Octave scale
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An octave scale is named for the musical note that begins and ends a musical scale. However, though the notes are the same they remain an octave apart, or in other words, the end note is double the frequency of the beginning note. Notes at the letters A, B, C, D, E, F, and G are used to name the musical notes. Using C major, the octave scale would be C, D, E, F, G, A, B, C. The octave number tells us which. As there are eight C notes on the 88-key piano the octave number signifies which C to start with.
A number (i.e seventh octave) or a note (C5) may be associated when referring to a particular octave scale.
[edit] Examples
The first note on the piano is 'A'. Since it is the first note, it is called A0. Note that it vibrates at only 27.5 Hz.
The next white note is B0. The black key in between is a half-step and is the sharp of A (A♯0) or the flat of B (B♭0).
The next white-key notes are C1, D1, E1, F1, and G1 respectively. The black keys in between are the flat of the note after it and the sharp of the note before it.
The next A is the second A, named A1. It vibrates at 55 Hz (double A0). This repeats again, to A2 (110 Hz).
[edit] Note
In Scientific pitch notation, octaves are numbered beginning with C and ending with B. In that notation (used in many Wikipedia articles - see Piano key frequencies and Soprano, Alto, Tenor, and Bass, as well as articles on specific instruments), the lowest piano keys play A0, A♯0, and B0. Followed by C1 through A1, B1, and C2, and Middle C is C4.