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There has been a fair bit of to-ing and fro-ing regarding consonance and dissonance lately here. What I cannot understand is that the two terms seem to encompass rather subjective opinions.

Looking at a recent list, I find myself disagreeing with a few of the rankings, and others would disagree with both my ideas and those in the list.

Apart from 'that sounds good/bad' (to somebody) what real parameters can be used?

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    On this page sethares.engr.wisc.edu/consemi.html the chapter "What Exactly is Consonance?" lists a few different definitions for consonance and dissonance. I guess a good StackExchange answer would require listing at least all of those meanings. – piiperi Sep 13 at 9:35
  • I think you are aware of the work of Helmholtz back in the 1880's. He tried to provide a physics based explanation of the ranking based on interference patterns in the harmonics of the intervals. While the application of physics in the analysis is objective the classification of intervals as being consonance vs dissonance is clearly subjective. People do differ in the ranking of intervals and trends within the European music culture have changed over centuries. The whole thing is, imo, very ethnocentric. – ggcg Sep 13 at 13:25
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    For context it ought to be mentioned that this question follows on the heels of another question, Just Intonation > Equal Temperament “Consonance and Dissonance”?. – phoog Sep 13 at 18:36
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    @Tim I just wanted to link to the actual question in case anyone wants to follow along at home. – phoog Sep 13 at 20:43
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    Irrespective of my opinions on tuning systems: I have to voice my disgruntlement with the community that this question has +9 (despite being borderline on both unclear what you're asking and primarily opinion-based), whereas the question from yesterday (which may be a bit XY-problem and overly long, but is certainly much more focused and has a lot of effort in it) was at -1 before I upvoted it. Does this by any means have something to do with the rep of the asker? Please everyone, don't vote based on appeal to authority! – leftaroundabout Sep 14 at 10:43
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Let me first quote from James Tenney's book, A History of Consonance and Dissonance:

There is surely nothing in the language of discourse about music that is more burdened with purely semantic problems than are the terms consonance and dissonance. A comparison of some of the definitions of these words to be found in current dictionaries, harmony textbooks, and books on musical acoustics indicates that there is considerable confusion and disagreement as to their meaning - if indeed there is any meaning still to be attributed to them.

The rest of the book can be read from the link above - but it's fair to say that there are various different definitions of consonance and dissonance. All of them are subjective to some extent - for example, the often-seen Plomp/Levelt curve, which attempts to quantify relative consonance/dissonance, is still based on experiments in which human subjects were asked to make judgements.

The 'causes' of dissonance include -

  • Critical band concerns: The human ear's inability to distinguish the frequency of pure tones that are very close, tending to hear 'beating' instead
  • tones not being related (or not being close to being related) by simple frequency ratios, meaning that the ear doesn't reconcile them as being part of the 'same sound'
  • expectations around how pitched notes will behave in a musical piece

Certainly the first of those (and possibly the second) is governed by human physiology, whereas the last is more a question of experience. Really, using the words 'consonance' and 'dissonance' risks us mixing up some very different concepts.

If we really want to talk precisely, it's best not to use the words at all, or be clear what definition we're using when we do use them if the context doesn't make it clear.

Are there objective criteria for classifying consonance v. dissonance?

I don't think there are in any general sense. There are ways that aspects of consonance/dissonance can be defined and measured, but they don't encompass all facets of what people mean by those terms.

It may also be possible to point tentatively to things that are considered consonant or dissonant within certain idioms, but classifying genres can be an inexact and subjective task in itself, so it doesn't seem to get us as far as an objective definition.

  • I disagree with your conclusion. The breakdown of what is consonant and what is dissonant can be not precise especially when looking at different cultures, but the ideas behind them are pretty solid. A very simple definition for them is stable vs unstable and this is how it will be viewed in any music theory class. Even post tonal concepts originated from the Emancipation of Dissonance essay which it was clear the author's goal was when talking about what dissonance was. – Dom Sep 13 at 12:24
  • @Dom you say that the breakdown cannot be precise - which is what I say in my last paragraph, so I'm not sure quite what the disagreement is..? If you're saying that roughly what these words mean is well-understood, I'd agree, but Tim asks "what real parameters can be used" - i.e. he's asking if these terms can really be pinned down, and I don't think they can. – topo Reinstate Monica Sep 13 at 12:42
  • The terms are defined. What they map to is not due to not everyone perceiving everything the same way. This is very different than your conclusion saying "If we really want to talk precisely, it's best not to use the words at all, or be clear what definition we're using when we do use them if the context doesn't make it clear." because the terms are defined. – Dom Sep 13 at 13:22
  • @Dom see my edit re. Tenney's book - he seems to agree that the terms are not well-defined. – topo Reinstate Monica Sep 13 at 13:28
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    "There is surely nothing in the language of discourse about music that is more burdened with purely semantic problems" -- I think that this is a fundamental issue that we encounter fairly often. In practice, artists are talking about something that can't be said in words, and resort to a sort of soft, metaphorical, personal language; in conversation with artists as part of the learning process, you make some sense of this to build your own views. But when people start inflicting rigorous reductionism we begin to lose meaning and run into problems. – ex nihilo Sep 13 at 13:50
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I'd like to re-use the opening from WillRoss1's answer

