Consonance and Dissonance      

copyright © 2003 by Larry J Solomon

The concept of "consonance and dissonance" (C&D) is an important technical issue in music. Unfortunately, common usage of the terms belies subjectivity, misconceptions, and contradictions. Surprisingly, even the respected Grove Music Online (2003) uses such terms as "pleasantness" and "unpleasantness" to define the duality {1}. Such subjective "definitions" cloud rather than clarify the issue and are not only unhelpful, but confusing. Sounds that are "unpleasant" to many listeners may be pleasant to others. Additionally, it is well known that the perception of C&D differs historically and culturally.

Acoustic Consonance and Dissonance

C&D must be considered in two different categories: contextual and non-contextual. Many scholars confuse these two, falling into the fallacy of equivocation. Acoustic C&D is non-contextual, i.e., it considers individual sounds isolated from any musical context. Theories of of acoustic C&D are commonly restricted to intervals and come under three categories:

  1. Pythagorean Theory. Consonant intervals are those with simple number ratios, although what constitutes "simple numbers" varies from author to author. The original Pythagoreans (5th Century BC) apparently restricted these to the numerals 1, 2, 3, and 4, whereby, 2:1 is the octave (P8), 3:2 is the perfect fifth (P5), and 4:3 is the perfect fourth (P4). Intervals having number ratios beyond that were considered dissonant; e.g., 5:4 the major third (M3), 6:5 the minor third (m3), etc. Later authors, e.g. Zarlino, expanded the consonant interval numbers to include those up to 6, with their inversions. This would include the perfect unison (1:1), P8, P5, P4, M3, m3, M6, m6. Other intervals would be dissonant.
  2. Harmonic Series or Beat Theory. This theory is represented by Helmholtz {2} and is often cited as the "beat theory", or "roughness theory". Consonant intervals are those without perceptible beats; e.g., an in-tune octave or fifth has no beats. The end results of this theory are not much different from the Pythagorean Theory. Carl Stumpf offered a convincing refutation of this theory in 1898{3}.
  3. Fusion Theory. Carl Stumpf {4} offered this theory. It is psychoacoustical, and assumes that amateurs will confuse various intervals for a unison. In his experiment, subjects are asked whether they perceive an interval as one or two sounds. Hence, the fusion theory may be aptly called the "confusion theory". Experiments by Stumpf yielded the following results, showing the percentage of confusion by amateurs: The problem with this theory is its subjective nature. Results vary wildly.

All these theories suffer from a lack of musical context. Even an octave can become dissonant within certain musical contexts. Therefore, a contextual definition of C&D is essential for music.

The Historical Variance of Consonance and Dissonance

The use of C&D has changed through history. In the ancient world only the perfect intervals were consonant, i.e., P8, P1, P5, P4. All other intervals were considered dissonant. This theory continued to be used in the Middle Ages when the perfect intervals were given religious significance. They were godly, holy, and pure, while the others were simply called “imperfect”. (The names for major and minor intervals did not yet exist.) Thus, they were "imperfect", impure, tainted, and corrupted in some way, i.e., dissonant. The major 3rd and 6th, for examples, were dissonant and initially were not used in early polyphony, which moved in parallel octaves, 4ths, and 5ths. Today 3rds and 6ths are the most consonant intervals as compared to the P4 or P5, that are now considered empty or “hollow” when heard alone. Even if we compare the treatment of dissonance in the Renaissance with that of, say, Bach, there is a profound difference. Whereas, Renaissance counterpoint is governed by the interval, Bach’s is governed by chords. Thus, we find many instances of practice in Bach’s music that actually violate the principles that governed Renaissance counterpoint.

Further, nineteenth century counterpoint found in Brahms, Wagner, and Strauss, etc., is freer in its treatment of dissonance than in any previous music. In the twentieth century we have heard composers speak about the “emancipation of dissonance”, where the distinction is either blurred or erased {5}. Recent studies suggest that even in much of the “dissonant” music of the twentieth century a new logic replaces the old; i.e., there are still consonances and dissonances, but they have been redefined and used in new ways.

