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Consonant 4th Music Definition Essay

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Consonance and dissonance

For the stylistic device often used in poetry, see Literary consonance .

In music. a consonance (Latin com-. "with" + sonare. "to sound") is a harmony. chord. or interval considered stable, as opposed to a dissonance (Latin dis-. "apart" + sonare. "to sound"), which is considered to be unstable (or temporary, transitional). In more general usage, a consonance is a combination of notes that sound pleasant to most people when played at the same time; dissonance is a combination of notes that sound harsh or unpleasant to most people.


Consonance has been defined variously through: With ratios of lower simple numbers being more consonant than those that are higher (Pythagoras ). Many of these definitions do not require exact integer tunings, only approximation.

  • Coincidence of partials. with consonance being a greater coincidence of partials (called harmonics or overtones when occurring in harmonic timbres ) (Helmholtz, 1877/1954). By this definition, consonance is dependent not only on the width of the interval between two notes (i.e. the musical tuning ), but also on the combined spectral distribution and thus sound quality (i.e. the timbre ) of the notes (see the entry under critical band ). Thus, a note and the note one octave higher are highly consonant because the partials of the higher note are also partials of the lower note. [ 1 ] Although Helmholtz's work focused almost exclusively on harmonic timbres and tunings, subsequent work has generalized his findings to embrace non-harmonic tunings and timbres. [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ]
  • 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). Harmonics may be perceptually fused into one entity, with consonances being those include:
  • Perfect consonances.
    • unisons and octaves
    • perfect fourths + and perfect fifths
  • Imperfect consonances.
    • major thirds and minor sixths
    • minor thirds and major sixths

+ The perfect fourth is considered a dissonance in most classical music when its function is contrapuntal .

Note that in the Western Middle Ages, only the octave and perfect fifth were considered consonant harmonically (see Interval (music) or Just Intonation for the explanation).

"A stable tone combination is a consonance; consonances are points of arrival, rest, and resolution."

—Roger Kamien (2008), p.41 [ 7 ]


Ernst Krenek 's classification, from Studies in Counterpoint (1940), of a triad's overall consonance or dissonance through the consonance or dissonance of the three intervals contained within [ 8 ]  Play ( help · info ). For example, C-E-G consists of three consonances (C-E, E-G, C-G) and is ranked 1 while C-D♭-B consists of one mild dissonance (B-D♭) and two sharp dissonances (C-D♭, C-B) and is ranked 6.

"An unstable tone combination is a dissonance; its tension demands an onward motion to a stable chord. Thus dissonant chords are 'active'; traditionally they have been considered harsh and have expressed pain, grief, and conflict."

—Roger Kamien (2008), p.41 [ 7 ]

In Western music. dissonance is the quality of sounds that seems "unstable" and has 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 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, all music with a harmonic or tonal basis—even music 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 partially responsible for what listeners perceive as beauty, emotion, and expressiveness 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, harmony is generally governed by chords, which are collections of notes defined to be tolerably consonant by the style. (Though there is likely to be a hierarchy of chords, with some considered more consonant and some 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), and 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 more emphatic 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 any style.

Dissonance in traditional music

Sharp dissonant intervals and chords play prominent role in many traditional musical cultures. Vocal polyphonic traditions from Bulgaria. Bosnia-Herzegovina, Albania. Latvia. Georgia. Nuristan, some Vietnamese and Chinese minority singing traditions, Lithuanian sutartines, some polyphonic traditions from Flores and Melanesia are predominantly based on the use of sharp dissonant intervals and chords. The most prominent dissonance in most of these cultures is the interval of the neutral second (which is between the minor and major seconds). This interval is known to create the maximum sharpness and is known in German ethnomusicology under the term "schwebungsdiaphonie". Joseph Jordania recently suggested that extremely loud group singing/shouting, based on dissonant intevals, augmented by stomping and drumming on external objects, threatening body movements and object throwing, was developed by the forces of natural selection during the early stages of hominid evolution in order to reach the state of the battle trance [ 9 ] .

