Harmony and dissonance

It is often thought that the essence of music is harmony - and, indeed, that the essence of human life is harmony. The goal of humanity is to live in harmony with ourselves, with each other and with our surroundings; let wars cease, let there be no anger, no suffering, no exploitation. The lion shall lie down with the lamb; “they shall not hurt or destroy in all my holy mountain”, as the Bible has it.

When humans who don’t know each other well sing together spontaneously, they sing in harmony. It’s quite surprising how rich that harmony can be, but it is ONLY harmony. No-one dares to step out of line, to be at odds with the group, so the basic harmony remains the same. Passing dissonances, blue notes and so forth may appear as transient variations, but they don’t effect change. If the singing started on a chord of D, it’s still on D after 5 minutes.

If the group knows each other better they may attempt more varied harmonies. They may even move from D to the dominant, A, and back again, maybe. But only a group of experienced musicians who know each other well are likely to attempt improvisation of more interesting harmonic movements and passing dissonances.

Simple harmony is very basic. And actually it is impossible to sustain for long. My group improvising on a chord of D would be unlikely still to be singing after 5 minutes: the fixed harmony would bore them rigid, so as none of them have the courage to do anything different they would gradually stop. I attended a meeting not long ago where the leader encouraged a very large group to sing together spontaneously; despite the leader’s best efforts to keep it going, the singing only lasted a few minutes then gradually faded away. Scripted singing, where people are singing known songs and improvising harmonies or singing in round, lasts for longer – but that too eventually fades and dies. Professional jazz musicians can improvise for a whole evening, but at the cost of considerable personal energy: group improvisation is a tiring activity. The energy to maintain harmony seems to dissipate over time.

People with a science background will recognise this as similar to the concept of entropy – the idea that the tendency of the universe is towards chaos, so maintaining order requires energy. Harmony is music’s equivalent of order – it takes energy to maintain it. Without energy, harmony quickly fades and dies. Contrary to popular opinion, harmony does NOT disintegrate into dissonance. Dissonance is not failed harmony. Dissonance is the energy source which makes it possible to maintain harmony.

Our cultural belief is that harmony is good and dissonance, bad. Those forms of music that have abandoned connection to what most people regard as “harmony” can be very difficult to listen to: for many people the onslaught of dissonance in much twentieth-century “serious” music amounts to torture, and they retreat to Mozart for relief. Yet music that has no dissonance is equally difficult to listen to, not because it is painful but because it is dull – particularly if it lacks rhythmic definition as well. Twentieth-century minimalist music is not as challenging to Western ears as twentieth-century serialism, but it is just as difficult to listen to attentively. After 5 minutes of unrelenting ostinato, the average listener is asleep.

Music requires both harmony and dissonance. Harmony is where we start and where we finish. It is the home to which we return. We are drawn to the sweetness of harmony. But energy and excitement is provided by dissonance, by excursions to remote keys, unexpected changes of harmony, clashing chords, harsh textures. It is astonishingly difficult to create excitement in a piece of music without creating some form of dissonance – causing pain, if you will. And without the excitement of dissonance, music lacks energy, lacks momentum, lacks direction. The pain of dissonance creates a yearning for resolution into harmony: without it, music can start anywhere, stop anywhere, doesn’t inspire, doesn’t engage. Without dissonance, music lacks meaning.

If you consider music to be an expression of all that makes us human, it is immediately obvious that music must have dissonance. No-one has a totally happy and peaceful life. Suffering is part of the human condition: music is one of the ways in which we express our pain. Music without the dissonance that expresses our anguish is inhuman. Unrelieved harmony is inhuman – it is the music of robots.

So what of economics? If music is a metaphor for human economic activity, where does the need for dissonance fit in? Surely our aim is to reach a state where there are no wars, no financial crises, no unsustainable booms leading to sudden collapses? If we could achieve that we would have the economic equivalent of unrelieved harmony. And unrelieved harmony is inhuman. We have booms, busts, wars and crises because we are human. Crisis is our nature –as it is the nature of nature itself, of which we are part. When we don’t have natural crises (or if the natural ones aren’t bad enough), we create artificial ones – because it is crises that give us energy and purpose. Without them we would stagnate and die. And for the whole of humanity to fade away through stagnation is a far worse prospect than some of us (or even rather a lot of us) suffering and dying in a crisis or a war.

So when the UK Prime Minister proclaimed that he had “ended boom and bust”, he was actually saying that we are no longer human. Fortunately he was wrong: very soon after that statement the world was engulfed by the worst financial crisis since the Second World War. That is not to say that the pain suffered by those who lost their money, their homes and their livelihoods in that crisis was a good thing. Clearly it was not. We cannot ever regard suffering as “intrinsically” a good thing: were we to do so, we would become immune to the pain of dissonance and lose the human yearning for harmony that gives us the energy to effect change. Permanent dissonance is just as inhuman as permanent harmony.

