Consonance and dissonance

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In music, a consonance (Latin consonare, "sounding together") is a harmony, chord, or interval considered stable and harmonized, as opposed to a dissonance, which is considered unstable and unharmonized. The strictest definition of consonance may be only those sounds which are pleasant, while the most general definition includes any sounds which are used freely.

Contents

1 Consonance

1.1 Source

2 Dissonance

2.1 Dissonance and musical style
2.2 Dissonance throughout the history of western music
2.3 The objective basis of dissonance
2.4 See also
2.5 Sources

3 External links
4 Further reading

Consonance

Consonance has been defined variously through:

Frequency ratios: with ratios of lower simple numbers being more consonant than those which are higher (Pythagoras). Many of these definitions do not require exact integer tunings, only approximation.
* Coincidence of harmonics: with consonance being a greater coincidence of harmonics or partials (collectively overtones) (Helmholtz, 1877/1954). By this definition consonance is dependent not only on the quality of the interval between two notes, but the partials and thus sound quality (timbre) of those notes themselves.
* Fusion or pattern matching: fundamentals may be perceived through pattern-matching of the separately analyzed partials to a best-fit exact-harmonic template (Gerson & Goldstein, 1978) or the best-fit subharmonic (Terhardt, 1974). Or harmonics may be perceptually fused into one entity, with consonances being those intervals which are more likely to be mistaken for unisons, the perfect intervals, because of the multiple estimates of fundamentals, at perfect intervals, for one harmonic tone (Terhardt, 1974). By these definitions inharmonic partials of otherwise harmonic spectra are usually processed separately (Hartmann et al., 1990), unless frequency or amplitude modulated coherently with the harmonic partials (McAdams, 1983). For some of these definitions neural-firing supplies the data for pattern-matching, see directly below (e.g., Moore, 1989; pp.183-187; Srulovicz & Goldstein, 1983).
* Period length or neural-firing coincidence: with the length of periodic neural-firing created by two or more wave-forms, lower simple numbers creating shorter or common periods or higher coincidence of neural-firing and thus consonance (Patternson, 1986; Boomsliter & Creel, 1961; Meyer, 1898; Roederer, 1973, p.145-149). Pure tones cause neural-firing exactly with the period or some multiple of the pure tone.
Critical band: Consonances are pitches farther apart than their critical bands.

In what is now called the common practice period consonant intervals include:

Perfect consonances:
* unisons and octaves
* perfect fourths and perfect fifths
Imperfect consonances:
* major thirds and minor sixths
* minor thirds and major sixths

This is as would be taught in a beginning music theory class, but intervals such as the thirds and sixths were once considered forbidden dissonances. Consonances may be used freely and unprepared, occurring on weak or strong beats.

Polyphonic cadences, requiring at least two voices, were created by successive dyads, the first an imperfect consonance on a weak beat, the second a perfect consonance on a strong beat, such as a major sixth moving to an octave (for instance, the major (imperfect) sixth D-B followed by the perfect octave C-C').

Source

Burns, Edward M. (1999). "Intervals, Scales, and Tuning", The Psychology of Music second edition. Deutsch, Diana, ed. San Diego: Academic Press. ISBN 0122135644.

Dissonance

In music, dissonance is the quality of sounds which seem "unstable", and have an aural "need" to "resolve" to a "stable" consonance. Both consonance and dissonance are words applied to harmony, chords, and intervals and by extension to melody, tonality, and even rhythm and metre. Although there are important physical and neurological facts important to understanding the idea of dissonance, the precise definition of dissonance is culturally conditioned — definitions of and conventions of usage related to dissonance vary greatly among different musical styles, traditions, and cultures. Nevertheless, the basic ideas of dissonance, consonance, and resolution exist in some form in all musical traditions that have a concept of melody, harmony, or tonality.

Additional confusion about the idea of dissonance is created by the fact that musicians and writers sometimes use the word dissonance and related terms in a precise and carefully defined way, more often in an informal way, and very often in a metaphorical sense ("rhythmic dissonance"). For many musicians and composers, the essential ideas of dissonance and resolution are vitally important ones that deeply inform their musical thinking on a number of levels.

Despite the fact that words like "unpleasant" and "grating" are often used to explain the sound of dissonance, in fact all music with a harmonic or tonal basis — even music which is perceived as generally harmonious — incorporates some degree of dissonance. The buildup and release of tension (dissonance and resolution), which can occur on every level from the subtle to the crass, is to a great degree responsible for what many listeners perceive as beauty, emotion, and expressiveness in music.

