Why Twelve Notes?
Why does every octave have exactly twelve notes? Start the Sound & Science module with two simple ratios: the octave is 2:1 and the perfect fifth is 3:2. Stack pure fifths from C and you visit all twelve notes, landing on B sharp, almost C seven octaves higher. Hear the tiny gap that is left, the Pythagorean comma, and learn to tell a pure fifth from one that beats.
In this lesson you'll
- Explain pitch as frequency in hertz and compute octaves and fifths: A 220 Hz, up an octave (× 2) to A 440 Hz, then up a fifth (× 3/2) to E 660 Hz.
- Count up the circle of fifths from C (C G D A E B F# C# G# D# A# E#) to find all twelve notes, and see why the twelfth fifth, B#, is almost but not exactly C.
- Hear the difference between a pure fifth (smooth and still) and a slightly out-of-tune one (beating, a wobble).
Remember
Pitch is frequency: doubling it gives the octave (2:1), multiplying it by three halves gives the perfect fifth (3:2).
Twelve pure fifths from C visit all twelve notes and land on B#, almost C seven octaves higher; five in a row give the black keys (pentatonic), seven the white keys (major).
B# comes out a little sharp, about a quarter of a half step: the Pythagorean comma. Twelve is the first number of fifths that comes this close, which is why the octave has twelve notes.