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Few single regularities explain as much at once. The harmonic series does: it accounts for why the octave is the most consonant interval, why the fifth comes next, why the major triad is the most stable chord, and why one pitch sounds different on different instruments.
What is hidden inside one tone
Strike a note and the ear believes it hears "one note". What actually sounds is a whole set of frequencies: a lowest fundamental, plus a stack of partials at whole-number multiples of it.
| Partial | Frequency | Pitch relative to C4 | Note name |
|---|---|---|---|
| 1 | 1x | the fundamental | C4 |
| 2 | 2x | one octave up | C5 |
| 3 | 3x | octave + perfect fifth | G5 |
| 4 | 4x | two octaves up | C6 |
| 5 | 5x | two octaves + major third | E6 |
| 6 | 6x | two octaves + perfect fifth | G6 |
| 7 | 7x | near two octaves + minor seventh | B♭6 |
| 8 | 8x | three octaves up | C7 |
These pitches are calculated, not chosen. Once the fundamental is fixed, the partials above it are exactly what they are — no more, no fewer.
Partial 7 does not coincide with any key of twelve-tone equal temperament. Convention writes it as B♭, but it sits lower than the tempered B♭. That small discrepancy is the first visible tension between the series and the keyboard.
Diagram: the ratios and pitches of the partials
Four things it explains
One: why the octave is the most consonant. Partials 2, 4 and 8 all carry the same note name. Two tones an octave apart share the most partials, so they sound like "one note". See octave.
Two: why the fifth comes second. The ratio 3:2 is the first non-octave overlap to appear (partial 3 against partial 2), with the fourth at 4:3 close behind. The simpler the ratio, the emptier the sound — which is where perfect intervals get their name.
Three: why the major triad is the most stable. Partials 4, 5 and 6 already form a major third stacked under a minor third: C, E, G. The major triad was not decreed by rule; it was in the series all along. This is where triads and all of harmony begin.
Four: where timbre comes from. Partials differ in strength. A strong fundamental with weak upper partials sounds round; prominent upper partials sound bright or piercing. How the partials behave in the first instant decides the instrument's attack. That is the physical floor under timbre.
Listen: picking out the partials
The row below is not a scale but different partials of one series, approximated by equal temperament. From the fifth tone on the match is no longer exact — listen for the shape.
Common misconceptions
- "Overtones are high, inaudible tones." They sound all the time, and a large part of them lies inside the audible range. Only the portion above the hearing limit is inaudible.
- "Timbre depends on the fundamental." The fundamental sets the pitch. Timbre is almost entirely determined by how strong each partial is.
- "The harmonic series was invented by music theory." It is a physical consequence of vibration. It came first; theory merely wrote it down.
- "Partial 7 is just B♭." Writing it as B♭ is a notational compromise; its actual frequency is lower. This is one reason keyboard tuning is stretched at both ends.
- "Every piano note sounds strictly in equal temperament." Real tuning stretches the extremes, because agreement between partials has to be factored in too.
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Listen in the library
All tracks from midicn-lib — inline badge is the license tier (C1 commercial / C2 non-commercial / C3 study only).
Sources
- {'泛音列的整数倍频率关系、前几个分音的音高、及 4': '5:6 与大三和弦的对应，属音乐声学与和声学通则'}
- 第七分音与十二平均律无完全对应，为已知事实
Used for fact-checking only; all prose is original.