Why is an Octave in music associated with the number 8 ?

Question

It is possible to have almost an infinite number of tones or frequencies between a given fundamental note and its octave. So why are there 8 notes in our musical scale. Any real reason ? Or is it just tradition ? 12 semitones is another case.

Answer 1

Astoundingly, the reason is not traditional, but the mathematical fact that 2^19 is so very nearly equal to 3^12. Watch how this turns out :-

Nice harmonic frequency intervals to Western ears are in the ratio of small integers. The very simplest is 2/1, and the next simplest is 3/2.

Start with any note, say 240 cycles. At twice its frequency, we have 480 cycles. At 3/2 times 240, we have a note of 360 cycles; and at 2/3 of 480, we have 320 cycles. So in our nice harmonic scale of notes, two notes in the centre have a ratio 9/8. This is what Western musicians call a "whole tone".

Now logarithmically, how many of those whole tones will fit into the 2/1 ratio? Almost exactly 6, because 3^12 / 2^18 is 2.0273... which is amazingly close to 2. And 6 tones means 12 semitones.

But we have a whole tone in the exact middle of our scale, so we need two and a half tones on either side of it. Choosing them to be two whole tones and one semitone gives us our eight-note scale, in which the frequency doubles over seven intervals of five whole tones and two semitones.

Mathematically the semitones have to be slightly "fat" at 16/15, and two of the whole tones have to be slightly "thin" at 10/9 instead of 9/8, but it all multiplies out nicely.

Answer 2

There is a mathematical reason behind the octave .

It all has to do with frequency.

Every seminote (or note) you go up (or down) the frequency changes by a twelth power of 2.

here's an example:
A has a frequency of 220hz
A# = 220 * 2^(1/12) hz (about 233 hz
C# = 220 * 2^(4/12) hz (about 277 hz)

Every 8 notes (or 12 seminotes) you go up or down the frequency doubles or halves. Thus creating the musical term of an octave.

Answer 3

Comes from Octo meaning Eight as in Octagon - 8 sided.

An octave is the interval between one musical note and another with half or double the frequency.

Answer 4

Because each note in the octave is another whole tone higher. The in betweens in music are the sharps and flats. When you are talkiing octaves higher or lower, to another musician, than he knows what (set of notes ) or octave to play.

Answer 5

There were arbitrary notes set way long ago. If you take into consideration the frequency of each note, you would not have a fixed interval... that's what them half-notes are for (C#, etc). Click on the reference below for a mathematical way of getting the frequency of a particular note...