But what the crisis did – briefly – was unite the world with a common purpose to seek an end to the crisis and relieve the suffering of those caught up in it. Crises draw people together to make change. The dissonance is resolved through common purpose and we return to harmony. At least, that’s what should happen – but how well it works does seem to depend on how bad the crisis is. By far the worst crisis in the last century was the Second World War, and there is no doubt that huge changes were made in our societies during that war and shortly afterwards as a direct response to the chaos and suffering that it caused. The recent financial crisis, despite all the rhetoric about how dreadful it was, was not bad enough for common purpose to be maintained for more than a few months. All too quickly the world sank back into bickering about the right way to deal with the problems, defending old beliefs even in the face of evidence that they are fundamentally wrong, and – perhaps most worrying – demonising those worst affected by the crisis in order to justify doing nothing to relieve their suffering, or even deliberately making it worse. Cruelty is our song at the moment. Just as 20th-century composers did, we are learning to love and accept dissonance, and in so doing we are becoming increasingly inhuman. It is no accident that the height of the 20th-century love affair with musical dissonance occurred in the period that encompassed the two World Wars and the Great Depression. Cruelty was our song in that period, even more than it is now.

It seems a terrible thing to say, but the financial crisis of 2008 did not cause enough suffering. The dissonance was not severe enough, and the yearning for harmony not strong enough, to create the common purpose needed to force through effective changes against the resistance of a powerful financial establishment. Instead, the energy for change fizzled out before real change could be effected, and we now have long-running, low-level dissonance that doesn’t generate enough energy to force change. This is depression, and if it becomes permanent, we stagnate and die. Perhaps that is the reason for our cruelty: we instinctively try to create the suffering needed to generate the energy to break out of our depression, because the alternative – slow economic death – is worse. People who self-harm know this all too well: pain is better than numbness, because at least if you can feel pain you know you are alive. Numbness is death.

Permanent dissonance is perhaps not quite as dangerous as permanent harmony. The soporific effect of unrelieved harmony can be disastrous, as anyone who has fallen asleep at a car wheel could testify. Listening to challenging music can be an effective way of warding off fatal sleepiness. Listening to undemanding musak can make sleepiness worse. When things are going well we are lulled into a false sense of security, which means that the crisis when it comes is all the worse because it is unexpected. In the recent financial crisis many people asked why it wasn’t predicted. The truth is that it WAS predicted, by many economists, but politicians and people alike didn’t want to listen to the Cassandras and wheeled out their own “experts” to “prove” that there would be no crisis, despite the mounting evidence that there was an unsustainable boom in house prices and credit expansion. They were asleep at the wheel, and the result was a crash.

Compare this with the present situation, where there is unrelieved suffering among the poor and the highly-indebted middle classes, and also a degree of pain among the well-off who are suffering capital destruction due to very low interest rates and house price falls. There is some energy for change, but it is fragmented and undirected: everyone has a different view on what should be done to restore the economy. There is a sense of frustration that we seem to be “boxed into a corner” due to high levels of public and private debt, and a desire for radical action to break the stalemate. This is dangerous, because radical action can be stupid action, and frustrated sufferers are a good recruitment source for extremists. But from that simmering anger could come the common purpose and energy required to make effective change. It is far, far harder to make effective change when everyone is enjoying the good life.

Currently we have a crisis bubbling away in Europe. But that too has not yet caused enough suffering to create the energy needed to make changes. And politicians are doing just enough economic and political management to prevent suffering increasing to the point where radical change becomes inevitable. They are, if you like, suppressing the natural progress of this crisis. You will remember that earlier in this post I said that if natural crises aren’t bad enough, we create artificial ones? When a crisis is artificially suppressed, eventually people take matters into their own hands, and the result is war. I fear the European crisis will end bloodily, because I can’t see how the breakup of the Euro, that is (to me, at any rate) very obviously the only long-term solution to this crisis, can be achieved in any other way. Economic suffering alone will not force politicians to abandon such a high-profile political project, any more than an emperor would voluntarily close down his empire – but war would. We are already seeing fragmentation of the financial infrastructure of the Eurozone, civil unrest in the poorer countries, and – most worrying – increasing support for nationalist political parties. What form the coming conflict will take remains to be seen: the pattern of recent empire breakup (Soviet Union, Yugoslavia) suggests that local wars re-establishing old territorial claims and tribal identities are most likely, but if pre-European Union allegiances prove strong then yet another pan-European conflict is not beyond the bounds of possibility.

