Portrait of Giuseppe Tartini, eighteenth century. Via Wikimedia Commons (public domain).
Ancona, 1714. A violinist of twenty-two, Giuseppe Tartini, plays a double stop, two notes together, and hears a third. It does not sit above the other two, as one would expect of a harmonic. It sits below, low, thin, stubborn. No string produces it. He hears it all the same, and he will hear it all his life.
For forty years he talks about it to his pupils and does not put a line of it into print. Then, in 1754, the Seminary Press of Padua publishes the Trattato di musica secondo la vera scienza dell’armonia (Treatise on Music According to the True Science of Harmony), and that phantom note becomes the hinge of an entire system. Tartini calls it the third sound. He treats it not as an acoustic curiosity but as a proof: if nature, when two sounds are true, adds a third that holds them up from below, then harmony is not a human convention. It is written into sound itself, and the bass is its foundation.
The treatise is difficult, at times obscure, dense with geometry and calculation. His contemporaries read it with more respect than comprehension. But someone takes it seriously: Jean-Jacques Rousseau, in his Dictionnaire de musique of 1768, devotes a long exposition to it and sets it against Rameau’s system. Tartini persists. In 1767 he publishes in Padua a second book, De’ principj dell’armonia musicale contenuta nel diatonico genere, again around the same note that nobody plays.
There is, however, a fact that the heroic version tends to omit. Tartini was not the first to write about it. In the mid-1740s a German organist, Georg Andreas Sorge, had already described the phenomenon, and in 1751 Jean-Baptiste Romieu had done so in Montpellier. Both came before the Trattato. The date of 1714 we know from the account Tartini himself gave of it forty years later, and historians have been arguing ever since over the order of the discoveries. What remains is that it was he who built a theory of harmony on it, and that the name that stuck to the note is his.
What did he hear, exactly? The answer is simple arithmetic. Take two notes a perfectly tuned major third apart: an A at 440 vibrations per second and a C sharp at 550. The difference between the two frequencies is 110, and 110 vibrations are another A, two octaves below the first. There is the third sound: a note that corresponds to the difference between the two real ones. With a perfect fifth, 440 and 660, the difference is 220, and the phantom falls an octave below the lower note.
Between the eighteenth and nineteenth centuries scholars such as Lagrange and Thomas Young tried to explain it by beats, that is, by interference between the two waves in the air. It was the wrong explanation. Today acoustics places the origin of the phenomenon largely inside us: the inner ear is not a neutral receiver, it reacts non-linearly to the vibrations that strike it and manufactures new frequencies, sums and differences of those it receives. Tartini really did hear a nonexistent note. Only the violin had little to do with it. His cochlea was playing it.
This also explains the practical use made of it, which violinists still keep. The third sound is a severe judge: if the two notes of the double stop are in tune, the phantom note falls exactly beneath them and supports them; if one of the two is slightly flat or sharp, the phantom shifts too, and the chord cracks. To check the intonation of a double stop, all you have to do is listen closely to what nobody is playing.
In today’s acoustics textbooks the phenomenon is called a combination tone, or difference tone. In violin studios, where it is still used to tune fifths and clean up thirds, it goes on being called Tartini’s third sound.