The distance between each block with 12 notes is called an octave. The term octave stands for that interval of notes where the frequency of the tone doubles.
In digital music, a number is added after the name of each note to describe the octave. “A4” stands for the note A in octave 4. A standard 88-key piano has seven octaves plus three lower notes (B0, B#0 and A0) below the bottom C1.
There are two special notes: C4 is also called middle C. It is in the centre of a piano keyboard and often used as the reference note for playing samples.
The note A4 is also called A440. It is the reference for the tuning instruments. This note is tuned to the frequency of 440Hz and the frequency of all other notes are derived from this reference point.
Octaves Double the Frequency of a Note
The frequency of a note one octave higher doubles its frequency.
The illustration above shows a tone (blue) at 440 Hz and another tone one octave higher (pink) at 880 Hz. Because the frequency doubles, both waveforms share two intercept points where they cross zero line.
If you play the same note in different octaves, like an A3 and A4, the waveform stays regular and just changes its shape.
For this reason, the second note just changes the sound, but not the perceived pitch of the tone. Most sounds are in fact a waveform with a base frequency and many layers of waveforms in doubled frequency steps above. These doubled frequency layers on top of the base frequency are called overtones.
Playing a note on different octaves will change its pitch, but it is the same note. The note A1, A2, A3, A4, A5, A6 are still the note A - just at a different pitch.
Overtones
Overtones are frequencies which are part of a sound and define the character of it. They do not alter its perceived pitch.
The image above shows a sound with many overtones. You see, the base frequency of the tone is C2, and there are strong overtones on C3, C4, C5 and C6.