I try hard to be open-minded. I think I succeed at that reasonably well, but I still regularly get surprised at the discovery of a prejudice I didn’t know I had.
I don’t know whether it’s possible to rid one’s self of all prejudice – I suspect it’s not. If so, the best I can aim for is to be on the alert for prejudices, try to rid myself of them when I discover them, and try to always remember that any opinion I have – regardless of how carefully thought out it may seem – may be inextricably tied up with some prejudice I don’t yet realise I have.
The Wikipedia article on Cognitive Biases has a very long list of them. With so many opportunities to go wrong, it’s hard to imagine one can escape all of them.
There’s a popular phrase ‘It’s good to have an open mind, but not so open that your brain falls out‘. I don’t like that phrase at all. It is most commonly used by bigots in an attempt to defend their bigotry while at the same time appearing rational. Nobody’s brain has ever fallen out from being open-minded, either literally or metaphorically. However, the rankest nonsense phrases often have a grain of truth of them, and there is a grain of truth even in that one. It is that, in order to achieve anything with our thoughts, we need a framework within which they can operate, and that framework will be made of rules and suppositions that are accepted without evidence. I agree that we need such a framework, but what is crucial is that we acknowledge the existence of the framework, that it has no supporting evidence, and that we hence have no basis on which to claim it is better than any other framework. That doesn’t mean we should refuse to act on conclusions drawn within our framework. But it does mean that (in my opinion, which was derived within my mental framework!) it is a good idea to regularly examine and challenge our framework, and consider alternatives. Sometimes that may lead to a radical change in worldview, which opens up whole new vistas.
It may lead to a Christian becoming a Buddhist, or vice versa. It may lead to a Socialist becoming a Libertarian, or vice versa. It may even (heaven forfend!) lead to personnel exchanges between Platonism and Existentialism. I may have my own preferences about which of those and other sets of ideas most people aligned themselves with but, regardless of the outcome of any migrations of beliefs, I see it as good that people regularly examine their beliefs, so that belief migration becomes a commonplace possibility. If we know what our prejudices are, we have the power to change them. But we cannot change a prejudice we don’t even know we have.
Here are two of my prejudices. The first is that it is preferable for there to be less suffering in the world. I know it’s a prejudice. I know I can’t prove it. But I’m going to hang onto it, for now at least.
The second prejudice is that if I have observed two phenomena to occur in close conjunction many, many times then, in the absence of strong reasons to the contrary, I should expect them to continue to occur in conjunction in future. Every self-supporting person on Earth has this prejudice. But nobody even realised it was a prejudice until David Hume pointed it out in the eighteenth century – his famous ‘Problem of Induction’. If you don’t believe me, think of how you use language. You speak English to somebody – say it’s Bertha, expecting them to understand it, because they have understood English when you spoke it to them in the past. But why should the fact that Bertha has always understood spoken English in the past indicate anything at all about whether she will understand it in the future? You might object that you know that Bertha learnt English as a child, so you know she knows English. But then you are relying on the association between the events ‘X has learned English‘ and ‘X understands English‘, which has been reliably observed in the past, but why should that tell us anything about whether it will be observed in the future? Whatever objection is raised, I (or rather David Hume) can find an answer to it. But I’m still going to hang on to this prejudice.
Prejudice in Music
I had been thinking over this in the context of musical styles. It’s hard to think of any other human activity, the study of whose history is so riddled with the use of the word ‘shocking‘. The most casual observer probably knows about how Rap was considered shocking when it emerged in the eighties, ditto Punk in the seventies, how Rock n Roll was considered shocking when it emerged in the fifties, and how Jazz was considered shocking in the early twentieth century.
But the history of people being shocked by music goes back much farther than that. The history of classical music in particular is regularly punctuated by shocks when some innovator broke hallowed rules. Working back in time we have Schoenberg, Stravinsky, Debussy, Wagner, Beethoven, Haydn and Monteverdi as major disruptors of established musical conventions.