Dissonance in history of Western music

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

Relaxation and tension have been used as analogy since the time of Aristotle till the present (Kliewer, p. 290).

In early Renaissance music. intervals such as the perfect fourth were considered dissonances that must be immediately resolved. The regola delle terze e seste ("rule of thirds and sixths") 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 introductio three or four, and Anonymous 11 (15th century) four or five successive imperfect consonances. By the end of the 15th century, imperfect consonances were no longer "tension sonorities" but, as evidenced by the allowance of their successions argued for by Adam von Fulda, 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. 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:

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 as such. 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":

The West's progressive embrace of increasingly dissonant intervals occurred almost entirely within the context of harmonic timbres. as produced by vibrating strings and columns of air, on which the West's dominant musical instruments are based. By generalizing Helmholtz's notion of consonance (described above as the "coincidence of partials") to embrace non-harmonic timbres and their related tunings, consonance has recently been "emancipated" from harmonic timbres and their related tunings (Milne et al. 2007, 2008; Sethares et al. 2009). Using electronically controlled pseudo-harmonic timbres, rather than strictly harmonic acoustic timbres, provides tonality with new structural resources such as Dynamic tonality. These new resources provide musicians with an alternative to pursuing the musical uses of ever-higher partials of harmonic timbres and, in some people's minds, may resolve what Arnold Schoenberg described as the "crisis of tonality". [ 10 ]

The Middle Ages
  • Perfect consonance: unisons and octaves
  • Mediocre consonance: fourths and fifths
  • Imperfect consonance: minor and major thirds
  • Perfect dissonance: minor seconds, tritonus, and major sevenths
  • Mediocre dissonance: major seconds and minor sixths
  • Imperfect dissonance: major sixths and minor sevenths
Physiological 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 understated.

For instance, two notes played simultaneously but with slightly different frequencies produce a beating "wah-wah-wah" sound that is very audible. Musical styles such as traditional European classical music consider this effect to be objectionable ("out of tune") and go to great lengths to eliminate it. Other musical styles such as Indonesian gamelan 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 (Vassilakis, 2005).

Sensory dissonance and its two perceptual manifestations (beating and roughness) are both closely related to a sound signal's amplitude fluctuations. Amplitude fluctuations describe variations in the maximum value (amplitude) of sound signals relative to a reference point and are the result of wave interference. The interference principle states that the combined amplitude of two or more vibrations (waves) at any given time may be larger (constructive interference) or smaller (destructive interference) than the amplitude of the individual vibrations (waves), depending on their phase relationship. In the case of two or more waves with different frequencies, their periodically changing phase relationship results in periodic alterations between constructive and destructive interference, giving rise to the phenomenon of amplitude fluctuations.

Amplitude fluctuations can be placed in three overlapping perceptual categories related to the rate of fluctuation. Slow amplitude fluctuations (≈≤20 per second) are perceived as loudness fluctuations referred to as beating. As the rate of fluctuation is increased, the loudness appears to be constant, and the fluctuations are perceived as "fluttering" or roughness. As the amplitude fluctuation rate is increased further, the roughness reaches a maximum strength and then gradually diminishes until it disappears (≈≥75-150 fluctuations per second, depending on the frequency of the interfering tones).

Assuming the ear performs a frequency analysis on incoming signals, as indicated by Ohm's acoustic law (see Helmholtz 1885; Plomp 1964), the above perceptual categories can be related directly to the bandwidth of the hypothetical analysis filters (Zwicker et al. 1957; Zwicker 1961). For example, in the simplest case of amplitude fluctuations resulting from the addition of two sine signals with frequencies f1 and f2. the fluctuation rate is equal to the frequency difference between the two sines |f1 -f2 |, and the following statements represent the general consensus:

a) If the fluctuation rate is smaller than the filter bandwidth, then a single tone is perceived either with fluctuating loudness (beating) or with roughness.

b) If the fluctuation rate is larger than the filter bandwidth, then a complex tone is perceived, to which one or more pitches can be assigned but which, in general, exhibits no beating or roughness.

