A musical haiku              Gunnar Johansson's `walking lights' demo, courtesy James Maas

Musical Fragments

In childhood and student days and occasionally in recent years, I have written very small amounts of music in various styles from twelve-tone to jazz-like. I think every musician should try it, just to learn something. In my case the idea was not to be revolutionary or influential -- still less to think I could ever aspire to the magic of a Toru Takemitsu, or a Carl Nielsen, or a György Ligeti, or any of the other great composers -- but only to experience for myself the organic growth of a piece, to follow where it wanted to go -- a wonderful spiritual exercise -- and to let it become as good-of-its-kind as it could be.

The great composer Leoš Janáček spoke of the silence in which `sounds shape themselves', and the great mathematician J.E. Littlewood of `giving the subconscious a chance'. Such exercises were also, in my case, part of a quest to understand the deeply mysterious phenomenon we call music, and the extent of its kinship with mathematics and with our unconscious power of abstraction. That in turn was part of a wider quest to understand what I like to call lucidity principles. Lucidity is the opening theme of some published essays of mine and of a book in preparation, whose ultimate concerns are the public understanding of science and its power to keep alive an optimist's hope for the future.

Here is a recent talk I gave at the 2013 Hay-on-Wye Philosophy and Music Festival of the Institute of Art and Ideas, touching on lucidity principles and the deepest connections between music and mathematics.

The silence in which sounds shape themselves has been a great joy to me. Thanks to the Internet I can share that joy with anyone in the world. No need for acknowledgement; I have no career that depends on it!

This little piece, `Fugue on a Telephone Number' (MP3 file for download, 2.5 Mbyte, duration 5'), is partly in memory of my father and is also for two dear friends, whose telephone number gave me the opening theme. There is a noticeable edit near the end, because after the recording I changed my mind -- or, rather, my mind was changed -- about how the piece wanted to end. (Here are pdf files of the revised score (7 pages, ca. 50 kbyte each), 1, 2, 3, 4, 5, 6, 7, and the string parts (2 pages each), v1, v2, c1, c2; a few other notes have been changed, since the recording, on page 6 of the score.) The new ending was inspired by a fascinating correspondence with the Israeli composer Yuval Shay-El. From that correspondence arose the idea of ending near the twin tonal centres, E and A, simultaneously -- a bit like the slow movement of Beethoven's op 132 string quartet, the famous hymn to convalescence that Beethoven thought of as being `in the Lydian mode', but which, to my ear, is nothing of the kind because it simply has the twin tonal centres C and F.

I happen to think that today's affluent societies are making a colossal mistake in downplaying the spiritual importance of artistic creativity in general, and of music in particular, and in supposing that scientific and mathematical creativity has nothing to do with artistic creativity. Lip service is paid, but the reality shows itself in, for instance, education priorities and education cuts, and above all in the unconscious assumption that if something can't be measured then it can't be important!   (That last assumption is also, it seems to me, part of what's leading to other insanities such as the patenting of people.) I happen to think, also, that an understanding of how music works has a great deal to say not only about lucidity principles but also, more generally, about human nature at its deeper levels.

Vocal music or proto-music could well be more ancient than language, perhaps many millions of years more ancient. It includes the vocal play between mothers and babies. Together with dancing and mimicry it seems to have been part of the emotional intelligence that bound groups of our ancestors together, permitting them to survive as ground-dwellers amongst large predators. It's no accident, I think, that within us there can be an unconscious `inner game' of music, played by an unconscious inner musician for whom singing and dancing are, and always were, nearly the same thing. Allowing that game to be played, after the removal of technical obstacles, is in my view the most important secret of success in musical performance. It is a game that can join heaven and earth.

There are many musical counterparts to the walking lights above. One is a tiny trombone `sketch' (40 seconds of mild irreverence, including a musical split infinitive somewhat like the emphatic split infinitive in `to boldly go'). The score is available here as a pdf file (20 Kbyte), and a `performance' of sorts is available here, as a computer-generated MP3 file, 1.3 Mbyte. But it's best with a real trombone. Like the walking lights it tellingly illustrates the brain's model-fitting processes, in which internal models are actively fitted to incoming sensory data.

