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 KeysAs 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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