Along with amplitude fluctuation rate, the second most important signal parameter related to the perceptions of beating and roughness is the degree of a signal's amplitude fluctuation, that is, the level difference between peaks and valleys in a signal (Terhardt 1974; Vassilakis 2001). The degree of amplitude fluctuation depends on the relative amplitudes of the components in the signal's spectrum, with interfering tones of equal amplitudes resulting in the highest fluctuation degree and therefore in the highest beating or roughness degree.

For fluctuation rates comparable to the auditory filter bandwidth, the degree, rate, and shape of a complex signal's amplitude fluctuations are variables that are manipulated by musicians of various cultures to exploit the beating and roughness sensations, making amplitude fluctuation a significant expressive tool in the production of musical sound. Otherwise, when there is no pronounced beating or roughness, the degree, rate, and shape of a complex signal's amplitude fluctuations are variables that continue to be important through their interaction with the signal's spectral components. This interaction is manifested perceptually in terms of pitch or timbre variations, linked to the introduction of combination tones (Vassilakis, 2001, 2005, 2007).

The beating and roughness sensations associated with certain complex signals are therefore usually understood in terms of sine-component interaction within the same frequency band of the hypothesized auditory filter, called critical band .

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

In human hearing, the varying effect of simple 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 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 waveforms, higher simple numbers creating longer periods or lesser coincidence of neural firing and thus dissonance (Patternson, 1986; Boomsliter & Creel, 1961; Meyer, 1898; Roederer, 1973, pp. 145-149). Purely harmonic tones cause neural firing exactly with the period or some multiple of the pure tone.
  • Dissonance is more generally defined by the amount of beating between partials (called harmonics or overtones when occurring in harmonic timbres ) (Helmholtz, 1877/1954). Terhardt (1984) calls this "sensory dissonance". By this definition, dissonance is dependent not only on the width of the interval between two notes' fundamental frequencies, but also on the widths of the intervals between the two notes' non-fundamental partials. Sensory dissonance (i.e.. presence of beating and/or roughness in a sound) is associated with the inner ear's inability to fully resolve spectral components with excitation patterns whose critical bands overlap. If two pure sine waves, without harmonics, are played together, people tend to perceive maximum dissonance when the frequencies are within the critical band for those frequencies, which is as wide as a minor third for low frequencies and as narrow as a minor second for high frequencies (relative to the range of human hearing). [ 11 ] If harmonic tones with larger intervals are played, the perceived dissonance is due, at least in part, to the presence of intervals between the harmonics of the two notes that fall within the critical band. [ 12 ]

Generally, the sonance (i.e.. a continuum with pure consonance at one end and pure dissonance at the other) of any given interval can be controlled by adjusting the timbre in which it is played, thereby aligning its partials with the current tuning's notes (or vice versa ). [ 13 ] The sonance of the interval between two notes can be maximized (producing consonance) by maximizing the alignment of the two notes' partials, whereas it can be minimized (producing dissonance) by mis-aligning each otherwise nearly aligned pair of partials by an amount equal to the width of the critical band at the average of the two partials' frequencies (ibid.. Sethares 2009).

Controlling the sonance of more-or-less non-harmonic timbres in real time is an aspect of dynamic tonality. For example, in Sethares' piece C To Shining C (discussed here ), the sonance of intervals is affected both by tuning progressions and timbre progressions.

The strongest homophonic (harmonic) cadence. the authentic cadence, dominant to tonic (D-T, V-I or V 7 -I), is in part created by the dissonant tritone [ citation needed ] created by the seventh, also dissonant, in the dominant seventh chord, which precedes the tonic .