The following story from a radio music presenter made a big impression on me. They told of how they had been working in the archives of a classical music operation, listening to, classifying and cataloguing recordings. After having been doing this for a few weeks they walked past a studio in where music was playing over the loudspeaker. Appalled at the terrible, disorganised racket they were hearing, they asked somebody what the noise was. It was JS Bach! [For the non-classical music buff, JS Bach was a genius who lived from 1685 to 1750, in the ‘Baroque’ period, and is as revered a part of the musical establishment as it is possible to be] The reason it sounded so terrible and formless was that the music the presenter had been listening to non-stop for the last few weeks was all pre-Baroque, and hence operated within a framework of rules and norms that Bach’s music ‘broke’. If they had heard it a few weeks earlier they would have likely thought ‘how lovely!‘ or maybe even ‘that’s a bit old-fashioned!‘
I want to pick on Schoenberg, because on the face of it he might seem to go as far as one can go in breaking rules. The Austrian composer Arnold Schoenberg rebelled against the tyranny of tunes having to be in a musical key, like G major or A minor. Although only classical pieces tend to state their key, with names like ‘String Quartet in E flat Major‘, nearly all pieces have one. Perhaps the most famous song of all, Lennon and McCartney’s ‘Yesterday‘, could have been called ‘Sad song in F major‘. Key changes do occur within a piece, but they have a big effect, because we become attached to the key in which the tune is set. That’s why key changes are often used towards the end of a song to build up the levels of excitement and energy towards a final climax.
Schoenberg’s project was to refuse to use any key at all, not even for one phrase at a time. To do that he invented his ‘Twelve-tone system’ in which he set a rule that every one of the twelve notes in a chromatic scale must be used exactly once within each short section of the piece (called a ‘tone row’). By giving every one of the twelve possible notes equal status, he prevented any note gaining prominence as the ‘Tonic’, the home note of a key. Unlike another famous Austrian, Schoenberg was very anti-racist: he wanted the black piano keys to get as much opportunity as the white piano keys in his pieces (note that’s a different use of the word ‘key’).
Here, from YouTube, is a Schoenberg piano piece using his twelve-tone system, for you to enjoy.
As I was musing over whether Schoenberg had achieved the ultimate in open-mindedness, I suddenly realised a hidden prejudice. Sure, he had proclaimed equality between all twelve notes. But a note is defined by a frequency – vibrations per second. So the number of possible notes is infinite, not only twelve per octave. Between any two different notes there are an infinite number of frequencies between them. In Western music, which is descended from Ancient Greek music, the smallest interval between two notes is a semitone, which means the ratio of the two frequencies is 21/12 or about 1.06.
In classical Indian music, the twelve Western notes are used, plus ten others, called ‘nadas’, giving twenty-two altogether, so that the average gap between adjacent permissible notes is just over a quarter-tone. A piece containing nadas sounds to a Western ear, which is not trained to understand those extra notes, like it is being performed on an out-of-tune instrument.
Here is a scale that goes up an octave in twenty-four quarter-tone steps (not exactly the same as an Indian scale, but closer to that than to a Western scale), then walks back down again. What does it sound like to you?
For comparison, here is the same thing using just the twelve notes in the Western scale.
Try to sing or hum along to first the Chromatic scale, and then the quarter tone scale. I’m a reasonably accurate singer and can do the first, but can’t even get started on the second.
But even writing music that includes nadas or quarter tones still involves a prejudice against the in-between notes. It’s just a smaller prejudice than Westerners like me have. I expect a piece involving eighth-tone intervals would sound just as weird to an Indian as one using quarter-tones does to us.
If we want to write music that is free from all prejudice, we need to go beyond Schoenberg, beyond Indian music, beyond even eighth tones, and write music in which each note can be any frequency at all, without limiting the choice to notes that are certain multiples and ratios of others.
I wrote a piece of such music. To be precise, I programmed a computer to randomly generate a series of frequencies and note-lengths and produce notes using those. I then produced another version of it, in which each note was rounded to the nearest semitone, so that only the twelve notes in the Western scale were used.
Can you tell which is which? They are both weird. Both break most of the rules we are used to. But one is a bit weirder, a bit more free, than the other.
Click here to find out which one is which.
The above is a long way from JS Bach, but is it free from any form of musical prejudice (aka structure)? No. For a start I have constrained the notes to be within the audible frequency range, even though it is entirely conceivable that notes that we cannot consciously hear may still have an effect on our body and thereby alter the sensory experience. I have also constrained the notes to not be very short or very long, in order not to frighten or bore the listener. The volume is also constant, rather than varying between notes, or even within notes. The shape of each sound wave is a perfect sine curve, whereas the wave shape could be allowed to change between and within notes too. That would not change the ‘tune’ but it would change the texture (‘timbre’ in musician-speak). I expect there are other prejudices in there that I have not yet realised.