(First off, I completely agree that "that sounds good/bad" has NOTHING to do with consonance or dissonance! I, for one, LOVE a good dissonance! But I digress...)

Consonance and dissonance are (mostly) objective, however they are not context-free.

The same chord can work as consonant in one piece of music and dissonant in another piece, but this different effect is not primarily due to subject-difference of the listener but object-difference of the musical context. (It can become subjective in the sense that a listener who hasn't had much exposure to the genre yet may have not completely ingested the context and thus “pastes it over” with context from another genre, in which the chords would indeed have different consonance.)

To pick one concrete example, consider the use of the major 7th in classical music and in Jazz. In classical, this is generally a strong dissonance leading to resolution to the octave, whereas in Jazz a maj7 chord is a super-sweet consonant sound. Why? Well, both genres work completely different.

In classical music, melodic counterpoint rules supreme. If the main melody uses the ⅶ note, then this is not merely a choice of colour or artistic freedom but it has a purpose, to drive the piece forward, highlight a conflict that needs to be, well, resolved. The other voices are in this case aides who support the development in a well-organised way. In the simplest case this is implemented by resolving from a harmony with complex frequency ratios to one with simple frequency ratios.

In Jazz, this kind of thinking is kind of opposed to the underlying philosophy of individual freedom: the leading voice isn't some kind of dictator that demands the lowly servants to propel it to its goal. Rather, the accompaniment starts out and gives a sonic landscape, within which the main voice has a lot of space for individual expression. This actually tends to get somewhat easier with jazzy chords like the maj7, because there aren't too strongs points of gravity – the root is often played only by the bass, not doubled through multiple octaves as often done in classical music which would make a strong friction of nearby harmonics for the ⅶ note. At the same time, the maj7 chord has ample notes to make it a properly rich/warm/groovy sound, not just a distant hollow drone as might be found in some folk genres that also have individual freedom in the main melody focus.

Further points could be made here about e.g. the way modulations are used in both genres.

Now, you could certainly say that it is subjective – one person likes Jazz, they hear the maj7 as consonant. Another might like Bohlen-Pierce, they'll perceive the octave as dissonant.
Except, this is then simply a frame challenge. If you don't like a genre, then you'll not want to adapt your ears to the intended context. The music won't work for you – which is fine! But it doesn't mean that consonant and dissonant have different meaning for you in the context of that piece than for people who like that genre, rather it means that you're not in the context of that genre.

An even starker example of different context is Gamelan music, which has an utterly different harmonic/melodic/scalar structure from most other genres. But this isn't just because people from Bali hear intervals subjectively different, it is because this music is built around instruments to which the harmonic-series arguments simply don't apply, because they don't have integer overtones.

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What I cannot understand is that the two terms seem to encompass rather subjective opinions.

You are close to musical enlightenment, Tim. What they "seem to encompass" is nothing.

Let's take a definite example of a specific musical instrument: the (Scottish) Highland Bagpipe. That is a capped reed instrument so (at least for time intervals measured in hours, if not days or weeks) the pitch is very stable. The blowing mechanism is completely mechanical, so there is no way for the player to modify the pitch of notes while playing. And played in the traditional way, the instrument only produces nine different notes, so theorizing about it is not overwhelmed by the quantity of information.

Does it sound "consonant" - at least to the many people who enjoy listening to it? Of course it does. The traditional intonation of the instrument hasn't changed for hundreds of years, as can be shown by examining (and playing) old instruments.

Does it match any mathematical theory of consonance? Not in the slightest. The 9-note scale is superficially "mixolydian" but it doesn't agree with any mathematical tuning system. Even the octaves between the top G and A and the corresponding bottom two notes are not remotely "in tune" by any theoretical definition - they two G's are about a quarter tone wider than a true octave, for example.

