Topmusicanswers
- Why is the twelfth the root of 2?
- What is a twelfth in music?
- Why does a 2 1 frequency ratio produce an octave?
Why is the twelfth the root of 2?
Every time we go up by a half-step in the chromatic scale, we increase the pitch by a ratio r. When we do this 12 times we go up an octave, so r12 must be 2. This says r is the 12th root of 2.
What is a twelfth in music?
twelfth / 12th / diatonic-12th
[Joe Monzo] A diatonic interval which traverses 11 steps in a diatonic scale, and covers a pitch distance bounded by 12 nominals inclusively, an octave plus a 5th.
Why does a 2 1 frequency ratio produce an octave?
If we divide each tone into two intervals, that are each close to a semitone, we get a 12-note scale. Therefore 12 semitones make an octave, a ratio of 2/1. This means that to get an octave we need to multiply a starting frequency twelve times in succession by a fixed amount that corresponds to a semitone.
