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Consonance and dissonance

In music, consonance and dissonance form a structural dichotomy, the terms of which define each other: a consonance is what is not dissonant, and reciprocally. A finer consideration shows that the distinction is one of gradation, from the most consonant to the most dissonant. Consonance and dissonance define a level of weetness/harshness, pleasantness/unpleasantness, acceptability/unacceptability, of the sounds or intervals under consideration. As Hindemith stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied."^[1]

The opposition can be made in different contexts:

In acoustics or psychophysiology, the distinction may be objective. In modern times, it usually is based on the perception of harmonic partials of the sounds considered, to such an extent that the distinction really holds only in the case of harmonic sounds (i.e. sounds with harmonic partials).
In music, even if the opposition often is founded of the preceding, objective distinction, it more often is subjective, conventional, cultural, and style-dependent. Dissonance can then be defined as a combination of sounds that does not belong to the style under consideration; in recent music, what is considered stylistically dissonant may even correspond to what is said consonant in the context of acoustics (e.g. a major triad in atonal music).

In both cases, the distinction mainly concerns simultaneous sounds; if successive sounds are considered, their consonance or dissonance depends on the memorial retention of the first sound while the second is heard. For this reason, consonance and dissonance have been considered particularly in the case of polyphonic Occidental music, and the present article is concerned mainly with this case.

Most historical definitions of consonance and dissonance since about the 16th century have stressed their pleasant/unpleasant, or agreeable/disagreeable character. This may be justifiable in a psychophysiological context, but much less in a musical context properly speaking: dissonances often play a decisive role in making music pleasant, even in a generally consonant context – which is one of the reasons why the musical definition of consonance/dissonance cannot match the psychophysiologic definition. In addition, the oppositions pleasant/unpleasant or agreeable/disagreeable evidence a confusion between the concepts of 'dissonance' and of 'noise'. (See also Noise in music, Noise music and Noise (acoustic).)

While consonance and dissonance exist only between sounds and therefore necessarily describe intervals (or chords), Occidental music theory often considers that, in a dissonant chord, one of the tones alone is in itself the dissonance: it is this tone in particular that needs "resolution" through a specific voice leading.

Acoustics and psychophysiology

Helmholtz (definition of dissonance by beating and roughness between harmonic partials; consonance = absence of dissonance)

Stumpf (definition of consonance by fusion of harmonic partials; dissonance = absence of consonance)

Modern versions of these.

The common idea that consonances are the intervals found between the lower partials, dissonances those found between higher partials is nonsense, because consonances and dissonances occur between complex sounds, each of which is made of a large number of partials.

History

Antiquity and Middle-Ages

In Ancient Greece, armonia denoted the production of a unified complex, particularly one expressible in numerical ratios. Applied to music, the concept concerned how sounds in a scale or a melody fit together (in this sense, it could also concern the tuning of a scale).^[2] The term symphonos was used by Aristoxenus and others to describe the intervals of the fourth, the fifth, the octave and their doublings; other intervals were said diaphonos. This terminology probably referred to the Pythagorean tuning, where fourths, fifths and octaves (ratios 4:3, 3:2 and 2:1) were directly tunable, while the other degrees (other 3-prime ratios) could only be tuned by combinations of the preceding.^[3] Until the advent of polyphony and even later, this remained the basis of the concept of consonance/dissonance (symphonia/diaphonia) in Occidental theory.

In the early Middle Ages, the Latin term consonantia translated either armonia or symphonia. Boethius (6th century) characterizes consonance by its sweetness, dissonance by its harshness: "Consonance (consonantia) is the blending (mixtura) of a high sound with a low one, sweetly and uniformly (suauiter uniformiterque) arriving to the ears. Dissonance is the harsh and unhappy percussion (aspera atque iniocunda percussio) of two sounds mixed together (sibimet permixtorum)."^[4] It remains unclear, however, whether this could refer to simultaneous sounds. The case becomes clear, however, with Hucbald of Saint Amand (c900), who writes: "Consonance (consonantia) is the measured and concordant blending (rata et concordabilis permixtio) of two sounds, which will come about only when two simultaneous sounds from different sources combine into a single musical whole (in unam simul modulationem conveniant) […]. There are six of these consonances, three simple and three composite, […] octave, fifth, fourth, and octave-plus-fifth, octave-plus-fourth and double octave."^[5]

Parallel survivance of the two conceptions: Consonance as a rational organization of the musical system (Guido); Consonance as a pleasing superposition of notes.

Progressive addition of imperfect consonances.

[Early rules for the usage of dissonances in counterpoint.]

[Margo Schulter makes a confusion between ratios of entire numbers and numbers in the harmonic series.]

Renaissance

5-limit, pure thirds (instead of Pythagorean ones): Schismatische verwechslung as a first attempt to produce pure thirds (refer to Lindley). Ramos de Pareja and the 5:4 major third.

Agent/patient

Common practice tonality

[Modern]

Schoenberg, Hindemith, Bartòk, Krenek, ...

Consonance as a tool for building musical systems and temperament

Pythagorean tuning

Principles of temperament

Irrational intervals

Just intonation

Prime limits

^ Paul Hindemith, The Craft of Musical Composition, vol. I, A. Mendel transl., New York, Associated Music Publishers, 1942, p. 85.
^ J. A. Philip, Pythagoras and the Pythagoreans, Toronto, University of Toronto Press, 1966, pp. 123-24.
^ Aristoxenus, Harmonics, ed. and transl. by H. Stewart Macran, Oxford, 1902, pp. 188-206. See James Tenney, A History of "Consonance" and "Dissonance", New York, Excelsior Music Publishing Company, 1988, p. 11-12.
^ Anicius Boethius, De institutione musica, vol. I, Ms Cambridge, Trinity College, R.15.22 (944), f. 13v. Electronic edition on [CHTML].
^ Hucbald of Saint-Amand, Musica, GS I, p. 107; Warren Babb, Hucbald, Guido and John on Music, New Haven, London, Yale University Press, 1978, p. 19.

[1] Paul Hindemith, The Craft of Musical Composition, vol. I, A. Mendel transl., New York, Associated Music Publishers, 1942, p. 85.

[2] J. A. Philip, Pythagoras and the Pythagoreans, Toronto, University of Toronto Press, 1966, pp. 123-24.

[3] Aristoxenus, Harmonics, ed. and transl. by H. Stewart Macran, Oxford, 1902, pp. 188-206. See James Tenney, A History of "Consonance" and "Dissonance", New York, Excelsior Music Publishing Company, 1988, p. 11-12.

[4] Anicius Boethius, De institutione musica, vol. I, Ms Cambridge, Trinity College, R.15.22 (944), f. 13v. Electronic edition on [CHTML].

[5] Hucbald of Saint-Amand, Musica, GS I, p. 107; Warren Babb, Hucbald, Guido and John on Music, New Haven, London, Yale University Press, 1978, p. 19.

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