Phantom notes played by violins turn out to be a real sound

For hundreds of years it's been known that a mysterious third note can be heard when playing two notes together on a violin – now we know why

Physics



1 November 2022

By Karmela Padavic-Callaghan

Violins can produce “combination notes”

Getty Images/Thomas Barwick

A musical sound once thought to be heard only in our heads as a quirk of the ear canal is actually real. Violins can produce these unusual tones – and higher quality violins can produce them more strongly.

In 1714, Italian violinist Giuseppe Tartini discovered that, when playing two notes simultaneously, he could unexpectedly hear a third sound. This third note was later named a combination tone because its frequency is a blend of the frequencies of the two original tones. It was thought that these tones arose entirely in our ears, due to the way sound is amplified by the cochlea, rather than actually emanating from an instrument.

Giovanni Cecchi at the University of Florence in Italy and his colleagues decided to investigate how different violins produce combination tones.

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They analysed recordings of a professional violinist playing selected pairs of notes on five violins of different age and quality using a computer. Motivated by the ideas of 19th-century physicist Hermann von Helmholtz who showed that some musical instruments may be able to produce combination tones on their own, they decomposed the sound waves made by the violins into parts with different frequencies. The team found that all violins produced combination tones, but the oldest instruments produced the strongest ones. The magnitude of the most prominent combination tone for the oldest violin, made in Bologna in 1700, was about 75 per cent larger than the one from a modern mass-produced instrument.

The researchers also wanted to know how clearly listeners could hear the combination tones produced by the three highest-quality violins. They invited a group of 11 professional and amateur musicians to listen to recordings of the violinist, some of which had the combination tones removed. The listeners could hear the difference almost every time: The least accurate heard it 93 per cent of the time, while the most accurate listener heard it every time.

Jim Woodhouse at the University of Cambridge says the experiment suggests that combination tones must come from the way that air vibrates and mixes inside the violin. When a note is played on a violin, it isn’t just the string that determines the tone but also the shape of the violin – which is more precisely constructed in a high-quality instrument. “It wouldn’t be difficult to find high-quality contemporary violins that would show this effect just as strongly,” he says.

The team now want to study even more violins to pinpoint exactly which part of the instrument is responsible for the combination tones, says Cecchi.

Journal reference: The Journal of the Acoustical Society of America, DOI: 10.1121/10.0014600

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