Why are there 12 tones/notes in an octave instead of 14?
For example, why isn't an octave of A: a, a#, b, b#, c, c#, d, d#, e, e#, f, f#, g, g#, a? I don't get it.
- 3 months agoFavourite answer
Because b# is the same note as c and e# is the same note as f
- MaxLv 53 months ago
That's like asking why the sky is blue, or why there are 7 colors in the rainbow. The answer is that it's the reality.
- Robert JLv 73 months ago
There are twelve equal-ratio steps (semitones) per octave - look at guitar frets as an example.
Each semitone step in a modern (western world) instrument is an increase in frequency of 12th root of 2 (about 1.059463); 12 increments give exactly double frequency or one octave increase.
That is the most fundamental basis of note steps.
It's the labelling or numbering that is weird and confusing, only assigning direct names to seven of them and labelling the rest as sharp/flat from those.
(Like the seven mnemonic vocal pitches - do re mi fa so la ti - they correspond to the named notes, not semitones).
And of course calling groups of seven an octave (which should be base 8, like a decade is base 10). It should be "septaves" with 7 or "unicals" with 12..
Just take it that the people that set out the note names etc. were not mathematicians - and the note names & white/black notes on a keyboard are a consequence of that.
We are stuck with it now, so make the most of it!
- HernandoLv 63 months ago
There is no B# or E#. Those notes don't exist in a 12-tone western scale.
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- Mr. SmartypantsLv 73 months ago
This is something nobody can explain. If you go from C to C on the white keys, to our western ears it sounds like 8 equal steps. (There are other scales in other parts of the world). But it's not equal steps--some are two half-tones, and some are only one--between b and c, between e and f.
Semitone are equally spaced, but not on a linear scale. Each note is higher than the one below by precisely the 12th root of 2. So you can use a calculator to figure out where the frets go on a stringed instrument. No music teacher can explain this, it just -is-. I suspect a physicist might be able to explain it, but I'd be afraid to ask one because I probably couldn't understand his answer.
About 100 years ago there was a movement in which composers used all twelve tones equally. They wrote music that, to this day, will make your cat put her ears back. It sounds like a piano rolling down a steep hill. And yet with the twelfth note of 2 system we can get Beethoven's 9th, Rhapsody in Blue, and Kitten on the Keys.