Somewhat in the same spirit -- and this time I dare to be irreverent to Beethoven and Nielsen -- is this joky little piano piece (MP3, 0.9 Mbyte). It grew out of another friend's telephone number endlessly repeated, which the number seemed to want to do. I call the piece `Half a cup of tea'. I imagine Beethoven pounding away at the piano (perhaps after hearing some bebop for the first time) with the tea forgotten and flying through the air. This is a revised version (2005) with the climax better timed. There is a slight allusion to some real Beethoven, the mighty Grosse Fuge, the natural and awesome ending to the great opus 130 string quartet. It popped up completely unplanned and unbidden. Make of it what you will. I haven't yet found time to tidy up the score, but will gladly supply it `as is' to anyone interested.

I still find occasional solace in a little six-minute string quartet movement written in spare moments, many years ago (from yet another friend's telephone number). It's a coy little piece about `walking lightly on this Earth'. It can be performed in the manner of Haydn's `Farewell Symphony', the four musicians slipping away one by one. The Delmé Quartet (Galina Solodchin, John Trusler, John Underwood, and Jonathan Williams) performed it in the Cambridge Summer Music Festival for my 60th birthday. A beautiful recording by them is available here as an MP3 file (6'15", 4.6 Mbyte). The printed score is available here as a gzipped postscript file (0.9 Mbyte), and the parts similarly: violin 1, violin 2, viola, 'cello (about 0.6 Mbyte each). Because of its `walking lightly' character it also works well as a flute quartet, after slight rearrangement. I stole the descending motif in bar 54 from a composition by my cousin Philippa Hemsley.

Another project in spare moments, spread over very many years, came from a love affair with the extraordinary first movement of the B flat Quintet written in 1932 by the late-romantic composer Franz Schmidt (1874-1939). Schmidt was in my view a wonderful, fascinating, and highly individual composer whose music has been unjustly neglected -- no `mere romantic', in my humble opinion, but a composer of great power and originality. He wrote the B flat Quintet shortly after suffering a terrible bereavement, the death of his daughter Emma, on top of deteriorating health and other personal difficulties. The B flat Quintet spoke to me at a time of personal stress of my own. The first movement, especially, transported me to an other-worldly landscape in which lost souls can find solace. It seems to have been new territory even for Schmidt himself.

The music is also fascinating technically, not only through Schmidt's extraordinarily clever and individual harmony and counterpoint, but also in his use of clarinet and string trio plus a very sparse piano line written for the left-handed pianist Paul Wittgenstein. The result is a rich yet delicate texture quite unlike that of most piano quintets. By far the best recording I've ever heard is that on catalogue number C 287921 A from Orfeo GMBH. The musicians are Rainer Keuschnig (left-hand piano), Ernst Ottensamer (clarinet), Josef Hell (violin), Peter Pecha (viola), and Leonard Wallisch (cello). In case you find yourself curious about my love affair with this music, and the surprising outcome, I've posted a few more details on a separate page here.

I'm grateful to Jeffrey Ginn Music Studios for valuable professional help, to the composers Robin Holloway and Yuval Shay-El for helpful comments and correspondence, and to my wife Ruth McIntyre, neé Hecht, for her supreme artistry as a musician, which has inspired me in many ways over the years. Her wonderful ways of using piano sonority inspired, in particular, this tiny piano piece à la Satie (5'25", score only, pdf, 116 kbyte, also gzipped postscript (106 kbyte), written for a much-loved colleague's Festscrift celebrations. (Guess what: it began with the colleague's telephone number -- though this time it was a tough nut to crack. It's fun to see whether unpromising material can turn itself into something that makes musical sense.) It's only light music -- a gymnopédie that immediately turns into a slow waltz -- and is meant to be played after dinner, in the late evening, while wearing rose-tinted spectacles. (And please make full use of the piano's sympathetic resonances.) The violinist Emma Wragg showed me that it also works beautifully as a violin-piano duet. Together with two deeply musical friends -- one of whom is Vivian Williams, the cellist on our Crighton Memorial CDs -- Ruth inspired me some time ago to a larger effort, a fourteen-minute trio for clarinet, cello and piano with clarinet doubling bass clarinet. It strongly complements existing repertoire. It's called `Frivolity', its opening telephone number is that of a drinking house in Worthing, West Sussex, and it is full of laughter and riotous dancing. Nevertheless, there's a still centre. Where that came from is another mystery. It's been recorded but I haven't yet got round to the editing.

