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Music and physics – the connections aren’t trivial

My ANU colleague John Rayner’s excellent recent article on the physics of music seemed to touch a nerve with the readership of The Conversation. Although beautifully framed by the personal and anecdotal…

“Physics permeates the language we use to describe music, and the concepts we use to understand it.” Ravages

My ANU colleague John Rayner’s excellent recent article on the physics of music seemed to touch a nerve with the readership of The Conversation.

Although beautifully framed by the personal and anecdotal – John’s piece was subtitled “a love song” – the issues he explores about the relationship between music and physics go back to the ancient Greeks, and are as old as the disciplines themselves.

It certainly inspired me – a musicologist – to write something from the other side, to meet my scientific colleague in the middle in a speculative conversation about the parallels between our two worlds.

Musical meaning is tantalising and elusive. For most of us, music has the power to reach us profoundly and directly. The temptation is to speak of music as a language: the notion of music as a kind of “language of the emotions” is pervasive, centuries old, and nowadays has some limited empirical experimental support.

Most theoretical work now done on musical semiotics treats music as just another flavour of discourse, another language of signs; albeit one with its own special characteristics.

But this runs against an age-old notion: that music is a natural law. The medieval concept of “music of the spheres” held that the movement of the celestial bodies – what we now describe as astrophysics – was, at root, musical: the planets move in the heavens according to principles of harmony and resonance, with a set of common Pythagorean ratios governing both music and cosmology.

Indeed, we music academics are rather nostalgic for the time (in medieval universities) in which music was considered one of the four core disciplines alongside astronomy, geometry and arithmetic, and we held pride of place above the three lesser (hence “trivial”) language-based disciplines of logic, grammar and rhetoric.

Highs and lows

Physics permeates the language we use to describe music, and the concepts we use to understand it. For instance we talk about “high” and “low” musical pitch, perhaps without realising how deeply metaphorical this is.

There is no altitude to musical pitch: “high” pitches are caused by faster vibrations than “low” pitches. But we don’t talk about “fast” and “slow” music with reference to pitch (we use those metaphors for something else entirely).

And yet, the notion of musical altitude makes sense if we think about the energy states of the music. If, as in the excerpt below from Puccini’s opera Tosca, we listen to a soprano sustain a top B flat (as at 2:40 into the recording below), we are aware that she is sustaining a high-energy state, which must eventually relax.

The pitch seems invested with the kinetic energy required to produce it (of course, in Tosca’s case she has a literal encounter with the force of gravity, but that’s quite another story).

Singers, wind and brass players expend energy to reach “altitude”, while string players, keyboardists, guitarists and all the rest work no harder for the high notes than the low.

Yet, perhaps because of the centrality of the human voice to all music, this idea of fighting against musical “gravity” is ubiquitous, whether in a Paganini violin concerto or a Jimi Hendrix guitar solo, as per the video below. In music, as in physics, what goes up must come down.

And it doesn’t come down just anywhere. Most systems of musical organisation have a fixed point of reference – a pitch that functions as an attractor, pulling the music towards it.

In Western music, we call this the “tonic”, and most people, regardless of their level of formal musical training, can hear and sing the note to which the music is “pulling”. This idea of gravitational or magnetic attraction to a pitch was arguably the single most important characteristic of Western music between 1600 and 1900, and much music thereafter.

This may be a characteristic of Western music, but in other cultures' musics, the idea of a point of attraction is often even more powerful, as in the example below from Classical Indian music.

Not all music has a tonic, a fixed point of reference – in 1908 in Vienna Arnold Schoenberg famously departed from the principle with the “atonal” concluding movement of his second string quartet (as per the video below), thereby heralding a new and controversial musical age.

By coincidence, three years earlier, across the border in Switzerland, Albert Einstein had thrown the world of physics into disarray by similarly demolishing the idea of a fixed point of reference, in a paper on electromagnetism that described what later would become known as the Special Theory of Relativity.

Questions and answers

It’s worth observing that language has nothing resembling this notion of gravity or attraction: to understand this principle in music the metaphors must come from physics.

There are other concepts that bridge the disciplines in the same way. Balance and symmetry are also ideas that are fundamental to musical structure, and that seem to have more of a physical than a linguistic origin.

In classical music, perhaps the most common phrase structure is often described informally (and somewhat puzzlingly, to me) as “question and answer” - or more formally, as “antecedent-consequent” - two phrases that complement each other structurally, as in two phrases that make up just the opening eights seconds of Mozart’s Sonata in C KV545 (below).

There’s no question that rhetoric plays a role in shaping the way in which these two phrases echo each other. But on a structural level, there is an identity that seems almost mathematical in nature.

The two phrases are in balance: their (gentle) energies are complementary; their shapes are an image of each other; they are like two sides of an equation.

Time and memory

For me, the most important parallels between music and physics happen on a more philosophical level.

