The series
Every pitched sound contains, besides the fundamental f, components at 2f, 3f, 4f… Starting from C2 (about 65.4 Hz):
- 1 C2 (65 Hz) – 2 C3 – 3 G3 – 4 C4 – 5 E4 – 6 G4 – 7 Bb4 (flat) – 8 C5 – 9 D5 – 10 E5 – 11 F#5 approximately – 12 G5…
Between harmonics 4, 5 and 6 the major triad appears (C E G); with the 7th you get the sound of a dominant seventh. The intervals narrow as you go up: octave, fifth, fourth, major third, minor third…
Timbre
Timbre depends on how much each harmonic weighs.
- Sine wave: fundamental only (sub, pure 808).
- Sawtooth: all harmonics, amplitude 1/n: bright, rich (supersaw, synthetic strings).
- Square: odd harmonics only, 1/n: hollow, “clarinet-like.”
- Triangle: odd harmonics only, 1/n²: soft, almost sine-like.
Filters, saturation and EQ work precisely on these harmonics.
Practical consequences
- Voicing: wide intervals in the low register, narrow ones in the high, as in the series. A third at C2 becomes mud; a fifth or an octave does not.
- 808 on phones: a bass at 45 Hz doesn't come out of a small speaker, but saturation generates harmonics at 90, 135, 180 Hz and the ear reconstructs the missing fundamental.
- Bernstein: in the first Norton lecture (“Musical Phonology,” Harvard 1973) he uses the series to argue that the major triad, the pentatonic scale and the circle of fifths have a common physical basis. The thesis has been criticized (not all musical cultures derive from the series), but it remains an excellent listening key.
Real example
The opening of “Also sprach Zarathustra” by Richard Strauss (1896): over a low pedal C the trumpets play C–G–C, that is, harmonics 2, 3 and 4. Right after comes the third (E/Eb), the 5th harmonic: the series becomes a dramatic gesture.