Dissonance

DISSONANCE, an unpleasant sensation for the ear, obtained depending on the relationship between the numbers of vibrations during the simultaneous reproduction of two sounds having different vibration frequencies (a pleasant sensation for the ear is called consonance). If we take a series of sounds that produce vibrations corresponding to a pure, or so-called harmonic scale, or the Zarlino scale, we obtain a series of the following numbers representing the intervals: C, D, E, F, G, A, B, C₃; 1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, 2. The combination of C and C₂ gives a ratio of 2; this is a common interval that merges in our perception, in which it is impossible to distinguish individual sounds. The ratio of the vibrations of C and G will be equal to 3/2; the ratio of the vibrations of C and E is 5/4; C and F is 4/3; and finally C and A is 5/3. Here there are simple ratios, and the simpler the ratio, the more perfect the consonance will be. The intervals that correspond to the intervals of C and G, C and E, C and F, and C and A represent a system of consonant intervals. The interval of C and D, which gives a ratio of 9/8, and C and B, which gives 15/8, represent a more complex relationship and give the impression of dissonance. The causes of consonance and dissonance, as Helmholtz showed, lie in the beats that two sounds produce. The number of beats is equal to the difference between the numbers of vibrations of the sounds creating these beats, and therefore, if we imagine that the fundamental note produces 100 vibrations, then the interval corresponding to C and D will constitute 9/8 of 100, i.e., about 113 vibrations, and 13 individual beats per second will be obtained, whereas the interval of C and G will give 50 beats per second (100 and 150), which will produce completely imperceptible beats that merge into a sound for which the fundamental tone (100) is an octave. Thus, in the first case, beats appear that irritate our ear, just as flickering irritates the eye. In the second case, there is no such irritation, because the beats merge with the fundamental tone. Helmholtz showed that in all individual cases where beats exist, phenomena of dissonance also always exist; his research clarified this question completely. However, another theory also arose—that of Stumpf, who examined this question statistically. Stumpf counted the number of people for whom a given chord is inseparable and showed that the greater the number of people who cannot separate two simultaneously sounding tones into their components, the more consonant the given interval is. Due to this, the second (C and D) and the seventh (C and B) appear dissonant, while all others appear more consonant. Later research, conducted by Rzhevkin at the Institute of Physics and Biophysics on individual sounds, directed one to the right ear and the other to the left ear, where the sensations of beats were excluded, showed that when beats are absent, the sensation of dissonance is also absent. Thus, the Helmholtzian theory regarding the connection between beats and consonance can be considered established.