idea
Ratios
If you halve a string, it sounds exactly an octave higher. Its frequency has doubled, so the two notes are in the ratio 2 to 1. This is the oldest idea in music theory: intervals are ratios of frequencies. The octave is 2:1, the fifth 3:2, the fourth 4:3 and the major third 5:4. To put one interval on top of another, you multiply their ratios. A fifth plus a fourth is 3/2 × 4/3 = 2, exactly an octave, and you can check this on any instrument.
Connects to
- The octave
- The fifth
- Logarithms and cents
- Rhythm and polyrhythm
- Harmony of the spheres
- Strings and pipes
- Music