One note, many notes
When you play C on a piano or a guitar, you do not hear just one frequency. The string also vibrates in halves, thirds and quarters, and each of these makes a quieter higher note called a harmonic (or overtone). The numbers are simple: harmonic n has n times the frequency of the fundamental.
Where the intervals come from
- 1 → 2: an octave (ratio 2:1).
- 2 → 3: a perfect fifth (3:2).
- 3 → 4: a perfect fourth (4:3).
- 4 → 5: a major third (5:4).
- 5 → 6: a minor third (6:5).
Harmonics 4, 5 and 6 are root, major third, fifth: a major chord is hidden inside every note. The octave, fifth and major third are the first intervals nature gives us, and they are the building blocks of nearly all harmony.
Timbre
Two instruments can play the same note and sound different because they put different amounts of each harmonic in the mix. A flute is almost pure (mostly harmonic 1 and 2); a violin or a trumpet has many strong upper harmonics. Use the slider above to hear it: more harmonics, brighter tone.
Tuning: a necessary compromise
The pure ratios do not line up perfectly. Stack twelve pure fifths and you overshoot seven octaves. Equal temperament shaves a little off every interval so all twelve keys sound acceptable. The fifth is two cents narrow; the major third is 14 cents wide; harmonics 7, 11 and 13 lie between piano keys. Instruments that can bend pitch (voice, violin, trombone) often drift towards the pure version.
Learn more
This is why the circle of fifths works, and why perfect intervals sound so stable. Hear each interval in ear training, and follow the Sound and Tuning program.
Frequently asked questions
What is the overtone series?
When a string or air column vibrates, it vibrates as a whole and also in halves, thirds, quarters and so on. Those faster vibrations are the harmonics (overtones), sounding at 2, 3, 4… times the fundamental frequency, much quieter than the main note.
Why do the first harmonics match the major chord?
Harmonics 4, 5 and 6 are in the ratio 4:5:6: root, major third and fifth. A major triad is literally contained in the sound of a single note.
Why is the 7th harmonic out of tune?
The seventh harmonic is about 31 cents flat of the equal-tempered minor seventh. Our tuning system is a compromise, so some natural ratios (7, 11, 13) do not land on piano keys.
What is the fundamental?
The lowest and loudest harmonic: the pitch you hear as "the note". The other harmonics give it its colour (timbre).
What is the difference between an overtone and a harmonic?
The first overtone is the second harmonic. The fundamental is harmonic 1 but is not an overtone. In practice people use the words interchangeably.