Today we will talk with you about an interesting phenomenon as combination tones, which are important both from the point of view of a deeper understanding of the nature of sound and different strings, and from a practical point of view, as they can be used to build up pure intervals, for example when playing the violin or singing in several voices.
The effect we will discuss was discovered by the German organist and music theorist Georg Andreas Sorge in 1745, described in more detail in 1754 by the Italian violinist and composer Giuseppe Tartini (hence their other name “Tartini tones”).
The scientific name for this effect is combinatorial tones.
When I heard how the combinational tones effect works, I was pleasantly surprised, as I was once again convinced that sound is one of the most complex phenomena in our life.
In the beginning, briefly what the essence of this effect is.
If we listen to two sounds at a sufficient volume, our brain begins to mix other sounds to their sound. They are divided into two kinds: subtraction tones and addition tones. As the name implies, we are talking about the subtraction or addition of frequencies. Addition tones are very faintly perceptible to the ear, so Tartini tones usually refer to subtraction tones.
Naturally, these tones do not exist, they occur as a consequence of the non-linearity of our hearing apparatus. Hearing non-linearity is expressed by the appearance of subjective harmonics.
What non-linearity is – the easiest way to describe it is as a mismatch between the outgoing signal and the incoming signal. When a sinusoidal signal is applied to the eardrum, harmonics occur that are not present in the original signal, these are subjective harmonics.
For example, if you play a sine wave at 400Hz, our eardrum also generates overtones at frequencies 800, 1600Hz, etc.
These harmonics are called subjective, because they occur only as a consequence of our auditory system and are not present in the original signal.
Phantom tones, which are Tartini tones, as I said, are due to the non-linearity of the auditory system.
When we hear two sounds at a sufficient volume, e.g. 200 and 600, our brain also perceives the difference between these sounds, which is 400. At the same time, if you remove any of the notes of the interval, the difference in their sound will disappear – I think this is obvious.
What is interesting is the following (This will be especially useful for those who like to claim that overtones and the nature of the sound have no effect on their perception of sounds in tonality).
If we subtract the difference from the sounds in the tempered string, we see that none of the combi tones we perceive are equal to the frequency of that sound in the RTS
But if for example in the major thirds we decrease the frequency to a pure scale, we will obtain the note C that coincides with its frequency in the RTS.
That is a simple and scientific situation, in which you need to exclude from the process of listening to music a) the eardrum and b) any sound-producing elements of a physical nature in order not to hear overtones, not to be influenced by combiatorial tones.
Otherwise, any music you hear
1) will always contain elements that are more or less distant from the temperament
2) it will always be influenced by the non-linearity of your hearing apparatus and the overtones
I also found it interesting to note that the frequency difference in the minor third, major and minor sextave intervals is supplemented in the combinational tones to a triad, which in a sense is further evidence in favor of the naturalness of the major and minor triads.
