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From: smoliar@vaxa.isi.edu (Stephen Smoliar)
Newsgroups: comp.music
Subject: Re: theory behind the scales
Message-ID: <14294@venera.isi.edu>
Date: 14 Jul 90 15:42:04 GMT
References: <8547@uhccux.uhcc.Hawaii.Edu> <10737@chaph.usc.edu>
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Reply-To: smoliar@vaxa.isi.edu (Stephen Smoliar)
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In article <10737@chaph.usc.edu> alves@castor.usc.edu (William Alves) writes:
>I don't think there is One True Scale that music then adheres to. Rather, I
>think that whether a composer or a culture decides to go with 12-tone equal
>temperament, or 43-note 13-limit just intonation (Partch), or 6-tone quasi-
>equal temperament (Thailand), or a whole multitude of heptatonic and penta-
>tonic systems (Indonesia) has to do with the music and the instruments first.
>In most cases, it is impossible to say what criteria were used or exactly how
>they developed historically. Also keep in mind that often theory does not 
>agree with practice. 
>
It is important to remember that, when it comes to trying to reconcile equal
temperament with the harmonic series, you will always have to contend with
mathematics.  Since all integer roots of two are irrational, you are never
going to get any which provide ratios which will line up with those of the
harmonic series.  What makes matters worse is that there will always be a
trade-off.  That is, as you improve your approximation to 3/2, you lose on
5/4 . . . unless you choose to go for some extremely fine division of the
scale, in which case you are no longer talking about anything which can be
resolved as an equally tempered gamut.

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