  Writing began with a single line representing Middle C or whatever pitch worked.  What we call ledger lines were added until we had the Great Staff-11 lines.  These were divided by various clefs into 5 line staffs.  The current note notion started around 1200 gradually adding more ways for the composer to denote performance.

Writing music by hand or computer, using all signs, best gets a composer's idea performed.  Multiple interpretations of the same piece still closely follow the Composer's intention.

You may have fantastic music in your mind, but you need the "tools" to have it performed!

I've never heard on anyone saying don't use naturals in atonal music. On the contrary, there are composers that say put an accidental in front of every not (except those immediately repeated). You can see this in scores by Boulez and (IIRC) Lutoslawski. I don't follow that theory, but I am liberal with my use of cautionary naturals. Better to be safe than sorry.

Concerning quartertones, most music notation programs have an array of common quartertone symbols available. I use equal-tempered quartertones, and I have had no problems conveying them easily to the performers. I know other composers who use 6th and 8th tones with easily found symbols. Btw, I use naturals to cancel those, too.

Interesting. I use the same methodology in atonal music and that using floating tonality.

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