When tuning the instrument, the drone pipes (two Ds and one A) are tuned to just intervals. But is the pipe that plays the melody (the chanter) also tuned to agree with those Ds and As? Well, obviously not, because the two As on the chanter are not even an octave apart! In fact, the chanter is adjusted to sound "in tune" when playing the note.... E. Go figure that, theoretically.

I rest my case, m'lud...

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    I'd prefer we discussed the question with reference to musical instruments..! – Tim Sep 13 at 14:07
  • I've never played the bagpipes myself, but to me it sounds like pretty close to Pythagorean tuning in practice. In which case it actually makes a lot of sense to tune the E to match the D and A drones, to get the frequency ratio 6:8:9 right. – leftaroundabout Sep 14 at 10:25
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Consonance and dissonance is not subjective, in fact it's mostly objective. There are real physical properties of tones that make them sound good or bad together.

There is a critical band within which two pure tones will sound bad two our ears. Outside that critical band, any pair of pure tones sound about the same.

The tones you play from your music instrument are not pure, they are complex tones. Meaning they have harmonic overtones that are integer multiples of the fundamental tone. The amplitude of these overtones, also called partials, is what defines the timbre of your instrument.

When you play two notes on your instrument, you hear a combination of all the overtones from each note you played. If those overtones fall within the critical band of each other, they will make the notes sound dissonant.

Mathematically, notes whose fundamental tones are integer ratios of each other will have overtones which either overlap (thus no dissonance) or fall far enough from each other that they are not within the critical band.

A note (say C) at 400Hz will have the following tones: 400, 800, 1200, 1600, 2000, 2400...etc. With decreasing amplitude.

Another note (say G) at 600Hz will have the following tones: 600, 1200, 1800, 2400, 3000...etc.

Notice that these two notes have overlapping overtones, and the notes that do not overlap are far away from each other that they fall outside of the band and don't cause dissonance.

This is why the consonant intervals are what they are. The fifth (3/2 or 1.5x the frequency). The fourth (4/3 or 1.33x the frequency) and so on.

Which intervals, and thus pairs of notes, are most and least consonant can be mathematically determined, far from being entirely subjective.

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    Thanks. So when the overtones come into the equation, it seems we can't even say x and y are/n't consonant/dissonant, due to the instrument we listen to them being played on! The plot gets thicker. – Tim Sep 13 at 10:11
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    @Tim definitely; and even where we play them on the instrument. Hence why chords sound muddier at the bottom end of the piano. Harmony and timbre ultimately aren't separate things. – topo Reinstate Monica Sep 13 at 10:27
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    The meaning of the words consonance and dissonance is subjective, just like the meaning of all words and interactions. There might be different opinions about an official true meaning, but if any particular opinion isn't widely shared, then for many intents and purposes, consonance and dissonance are subjective. – piiperi Sep 13 at 10:31
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    "There are real physical properties of tones..." yes; "...that make them sound good or bad together." No. Different people have differing views on what sounds good or bad, and one view isn't wrong with respect to another based on a mathematical definition; different cultures treat combinations of sounds differently; even Western music has shifted around on this front. You can create definitions for any term you like, but that doesn't mean that everyone is using it, or that you are using it correctly, or even make it a meaningful definition. – ex nihilo Sep 13 at 13:35
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    @Dom ask 100 people here about their ideas on what consonance and dissonance mean, the mileages will probably vary – piiperi Sep 13 at 13:46
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(First off, I completely agree that "that sounds good/bad" has NOTHING to do with consonance or dissonance! I, for one, LOVE a good dissonance! But I digress...)

Consonance and dissonance form a structural dichotomy, a kind of sliding mutual exclusivity in which one is defined by absence of the other. This is similar to light and dark or hot and cold. They have an objective, metered scale to definitively mark an exact value if necessary, but our day to day interactions with them are very subjective and can change drastically depending on context. A cool pool feels freezing if you've just been in a hot tub. Sunlight on a pleasant day can feel like a flashbang just went off after being in a dark room for a while. Someone that grew up in a frigid climate might be perfectly comfortable in 40-50 °F, but someone that just moved there from an extremely hot area might think they are going to die of hypothermia.

Consonance and dissonance work in a very similar manner. Many Jazz harmonizations would be unbearably dissonant in a highly structured classical context. Even a major second would sound very dissonant in a baroque piece, but warm and somewhat consonant in more modern works. Try playing a Major chord and adding the 2nd (C-D-E-G). This chord has not 1, but 2 major second intervals so it should sound dissonant, but it doesn't. It is warm and pleasant and, in many ways, consonant.

