Combination Tones in Violins

Abstract

In this study we investigate the appearance of combination tones in violins. Most authors in recent times have emphasised that combination tones occur inside the ear exclusively (intra-aural). This assumption will be subjected to scrutiny based on evidence found in an empirical study in which combination tones were measured outside the ear (extra-aural). Measurements were performed in which a violinist played two tones of a partic- ular musical interval simultaneously. This was recorded and subsequently analysed using a Fourier Transformation. In addition to the partial tones of the primary interval, the resulting spectrum showed frequencies corresponding to combination tones. Similar measurements on the viola and violoncello also revealed the exis- tence of extra-aural combination tones. Such frequencies may influence the timbre of simultaneous intervals played on string instruments. In another experiment the violin was excited using an electrodynamic mini-shaker with the aim of localising the origin of extra-aural combination tones. A newly devised tone matrix was used as a theoretical approach which computes all potential combination tones that may occur between any pair of partial tones. The detailed analysis of musical intervals by both the frequency spectrum and the tone matrix shows characteristic mirror and point symmetries in the partial tone structure. The discussion focuses mainly on the audibility of extra-aural combination tones and on ‘the combination tone 1’. This research opens up new perspectives and questions relevant for interpreters, composers, violin makers and violin acousticians.