Brief audio (MIDI) musical examples of the interaction and effect of consonance and dissonance upon each other can be found here: ["The effect of context on dissonance'"] and here: [''The role of harmony in music"].

Dissonance and musical style

Understanding a particular musical style's treatment of dissonance — what is considered dissonant and what rules or procedures govern how dissonant intervals, chords, or notes are treated — is key in understanding that particular style. For instance, in the common practice period, harmony is generally governed by chords, which are collections of notes generally considered to be consonant (though even within this harmonic system there is a hierarchy of chords, with some considered relatively more consonant and some relatively more dissonant). Any note that does not fall within the prevailing harmony is considered dissonant. Particular attention is paid to how dissonances are approached (approach by step is less jarring, approach by leap more jarring), even more to how they are resolved (almost always by step), to how they are placed within the meter and rhythm (dissonances on stronger beats are considered more forceful and those on weaker beats less vital), and to how they lie within the phrase (dissonances tend to resolve at phrase's end). In short, dissonance is not used willy-nilly but is used in a very careful, controlled, and well circumscribed way. The subtle interplay of different levels of dissonance and resolution is vital to understanding the tonal and harmonic language of this period.

Dissonance throughout the history of western music

Dissonance has been understood and heard differently in different musical traditions, cultures, styles, and time periods.

In early Renaissance music intervals such as the perfect fourth were considered strong dissonances that must be immediately resolved. The regola delle terze e seste ("rule of sixths and thirds") required that imperfect consonances should resolve to a perfect one by a half step progression in one voice and a whole step progression in another (Dahlhaus 1990, p.179). Anonymous 13 allowed two or three, the Optima intorductio three or four, and Anonymous 11 (15th century) four or five successive imperfect consonances. By the end of the 15th century imperfect consonances where no longer "tension sonorities" but, as evidence by the allowance of their successions argued for by Adam von Fulda, but independent sonorities, according to Gerbert (vol.3, p.353), "Although older scholars once would forbid all sequences of more than three or four imperfect consonances, we who are more modern allow them." (ibid, p.92)

In the common practice period all dissonances were required to be prepared and then resolved, occurring on weak beats and quickly giving way or returning to a consonance. There was also a distinction between melodic and harmonic dissonance. Dissonant melodic intervals then included the tritone and all augmented and diminished intervals. Dissonant harmonic intervals included:

minor second and major seventh
augmented fourth and diminished fifth (tritone)

Thus, Western musical history can be seen as starting with a quite limited definition of consonance and progressing towards an ever wider definition of consonance. Early in history, only intervals low in the overtone series were considered consonant. As time progressed, intervals ever higher on the overtone series were considered consonant. The final result of this was the so-called "emancipation of the dissonance" (the words of Arnold Schoenberg) by some 20th-century composers. Early 20th-century American composer Henry Cowell viewed tone clusters as the use of higher and higher overtones.

Despite the fact that this idea of the historical progression towards the acceptance of ever greater levels of dissonance is somewhat oversimplified and glosses over important developments in the history of western music, the general idea was attractive to many 20th-century modernist composers and is considered a formative meta-narrative of musical modernism.

One example of imperfect consonances previously considered dissonances in Guillaume de Machaut's "Je ne cuit pas qu'onques":

One example of baroque dissonance:

One example of classical era dissonance:

One example of modernist dissonance:

The objective basis of dissonance

Musical styles are similar to languages, in that certain physical, physiological, and neurological facts create bounds that greatly affect the development of all languages. Nevertheless, different cultures and traditions have incorporated the possibilities and limitations created by these physical and neurological facts into vastly different, living systems of human language. Neither the importance of the underlying facts, nor the importance of the culture in assigning a particular meaning to the underlying facts, should be minimized.

For instance, two notes played simultaneously, with the same timbre but slightly different frequencies, have a beating "wah-wah-wah" sound that is very audible. Some musical styles consider this to be objectionable ("out of tune") and go to great lengths to eliminate this effect. Other musical styles consider this sound to be an attractive part of the musical timbre and go to equally great lengths to create instruments that have this slight "roughness" as a feature of their sound.