I do not think that smoothing out the business cycle and eliminating booms and busts is either achievable or desirable. We are part of the natural order, and our economic system, like our music, reflects the way the natural order works. Steady-state is not a natural state in nature, and it is not a natural state in human life, either. Wave forms – peak and trough, climax and release, compression and rarefaction, boom and bust, domination and extinction – are how our natural world works, and it is how our human systems work too.

It is time to embrace the cyclicality of human systems, and understand that individuals – particles, if you like – suffer and die in the “creative destruction” phase of the business cycle. At present we attempt to mitigate their suffering by dampening certain aspects of the cycle itself – usually those parts that special interest groups are most concerned about, not those that most impact the poor and disadvantaged. But I suspect the effect of this is merely to displace creative destruction from where we were expecting it to somewhere we didn’t expect where the impact is much greater, or delay it to a later date when the boom is even bigger and the collapse much worse. We still have no idea how to protect people from suffering without also dampening creative energy, and I admit I have no solution to this conundrum. Yet the people who suffer and die in crises are often innocent of the excesses that cause them. We owe it to the innocent to find ways of redirecting their suffering to those actually culpable, and avoid protecting the rich and powerful at the expense of the poor and weak. And we owe it to them to avoid unnecessarily increasing their suffering, and to address economic crises in ways that reduce, rather than increase, the likelihood of war.


  1. Given economic, social and international harmony, the human race would find plenty to do and keep itself occupied . . . . . if the human race was wise. But of course it isn’t.

    Give people a smoothly functioning bank system, and they’ll think of ways of taking ever increasing risks, till the bank system blows up. Give them full employment, and they’ll introduce rules and regulations that mess up the labour market and raise unemployment.

    As Elvis Presley rightly observed: “You don’t know what you’ve got untill you lose it.” Or as the 17th century Spanish writer Baltasar Gracien said, "New mediocrity is preferred to traditional excellence."

  2. Music's a nice metaphor but I'd have used the difference between a sweet cider and sharp beer :)

  3. Thanks Frances. I agree with this one 100%.

    Evolution just takes time. To achieve harmony, imo human kind not only has to seperate church and state, we also have to seperate market and state.
    My background is IT. I'm a programmer. You just make a mess of the flow if you don't split functionality. This is fractal, as it works this way on all levels and in all systems. Economy or biomass no different.

    We can only achieve harmony if we set up the collective arcitecture to fascilitate. without double functionality.
    or we will just create another third world on another place.
    if you don't cure the cancer, it will just grow another tumor ...

    where blood is needed for on organism, economy needs money. without the double functionality. Our friends the freegolders stopped with splitting just two monetary funcions. we need to split all three !
    Just as we will do with religion, state and market. we will do this with medium of exchange, store of value and unit of account. Harmoney(c)
    We could do this easily with a Bretton Woods 2.0, it could also take another dark ages but I am not a doomsday regression guy. As time moves only in one direction, I believe we will also move forward. When things get really rough in a year or two we will have the restructuring of our systems. we do not have a choice. its the invisible hand.

    markets will decide so.
    you speak chinese yet ?

  4. Your a gettin' all preachy on us, Francis.

    I see it like this, History is a series of accidents (good and bad) that from a distance look to have some sort of order in them. They don't. History like economics is not a science. That's not to say its not useful or important it is. But I think our will to shape the future is actually very harmful.

    And just as when You are playing a piece of music you don't want to get too far in front of yourself. You need to be in the moment to let the music flow or you just lose your rhythm or the whole thing becomes either wrong of bad, and sometimes both.

    I hate the happiness metrics. How do you know what happiness is if you have never experienced sadness? Harmony is contentment, not replacing your kitchen every other year on the back of a property credit card. I am not saying we need to banish happiness, it does need putting in its rightful place though.

    We need to be lucky as well as good, you cant force luck. Even if we get everything right we still need to be lucky.Its not an admission of failure to admit that.

    1. I think economic forecasting is pretty similar to weather forecasting. One week ahead is pretty accurate. But the further ahead you attempt to forecast, the more it becomes like divination - and if you base policy on it, you are behaving like the kings of old who consulted sages to tell them the most propitious times and places to hold battles.

      I don't mean to preach. I just don't think we understand our system anywhere near well enough to be able to change the way it works.

  5. Frances, I disagree strongly that we need economic crises. There's enough grief in life already to stop us getting too comfortable.

    But I agree strongly with your last paragraph - too much smoothing is a bad thing, because stopping the small crises can lead to big crises. There's an analogy with forest management - if you put out all the small fires you leave fuel for an eventual big fire.

    And then again, I'm rather uncomfortable with your talk of cycles, which tends to give the impression that these fluctuations are much more reliable than they really are.

    1. Paul,

      really in this piece I'm sort of thinking aloud - it's not a set of finished ideas by any means - so your feedback is helpful.

