Combination tones (also a combination tone , from it. Kombinationstöne ) arise in a non-linear acoustic system when exposed to two or more sinusoidal sound vibrations [1] .
There are subjective and objective combination tones. Subjective occur in the human hearing aid with a sufficiently high intensity (continuous) sound. Objective are called combinational tones that are formed outside the human ear, for example, due to the nonlinearity of the sound source itself or the sound-conducting medium.
There are difference (with frequency ω 1 -ω 2 ; German. Differenzton ) and sum (frequency ω 1 + ω 2 ; German. Summationston ) combination tones. Difference tones are practically more significant: they are of great importance in the design of musical instruments, are used (mostly unconsciously) by composers, are used to explain harmony by music theorists (as, for example, in P. Hindemith’s theory ). Sum tones are much weaker and often lie outside the audible frequency range.
Content
Historical essay
Difference combinational tones were discovered by German organist and music theorist Georg Andreas Sorge in 1745 [2] ; in 1754, they were described in more detail by Italian violinist and composer Giuseppe Tartini (hence their different name “Tartini tones”). In the second half of the 19th century, Hermann Helmholtz gave the holistic theory of combination tones, which explained their appearance only by the nonlinearity of the mechanical system of the hearing aid, namely the eardrum . According to modern ideas about the perception of sound, the nervous apparatus of human perception itself is essentially non-linear, and it serves as the main reason for the formation of subjective combination tones.
Notes
- ↑ Pozin and Others 1978, p. 176 : “In general, the nonlinear function F (a) can be represented as a series expansion in powers of a: F (a) = c₁a + c₂a² + c₃a³ + c₄a⁴ + c₅a⁵ + ... The corresponding system generates higher order harmonics from each input component and high-order combination tones with frequencies fk = k₁f₁ ± k₂f₂, k₁, k₂ = 1, 2, 3, ... " (see in unedited text form) .
- ↑ In the first part of his extensive treatise “Vorgemach der musicalischen Composition”.
See also
- Basic tone
- Unterton theory
Literature
- Combinational tones // Great Russian Encyclopedia . T. 14. Moscow, 2009, p. 604.
- Elements of the theory of biological analyzers, ed. N.V. Pozina. Moscow, 1978, p. 176-177.
Links
- Pozin N.V. (Editor). Elements of the theory of biological analyzers : [] . - Moscow, 1978.