Re: musical grammar

From: Bill Spight (
Date: Thu Apr 18 2002 - 19:06:16 BST

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    From: Bill Spight <>
    Subject: Re: musical grammar
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    Dear Wade,

    > > why do we have a 12 tone scale.?
    > Well, we do, most definitively after Schoenberg, but I don't think
    > twelve-tones are quite as universal as all that. Tonics and harmonics
    > are more important, with five and seven tone systems.

    In the West, the well tempered 12 tone scale dates to classical times. I
    believe that the Chinese had discovered it several centuries before. :-)

    Why 12 tones? Because the log(1.5) base 2 = 0.585, which is close to
    7/12 = 0.583. 1.5 is the ratio of the fifth to the dominant. A cycle of
    12 5ths will take you back to back to the dominant (about 2% sharp). If
    you flatten the 5th slightly, it takes you back exactly. That enables
    you to have a piano-forte with 88 keys covering a bit over 7 octaves,
    and play in any key. To get closer you need a 41 note well-tempered
    scale. A cycle of 41 5ths takes you back to the dominant (about 2%
    flat). But that would give you a piano range of a little more than 2

    Does tempering make a musical difference? Yes, as Wade indicates. I once
    met a music professor who would not let his singing students practice to
    piano accompaniment for that reason. ;-)



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