A piano has approximately seven octave patterns. For notation of notes I'll use {A, B, C, D, E, F, G} and the so called accidental signs (b for flat) and (# for sharp). The repeating octave pattern can be visualized as


           C#  Eb      F#  Ab  Bb
           |-| |-|     |-| |-| |-|         Black Keys
        |---|---|---|---|---|---|---|
          C   D   E   F   G   A   B        White Keys

As far as a modern keyboard with well tempering goes:

           C# = Db,   D# = Eb,  F# = Gb,  G# = Ab,  A# = Bb
           B  = Cb,   E  = Fb,  C  = B#,  F  = E#,

   The "ascending chromatic sequence" is

      ...  C C# D Eb E F F# G Ab A Bb B (C)  ...

   where the ratios of frequencies: (C# / C), (D / C#), (Eb / D), ...

   are all equal to the 12th root of 2.

   This defines "well tempering".



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The URL for this document is:
http://graham.main.nc.us/~bhammel/MUSIC/8ve.html
Created: September 1997
Last Updated: May 28, 2000
Last Updated: March 1, 2011