Most modern, full size pianos have a row of 88 black and white keys, 52 white keys for the notes of the C major scale (C, D, E, F, G, A and B) and 36 black keys (needed to play other scales). This means that the piano can play 88 different fundamental frequencies (pitches or "notes"), going from the deepest bass range to the highest treble. The notes sound musical because each piano string vibrates with other frequencies that are a multiple of the fundamental frequency (pitch or note). The fundamental note will also induce neighbouring strings, tuned to a harmonic frequency, to vibrate if they are not damped.
The following table shows the lowest 16 keys on the piano with the fundamental frequency and corresponding note letter.
Fundamental Note
Key Hz 16 65.40639 C
15 61.73541 B
14 58.27047
13 55.00000 A
12 51.91309
11 48.99943 G
10 46.24930
9 43.65353 F
8 41.20344 E
7 38.89087
6 36.70810 D
5 34.64783
4 32.70320 C
3 30.86771 B
2 29.13524
1 27.50000 A
Notice that for one octave the frequency is exactly doubled.
The A key 1 is 27.50000 Hz while the A key 13 is 55.00000 Hz. The B key 15 is also exactly double the frequency of the B key 3 and this applies to every pair of keys separated by 12 intervals.
This means that key 13 produces a harmonic frequency of key 1 and so on. It gets more complicated as the octave is divided into thirds and fifths so that each fundamental note has harmonic frequencies that are double, triple and quadruple the fundamental frequency.
For example multiply 32.70320 (key 4 C) by 1.5 = 49.0548, it is almost exactly the frequency of key 11 G at 48.99943. G is therefore a harmonic of C.
Early musicians realized that their instruments had to be tuned to the same set of frequencies. This was relatively simple with instrument like the violin, that can be adjusted easily, but flutes had to be made so that they emitted exactly the same notes. As more musicians started to play together, they agreed on a set of frequencies exemplified by the piano. They also realized that not everyone could remember every note of a piece of music and started to write down notes as a way to aid their memories.
As music pieces became longer and more complex and especially when dozens of musicians were required to play or sing together this evolved into the musical notation systems used since the 16th century in Europe.
The earliest form of musical notation found, was marked on a cuneiform tablet about 1400 BCE in Nippur, Babylonia (Iraq). It is a fragment of instructions for performing music composed in harmonies of thirds. The fragment named the strings on a lyre (a stringed, harp-like instrument) and other tablets described the method of tuning each string.
Yohan Kim playing Isn't She Lovely by Stevie Wonder on an electronic piano.
Modern music notation generally uses a staff which is set of five horizontal line on which notes (pitches) are shown by oval marks on, or between, the lines. Read from left to right, a staff begins with a clef, which indicates the position of one particular note on the staff. The treble clef or G clef normally identifies the second line up on the five line staff as the note G above middle C on the piano. The bass clef or F clef shows the position of the note F below middle C.
Immediately after the clef is a time signature (for example a 4 above a 4 indicates that there are four beats to a bar). The duration (note length) is shown as:-
a hollow oval, a whole note (the note is held for four beats in 4:4 time),
a hollow oval with a vertical stem is a half note (the note is held for half of a whole note),
a black oval with a vertical stem is a quarter note (held for a quarter of a whole note),
a black oval with a vertical stem and a flag is an eighth note (held for an eighth of a whole note),
a black oval with a vertical stem and two flags is a sixteenth note (held for a sixteenth of a whole note).
Notice that the time increment is doubled with each symbol, 1, 2, 4, 8, 16 etc. Additional symbols such as dots and ties lengthen the duration of a note. A rest symbol indicated that no note is played for the duration of the rest.
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