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Pitch and timbre
Published in Stanley A. Gelfand, Hearing, 2017
The cubic difference tone (2f1 − f2) is another significant and frequently encountered combination tone. These distortion products appear to be generated by the active processes in the cochlea, and have already been encountered when distortion-product otoacoustic emissions were discussed in Chapter 4. For the 800- and 1000-Hz primary tones in Figure 12.7, the resulting cubic difference tone is 2(800) − 1000 = 600 Hz. A particularly interesting aspect of the cubic difference tone is that it is audible even when the primaries are presented at low sensation levels. For example, Smoorenburg (1972) demonstrated that 2f1 − f2 is detectable when the primaries are only 15 to 20 dB above threshold, although he did find variations among subjects.
Hermann von Helmholtz and the aesthetics of the acoustics
Published in Hearing, Balance and Communication, 2021
Marta Mion, Alessandro Martini
Helmholtz's first work in the acoustic field concerned the study of combination tones [8]. The difference tones, which occur when two sounds with different frequencies are in agreement and each has a high intensity, have been well known for a long time to musicians and organ builders. They are often called ‘Tartini's tones’ as mentioned by the Italian violinist Giuseppe Tartini in his ‘Treatise on music according to the true science of harmony’, published in Padua in 1754 [9]. Tartini reported that sometimes he heard a third note while he was playing only two, and this additional tone was higher when the first two notes were farther apart. Gerhard Vieth from Dessau in 1805 renamed this third sound ‘combination tone’ (today the combination tones are called ‘difference tones’, since their frequency corresponds to the difference between the two original sounds’ frequencies) [10]. Helmholtz found that different tones occur in systems characterized by the presence of distortion during the transmission of the sound (nonlinear systems).