Comment Consonance (Score 3, Informative) 183
It's perhaps not obvious but there is no such thing as perfect consonance in music:
- Tone C3 is an exact second harmonic of C2 and a fourth harmonic of C1. That's why the sound so nice together.
- Tone G2 is a third harmonic of C1, but (surprise) not an exact one. That's because if you take 13 third harmonics (C G D A E B F# C# G# D# A# F C') you are supposed to arrive at the same tone. But you don't, there is a slight frequency offset. In practice, this offset is distributed among all 13 intervals so we are generally unable to notice it.
- The fifth harmonic tone (C1 -> E3') is also inexact. It is fairly close to the sound (here E) obtained from the scale above but again there is a slight frequency offset.
- The sixth harmonic (C1 -> G3) is 2*3 times the fundamental frequency, so is as (in)exact as the third harmonic.
- The seventh harmonic (C1 -> ~A#3, noticeably lower) is not on the (twelve tone) scale but it still sounds nice.
- The eight harmonic is exact (2*2*2, C1 -> C4). And so on...
The twelve tone scale is a rather clever invention, it manages to approximate a rather large number of harmonics with a small number of tones. But it is still only an approximation - a perfect consonance can only be obtained for octaves.