Scarlet & Grey
Ohio State University
School of Music

Consonance and Dissonance - Tonal Fusion Theory

Carl Stumpf carried out a seminal experiment investigating the tendency for some sound combinations to cohere into a single sound image through a process of Tonverschmelzung or tonal fusion. Listeners heard two concurrent tones and were asked to judge whether they heard a single tone or two tones. Stumpf found that the pitch interval that most encourages tonal fusion is the aptly named unison. The second most fused interval is the octave, whereas the third most fused interval is the perfect fifth (Stumpf, 1890). (There is no general agreement in the literature concerning the rank order for subsequent intervals. Some commentators consider the perfect fourth (3:4) to be the next most fused interval, whereas others have suggested the double octave (1:4). Experimental data collected by DeWitt and Crowder (pp.77-78) paradoxically suggests that major sevenths are more prone to tonal fusion than perfect fourths.)

Stumpf was struck by the similarity of these judgments to judgments of the degree of consonance. In his Tonpsychologie of 1890 Stumpf proposed that consonance is caused by tonal fusion. That is, the greater the tendency for sounds to cohere, the greater the consonance. At first glance, this theory seems to hold considerable merit. For example, since harmonically-related partials are more likely to fuse and sound like a single complex tone, the resulting tone should be relatively free from dissonance.

Stumpf later abandonded his own theory as unsatisfactory. There are a number of good reasons supporting Stumpf's decision to abandon the theory. Here we will note three sample problems.

Consider first, a complex harmonic series consisting of the first ten partials: 100 Hz, 200 Hz, 300 Hz, 400 Hz, 500 Hz, 600 Hz, 700 Hz, 800 Hz, 900 Hz, 1,000 Hz. This spectrum will produce a highly fused complex tone with a pitch corresponding to roughly a 100 Hz fundamental. Now compare this with the subset consisting of just the 2nd and 3rd partials: 200 Hz and 300 Hz. Most listeners will tend to judge this dyad as less fused than the complex tone, yet most listeners will also judge the dyad to sound more "pleasant", "euphonious" or "consonant" than the full-spectrum tone.

Another simple demonstration involves taking any complex sonority and passing it through a commercial "phaser" or "chorus" device. Phasing involves making a duplicate copy of a signal, phase-shifting it, and adding the shifted copy to the original signal. In addition, the amount of phase shifting is constantly varied. A "phase shifter" has two immediate perceptual effects. The first effect is to make the sound more "pleasant" or "euphonious". The second effect is to make the sonority sound like there are more instruments. That is, a process that increases the apparent numerosity in the sound field, also causes an increase in perceived consonance. Said another way, the Tonal Fusion theory of consonance fails to explain by a "string section" often sounds more pleasant that a single violin.

A third problem for the Tonal Fusion theory comes from a multiple regression analysis of the interval distributions in the polyphonic writing of J.S. Bach. In a review of the published experimental data, Huron (1991) noted that the distributions for judgments of consonance/dissonance differ significantly from the judgments for tonal fusion. Huron (1991) went on to compare these published distributions against the interval distributions for intervals in the music of J.S. Bach. For a large sample of music, there is a positive correlation between the consonance distributions and Bach's interval prevalence. However, there is a negative correlation between Bach's interval use and the tonal fusion distributions. Moreover, the best correlations were found using a multiple regression combining tonal fusion and consonance. In short, there is strong evidence that in his polyphonic writings, Bach was endeavoring to promote sensory consonance while simultaneously avoiding tonal fusion. For example, unisons, octaves, and perfect fifths occur less frequently in Bach's polyphonic music than would occur in a purely random juxtaposition of parts. Moreover, unisons occur less frequently than octaves, which occur less frequently than perfect fifths, which occur less frequently than other intervals. Note that this observation is independent of the avoidance of parallel unisons, fifths, or octaves. As simple static intervals, these intervals are actively avoided in Bach's polyphonic works.

Bregman (1990) has pointed out that it is important not to conflating two different auditory experiences: "smooth sounding" versus "sounding as one." Huron (1991) showed that Bach's polyphonic music is organized so as to minimize "sounding as one" while maximizing "sounding smooth". Bach's musical organization is inconsistent with the theory that consonance is caused by tonal fusion.