The late musicologist Jonathan Kramer started his book The Time of Music with the observation that small children play with blocks and toys to learn the fundamental concepts of space; by contrast, by singing and clapping, they play with music to learn about time.

There is something profound about the way in which music can accelerate, retard, bend and colour our sense of time’s passing. We can sit in a concert hall or opera theatre for an hour and hear 90 different people make thousands of noises on bits of wood, metal and flesh, and yet walk away with the impression we have heard one thing - a symphony, or an opera.

Music joins up time, and allows us to hear time as patterned and organised. These patterns allow us to predict the future - we listen in anticipation: that a melody will come to rest, or a harmony will move in ways that make sense to us, wordlessly.

Music is also a powerful stimulus of memory - overhearing a piece of remembered music can instantly rekindle long-forgotten memories.

It is much easier for most of us to memorise a song (words and all) than it is to memorise a poem. Music is a tool for grasping the order and sense between what has happened in the past, what is happening now, and what will happen in the future.

And to me, that sounds suspiciously like a definition of physics.

Threat and survival

Sadly, there is one last way in which music and physics are currently bedfellows. Worldwide, both disciplines are under threat at universities. In America and the UK, several physics departments have closed or are in danger.

Music education no longer receives government funding at UK universities, and in Australia recent controversies at ANU and Edith Cowan are symptomatic of the fact government funding for music is problematic.

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And the provision and quality of music and physics education in our secondary schools, crucial to support and enable undergraduate study, are always competing with the demands for more and more literacy and numeracy in the curriculum.

There is not yet a crisis - at least, not at the high end: it remains, at least for the moment, sexy enough in policy terms to fund the elite practitioners.

The select few physics virtuosi who will discover whatever comes after the Higgs boson, or their musical equivalents who will perform the Queen of the Night aria at the Sydney Opera house or Covent Garden, still capture both the public imagination and the public purse.

But the opportunities for students to study fundamental and abstract ideas - such as music and physics - as part of a liberal arts education that supports a civilised and educated society are becoming fewer and fewer.

John Rayner was right to call the relationship between music and physics a love song. Let us just hope it’s not also a swansong.
Further reading: This is a love song: the physics of music and the music of physics

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20 Comments sorted by

  1. Dennis Alexander

    logged in via LinkedIn

    Nice article Jonathan. A small correction: the trivium is derivative of three not lesser: the meaning of "trivial" grew out of the relation of the trivium to the quadrivium as the former is preparatory for the latter and hence regarded as lesser. The ancient universities taught the quadrivium (and in some cases also the trivium) as part of the Artes Liberales (Liberal Arts) Degree of whatever nomenclature (Bachelor or even Dottore), which was the prerequisite for admission to the postgraduate vocational studies of Theology, Law and Medicine. In some cases, universities would only accept students who had graduated from grammar schools which had examined them in the trivium.

    My apologies for nitpicking, but these things do have some historical and grammatical importance in universities (;-)).

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    1. Jonathan Powles

      Associate Professor and Director, Academic Skills at the University of Canberra at University of Canberra

      In reply to Dennis Alexander

      Thanks for your comment, Dennis. You needn't apologise for nitpicking to a pedant like me! But I am well aware of the derivation of "trivial" - you'll have seen much of your background if you click through to the link I gave to the quadrivium, and the original meaning is important if you are to understand the title I gave to my article.

      But perhaps my reference was a little abrupt. When I wrote tThe three lesser (hence "trivial") language-based disciplines' I was employing an etymological shorthand…

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    2. Jonathan Powles

      Associate Professor and Director, Academic Skills at the University of Canberra at University of Canberra

      In reply to Dennis Alexander

      PS Our little exchange reminded me of the motto of the august institution for which we both work. I have heard "naturam primum cognoscere rerum" translated in many fine ways. But my favourite, and often the most apt, remains "First, to find out the best nits to pick"

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    3. Byron Smith
      Byron Smith is a Friend of The Conversation.

      PhD candidate in Christian Ethics at University of Edinburgh

      In reply to Jonathan Powles

      From the link in question:

      "In turn, the quadrivium was considered preparatory work for the serious study of philosophy (sometimes called the "liberal art par excellence") and theology".

      Two more chronically underfunded subjects. Either our university administrators are much, much smarter than the brightest minds of the medieval period. Or the opposite.

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  2. Mark Harrigan

    PhD Physicist

    Charming and erudite. Thank you.

    Physics is the "music of the spheres" and (for me) so much of the experiential "resonance" we have with, and apprecoation for, music perhaps reflects this.

    One of my undergraduate physics lecturers was fond of saying that "everything in physics can be reduced to a simple harmonic oscillator". An exageration of course and absurdly reductionist but quite deliberate on his part. It made a telling point.

    Almost every way we "measure" the passing of time in…

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  3. Darragh Murray

    Self employed

    As much as I realise the connection between music and science, connecting them does seem to suck the joy from this form of artistic work. I prefer to remain ignorant.

