Where I live, near Sydney’s Eastern beaches, we have something we call mud. But it is not proper mud. Sure, it marks clothes, necessitating a wash, but is otherwise unremarkable.

I am currently in North Devon in England, where it has drizzled on every one of the six days since I arrived here.

Here they have PROPER mud.

It is sticky yet somehow also slippery. It makes squelchy noises when you tread in it. I went jogging beside a canal in Stratford-upon-Avon and, after the path ended, there was only grass interspersed with boggy bits of naked mud. I did my best to skirt around them, but that wasn’t possible in all cases and once or twice I had to actually tread in the mud. It looked very precarious, especially with the freezing canal only a metre away, ready to gobble me up if I slipped. As it happened, I only slipped once, falling away from the canal rather than towards it. My glove is now coloured by a souvenir of that special mud.

Sydney mud has too much sand in it.

English mud seems much more fertile. Mud is quickly regrown by vegetation if left undisturbed. Wherever I see mud I also see lush, fertile grass or close-packed, flourishing vegetable crops just nearby.

In that sense, mud is great – it is life.

But it is also death. The Great War, at least on the Western Front, seemed to be all about mud. It contaminated water to help spread disease, afflicted soldiers with Trench Foot, and it trapped horses, gun carriages and even soldiers, who could find themselves stuck in a position that was exposed to opposition gunfire. The bodies of soldiers killed by machine-gun fire, where they weren’t suspended on rolls of barbed wire, were soon partly or wholly swallowed up by mud. It was part of the horror.


There is something extraordinary about European mud. It is mythical. That’s why they write songs about it.

Perhaps it’s not just European mud. The song I had in mind was ‘Mud, Mud, Glorious Mud’, which I find is called ‘the Hippopotamus Song’ and is by Flanders and Swann (I had always assumed it was supposed to be a song for pigs). But a bit of web-searching informs me there are also lots of songs about American mud, although mostly in the South.

As the spine-chilling Maori Haka says, ‘It is death it is death it is life it is life…’ (‘Ka mate Ka mate Ka ora Ka ora’). One can imagine that life on Earth first originated in mud. There is so much richness in good mud, it would be difficult for life not to arise.

I realise that may not be scientific. I think a key reason why mud is so fertile is that it’s mostly organic, made up of lots of decayed organisms, animal and vegetable. So maybe they didn’t have mud on Earth before life arose, what with there being no decayed organisms around. Who knows, there was nobody there to write it down.

But even if life didn’t originate in mud, I bet that, once originated, it did an awful lot of evolving in there. We humans evolved in Africa, so I bet they have really impressive mud there. I’ve only been to North Africa, which is sandy, like Sydney, so I have never encountered real, proper African mud, of the sort that Joseph Conrad describes in Heart of Darkness.

If you are fortunate enough to live in a place where they have proper mud, I urge you to give it a thought next time you get caught in or covered by it, rather than just cursing as you head for the washing machine. Mud is magical stuff. No wonder little children loving playing in it.

Andrew Kirk

Woolacombe, North Devon, December 2017

Challenging my prejudices, in life and in music

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?

Quarter-tone scale.

For comparison, here is the same thing using just the twelve notes in the Western scale.

Chromatic scale (semitones)

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.


Sound File Freda

Sound File Bob

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.

Andrew Kirk

Bondi Junction, July 2017


Thought Association

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.

Thought association.

Andrew Kirk

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.

Acoustic ‘beats’ from mismatched frequencies

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.

Andrew Kirk

Bondi Junction, August 2016

I think my spaceship knows which way to go

Miss Honeychurch piano

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‘.

Mr Beebe3.jpeg

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.

Andrew Kirk

Bondi Junction, July 2016

Miss Honeychurch piano 2