I like most of my prejudices. I prefer Bach to Schoenberg most days of the week. But it’s good to challenge oneself every now and again with a bit of Schoenberg (or its equivalent), and then to occasionally challenge the Schoenberg with something even more radical.
Bondi Junction, July 2017
I was jogging on the beach, trying to think of something else because the last couple of days had been rather upsetting. I settled on thinking about an essay I am trying to write about The End of The World. Very soon I found that I had the REM song It’s the end of the world as we know it running through my head on repeat.
After a while I noticed somebody running along next to the concrete promenade, where the sand is softest because it is furthest from the water and almost never gets wet from the sea. The sand was pretty soft where I was, about halfway between the promenade and the water. But maybe it was softer over near that other guy. In any case, we’d had heaps of rain recently, so if water makes sand pack together harder, presumably where I was would be just as water-hardened as next to the promenade.
But then maybe seawater has a different effect. Perhaps it makes the sand stick together better than rainwater does. If so then the sand next to the promenade really would be softer, unless the sea ever gets up to there.
That led to me wondering about whether, in the wildest sorts of weather, the sea ever came all the way up to the concrete wall below the promenade (about fifty metres from the high tide mark).
Thinking of stormy weather made me think of the scene in the movie The French Lieutenant’s Woman where the female lead stands at the end of a long jetty in a storm, only a metre or two above the rough sea – a precarious position, deeply evocative.
That led me to wonder whether it is sexist to refer to the character as somebody’s ‘woman’, thereby seeming to suggest ownership. That led to my thinking about the reverse phrase ‘somebody’s man’, which led me to think of the Tammy Wynette song Stand by your man.
And without any conscious decision to do so, there I was, jogging along the beach, mentally humming Stand by your man instead of It’s the End of the World as we know it.
Bondi Junction, April 2017
Featured Image is from the 1981 movie The French Lieutenant’s Woman, showing the jetty called ‘The Cobb’ at Lyme Regis UK.
Here’s a piece I wrote explaining the mathematics behind the peculiar phenomenon of acoustic ‘beats’.
It’s a bit maths-y. But for those that don’t love maths quite as much as I do, it also has some interesting graphics and a few rather strange sound clips.
Bondi Junction, August 2016
I am re-committing to memory my old piano repertoire which, 25 years ago, comprised somewhat over an hour of music.
Playing complex piano pieces from memory amazes me. Any form of memorised material is impressive, but piano seems weirdest because one doesn’t have to just memorise a melody, but all the chords and counterpointal parts as well. There are usually three to eight notes being played at once, so superficially it sounds as though one has to memorise three to eight separate parts and play them simultaneously. It’s not really that hard (unless it’s a five-part fugue by JS Bach, and I haven’t memorised any fugues yet) because while there may be three notes in an A major triad in second inversion, they are not just any old three notes. They are three notes that nearly always go together. So one can just remember that there’s a triad there, rather than remembering three separate notes.
But still, there’s an awful lot of stuff to remember. I think concert pianists and Shakespearean actors are the most impressive to me in terms of memory feats.
I find it astounding to what extent the fingers – after a fair bit of effort at memorising – just know which notes to play. If you asked me what the next chord was, I could play it, but I couldn’t tell you beforehand what it was. I might even need a run-up to play it, because it seems that playing the chords leading up to it set the context that enables my fingers to ‘know’ what comes next. I know this because if I get lost and have to get re-started, there are only certain points in the piece from which I can start cold.
I have read that it’s really the Cerebellum that ‘remembers’ what to play, not the fingers. But it feels like it’s the fingers.
One can commit a piece to memory either consciously, so that one can say out loud what comes next – what chord it is, which notes and perhaps which of passages A, B, C or D it is in a Rondo structure – or unconsciously, by just playing it over and over from sheet music until it gets programmed into one’s subconscious.
I think it is safest to learn both ways.
Committing the piece to conscious memory is a safeguard against a crisis of faith or a sudden disorientation. Playing unconsciously relies on context to know what comes next and it needs faith so that one trusts one’s fingers to do the right thing. As soon as one loses context or faith – easy to do when under pressure in a performance – one can lose the ability to let one’s fingers do the work.