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    1. Jonathan Powles

      Associate Professor and Director, Academic Skills at the University of Canberra at University of Canberra

      In reply to Darragh Murray

      That's a response I have met before, although I find it curious. For some (including me) the natural world is a source of wonder and beauty, and science is like the poetry that describes it. For me, connecting science and music enhances the joy of this beauty, just as I find sunsets no less spectacular, and perhaps appreciate them more, knowing that they are caused by "Rayleigh scattering" of the shorter wavelengths of light.

      But others seem to find science deadening. I hear what you say, but I can't connect to it on an emotional level.

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    2. Darragh Murray

      Self employed

      In reply to Jonathan Powles

      It depends on who you talk to I guess.

      One thing I think you neglect to speak about above is the connection with words and lyrics with the science of music. How do these lyrical structures fit in? Is the meaning words have integral to the appreciation of music? While I personally think melodies are the key features that draw me to a particular song, things like lyrics are very important, and I think stand to the side of the science behind the music.

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    3. Darragh Murray

      Self employed

      In reply to Peter Ormonde

      Well, when people are creating good songs, do they ever analyse their work at a scientific level? I doubt that.

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    4. Peter Ormonde

      Farmer

      In reply to Darragh Murray

      Might be surprised there Darragh - I don't think great composers so much analyse - but rather have an intuitive, innate understanding of what makes a good "hook" ... what it is that makes one tune over all others "stick in your head" all day. The Beatles were particularly good at it, as were the Gershwins and Col Porter. A complex business - and sadly perhaps there is a science to it and in it. Bloody physics.

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    5. Darragh Murray

      Self employed

      In reply to Peter Ormonde

      Oh I agree with this - totally. My point is that I don't need to know the physics behind it to appreciate it as a work of art. It's like knowing the precise direction of the brushstrokes used to paint the Mona Lisa - knowing that, I think, takes away some of it's aesthetical magic.

      Not to devalue Jonathan's interesting article, which many, I suspect, will find very enlightening.

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    6. Jonathan Powles

      Associate Professor and Director, Academic Skills at the University of Canberra at University of Canberra

      In reply to Darragh Murray

      I totally agree. The relationship between music and words is a deep one, and has a long history of philosophy, speculation and scholarship around it. Maybe the editors could run some pieces on "words and music" after this current crop of "science of music" papers ...

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    7. Jonathan Powles

      Associate Professor and Director, Academic Skills at the University of Canberra at University of Canberra

      In reply to Darragh Murray

      I don't think we are in as much disagreement as it seems. When Benji Marshall throws a perfectly-timed flick pass to put Beau Ryan over the try line, does he calculate the angles, velocities, force, momentum and trajectories required for himself, Ryan and the ball, factor in air resistance and the force of gravity, and calculate the reaction times of the opposition players to ensure that the try is scored?

      Consciously, of course not. If he stopped to think about all this, he'd be flattened by…

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    8. John Rayner

      Visiting Fellow in Science Communication at Australian National University

      In reply to Jonathan Powles

      Thank you for a fascinating and symmetrical article. Ideas about symmetry have a deep emotional and aesthetic appeal for us, whether in art, design, golden ratios, musical structures, mathematics, space, time, processes or ideas. In my own area of physics I have often been struck by the power of a "symmetry of ideas" as a creative force. For example, Michael Faraday knew that a wire carrying an electric current produced a magnetic field. Driven by a deep belief in the symmetry of nature, and…

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    9. Peter Ormonde

      Farmer

      In reply to John Rayner

      Just so John.

      Bela Bartok was interested in the maths of music ... you might be too.

      This is worth a read and then a listen:http://en.wikipedia.org/wiki/String_Quartet_No._4_%28Bart%C3%B3k%29

      And the wikipedia entry on Bartok himself has a serious jargon laden section about his compositional symmetry ... and a host of erudite words I will not ever understand. Look at the "analysis" section. And don't ever use words like that in public.

      He had a particular fascination for the Fibonacci sequence - seeing it reflected in the design of nature. He wrote a few pieces structured around that magical set of numbers as well. I'll try and remember a couple.

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    10. Mark Harrigan

      PhD Physicist

      In reply to Peter Ormonde

      Thanks, good links Peter. The book, "Godel, Escher, Bach" by Douglas Hofstadter covered some of this territory very well

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    11. Fred Pribac

      logged in via email @internode.on.net

      In reply to Darragh Murray

      Sorry to wade in so late but I just wanted to make a comment here. I, like Darragh Murray, really appreciated this article and the preceding one from John Rayner.

      However I have never bought the argument that knowing more about something somehow dimishes aesthetic enjoyment!

      It's been my experience that, almost invariably, greater knowledge brings cognisance of deeper mystery and beauty that was not previously visible. Nor is the original appreciation lost - instead it becomes possible to tune…

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