Combination tones (CTs) generated by the inner ear have been widely investigated in the past, starting from the famous Tartini's "third tone." Instead, much less attention has been dedicated to the CTs generated by musical instruments. In this paper, the CTs generated by a set of violins of different quality and age have been investigated when playing a selected set of dyads. CTs were found in all of the violins, and the strongest of them occurred at a frequency below the lower note of the dyad. Its amplitude was strongly dependent on violin and dyad played and was greatest in two old Italian violins and decreased down to a minimum in a factory-made violin. All of these findings are well explained by the boosting action of A0, the main air resonance of the violin that correlates well with the strongest CT. A listening test, performed using selected dyads and violins, showed that the differences between dyads with and without CTs were correctly recognized by a group of professional and amateur musicians, suggesting a possible musical significance of the main CT. The results investigating the possible source of violin nonlinearity are also described.