Harmonic series scale
The harmonic series scale consists of the natural tones, that is, the partials of the overtone series above a fundamental. On instruments without valves or keys, such as the natural trumpet, the valveless horn or the alphorn, these are the only notes that can be played.
- Basis
- overtone series, frequencies 1 : 2 : 3 : 4 : …
- Example
- natural tones above C
- Peculiarity
- 7th, 11th and 13th partials deviate most from equal temperament (over 30 cents)
- Playable on
- natural trumpet, alphorn, natural horn
The overtone series as a scale
Every sound consists of a fundamental and its overtones, whose frequencies are whole-number multiples of the fundamental frequency: single, double, triple and so on. If you play exactly these notes one after another you get the harmonic series scale. On the natural trumpet and the alphorn the player determines the note only by lip tension; there are no valves or finger holes. That is why the natural tones are the only notes available there.
Partials 1 to 5 above the fundamental C
Fundamental, octave, twelfth, double octave and major third. The first natural tones form the major triad.
Partials 6 to 16: the scale becomes denser
The higher the partials, the closer they lie. The marked notes (7th, 11th, 13th and 14th partials) are only approximated on a piano: they lie between the keys. The listening example plays, like any piano, the nearest equal-tempered pitch.
In the glossary: Harmonic series · Natural tones · Natural trumpet
A scale that thickens
The gaps between natural tones get ever smaller going up. Between the 1st and 2nd partials lies an octave, between the 2nd and 3rd a fifth, then a fourth, major third, minor third, and so on. Only from the eighth partial on do steps arise that you hear as a scale. That is why fanfares for natural trumpets have their character: they consist essentially of triad notes.
| Partial | Note above C | Distance from the fundamental | Deviation from the piano key |
|---|---|---|---|
| 1 | C2 | fundamental | – |
| 2 | C3 | octave | 0 |
| 3 | G3 | octave + perfect fifth | +2 cents |
| 4 | C4 | double octave | 0 |
| 5 | E4 | double octave + major third | −14 cents |
| 7 | B♭4 | double octave + minor seventh | −31 cents |
| 11 | F5/F♯5 | three octaves + augmented fourth (alphorn F) | +51 cents above F |
| 13 | A♭5 | three octaves + minor sixth | +41 cents above A♭ |
Notes between the keys
The deviations in the table show that the natural tones do not fit the equal temperament of the piano. The fifth (3rd partial) lies almost exactly on the key. The major third (5th partial) is 14 cents too low. The 7th partial lies 31 cents below the B♭. The 11th partial, the so-called “alphorn F”, lies between F and F♯ and fits neither key. This is exactly where the problems of tuning theory begin: pure intervals and keyboard instruments do not quite get on. More on this in the article Equal, meantone, just: why your piano is slightly out of tune.
Continue on Maikstrings
Related terms
Harmonic seriesNatural tonesNatural trumpetTwelfthScaleOctavePerfect intervalsTritone
Editor: Maik Krohm · reviewed on 3 October 2026
← Back to the glossary