Scarlet & Grey
Ohio State University
School of Music


Consonance and Dissonance - Stream Incoherence Theory

Wright and Bregman suggest that when two concurrent tones are captured by independent streams, their potential dissonance is suppressed or neutralized. Thus the degree to which a major seventh interval is perceived as dissonant depends upon how well the constituent tones are integrated into their respective horizontal voices.

"I think that if we were to hear, over headphones, a violin partita by Bach in one ear and piano sonata by Beethoven in the other, and if these were well segregated perceptually, a combination consisting of one note from the Bach and one from the Beethoven would be neither consonant nor dissonant." (p.521).
The theory is illustrated in Figure (from page 513). Due to the close within-voice pitch proximity the two diatonic scales in Figure 1a segregate well from each other. At the same time there is little or no perceived dissonance in example 1a. However, if the four through seventh intervals are extracted and rearranged so as to reduce the pitch proximity (and so reduce the horizontal streaming) the dissonances become evident (Figure 1b).

Figure 1a.


Figure 1b.

From this principle a full-fledged theory of non-chordal notes is developed. Wright and Bregman propose that the potential dissonance arising from non-chordal notes is controlled by ensuring good streaming. In practice, this means that most non-chordal notes will maintain close within-voice pitch proximity (i.e. antecedent and consequent step motion), and will be given asynchronous onsets. Passing notes, neighbor tones, suspensions, and anticipations all conform to these stringent streaming conditions -- whereas appoggiaturas and escape tones conform less well to the pitch proximity constraints. The most common types of non-chordal tones appear to be those that most contribute to the within-voice stream fusion.

Wright (1986) has suggested that the increasing dissonance over the course of the history of western music is reflected in the manner by which dissonant intervals are prepared. Over time, dissonances have been heightened by the dual practices of increasing the onset/offset synchronization of the tones forming the dissonant interval, and by decreasing the antecedent and consequent step motion. In short, the historical increase in musical dissonance is less attributable to the increasing prevalence of dissonant vertical moments, and more attributable to the weakening of horizontal streaming.

Interestingly, the Wright/Bregman theory is diametrically opposed to the theory of consonance proposed by Carl Stumpf (1898). Stumpf argued that the degree of perceived consonance in intervals is proportional to their tendency to fuse into a single percept. Intervals exhibiting simple frequency ratios are especially prone to tonal fusion (Verschmelzung) -- and hence are perceived as being most consonant. Stumpf (1926) later retracted this explanation. With the classic paper by Plomp and Levelt (1965), Helmholtz's theory of consonance and dissonance arising from the aggregate beating of adjacent partials was vindicated -- with an important modification arising from the influence of critical bands. The Wright/Bregman theory does not contradict the work of Plomp and Levelt.

Nevertheless, a number of issues arise from the Wright/Bregman theory. First, consider the notational examples in Figure 2. There is little difficulty hearing the two tones constituting the major seventh interval in Figure 2a. By adding the "e" and "g" in Figure 2b, two things happen: the individual notes are no longer easily resolved -- the sonority sounds more like a single chord rather than 4 notes. More importantly, by adding pitches, the dissonance of the major seventh interval has been considerably softened. This example poses a problem for the Wright/Bregman theory since a decrease in dissonance appears to accompany a decrease in the segregation of the auditory images.

Figure 2.

Second, Wright and Bregman argue that the existence of a good horizontal streaming permits the addition of non-chordal tones without suffering the penalty of undue dissonance. but the cause and effect may be reversed here. It may be that the goal of good horizontal streaming leads composers to add non-chordal tones in order to enhance the voice segregation. In short, the purpose of non-chordal tones may not be to add the spice of dissonance (without being too spicy); an equally plausible explanation may be that non-chordal tones are used to enhance the horizontal fusion of individual voices. The fact that even monophonic melodies make use of "non-chordal" tones (such as passing tones) lends credence to the idea that part of their purpose is to enhance horizontal streaming rather than to add dissonance. The Wright/Bregman theory of dissonance is nevertheless an important theory, and certainly worthy of experimental investigation.






References

Plomp, R. and Levelt, W.J.M. (1965). Tonal consonance and critical bandwidth. Journal of the Acoustical Society of America, Vol. 38, pp. 548-560.

Stumpf, C. (1898). Konsonanz und Dissonanz. Beiträge zur Akustischen Musikwissenschaft, Vol. 1, pp. 1-108.

Stumpf, C. (1926). Die Sprachlaute. Berlin: Verlag J. Springer.

Van Noorden, L.P.A.S. (1975). Temporal Coherence in the Perception of Tone Sequences. Eindhoven University of Technology, doctoral dissertation.

Wright, J.K. (1986). Auditory Object Perception: Counterpoint in a New Context. McGill University, Master's thesis.