The harmonic series gives an objective point of reference, but what really matters (in terms of composing, performing, listening, analyzing and basically everything else) is how it feels. The harmonic series can be a nice reference point, but is worthless if you don't take into account how it will actually feel. Lap pools are often kept significantly colder than recreation pools because a comfortable temperature for someone playing in the water is uncomfortably warm for someone exercising.

In the end, it is very subjective to the context and the listener, hence why there are so many different opinions. As a very warm person I am baffled when someone bundles up in September because it is "freezing" outside, and they, in turn, think I'm completely nuts when it's the middle of January and I'm in shorts and flip-flops eating an ice cream cone!

  • There's no need to use the conditional in discussing major seconds in baroque pieces. They are used regularly, as they were in the renaissance before. – phoog Sep 13 at 16:33
  • @phoog I didn't say they were not used, just that they were used to create dissonance as opposed to a lot of modern pieces that use them to create consonance. – WillRoss1 Sep 13 at 17:22
  • Hm, I read the "would" as implying "...if it had been used." If it doesn't imply that then so much the better :) But again this goes to the question of melodic (i.e., contrapuntal) considerations, for a major second in renaissance counterpoint or baroque voice leading typically has a very different context from a major second in a jazz chord (a major chord with an added 9th or 6th, for example). This is especially true when that chord functions as a consonance with the second or ninth providing texture. – phoog Sep 13 at 18:33
  • Oh, yeah, I see what you mean! Thanks for helping to clarify that! – WillRoss1 Sep 13 at 19:07
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I personally think the concept of consonance/dissonance is hard to define because of historical reasons. It is clear that the (Western) cultural concept of consonance has changed over time. It is well-known that when Igor Stravinsky's "The Rite of Spring" premiered in Paris, there was a huge backlash due to its "dissonant" nature. Does it sound "dissonant" to an average ear in 2019? I highly doubt it. And that work is only from 106 years ago (the premier was in 1913). The further we delve into the annals, the more "strict" the notion of consonance becomes. If we go back to the times of Guido d’Arezzo, we will find that the purpose of music and notes that were "allowed" to be used were even more restricted.

Things become even more messy if we add Eastern systems to the plate, where the concept of consonance developed in a completely different way (perhaps, partially due to the difference in how languages are spoken, as the human concept of dissonance depends on how one's language sounds as well).

The notion of consonance/dissonance can also be linked to environmental and biological factors. I see a clear correlation between the Second Industrial Revolution and the changes in music. As evolution went on, certain birds required more sophisticated calls to attract mates as well (I am mentioning this with a reference to Olivier Messiaen who famously based some of his melodies on bird calls). We simply got used to more "jarring" sounds, because they became a part of our everyday lives.

I personally grade certain intervals based on "classical" interpretations and how they sound into groups of weak/strong dissonances and imperfect/perfect consonances. Here is the table I use:

Semitones | Name             | Consonance/Dissonance
----------------------------------------------------
0         | Unison           | Perfect consonance
1         | Minor second     | Strong dissonance
2         | Major second     | Weak dissonance
3         | Minor third      | Imperfect consonance
4         | Major third      | Imperfect consonance
5         | Perfect fourth   | Perfect consonance
6         | Augmented fourth | Strong dissonance
7         | Perfect fifth    | Perfect consonance
8         | Minor sixth      | Imperfect consonance
9         | Major sixth      | Imperfect consonance
10        | Minor seventh    | Weak dissonance
11        | Major seventh    | Strong dissonance
12        | Octave           | Perfect consonance

Naturally, how consonant/dissonant those intervals sound depends on whether they are part of a larger chord and what instruments play them (whether their overtone sequences overlap or not) and plenty of other things, but in the most primitive form this table serves its purpose. I am assuming you were looking for something of that nature.

It is also worth noting, that the further away notes are from each other, the less dissonant they sound. A minor second in the same octave (C5 + C#5) sounds very different compared to notes that are 2 or more octaves apart (C5 + C#7, for example).

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    Um, “does The Rite of Spring sound dissonant to the average ear today”? You bet it does! – leftaroundabout Sep 14 at 10:33
  • (That's of course not to say I don't like it, it's one of the greatest works of all time... but it wasn't intended to sound very consonant, and still doesn't.) – leftaroundabout Sep 14 at 10:35
  • @leftaroundabout, to me it does sound extremely consonant in comparison to later works by other composers, like Threnody for the Victims of Hiroshima and Pithoprakta. Not to mention noise rock and no wave giants like Arab on Radar and U.S. Maple. – Pyromonk Sep 15 at 0:14

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