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".
Email me, Bill Hammel at