Look at other dictionaries:

consonance and dissonance — Perceived qualities of musical chords and intervals. Consonance is often described as relative stability, and dissonance as instability. In musical contexts, certain intervals seem to call for motion by one of the tones to resolve perceived… … Universalium

Dissonance — has several meanings, all related to conflict or incongruity: Consonance and dissonance in music are properties of an interval or chord Cognitive dissonance is a state of mental conflict Dissonance in poetry is the deliberate avoidance of… … Wikipedia

consonance — /kon seuh neuhns/, n. 1. accord or agreement. 2. correspondence of sounds; harmony of sounds. 3. Music. a simultaneous combination of tones conventionally accepted as being in a state of repose. Cf. dissonance (def. 2). See illus. under… … Universalium

dissonance — /dis euh neuhns/, n. 1. inharmonious or harsh sound; discord; cacophony. 2. Music. a. a simultaneous combination of tones conventionally accepted as being in a state of unrest and needing completion. b. an unresolved, discordant chord or interval … Universalium

dissonance — dis|so|nance [ˈdısənəns] n [Date: 1400 1500;. Latin; Origin: dissonare, from sonare to sound ] 1.) [U and C] technical a combination of notes that sound strange because they are not in ↑harmony ≠ ↑consonance 2.) [U] formal lack of agreement… … Dictionary of contemporary English

dissonance — /ˈdɪsənəns / (say disuhnuhns) noun 1. an inharmonious or harsh sound; discord. 2. Music a simultaneous combination of notes conventionally accepted as being in a state of unrest and needing resolution (opposed to consonance). 3. disagreement or… … Australian English dictionary

tuning and temperament — In music, the adjustment of one sound source, such as a voice or string, to produce a desired pitch in relation to a given pitch, and the modification of that tuning to lessen dissonance. Tuning assures a good sound for a given pair of tones;… … Universalium

List of post-industrial music genres and related fusion genres — The term Industrial music was first used in the mid 1970s to describe the then unique sound of the Industrial Records label artists, a wide variety of labels and artists have since come to be called Industrial. There is much disagreement between … Wikipedia

Emancipation of the dissonance — The emancipation of the dissonance was a concept or goal put forth by Arnold Schoenberg (composer of atonal music and the inventor of the twelve tone technique) and others, including his pupil Anton Webern. It may be described as a metanarrative… … Wikipedia

Other articles

Are octaves, fifths, fourths and thirds considered as - consonant - in all music cultures? Music: Practice - Theory Stack Exchange

Our western music culture revolves around the rule that certain intervals are very consonant, and others (such as the interval between a B and F) are dissonant. The octave is the most consonant interval we have, and we are able to use notes from different octaves interchangeably, considering them to be the same in some contexts.

Is this the case in all music cultures? Are there any cultures where octaves have absolutely no particular meaning, and where completely different tonic systems exist?

asked Jul 11 '14 at 11:40

No, they are not considered consonant in all music cultures. The perception of consonance and dissonance can be different among cultures. The same interval can be perceived (and labeled) differently by different cultures. This is influenced by many factors (and the harmonic series is not the only one!)

For example, in medieval times major thirds were considered dissonances unusable in a stable final sonority. (from wikipedia)

A very interesting text is A History of 'Consonance' and 'Dissonance' by James Tenney. He goes through many eras to analyze what was going on with dissonances and consonances.

There he quotes Paul Hindemith:

The two concepts have never been completely explained, and for a thousand years the definitions have varied. At first thirds were dissonant; later they became consonant. A distinction was made between perfect and imperfect consonances. The wide use of seventh-chords has made the major second and the minor seventh almost consonant to our ears. The situation of the fourth has never been cleared up. Theorists, basing their reasoning on acoustical phenomena, have repeatedly come to conclusions wholly at variance with those of practical musician.

The whole text answers your question, so I really recommend you to give it a read. Some examples:

In most pre-9th-century theoretical sources, the cognates of consonance and dissonance-or of related words like concord and discord, symphony and diaphony, and even our more general term harmony-refer neither to the sonorous qualities of simultaneous tones nor to their functional characteristics in a musical context but rather to some more abstract (and yet perhaps more basic) sense of relatedness between sounds which-though it might determine in certain ways their effects in a piece of music-is logically antecedent to these effects.

The contrapuntal and figured-bass periods, ca. 1300-1700:

The new system of interval-classification which emerged in theoretical writings sometime during the 14th century differs from those of the 13th century in several ways, but the most striking of these differences is that the number of consonance/dissonance categories has been reduced from five or six to just three- "perfect consonances," "imperfect consonances," and "dissonances." Both the major and the minor sixth (as well as the thirds) are now accepted as consonances (albeit "imperfect" ones), the fifth has been elevated from an intermediate to a perfect consonance whereas the fourth has become a special kind of dissonance (or rather, a hlghly qualified consonance). All of the other intervals-if allowed at all in the music-are simply called "dissonances."