It is like the art of flying in the fourth HitchHiker book (‘So long and thanks for all the fish‘) or a Roadrunner cartoon where Wile E Coyote accidentally runs over a cliff but only falls when he looks down and realises where he is. You only lose the ability to fly when you remember that it is impossible. Then you suddenly plummet.
There is a very long trill in a Chopin Nocturne that mixes me up because it covers three notes and is more complex than an ordinary trill. I can play it fine, and very fast, as long as I don’t think about it. But because it’s long, I usually end up inadvertently thinking about what my fingers are doing about halfway through and then getting muddled. The last few times I have succeeded in playing it right through without mistake by looking around the room as I play it, focusing on things I see – keeping my mind occupied by anything except what my fingers are doing.
My fingers playing music are like me doing maths. They are very good at it as long as nobody is watching. But as soon as somebody is watching it turns to mud. Young children enjoy tormenting me by sidling up to me and asking me something embarrassingly easy like ‘differentiate x squared!‘ and then staring at me intently so that my brain won’t work (like a watched pot).
But if one also knows consciously what comes next, one can silently tell oneself to play an E flat diminished chord in the second inversion, or to reprise theme B, one octave higher. One knows how to do that, so one does it – no faith required. The conscious brain acts as scab labour to supplant the striking union of the unconscious fingers.
Although both conscious and unconscious memory always have a role to play, I feel that this time I am learning a lot more unconsciously than I did 25 years ago. I can see how much conscious involvement there was in 1991 because some of the scores still have the pencilled notes I wrote on them to help me categorise and memorise the thematic and harmonic structure of each piece. It’s more enjoyable learning subconsciously. But it’s higher risk to do only that, if one has to perform.
I have been finding that, once one has committed a piece thoroughly to memory, it is quite peaceful and meditative to play without thinking about the notes one is playing. One thinks about the music, because one puts the feeling into the piece by variations in loudness and pace, but not about the microstructure of the notes. That is beyond one’s gaze, being taken care of by the fingers/cerebellum.
It is important to keep one’s mind on the music though, otherwise the relentless, angst-ridden chatter of the modern monkey mind comes in to disturb the peace. I can remember occasions of playing pieces in the past, whether from sheet music or from memory, with my mind completely oblivious to the music and instead working philistinically though every grievance, anxiety and obsession it could find, re-running past conversations and projecting future ones at a rate that would make a Boddhisattva wince and that could generate material for at least three psychology PhD theses.
I wonder what concert performers do – whether they do both, or just one and if so which one? Or does it vary between performers?
In case anyone is interested, here are the pieces from the 1991 repertoire, showing which ones have so far been re-learned:
- Beethoven Pathetique Sonata, all three movements (2nd and 3rd re-learned so far)
- Mozart C major sonata, all three movements
- Beethoven Moonlight Sonata First movement (the famous one)
- Beethoven Fur Elise (re-learned)
- Debussy First Arabesque (re-learned)
- Debussy Clair de Lune
- Chopin Nocturne in E flat major (re-learned)
Mr Beebe would say ‘Too much Beethoven‘.
But I will never be able to competently play the fiendishly difficult Opus 111 sonata whose crashing rendition by the troubled Miss Honeychurch prompted those immortal words.
I have vague aspirations to extend the list if I manage to re-learn all of it. I have in mind to do one of Faure’s three lovely impromptus. Given my comment above, I am tempted to also take up the challenge of attempting to memorise a Bach fugue. I probably shall. Sadly, nobody in my circle of friends and family seems to really like Bach fugues. Perhaps he really wrote them for the enjoyment of the performer rather than for the listener.
Bondi Junction, July 2016
Although this third movement is less “pathetic” than the preceding ones, the player alone will be to blame should the Pathetic Sonata end apathetically.
Thus writes the author of Schirmer’s Library of Musical Classics, at the foot of the first page of the score of the last movement of Beethoven’s Sonata Pathetique (That’s ‘Pathetic’ as in pathos, ie emotionally moving, not as in contemptible, in case you were wondering). The bold font emphasis was added by me, by the way – it’s not in the original.
Many were the admonitions of this type that one used to encounter in learning, performing and reading about music. I don’t know if such admonitions still abound, but I used to take them very much to heart.
