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<appendix id="aharmonies" revision="$Revision: 1841 $ $Name$" userlevel="adv"
  vendor="1.12" xmlns:xi="http://www.w3.org/2003/XInclude">
  <title id="atharmonies">The harmonic principle</title>
    
  <para>The Harmonies Attributes came from a principle known from
    Antiquity and named harmonics.  Harmonics are used in music as
    what we known as scales.  A scale contains twelve notes (when we
    count the black notes on piano keys) which repeat infinitely.
    Between one note and the next one with the same name, there is a
    difference of pitch (the frequency of the notes) which is exactly
    the double.</para>

  <para>In the Harmonies, the recipe is the same except that we only
    kept ten notes and that the value is multiply by 10 at each
    repetition.  This scale is called the logarithmic decimal scale
    and <xref linkend="tmesures"/> only gives you an approximation of
    it.</para>

  <para>The important values to remember in this scale are those
    associated with the value 0, 3, 5 and 10, which are 1, 2, 3 and 10
    respectively.  From those ones, you can find back the full table
    simply by adding and subtracting the empty spaces from the known
    values, and then to replace additions with multiplications, and
    subtraction with divisions.  For example, to get back the value of
    2, we can observe that 5-3=2, so, once the substitution done, we
    have 3/2=1.5.</para>

  <para>Note that those numbers are only approximation except for 0
    (which equal exactly 1) and 10 (which equal exactly 10).  A 3
    points difference is equivalent to a factor of 2.01, and a 5
    points difference is equivalent to approximately 3.2.</para>

</appendix>
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