explain the octave law?

Question

the law should be based on the music

Answer 1

The animated link shows how a given length of string (on a guitar?) can vibrate as though the string was divided into various shorter lengths. When the string is plucked, the longest wave forms the deepest tone (the fundamental) while smaller divisions produce higher (over)tones. Tones that are exactly twice the frequency of the fundamental are an octave higher. Octave means eight (an octopus has eight arms and October at one time was the eighth month, right?). It is called an octave because on a modern piano, if you play a note and find the eighth white key higher you can play a tone one octave higher with twice the frequency. Usually the piano string that is one octave higher is shorter and perhaps thinner and under more tension than the lower note and must be tuned (by a piano technician) to have exactly twice the frequency. The loudest tone of every piano string is its fundamental, however there are also higher and softer tones called overtones (as in the guitar) because the string is struck by the hammer near one end. Plucking a string dead center should produce only the fundamental (without overtones). You can easily hear the difference on a guitar.

Answer 2

An octave is always the multiple of a frequency.
For example: Tone A = 440 Hertz, one octave higher is 880 Hertz, then 1760 Hertz and so on....