      I don't think I mean that we "need" economic crises, just that it's hard to maintain common purpose and creative energy without some form of stress, and sometimes that stress has to be a LOT of stress - such as a war. If we could find a way of maintaining common purpose and creative energy without the stress, that would be far better, obviously.

      I think we live within an oscillating system, rather than a system in simple equilibrium, but we don't see the oscillations clearly because they appear infrequent and we also have shocks which disturb their frequency and amplitude. The business cycle is the best-known example of economic oscillation, but I reckon there are others - a whole set of waveforms, if you like.

      I read something recently that suggested that there is a financial cycle which is longer than the business cycle and has greater amplitude: from time to time the two combine and the result is a mega-crash, but the intervening period is a "moderation" caused by one negating the other (in other words, an interference pattern). This is econophysics,really, and I'm more than slightly out of my depth as my physics doesn't go beyond A-level. But I thought it was an interesting idea.

    2. There are economic feedback mechanisms that tend to produce oscillatory behaviour, but I think it's a mistake to treat the economy as if it were a physical system. A musical instrument for example is usually much the same from one day to the next, and behaves always according to the same laws of physics. It will therefore produce much the same note if plucked in the same way. But the properties of the global economy change with every technological development and every change in the availability of resources. The properties of the economy of one country change also with every change in the economies of its trading partners. There's therefore no reason why any particular cycle should persist.

    3. Paul, you're making the same mistake as the person in a previous post who dismissed music as "just maths".

      Music is as much a human system as a physical system, and it is constantly changing - it is dynamic, not static. You never hear the same piece of music twice (except recordings): every piece of music is to a degree "re-composed" in every performance. Even what we define as "music" changes over time. And music technology changes all the time - even acoustic instruments vary from day to day because of the influence of temperature and humidity, and the sounds they make depend on the skill, personality and mood of the player. In these ways it resembles economics.

      However, it's true that you can only stretch an analogy so far. Economics doesn't have much of a physical component at all, unlike music. It is a human system which mimics a physical system. There is a limit to our ability to change music, because as you say the sounds themselves are bound by physical laws. But economics we could change completely if we choose. The question is whether we want to.

    4. Let me try an extended analogy. The fundamental frequency - the pitch - of a guitar string is determined by its length, its tension, and its linear density. I propose a thought experiment by which I measure the frequency (by plucking the string) once an hour, for many years. The frequency will tend to drift down slightly as the string slackens, then go up when the guitar is tuned. However, the tuning will not exactly restore the frequency (at least not if someone with my ear does it), so the frequency will drift around until, from time to time, the guitar is tuned with reference to some frequency standard, or by someone with perfect pitch. And, from time to time, the string will break, so that, until it's replaced, there will be a few observations where the frequency has fallen to zero.

      All these cycles will create what seems to be a roughly predictable pattern. But there is no reason why any of them shouldn't change unexpectedly - a change in habits by the guitar's tuner, or a new owner, or the invention of a new sort of guitar spring that breaks less often...

      And then one day some oaf will come along and tread on the guitar, breaking its neck. There's nothing in the historical data that would predict that.

    5. Plucking a guitar string is not making music. It's making tuned sound, that's all. So it's physics, not music. The Pythagorean monochord does pretty much what you describe - we tune it using resonant frequencies, actually (although I always cheated and tuned it by ear, because I do have perfect pitch!)

      However, let's assume that rather than a single note being plucked, a known piece of music were played once an hour. The pitch and quality of sound would vary, not only as the strings slackened but simply due to weather conditions, the player's mood, the guitar tuner going deaf. If the guitar were not tuned, there would be a gradual increase in dissonance as the strings slackened, which would make the player less willing to play, since he would not be able to avoid making sounds that cause him pain. If he is forced to continue playing, eventually he will find the pain so bad that he will call in a guitar tuner. Tuning the guitar restores both harmony and the player's pleasure in playing (and hence his willingness to play). This is a more passive example of dissonance than the examples I used, where dissonance is deliberately created to make music exciting and give it momentum. But it is none-the-less a good example of what I meant when I said that the pain of dissonance eventually forces change.

      Music does change over time, and as I said, every performance is different. But sudden changes in music are almost impossible: the "black swan" event in your example would not necessarily cause the music to stop, unless that were the only guitar in the world. The music could continue with a different instrument. There would be a qualitative difference in the sound, but the "shape" of the music - its skeleton, if you like - would be the same.

      Music is a human system built upon a physical system. And I'm certainly not disputing that cycles of human behaviour can and do change, both gradually and suddenly. But the physical laws underpinning music don't change, or if they do the rate of change is far, far slower. My problem with economics is that it is almost entirely a human system and therefore change, including sudden change, is INNATE to it. It's much more like a living system: perhaps econobiology would be closer to the truth than econophysics.


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