Subjective acceptability of various regular twelve-tone tuning systems in two-part musical fragments

Musically trained subjects rated the overall acceptability of the performance of two-part musical fragments. With the help of a computer these fragments were produced with intonations according to various regular 12-tone tuning systems: Pythagorean tuning (tempering T of the fifths equal to 0.0 cent), equal temperament (T = -2.0 cents), Silbermann (T = -3.9 cents), mean-tone (T = -5.4 cents), and Salinas tuning (T = -7.2 cents). In experiment 1, two systems in which T = 2.0 or T = -10.0 cents were also included. In both the lower and the higher parts of the fragments we used complex tones with a spectral-envelope slope of -6 dB/oct. Mean acceptability ratings were about the same for -5.4 less than or equal to T less than or equal to 0.0 cent, whereas for T greater than 0.0 and T less than -5.4 cents the ratings strongly decreased. This effect of tuning system was also found when acceptability was determined by means of the method of paired comparisons. The specific effect of tuning system was not affected by the tempo of the fragments. The perception of beats in the harmonic intervals was manipulated in experiment 2 by varying the spectral content of the tones. The condition in which the interference of the nearly coinciding harmonics was canceled resulted in higher acceptability. The effect of tuning system was the same as in experiment 1. In both experiments overall acceptability could be accurately predicted from a linear combination of the purity ratings of the isolated harmonic fifths and major thirds. It is not precluded, however, that for T greater than 0.0 and T less than -5.4 cents, the subjects based their acceptability ratings partly on the subjective purity of the melodic intervals.