Combination tone
A combination tone is an additional note that you hear when two notes sound loudly together, although nobody plays it. The most important is the difference tone, whose frequency is the difference of the two notes played. It arises only in the ear.
- Difference tone
- f₂ − f₁, the difference of the frequencies
- Summation tone
- f₁ + f₂, weaker and harder to hear
- Also
- Tartini tone, after the violinist Giuseppe Tartini
- Prerequisite
- two strong, pure notes at high volume
A note that nobody plays
If you play two notes loudly and purely together, for example on two recorders or two violin strings in a double stop, you can perceive a third, low note beneath them. It does not sound from the instruments but arises in the hearing system itself, because at high sound pressure the ear does not respond quite evenly to vibrations. This is called a combination tone. Its frequency is, in the simplest case, the difference of the two notes.
Fifth A–E and its difference tone
First A (440 Hz) and E (660 Hz) sound together. Their difference is 220 Hz, the A an octave lower. This A3 is notated behind them here for orientation; when the two notes sound together you hear it only faintly and in the ear, not as a played note. In equal temperament the difference lies just below, at 219.3 Hz.
How it is calculated
The calculation is simple: subtract the lower frequency from the higher. If you play 440 Hz and 660 Hz, that is, a fifth with the ratio 3:2, you get 220 Hz. The table works out four pure intervals. A rule stands out: with intervals of neighbouring partials like these the difference tone is the common root of both notes, that is, the note whose overtones are the notes played. For the fifth, 440 Hz is the second and 660 Hz the third partial of 220 Hz.
| Interval (pure) | Ratio | Example | Difference tone | Lies at |
|---|---|---|---|---|
| Octave | 2:1 | 440 and 880 Hz | 440 Hz | equal to the lower note |
| Fifth | 3:2 | 440 and 660 Hz | 220 Hz | an octave below the lower |
| Major third | 5:4 | 440 and 550 Hz | 110 Hz | two octaves below the lower |
| Minor third | 6:5 | 440 and 528 Hz | 88 Hz | about F2, two octaves and a major third below A4 |
That explains why pure intervals fuse so well: both notes belong to the overtone series of the same imagined root, and the difference tone supplies this root as well. With impure intervals no common series fits any more, and the difference tone lies beside it.
In practice
The violinist Giuseppe Tartini made use of the phenomenon: anyone who hears a difference tone in a double stop can check by it whether the interval is pure. That is why the effect is also called the Tartini tone. In organ building it is used as an “acoustic bass”: two stops a fifth apart, for example a 16-foot and a 10⅔-foot pitch, let you hear the octave below, the 32-foot pitch, without the huge pipe having to be built for it.
Common mistakes
- Taking the difference tone for a fault in the instrument: it arises in the ear, not in the instrument.
- Calculating the difference in cents: it is calculated in hertz.
- Expecting every interval to produce it clearly: it is clearest with loud, pure notes and well-tuned intervals.
Continue on Maikstrings
Related terms
InterferenceBeatingHarmonic seriesPerfect fifthFifthPartialOctaveVibrationInterval
Editor: Maik Krohm · reviewed on 3 October 2026
← Back to the glossary