Archives of Acoustics, 36, 4, pp. 727–740, 2011

Combination Tones in Violins

Angela LOHRI
University of Music and Performing Arts Vienna, International Centre of Harmonics

Sandra CARRAL
University of Music and Performing Arts Vienna, Institute of Musical Acoustics

Vasileios CHATZIIOANNOU
University of Music and Performing Arts Vienna, Institute of Musical Acoustics

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.
Keywords: combination tones; extra-aural; intra-aural; string instruments; measure- ments of simultaneous intervals; nonlinearity; virtual pitch
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