Here are some of the physical, physiological, and neurological facts that influence the idea of dissonance in all musical languages:

In general, for two pitches that are quite close in frequency, the closer the frequencies of two pitches the more "roughness" there is in the resulting composite waveform. As two pitches approach each other they begin to produce beat oscillations, which are caused when the two pitches cause interference, or reinforce and cancel each others amplitudes. Most listeners experience these beat oscillations and interference as a roughness in the sound that is unpleasant or dissonant. The roughness increases to a certain point as frequencies of the two pitches become closer together, reaching a high point of roughness, then decreasing as the frequencies become perceptually indistinguishable.

[Two pitches moving from the interval of a Major 2nd to a unison] ([file info])
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* Problems listening to the file? See [Media helpmedia help].

Frequency ratios: ratios of higher simple numbers are more dissonant than those which are lower (Pythagoras).

Diverging tones

Spectral analysis of two diverging tones

[Two diverging sinusoid-like tones] ([file info])
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* Problems listening to the file? See [Media helpmedia help].

[Two diverging tones with sawtooth waveform] ([file info])
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* Problems listening to the file? See [Media helpmedia help].

The physical basis for Pythagoras's observation can be seen in the spectral analysis above and heard in the accompanying sound file. At the points where the ratios of the frequencies of the tones are more simple (indicated by arrows near the top of the graph), the overtones as observed in the spectral analysis are more ordered and simple. Most listeners perceive the tone of the interval at these points to be more "pure" or "harmonious".

By contrast, when the ratios of the frequencies are not simple, the overtone situation appears complex and chaotic in the spectral analysis. Most listeners perceive the intervals at these points to be "rougher" or more "disharmonious".

In human hearing, the varying effect of these different ratios may be perceived by one of these mechanisms:

* Fusion or pattern matching: fundamentals may be perceived through pattern-matching of the separately analyzed partials to a best-fit exact-harmonic template (Gerson & Goldstein, 1978) or the best-fit subharmonic (Terhardt, 1974) or harmonics may be perceptually fused into one entity, with dissonances being those intervals which are less likely to be mistaken for unisons, the imperfect intervals, because of the multiple estimates, at perfect intervals, of fundamentals, for one harmonic tone (Terhardt, 1974). By these definitions inharmonic partials of otherwise harmonic spectra are usually processed separately (Hartmann et al., 1990), unless frequency or amplitude modulated coherently with the harmonic partials (McAdams, 1983). For some of these definitions neural-firing supplies the data for pattern-matching, see directly below (e.g., Moore, 1989; pp.183-187; Srulovicz & Goldstein, 1983).
* Period length or neural-firing coincidence: with the length of periodic neural-firing created by two or more wave-forms, higher simple numbers creating longer periods or lesser coincidence of neural-firing and thus dissonance (Patternson, 1986; Boomsliter & Creel, 1961; Meyer, 1898; Roederer, 1973, p.145-149). Pure tones cause neural-firing exactly with the period or some multiple of the pure tone.
Dissonance is also then defined by the amount of beating between non-common harmonics or partials (collectively overtones) (Helmholtz, 1877/1954). Terhardt (1984) calls this "sensory dissonance". By this definition dissonance is dependent not only on the quality of the interval between two notes, but the harmonics and thus sound quality (timbre) of those notes themselves.
Dissonances are pitches that fall within each other's critical bands.

The strongest homophonic (harmonic) cadence, the authentic cadence, dominant to tonic (D-T, V-I or V⁷-I), is in part created by the dissonant tritone created by the seventh, also dissonant, in the dominant seventh chord which precedes the tonic.

Sources

Burns, Edward M. (1999). “Intervals, Scales, and Tuning”, The Psychology of Music second edition. Deutsch, Diana, ed. San Diego: Academic Press. ISBN 0122135644.
Dahlhaus, Carl. Gjerdingen, Robert O. trans. (1990). Studies in the Origin of Harmonic Tonality. Princeton University Press. ISBN 0691091358.

External links

[Atlas of Consonance]
[Babies react: Tonality and dissonance/consonance] — News clipping
[Tonalsoft Encyclopaedia of Tuning]
[Consonance and Dissonance — Index to Notes] by David Huron at Ohio State University School of Music
* [Bibliography of Consonance and Dissonance]
[The Keyboard Tuning of Domenico Scarlatti]
[Natural forces in the evolution of the Scale]
[Role of the drone in the evolution of counterpoint & harmony]
[Stages in the Evolution of Music]