Consonance is metaphorically resolute, static, and restful, whereas dissonance is dynamic, moving, and energetic. Both are necessary. Without the dynamic power of dissonance, consonance becomes impotent. Throughout history it seems that as the old dissonances lost their energy and strength, listeners became used to them. Composers then compensated by strengthening the level of dissonance, using the old dissonances as consonances -- thus, the perennial complaint that modern music is "too dissonant". Beethoven’s music was deemed dissonant by many of his contemporaries. His Ninth Symphony was considered so incomprehensible by some that they blamed it on his deafness; he was totally deaf when he wrote it.

So we see that the concept of C&D is neither rigid nor universal. This is to say nothing of the music found in other cultures, where even microtones are frequently used. How then can we define what is consonant or dissonant?

Contextual (Musical) Consonance and Dissonance

Working definition: Any sound that is restricted in its treatment is dissonant. Any sound that is used freely is consonant.

Each practice of music composition has its rules or restrictions. Without these there would be only chaos; i.e., any music that is organized has restrictions (a virtual tautology). Therefore, C&D is relative to each practice. Eighteenth century counterpoint has its restrictions which are different from sixteenth century counterpoint. Later music accepts new consonances that earlier music regarded as restricted sounds, i.e., dissonances.

An example of a "sound" that is restricted in its "common practice" treatment is the dominant seventh chord, which is expected to resolve to its respective tonic. It may or may not do so, but that does not change its expected resolution. Why is V to vi called a deceptive cadence? -- because the expected resolution is to tonic. If V does not go to tonic (in a cadence) it is "deceptive". Dominant, due to this restriction is dissonant. Any dominant function chord would also be dissonant; e.g., viio7.

Tonic, on the other hand has no expected resolution or implied movement. It can go anywhere. Therefore, it is unrestricted, and thereby consonant. In Bach's countrapuntal practice some intervals have restricted treatment. Any such intervals are dissonant by definition. Intervals, such as P8, M3, M6 are relatively unrestricted, and are therefore, consonant. Others such as seconds, sevenths, tritones, and augmented intervals are dissonant, due to their restricted treatment. In keeping with this, the restrictions on parallel fifths and octaves make them dissonant. The same would be true for parallel seconds and sevenths. Open cadential fifths are dissonant in Bach's counterpoint; they are infrequent. Therefore, any rule of contrapuntal practice is a restriction that bestows dissonance.

C&D, thereby, may be represented by a gradual scale from consonance to dissonance, from the freest sounds to the most restricted. There are no absolute consonances or dissonances, only observable practices. Finally, there is normally no strict dividing line even within a single practice.

Notes

  1. Grove Music Online, 2003
  2. Helmholtz, H. von. (1877)
  3. Stumpf, C. (1898). "Konsonanz und Dissonanz"
  4. Ibid.
  5. Schoenberg, Arnold. Theory of Harmony

References

  1. Grove Music Online ed. L. Macy (Accessed 27 Dec 2003), <http://www.grovemusic.com>
  2. Helmholtz, H. von. (1877). Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik. 1877, 6th ed., Braunschweig: Vieweg, 1913; trans. by A.J. Ellis as On the sensations of tone as a physiological basis for the theory of music" (1885). Reprinted New York: Dover, 1954.
  3. Stumpf, C. (1898). "Konsonanz und Dissonanz". Beitr. Akust. Musikwiss. Vol. 1, pp. 1-108. and (1883-1890). Tonpsychologie.
  4. Schoenberg, Arnold. Theory of Harmony, (originally Harmonielehre, Third edition,1922 ), translated by Roy E. Carter, Faber & Faber Ltd, 1978, reprinted by University of California Press, 1983.
  5. Tenney, J. (1988). A History of "Consonance" and "Dissonance." White Plains, NY: Excelsior, 1988; New York: Gordon and Breach, 1988.

see also: Bibilography of Consonance and Dissonance

  
2003 GUEST