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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?

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No. In Gamelan music, nothing smaller than a fourth is considered "consonant." Octaves tend to be very sharp (10 to 30 cents typically). In Pelog, the "fifths" are around 20 cents flat, whereas in Slendro the "fifths" can be as much as 50 cents sharp (but are typically 20 cents sharp). This is enough of a deviation that I would no longer consider these intervals to be fifths or fourths, from a Western perspective. –  Ryan Sep 16 at 1:29
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Fourths are only considered consonant when they are supported. –  American Luke Oct 6 at 14:46
    
What do you mean with that, @AmericanLuke? –  Lee White Oct 7 at 5:52
    
When there is one or more note below the fourth in pitch, the fourth is considered consonant. Otherwise (i.e., when the fourth has no notes below it in pitch), the fourth is considered dissonant. –  American Luke Oct 7 at 13:22

4 Answers 4

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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:

Pre-polyphonic era:

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)

He mentions:

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.

More on this:

Moran, H., & Pratt, C.C. (1926). Variability of judgments of musical intervals. Journal of Experimental Psychology, Vol. 9, pp. 492-500.

Lundin, R.W. (1947). Toward a cultural theory of consonance. Journal of Psychology, Vol. 23, pp. 45-49.

Guernsey, M. (1928). The role of consonance and dissonance in music. American Journal of Psychology, Vol. 40, pp. 173-204.

Cazden, N. (1960). Sensory theories of musical consonance. Journal of Aesthetics and Art Criticism, Vol. 20, No. 3, pp. 301-319.

Consonance and Dissonance - Effect of Culture, Ohio State University School of Music

Musical chord preference: cultural or universal? Data from a native Amazonian society.

The basis of musical consonance as revealed by congenital amusia.

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... One of the most interesting posts I have seen in a long time. –  Lee White Jul 11 at 20:54
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+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 at 21:11
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@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) –  JCPedroza Jul 11 at 21:57
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@leftaroundabout Read the whole text before emitting judgment (it's only 9 pages long). I definitely left out important parts that further explain, sustain, and complement what I posted here. –  JCPedroza Jul 11 at 23:05
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Very interesting. Thanks for putting it together. –  BobRodes Jul 12 at 6:11

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.

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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? –  JCPedroza Jul 11 at 18:13
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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 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.

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Bach was not an advocate of equal temperament (12-edo), that wasn't even developed in Europe yet. He was an advocate of well-tempered tuning, which though it allows playing in all keys doesn't treat them all the same. WT has some fifths much more notably flat than in 12-edo, whose fifths are actually extremely close to Pythagorean; but in the "white keys" WT has sweeter major thirds, more narrow than the somewhat agressive ones 12-edo gives you. –  leftaroundabout Oct 6 at 19:46
    
Hang on... 12-edo was actually developed in Europe by Bach's time, that bit was wrong. –  leftaroundabout Oct 6 at 19:58

Octaves and fifths will usually be consonant in any music culture, simply because that's the intervals their tuning systems is based on. In traditional western music this is Pythagorean tuning. Thirds only appear as ditones in that system, and they are so sharp they're normally considered dissonant. Thus styles such as Gregorian chant avoid them.

You might say harder rock styles also allow only fifths as consonant intervals, because though 12-edo tuning gives guitars thirds which most listeners accept as consonant 5/4, these aren't good enough to sound well through heavy distortion.

Where even octaves, I believe, don't play a role is in Gamelan music – this is played on instruments with very short range. Also, I don't think it "permitted" readily to switch between octaves in Arabic music. But I don't know enough about these to be able to tell the exact relevance.

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The tuning system -- which tuning system? Is this an encompassing tuning system that every music culture in the world uses? –  Lee White Jul 11 at 16:10
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Have all tuning systems in the history of music, in all cultures and places around the world, have been based on octaves and fifths? I'm confused by your first line. Can you provide a source for that claim? –  JCPedroza Jul 11 at 18:17

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