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.

1.
Bissinger
,
G.
(
2008
). “
Structural acoustics of good and bad violins
,”
J. Acoust. Soc. Am.
124
(
3
),
1764
1773
.
2.
Caselli
,
G.
,
Cecchi
,
G.
,
Malacarne
,
M.
, and
Masetti
,
G.
(
2020
). “
Analysis of violin combination tones and their contribution to tartini's third tone
,”
Savart J.
1
(
9
), available at https://SavartJournal.org/articles/29/article.pdf (Last viewed 2 September 2022).
3.
Crowder
,
R.
(
1982
). “
The demise of short-term memory
,”
Acta Psychol.
50
,
291
323
.
4.
Curtin
,
J.
(
2006
). “
Taptones and weight of old Italian violin tops
,”
J. Violin Soc. Am.
1
(
2
),
1
13
.
5.
Dünnwald
,
H.
(
1991
). “
Deduction of objective quality parameters on old and new violins
,”
J. Catgut Acoust. Soc.
Ser. II
1
(
7
),
1
5
.
6.
Fritz
,
C.
,
Moore
,
C. G.
, and
Woodhouse
,
J.
(
2007
). “
Perceptual threshold for detecting modifications applied to the acoustical properties of a violin
,”
J. Acoust. Soc. Am.
122
(
6
),
3640
3650
.
7.
Goldstein
,
J. L.
(
1967
). “
Auditory nonlinearity
,”
J. Acoust. Soc. Am.
41
(
3
),
676
689
.
8.
Gough
,
C.
(
2014
). “
Musical acoustics
,” in
Springer Handbook of Acoustics
, Springer Handbooks, edited by T. D. Rossing (
Springer
,
New York
).
9.
Gough
,
C. E.
(
1980
). “
The resonant response of a violin G-string and the excitation of the Wolf-note
,”
Acustica
44
(
2
),
113
123
.
10.
Hallstrôm.
(
1832
). “
Von den combinationstonen
” (“On the combination tones”),
Ann. Phys. Chem.
24
,
438
466
.
11.
Helmholtz
,
H. L. F.
(
1877
).
Cambridge Library Collection—Music On the Sensations of Tone as a Physiological Basis for the Theory of Music
, 3rd ed. 2009, translated by
A. J.
Ellis
(
Cambridge University Press
,
Cambridge, UK
).
12.
Hindemith
,
P.
(
1942
).
The Craft of Musical Composition
.
Theoretical Part
(
Associated Music Publisher
,
New York
), Vol.
1
.
13.
Hutchins
,
C. M.
(
1962
). “
The physics of violins
,”
Sci. Am.
207
(
5
),
78
93
.
14.
Hutchins
,
C. M.
(
1983
). “
A history of violin research
,”
J. Acoust. Soc. Am.
73
(
5
),
1421
1440
.
15.
Lohri
,
A.
(
2016
).
Kombinationstöne Und Tartinis Terzo Suono
(Combination Tone And Tartini's Terzo Suono) (
Schott Music GmbH and Co.
,
Mainz, Germany
).
16.
Lohri
,
A.
,
Carral
,
S.
, and
Chatziioannou
,
V.
(
2011
). “
Combination tones in violins
,”
Arch. Acoust.
36
(
4
),
727
740
.
17.
McIntyre
,
M. E.
, and
Woodhouse
,
J.
(
1978
). “
The acoustics of stringed musical instruments
,”
Interdiscip. Sci. Rev.
3
(
2
),
157
173
.
18.
Meinel
,
H.
(
1957
). “
Regarding the sound quality of violins and a scientific basis for violin construction
,”
J. Acoust. Soc. Am.
29
(
7
),
817
822
.
19.
Pierce
,
J.
(
1983
).
The Science of Musical Sound
(
Scientific American
,
New York
).
20.
Plomp
,
R.
(
1965
). “
Detectability threshold for combination tones
,”
J. Acoust. Soc. Am.
37
(
6
),
110
123
.
21.
Reinicke
,
W.
, and
Cremer
,
L.
(
1970
). “
Application of holographic interferometry to vibrations of the bodies of string instruments
,”
J. Acoust. Soc. Am.
48
(
4B
),
988
992
.
22.
Robles
,
L.
, and
Ruggero
,
M. A.
(
2001
). “
Mechanics of the mammalian cochlea
,”
Physiol. Rev.
81
(
3
),
1305
1352
.
23.
Rodgers
,
O. E.
(
2005
). “
Tonal tests of prizewinning violins
,”
J. Violin Soc. Am.
(
75
), 2004,
VSA competition
,
Portland, OR
.
24.
Schelleng
,
J. C.
(
1963
). “
The violin as a circuit
,”
J. Acoust. Soc. Am.
35
(
3
),
326
338
.
25.
Smoorenburg
,
G. F.
(
1972
). “
Audibility region of combination tones
,”
J. Acoust. Soc. Am.
52
(
2B
),
603
614
.
26.
Tartini
,
G.
(
1754
).
Trattato Di Musica Secondo La Vera Scienza Dell'Armonia
(Treaty of Music According to the True Science of Harmony) (
Stamperia del Seminario
,
Padova, Italy
).
27.
Vieth
,
G.
(
1805
). “
Ueber combinationstöne, in beziehung auf einige streitschriften über sie zweier englischer physiker
” (“About combinations tone, in relation to some polemical writings about them by two English physicists, Th. Young and Jo. Gough”)
Ann Phys.
21
(
11
),
265
314
.
28.
Wegel
,
R.
, and
Lane
,
C.
(
1924
). “
The auditory masking of one pure tone by another and its probable relation to the dynamics of the inner ear
,”
Phys. Rev.
23
,
266
285
.

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