from the book " euphony. objective prerequisites consonance in music. " Jaan Ross.
Several experimental studies have questioned a priori recognized by the assertion that the ideal from the standpoint of human hearing are intervals with simple frequency ratios. In particular, Lindqvist and Sundberg (1971) investigated the perception of melodic octaves (as an incentive to use both simple and complex sounds) and found that the ideal net is an interval, the frequency components of which are on a somewhat larger, than 2:1 (regardless of whether it is ascending or descending octave). Similar results for harmonic intervals were also Terhardt (1971a) and Ward (1954). As noted by Lindqvist and Sundberg, "for the extension of the intervals the subjects vary considerably in quantity, but not in quality (Lindquist and Sundberg 1971: 620). Terhardt (1971b) explains the expansion of octave masking, which occurs in the spectrum of sounds between the harmonics. This explanation is confirmed опытами (Терхардт и Фастл 1971), в которых через небольшой промежуток времени к одному синусоидальному звуку добавляли другой, октавой вверх или вниз от начального, which led to a slight shift in the height of the initial sound.
To study the phenomenon of expanding intervals, we also conducted an experiment (see: Lippus et al 1977) with a harmonic musical intervals, consisting of two pure tones. The experiment involved nine subjects with musically trained hearing. Incentives serve as a signal, the frequency of the lower tone of which was recorded and was 220, 440, 880 or 1760 Hz, and frequency of top-mounted experimenter an octave, fifth, quart, major third and major second, and then controlled the subjects within ± 5% of the frequency corresponding to a given tone on the net system. The experiment was performed in the anechoic room, the signals were fed through two speakers - left and right of the auditor, at a distance of 40 cm Intensity colors match 60, 70 or 80 dB. Was obtained 540 (9h4h5k3) reactions to stimuli.
experimental results are shown in Fig. 12 and 13 (data averaged for the three intensity levels). The vertical axis represents the variation in the ranges from standards of pure system (Fig. 12) or from the tempered scale (Fig. 13). On horizontal axis represents the frequency of the lower tone.
Based on these results the following conclusions.
1. It can be argued that the discrepancy between mathematically clean and pure perceptual values takes place not only in the case of an octave, but also at other intervals.
2. With increasing frequency octave range tends to increase, and the rest intervals - to decrease, which is most pronounced for the major second and perfect fourth. When crude interpolation line between pure mathematics and perceptual intervals takes place for the next lower frequency sound range: pure octave - 250 Hz, the perfect fifth - 1500, perfect fourth - 1100, major third - 5000, more than a second - 700 Hz.
Fig. 12. Differences in values between the mathematically harmonic and clean on the perception of intervals, depending on the frequency range.
Abscissa - frequency, Hz; ordinate - the deviation of the interval cents. solid line - pure octave, dash-dotted line with one point - perfect fifth, dot-dash with two dots - perfect fourth, dotted line - large third, dotted - more than a second.
Fig. 13. Differences in values between the evenly-tempered and clear on the perception of intervals, depending on the frequency band. Designations as in Fig. 12.
3. Of the net on the perception of intervals, in most cases do not coincide with the values of the intervals simple numerical relationships. We emphasize that the frequency of invisibility here can not be discussed - the minimum deviation of the perceived sound frequency of 500 Hz at 70 dB is only 2 Hz (see: Tsviker and Feldkeller 1971: 78). Therefore, can not be considered reliable enough common view that the transition from pure to a uniformly-tempered scale is negative because of failure of the principle of simple numerical relationships (excluding pure octaves). All the above-noted construction - Pythagoras, clean and evenly-tempered - to some extent theoretical constructs, neither of which does not satisfy fully the criteria of perception.
4. Finally, attention is drawn to a rather interesting parallel between the increase (or decrease) the intervals and functioning scale in the Yakut folk music (see: Alekseev 1976: Ch. 1). In folklore (apparently, not only in the Yakut) survived tunes, where the support is gradually "Parted" in height from verse to verse, ie, a sort of extension of the scale. We can assume that there is a connection between the phenomena extension and expansion of the scale intervals. However, the causes of these phenomena on the basis of these experiments can not be judged yet.