Norman Cazden dives into this subject in many occasions, including the text Musical Consonance and Dissonance: A Cultural Criterion. The Journal of Aesthetics and Art Criticism Vol. 4, No. 1, pp. 3-11. (paywall, but you can read online for free if you register)

In the musical system of ancient Greece, there were no "imperfect" consonances. Major and minor thirds and sixths were considered dissonant. The fourth was the basic consonance for the formation of modes and systems of tetrachords.

(. ) Resolution is a criterion that has no application to the pentatonic scales. That is one reason why, to our perceptions, Chinese music sounds so inconclusive, so lacking in tendency and definition. The acoustically "perfect" consonances are the rule in some musics, but are not inevitable foundations, for nothing close to the ratio 3:2 is found in certain Javanese and Siamese scales. Intervals which bear no resemblance to any in our diatonic system form melodies which to their users seem "instinctive" and self-evidently natural. (…) In the Icelandic "Tvisöngvar" the third appears to be treated as dissonance.

He proposes that the perception of dissonance and consonance is not entirely based in ratios, harmonics, acoustics, etc; the perception can be trained, influenced.

The natural phenomena of vibratory wave-motions and their reception by the ear may be seen as limiting, rather than as a determining, factor in the perception of consonance and dissonance.

Studies of the psychology of musical perception have produced important negative results regarding consonance and dissonance. The naive view that by some occult process mathematical ratios are consciously transferred to musical perception has been rejected. Fusion, or "unitariness of tonal impression" has been found to produce no fixed order of preference for intervals, with the remarkable exception of the octave. It has been discovered that individual judgments of consonance can be enormously modified by training. Perceptions of consonance by adult standards do not seem generally valid for children bellow the age of twelve or thirteen, a strong indication that they are learned responses.

He suggests that the social factor is much more important.

In musical harmony the critical determinant of consonance or dissonance is the expectation of movement. This is defined as the relation of resolution. A consonant interval is one which sounds stable and complete in itself, which does not produce a feeling of necessary movement to other tones. A dissonant interval causes a restless expectation, or movement or movement to a consonant interval. Pleasantness or disagreeableness of the interval is not directly involved. The context is the determining factor.

For the resolution of intervals does not have a natural basis; it is a common response acquired by all individuals within a culture-area. It becomes evident that the science of music is not primarily a natural science. It is a social science devoted to the properties of a musical system or language belonging to a specific culture-area and a certain stage of historical development.

Due to the tonality relation, probably the most powerful systemic structure in our musical culture of the past few centuries, the most familiar consonant harmonies may act as dissonances. The C major triad is a dissonance in the key of F; as the dominant harmony, it requires resolution to the tonic. The requirement is a psychological imperative resulting from our conditioning; it has no basis on the nature of tone.

The origin of the minor mode and the minor triad in the overtone series has puzzled theorists for centuries. The ratios involved are, to say the least, rather more complicated than those of many "dissonances". (…) The minor harmony is accepted as frankly consonant, and as fundamentally so as the major.

The tempered major third, which is acoustically most badly out of tune, functions as the basic consonance in our system harmony. Where untempered intervals are possible (..) the skillful musician will produce thirds still more out of tune, in order to emphasize the major-minor contrast.

Perception and preference changes, varies.

During the 11th century, apparently, the preference for the fourth gave way to an increasing and almost exclusive use of fifths and octaves. In the period when our modern musical system came into existence, with its dependence on tonality and the major and minor modes, thirds and sixths became consonances and fourths dissonances, the full triad replaced the empty neutrals, and the functional value of resolution crystalized.

He has some interesting things to say about octaves, fifths, and fourths.

Octave and perfect fifth are noncommittal in respect to resolution tendencies, they are not in reality consonances within the meaning of harmonic relations.

