We have 12 different 'notes' per octave on a musical keyboard. They are set up so that every 'note' (A, B,C etc) is a second harmonic of the same 'note' in the next higher octave. With this ratio in place, it seems that everything on a keyboard should be divided up into equal groups of 2,3,4 or 6. However, the keyboard seems to be divided up into groups of 5 and 7 (one group of 2 black & 3 white keys, and another group of 3 black & 4 white keys). This does not make much sense to me. However, when I play scales, the layout is very helpful. I'm guessing that the design of the scale is related to physics and therefor the layout of the keys must be too. What is the connection between physics, scales and the layout of the piano keyboard?
[Physics] Is there physics behind the layout of a piano keyboard
acousticsfrequency
Best Answer
12 notes per octave comes from the history of Western music. Other cultures are different. For example, Arabic music has 5 notes per octave. India has 22.
The physiology/physics is that pleasing chords are produced by frequencies that can be expressed as the ratios of small numbers. If two frequencies have a ratio of 2:1, they are an octave apart. 3:2 is a fifth. A slightly different ratio produces beats.
This makes it difficult to tune a piano satisfactorily. Equally spaced frequencies do not produce perfect chords. But the piano can be played in any key equally well. Or perhaps equally not so well.
Tuning was a controversial question among musician in the time of J. S. Bach. Bach took an active interest in it. He developed his own tuning. He wrote the Well Tempered (i.e. well tuned) Clavier, a set of 24 short pieces in all 24 keys, to show the advantages of his preferred tuning.
Today, frequencies are in theory equally spaced on a logarithmic scale. In practice, a piano tuner may "stretch" some notes.
Some references:
Piano tuning,
The Well-Tempered Clavier,
The Ongoing Quest for Bach's Temperament