Here’s another gem from the last page of the same movement:
In proportion to the greater or lesser degree of passion put forth by the player before the calando, this latter is to be conceived as a diminuendo and ritardando. Excess in either direction is, of course, reprehensible.
A piano teacher once told me that, while Mozart piano sonatas seemed easy to play, especially the slow movements, they were actually especially difficult because their smooth lightness and sustained notes would ‘expose’ the inadequacy of any player whose touch upon the keys was not delicate and even. I interpreted this as meaning that only an impostor would attempt to play a Mozart Sonata without first obtaining the very highest degree of musical performance qualification possible. Their crime of trying to hide their lack of skill behind the apparent simplicity of the score would be exposed by the very first unplanned variation in pressure ( a ‘plonk’ in lay terms) leading to their justly deserved shame and humiliation and, it is to be hoped, excommunication from any future association with decent, honest, genuine music lovers.
Although I did take this sort of sermon to heart, I nevertheless dared to play sonatas by Mozart. I enjoyed it. But I just had to secretly hope that no true music connoisseurs would ever hear me, perhaps as they walked past the open window of the room in which I was playing, and be goaded into a rage by my lack of finesse – not to mention the unmitigated temerity of presuming to play Mozart. I imagined they would feel it were as though I had reanimated the corpse of Wolfgang Amadeus himself, just so I could slap him in the face and jeer at him.
I don’t think that any more. In fact, I may have swung so far to the opposite extreme that I have to remind myself not to be too intolerant of those poor souls that do happen to be internationally renowned piano virtuosi.
In short, I love amateur music. There is a point at which it may become difficult to listen to, as with a tone deaf singer or the tuneless screeching of a child unwillingly doing their ten minutes a day practice on the clarinet or violin. But short of that (and even that isn’t too bad, but that’s another essay) I find that musical flaws enhance rather than detract from the performance, as long as the player’s heart is in it. Sincerity and enthusiasm is all that’s needed to make a performance truly marvellous.
My youngest daughter will graduate this year from high school, after which I will no longer have a socially acceptable reason to attend performances of school musical ensembles, whose enthusiasm is often in inverse proportion to their skill. What a pity! Like a Persian carpet, where (it is said) the maker always includes a deliberate flaw because only Allah is allowed to be perfect, the flaws in an amateur musical performance are an essential ingredient, without which the performance would lack – I don’t know, maybe ‘soul’?
For ensembles of young children, the many mistakes, constantly varying level of pitch accuracy and plodding pace are, of course, adorable. But my liking for amateur music is not limited to a sentimental fondness for kitsch cuteness. I feel just as warmly about performances by tall, spotty adolescents in rock bands – as long as they have not been stage managed by Simon Cowell and do not have PR agents in tow. What is important is sincerity and enthusiasm. The occasional (or frequent) mistake emphasises the humanity of the performer.
And in any case, a liking of cuteness could not explain my recently acquired toleration of my own mistakes since, if I recall correctly, some biologist or other (was it Richard Dawkins? Or perhaps Francis Collins? I get them mixed up. Goodness knows they have so much in common) has proven conclusively that it is impossible for any individual member of any mammalian species to find itself cute. I’m not talking about pretending to be cute. All humans seem to do that at a certain age. But pretending to be cute is not the same as finding oneself cute. Indeed, it requires a healthy dose of cynicism to pretend to be naively clumsy and inarticulate just to manipulate the emotions of those around you. It must be done with a cold, clear, calculating mind and a total awareness of what one is doing, and leaves no possibility open for being taken in by one’s own deception. Or so I imagine. It is many years since I discarded any hope of garnering positive attention by feigning sweet ingenuity.
I digress. Refocussing: I think perhaps it is the humanity revealed through their imperfections that make amateur performances so valuable. We have had flawless performances available ever since the piano roll was invented. No doubt it is now possible for a computer to produce a virtuoso performance of a piece of music direct from the written score. I’m not knocking that. Even when that is done, we still have the human element provided by the composer. I doubt the day will ever come when a computer can write something like Beethoven’s fifth symphony. And if it does, I may find myself believing that the computer has attained consciousness.
