Monday, February 11, 2013

Get used to it

Here’s my latest piece for BBC Future, pre-editing. More to follow shortly.


Post-modernism has been pronounced dead even before many of us made our peace with modernism. Picasso we can handle now; James Joyce’s Ulysses gets grudging genuflection, even if few people actually want to read it. But mention Arnold Schoenberg’s atonal music and you’ll still set many music-lovers snarling about an “ungodly racket”. The Austrian composer’s dissonant chords, unleashed more than a century ago, are denounced as unnatural, a violation of what music is meant to be.

This aversion to ‘dissonance’ has been lent some apparent support by theories of music cognition which propose that we have an innate preference for consonance: for musical tones that sit together comfortably like the soothing harmonies of Mozart. But a team of psychologists in Melbourne, Australia, led by Neil McLachlan have just taken a hatchet to that idea. Their findings support Schoenberg’s contention that consonance and dissonance are merely matters of convention: every culture develops its own rather arbitrary rules for what sounds ‘right’ and ‘wrong’. The Australian team shows that perceptions of dissonance can be shifted with even just a little training.

This might surprise no one who takes a close interest in so-called ‘world music’, meaning anything outside the cultural hegemony of the Western tradition. There are plenty of cultures that enjoy listening to chords and harmonies that might jar the ear of anyone brought up on Berlioz or Bacharach, from the metallic timbres and unusual scales of Indonesian gamelan to the semitone intervals (two notes a semitone apart, like C-C#) of some Bosnian folksong.

Nonetheless, the notion that consonant chords fall more smoothly on the human ear is deeply rooted. Pythagoras claimed that the most perfect harmonies are those in which the component tones have sound frequencies related in simple mathematical ways. A musical pitch consists of a sound wave with a particular frequency – the number of acoustic waves excited each second. Pythagoras noted that combinations of notes thought to be pleasing and consonant – for example, in modern terms an octave or C-G – have frequency ratios that are simple, whole numbers, in those cases 1:2 and 2:3.

This seems to imply that Mozart’s consonances are merely observing a law of nature: they are dictated by acoustic physics. This idea was refined in the nineteenth century, when the German physiologist and physicist Hermann von Helmholtz took into account the fact that musical instruments don’t generate ‘pure’ notes with a single frequency, but complex notes in which the ‘fundamental’ frequency that we register is supplemented by a whole succession of overtones, which are whole-number multiples of the fundamental frequency.

Helmholtz argued that consonance depends on how well all of these overtones fit together for all the notes of a chord. If two pure tones with just very slightly different frequencies are played together, their acoustic waves interfere with one another to cause an effect called beating, in which we hear not two separate tones but a single tone that is rising and falling in loudness. If the frequency difference is very small, the beats are very fast, creating a rattling or grating sound called ‘roughness’ that seems genuinely unpleasant. Helmholtz worked out the amount of beating for all the pairings of notes in the Western scale and argued that there is less roughness for traditionally consonant pairs, which have fundamental frequencies in simple ratios.

But it’s not that simple. For one thing, in the West notes are not tuned to have these simple ratios. The conventional equal-tempered scale, with equal steps between each successive note, is a compromise that slightly distorts frequency ratios compared to their ‘ideal’ Pythagorean tuning. Yet we don’t seem to mind. What’s more, Helmholtz’s idea implies that our sense of dissonance should depend on what instruments the notes are played on, since different instruments produce different overtones. But that’s not so. And the differences in roughness turn out to be insignificant for note pairs traditionally considered pleasing (C-F, say) and jarring (C-F#).

For all these and other reasons, the question of whether dissonance is innate or learnt has remained hotly debated. One of the key questions is whether our perceptions shift as our musical experience evolves. Some studies have claimed that very young infants show a preference for traditional consonance, but it’s hard to rule out other influences in these studies, especially the possibility that we start learning, from encountering music at an early age (even in the womb), what is ‘normal’.

McLachlan and his colleagues have subjected these ideas to careful testing. Using a group of 66 volunteers from the university and music conservatory of Melbourne, with a range of musical training from none to lots, they have devised a suite of tests to look for the roles of Helmholtz-style overtone matching, and of learning, in our judgements of dissonance.

In the first test, they found that the subjects’ ratings of the dissonance of two-note chords was not significantly different if the notes were pure, single-frequency tones or included various combinations of overtones. If beating was the cause of these judgements, the complex tones should have elicited a stronger sense of dissonance.

So much for Helmholtz. The team also tested and dismissed a somewhat related theory proposed in 1898 by the German philosopher Carl Stumpf, who argued that if the harmonics of the notes in a chord have several coincident frequencies, the brain interprets these as the overtones of a single pitch: it fuses the notes into one.

McLachlan has previously suggested that we ‘hear’ chords in a complex, two-stage process (N. M. McLachlan, Journal of the Acoustical Society of America 130, 2845–2854 (2011)). First, we pick out a single most salient pitch. Then, a long-term memory of the ‘quality’ of that chord – think of the instant recognition we have of a simple major or minor chord, even if we don’t know those terms – fills in the rest. Dissonance then arises as a sense of discomfort or unease when we don’t have a good ‘chord template’ to work from, and so experience expectations inconsistent with what we actually hear.

If that’s so, musical training should reduce the sense of dissonance, because this supplies a wider, more varied range of common ‘chord templates’. That’s more or less what the researchers found, but with a curious addition: a little musical training seems to increase the perception of dissonance for less-common chords, whereas this effect vanishes with more training. It seems that non-musicians lose any real sense of right or wrong when on unfamiliar harmonic territory, while slightly-trained musicians develop the somewhat rigid right/wrong distinction familiar in young learners, which relaxes with experience.

As these findings lend some support to McLachlan’s learning model of dissonance, they imply that perhaps we can learn to love what jars at first. In a final set of experiments, the Melbourne team showed that this is so. They asked the non-musicians to take ten daily sessions in which they trained to match the component pitches of certain two-note chords to single test pitches. This improved their ability to process the chords, and after the ten days they rated these chords as less dissonant than when they began.

These findings are sure to stir up more debate about why we find some music more dissonant than others, but you can be sure it won’t be the last word. In the meantime, perhaps you should give Schoenberg another listen – or ten.

Reference: McLachlan, N., Marco, D., Light, M., & Wilson, S., Journal of Experimental Psychology: General, advance online publication doi: 10.1037/a0030830 (2013). Paper here.

1 comment:

JimmyGiro said...

"If the frequency difference is very small, the beats are very fast..."

You might want to revise that, since the beat frequency is simply the difference between the combined frequencies; hence being closer makes their difference smaller, thence the beat a lower frequency.

Change it to: the beat becomes more distinctive...

As for your article, measuring dissonance is like eating a piece of garlic on its own, of course it's yuk, but sparingly in a simple Bolognese sauce, and it works.

Similarly to humour, it works because it brings unexpected dissonance. And like humour, it is very culturally divisive. No wonder Adorno and his fellow subversives warmed to the dulcet tones of un-music.