Another "perfect consonance", the fourth, is actually a dissonance in musical practice; and what is worse, not consistently so.

+1 for a proper source, but I don't agree with some of the conclusions. Octaves and fifths certainly are consonant in western music, only, consonant plus dissonant makes dissonant and 8ve and 5th take part in both kind of chords. Perfect fourths are also never dissonant on their own (though they may become so by addition of a fifth, implied or real, to make a suspended-4th chord). – As for "the skillful musician will produce thirds still more out of tune"; yes, there is "expressive intonation", but its purpose is not emphasising major vs. minor. but consonant major vs. dissonant major. – leftaroundabout Jul 11 '14 at 21:11

@LeeWhite Added -A History of 'Consonance' and 'Dissonance' by James Tenney- excerpts. If you are interested in the subject, you should definitely give it a read (the text seems to no longer available or printed, but there are many PDFs available online) – Teental Jul 11 '14 at 21:57

This is an excellent post. Although I agree that historical factors trump purely acoustical ones, I think @leftaroundabout's post below is correct in pointing out that in medieval Pythagorean tuning the "thirds" are considerably wider than just- or equal-tempered thirds, and so have more beats or acoustical "dissonance". So the idea of a dissonant third is not as strange as it might seem. Kyle Gann has a good page about this and other historical tunings here. – Jon O. Jul 17 '14 at 19:52

Octaves and fifths are very prominent physical properties of sound-making objects.

The octave is the first harmonic, the fifth is the 2nd harmonic. Very closely related: the octave is what you get from halving the length of a string, the 5th is one-third.

This means that you hear the octave and the fifth prominently within single notes, even for primitive instruments like simple string instruments or ocarinas -- and even for "accidental" instruments like wind whistling across a cave entrance.

I therefore find it very likely that these intervals are almost universally used.

Of course the circle of fifths shows that by hopping through fifths you can reach any note, but the further out you go, the less "primal" the interval is. And there are more harmonics - but they are less prominent. I think the third is far enough removed from those "primal" intervals to not necessarily be universal.

answered Jul 11 '14 at 15:35

I don't think this answers the question. The question is not if the octave and fifth intervals are being used, the question is if octaves, fifths, fourths, and thirds are considered consonant in other music cultures. Also, you only talk about two intervals, what about fourths and thirds? What is the view of other cultures regarding those four intervals? Are they considered equally consonant? What's the array of distinctions given to those intervals? Which cultures are these? – Teental Jul 11 '14 at 18:13

The harmonic series is really a physical property of particular kinds of sound-making objects, such as idealised strings with no lateral stiffness. Stiffer strings, as on a piano, have some 'disharmonicity', or a slightly different relationship between the fundamental and overtones. Metal percussion instruments and bells differ even more from the harmonic series' integer ratios. This page argues that the disharmonicity of gamelan instruments influences the set of intervals in the /pelog/ scale, which includes octaves, but not fifths. – Jon O. Jul 17 '14 at 20:10

My response is intended as a useful supplement, not a direct answer nor oblivious tangent:

Different cultures have different traditions of which intervals they use most, but psychology aside, consonance can be measured quantitatively by nearness to a low whole-number ratio, another way of describing how regularly notes' vibrations criss-cross.

Octaves and fifths fit a 1:2 and 2:3 ratio, respectively, though in Western music we've adopted the Equal Tempered scale which divides the octave into twelve equal multiplicative steps (the ratio for each chromatic step, or minor 2nd or fret, is two to the one-twelfth power, so that a thirteenth note will be double the frequency of the first). For this reason the fifths are a little flatter in Equal Temperament. ET was adopted as a good compromise (Bach was an advocate) to allow key changes and transposition yet still have consonant intervals.

Harry Partch and other composers have worked out music based on the low whole-number ratio approach, extending to more notes. A few pieces on Wendy Carlos's Beauty in the Beast extended the harmonic series (rather than using the Equal Temperament scale's near-misses to most of the harmonics), including a circle of fifths which is famously difficult to do with truly perfect fifths.

answered Sep 15 '14 at 17:20