But music is an activity for participation, not passive observation. Even apparently passive listening often involves participation of some sort. If one taps one’s foot, sways a little to the rhythm, or hums along, maybe out loud or maybe silently inside one’s head, one is participating. If that mild level of participation is enjoyable and life-affirming, how much more so when one is fully involved in producing the music? Churches seem to have understood this for a long time, with hymns that all the congregation participates in singing. I also think of the wonderful chants that some African villagers do, and of Australian Aboriginal corroborrees. As I understand it, these are social activities, in which all tribe members participate, rather than demonstrations of skill.
When one is learning to play an instrument or, having learned the instrument, trying to master a difficult new piece on the instrument, it can be disheartening to think that, however much effort one might put in, one will never be able to perform the piece as well as a computer program programmed by a mildly competent computer nerd, regardless of whether they have any musical ability. It is a little sad to think that the role of musical performance could be supplanted by instruments played by computers. My response to such negative thoughts is to remind myself that a critical part of any performance is the personal experience of the performer. It will be many centuries before they can program a computer to not only perform Scott Joplin’s ‘The Entertainer’, but to enjoy playing it as well.
That experience of playing multiplies when one is part of an ensemble. It is especially so in a choir, when one can feel the harmonies with the other singers resonating throughout one’s body.
I think the knowledge that there is an important experience of the performer is part of the experience of the listener too. If we reflect on it, we can feel that the performer is feeling the music and, in a way, communicating to us through the music. It would be different, a less complete experience, if the music were being performed by a (non-sentient) computer and we knew that to be the case.
And that’s why I think international piano competitions are bad! Does that opinion follow smoothly enough from the previous paragraph? No? Well, never mind, that’s how I feel. Like many of my opinions, that particular one (which is only a minor aspect of my overall preference for amateur music) was planted in my head by another. It was a talk given by an Australian that was an internationally renowned concert pianist – I forget their name – about how damaging the world of international piano competitions is to musical appreciation, as well as to the lives that compete in them. Most of the contestants are virtuosos, whose difference in skill can only be discerned by the most experienced of connoisseurs. Yet one person will win and be declared ‘better’ than the others. What nonsense. Perhaps the problem is that there are too many virtuoso pianists and not enough paid jobs for them.
The Berlin Philharmonic is an amazing orchestra and tremendous to listen to. But I wonder whether my daughter’s high school orchestra sounds more like the orchestras that premiered works by Beethoven, Mozart, Haydn or Schubert, than the Berlin Phil. From what I have read, the musicians of late eighteenth century Vienna were poorly paid, possibly ill and malnourished and distracted by the worldly cares that beset the financially insecure. They frequently had insufficient opportunity to learn and practice a new piece – sometimes with score changes occurring mid-rehearsal – and the halls in which they performed were irregularly heated, which would have driven constant variations in tuning. My brother and sister-in-law married in a small, freezing stone church in the midst of a dark Oxford winter. I remember the sounds of the string quartet drifting in and out of tune as they played ‘Jesu Joy of Man’s Desiring’. The pitch went up when an eddy blew warm air from the bar heater towards them, and down when the warmth moved away. When I think about it, I realise that that is probably the way the piece was meant to be played. From what we know of JS Bach, the Leipzig churches in which his pieces were performed were probably even colder and draftier than the one in Oxford. There were no electric bar heaters in 1725.
And yet, even though the premier performances of those works may have been riddled with faults, the audiences still responded with adulation and rapturous applause. They could see past the occasional wrong note, loss of synchronisation and variation in pitch, to the underlying genius and emotional power of the composition, and the sincerity of the performers.
I don’t want to sound critical of virtuoso performers and ensembles. They are valuable too and have a key role to play in the world of music. I have no reason to doubt their dedication and sincerity or their enjoyment of the music they play. It is marvellous to hear every now and then a highly skilled performance of some challenging orchestral work. There are some, like Mahler’s second symphony (‘Resurrection’), that are so gargantuan – in both length and number of musicians and different instruments required – that it’s just not feasible to perform it with anything other than a top-level, fully professional orchestra. But they are not what music is about, just as teams like the All Blacks or Manchester United are not what sport is about. Attending an FA Cup Final or a Super Bowl would be a great experience but, given a choice between never being able to watch professional sport again and never being able to watch my children play sport, or play sport myself, I would give up watching professional sport in an instant. And it’s the same with music.