By the way, I should have acknowledged that Ruth and Vivian are the pianist and cellist playing along with me in the little Fugue on a Telephone Number above. (Of course it's not their fault that I changed my mind -- sorry, my mind was changed -- about the notes on page 6.) And I'd like to thank Virginia Seay Ploeser for some kind and wonderful first lessons in composition when I was a little kid in New Zealand.

And what's that fragment at the top of this web page? Not a telephone number that I'm aware of! Just a musical haiku that touches me. My late aunt, the Australian poet Anne Edgeworth, first showed me such things. In the last few years it's been growing into something more, a palindrome of the form ABCDE WXYZYXW EDCBA, about 4-5 minutes' worth, each letter being a haiku with Z itself palindromic. Who knows, it might finish itself before I die.

This page is at http://www.atm.damtp.cam.ac.uk/people/mem/papers/LHCE/music-index.html
Back to the Crighton memorial concert and recording, http://www.atm.damtp.cam.ac.uk/people/mem/crighton.html
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First posted 2000. Last updated 30 June 2015
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Footnote for composers:  My take on harmony and temperament -- the extended Note 58 from Lucidity Part I on musical hyperspace, etc. -- is available here as a pdf file (0.37 Mbyte), though due for a thorough rewrite before publication. I argue in particular that most of what's in the harmony books, and much that isn't, can be condensed into one sentence. This is done noticing something that might not be obvious at first sight -- at least I haven't seen it mentioned in the harmony books -- the precise way in which the organic-change principle applies to harmony. (I think Claude Debussy, who first discovered all this, kept it as a trade secret. I don't blame him at all. Even for the very greatest talents, it's tough trying to survive financially as an innovative composer. I do like Igor Stravinsky's aphorism `revolution is one thing, innovation another.')

I'm keeping the Note available in case it interests a young composer who'd like to get away from the usual nonsense about temperament and atonality, while respecting our inner nature. Please skip the elementary stuff on page 2, written for my scientific colleagues. Please also notice a mistake in the footnote on page 4: the circle of fifths is one thing, and harmonic-series proximity is another, albeit somewhat related. It's correctly explained on page 2. (To say nothing of the equally important circles of major and minor thirds...)

Footnote for musicians interested in the inner game:  Have you come across the wonderful article `Phrasing in Contention', by the clarinettist and conductor Antony Pay, available here? The article first came out in May 1996 in the periodical Early Music. It contains profound insights into -- among many other things -- the likely meaning of the vertical dashes in Mozart's autographs.
Footnote for violinists:  If you're a violinist looking for violin duos to play for fun, here's a frivolous, superficial little thing that some people enjoy. It's seriously silly. It was written ages ago, around 1960, in my dissipated student days. It had its first public performance, by the Parry-Mikelic Duo, in London on 28 March 2000, providing some of the light relief in an all-20th-century concert programme. A recording of the Parry-Mikelic performance is available here as an MP3 file (1'15", 1.2 Mbyte). A higher-quality MP3 file of the same recording is here (3.1 Mbyte). The printed score is available here as a gzipped postscript file (80 kbyte).
My anonymous ftp site:  This is here mainly for use during personal correspondence; there are some musical bits and pieces from ongoing projects...