Combination tone

Combination tones can occur with simultaneous sounding of two different tones.

Combination tones appear particularly clearly the difference frequency of the output tones.

Trained musicians hear more combination tones as differences and sums of multiples of the frequencies.

Combination tones were occasionally also the subject of music theory, such as Hindemith instruction in music theory.

Difference tones

Difference tones are also known under the name Tartini tones, as they have been described by the Italian violinist Giuseppe Tartini, who heard loudly played in double stops on his violin. It is in these difference tones to the subgroup of combination tones, indicating their frequencies by calculating the difference between the primary frequencies or their multiples.

The best known and most easily audible difference tone is the so-called "square" difference tone. Its frequency is the beat frequency, which is the difference between the basic frequencies of the two tones output:

Example:

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Are two primary tones to an observer of the frequencies f1 and f2 performed under the condition of f1 < f2, as arise in the ear, especially of quadratic difference frequency f2 - f1 and the cubic differential tone 2 × f1 - f2. However, under appropriate conditions and difference tones of higher order are perceptible. In the ear formed quadratic difference tones behave like regular distortions, that is, with increasing sound level of the primary tones also increases the level of the quadratic difference tone at. However, in the ear formed cubic difference tones demonstrate Eberhard Zwicker an " unusual amplitude response " on. With increasing level of the higher level of the primary tone of the cubic difference tone increases initially, as this is to be expected in normal distortion. However, where the level of the higher level of the primary tone of the lower primary tone, the level of the cubic difference tone decreases. From numerous measurement results it can be seen that the difference tones generated in the ear, in principle, behave exactly like the ear supplied from outside sounds. As of origin of the difference tones hence the peripheral part of the auditory system is assumed.

Observation

Inexperienced users often find it difficult to distinguish the existing sounds from the combination tones. When producing a constant tone of frequency f1 and superimposed him f2 a tone of increasing frequency, the observation is easier: In addition to the frequency f1 and the increasing frequency f2 can be heard at high volume low the quadratic combination tone of frequency f2 - f1 and even quieter the cubic combination tone frequency 2 × f1 - f2.

Sample

They will play two tones with the frequencies and (in Hz):

When you play this loud, quietly listening to the square and even quieter cubic difference tones.

In the following example, the quadratic combination tones are reinforced with the frequencies for clarity. (The quadratic combination tone is heard from the depth coming in ascending order. )

In the following example, the cubic combination tones are reinforced with the frequencies for clarity. (The cubic combination tone is heard, first becoming deeper and then ascending again. )

Discovery

Combination tones, at the time referred to as difference tones were discovered in 1740 by Georg Andreas Sorge and incoming 1754 by Giuseppe Tartini, later Röber and Hermann studied by Thomas Young, of Helmholtz. Helmholtz has also discovered with the help of the theory of difference tone an analogous higher tone whose rate of vibration of the sum of the frequencies of the exciting tones corresponding to ( summation tone ).

Causes

The ear is able to analyze the envelope of a signal. The result of this evaluation, would then be an oscillation at the frequency of the difference tone.

Particularly at frequencies above 1600 Hz, the human auditory system, the exact function of time of the signals is no longer capture. Herein can be evaluated as information about the timing of the sound signals, only the envelope. And this evaluation gives an oscillation with the frequency of the difference tone.

Furthermore, also play a role in non-linear distortion of the sound source itself, ie, the acoustic transducer, the instrument or in the ear.

Consequences for musicians

This effect makes the musicians tuning instruments exploit in which the tone generator (eg, strings, pipes ) are to vote at a distance of a perfect fifth. The difference tone sounds an octave below the lower tone generator. In organ building an acoustic phenomenon is mistakenly called difference tone. Actually, it is here to Residualtöne; see also Acoustic deception.

From the phenomenon of " combination tone " but also arise consequences for the theory of music. Comparing the major third in just intonation and gleichstufiger mood, so you will notice a roughness at the same stage atmosphere that is enhanced by the difference tone. The difference tone in the pure Great third is exactly two octaves below the lower tone. In the equal temperament tuning of the difference tone is a semitone higher and this results in a dissonance to the interval sound.

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