Silver on Silver Thrills Itself to Ice
Music survives, composing her own sphere,
Angel of Tones, Medusa, Queen of the Air,
and when we would accost her with real cries
silver on silver thrills itself to ice.
Geoffrey Hill, Tenebrae
Reading reviews in JMI (Jan/Feb & Mar/April, 2002) by Patrick Zuk and in Magill (April 2002) by Barra Ó Seaghdha, of Harry White’s books The Keeper’s Recital (Cork, 1998) and Musical Constructions of Nationalism (Cork, 2001) and White’s article in the Oxford Companion to Irish History, one could be excused for thinking that there must be a misunderstanding about the term ‘music’.
Having been asked by the Irish World Music Centre at the University of Limerick to address a seminar (10 April 2002) where the other speaker was Professor White, I found myself toying with the following notions which I would like to share with JMI readers for some critical appraisal.
It seems to me that ‘music’ is a very wide and comprehensive category which can be compared with ‘mathematics’, whereas ‘classical music’ can be described as an area within that genus which is separate and distinct, in something of the way in which algebra forms a separate discipline within the overall category of mathematics.
Mathematics came into existence as a way of counting. If we didn’t have fingers it is unlikely that we would have learned to count in the way we do. Fingers are visual aids to counting. Digit(us) is the latin word for ‘finger’. Five fingers on each hand allow us to proceed to the ‘decimal’ (Latin for ‘ten’) system in the most natural way. In some archaic languages the word for six is equivalent to the word for ‘jump’, because you are jumping from one finger to the next hand to make your calculation. 5 + 5 = 10. We’re all pretty competent as far as that goes. 5 x 5 = 5+5+5+5+5. That switch of combining symbolism causes too much of a handful even if you use all toes (also digitus in Latin) on both feet as well. So, you have to find ways of compressing: e.g. 5 to the power of 5 = 5 x 5 x 5 x 5 x 5, which is the equivalent of: (5+5+5+5+5)+(5+5+5+5+5)+ (5+5+5+5+5)+(5+5+5+5+5)+(5+5+5+5+5)
When you begin to count in billions you need a more sophisticated form of calculation.
When mathematics gets into the land of subtraction, it delivers the thought of negative numbers; division leads to fractions; and roots reveal the possibility of surds. Each leads to another viewpoint. Mathematics develops its own complications within the confines of its own system. However, we are still within the recognisable terms of quantity, still in touch, no matter how distantly, with the tangible world of digits. With algebra, on the other hand, we cut that reference grid and move into an autonomous world of referentiality as a world of its own. Cutting the linkage to the original source of reference we concentrate on the system of interconnection between signs themselves.
Again, if we borrow a working description of signs, we can say that signs are either suggestive (a knot in your handkerchief), expressive (language), or substitutive (a counter game or a mathematical calculus). The difference between the last two is that a word is an instrument for thinking about the meaning which it expresses whereas a substitute sign is a means of not thinking about the meaning which it symbolises. This last is where algebra would, perhaps, situate itself.
Harry White in The Keeper’s Recital (p. 259) quotes Lydia Goehr: ’the distinguishing feature of European art music in the nineteenth century is that the musical work itself becomes an autonomous object, a self-subsisting idea which is independent of the circumstances which bring it into being’.
Such a suggestion make one think of algebra as compared with mathematics as a system. Which does not imply inferiority or superiority; nor does it make one system better or ‘higher’ than the other.
In Euclidean geometry (Greek for ‘measurement of land’), another such system within the overall category, the assumptions are explicit: the premises and conclusions are formulated in words. But in Algebra (Arab word jabara, meaning to ‘reunite’) the link between words and operations and between objects and symbols are cut so that the operations and symbols can be brought into a closer mutual configuration. It is a language, but not one connected to ‘the real world’ and it restricts itself to defining relationships between signs and symbols.
Suzanne Langer puts the difference between mathematics and algebra with her usual clarity:
Every mathematician knows how hard it is to convince the naïve beginner in algebra that its letters have any meaning, if they are not given specific denotations: ‘let a = 5, let b = 10, etc.’ Presently the novice learns that it makes no difference to the validity of the equation how the meanings of terms have been assigned; then he understands the generality of the symbolism. It is only when he sees the balance of the equation as a form in itself, apart from all its possible arithmetical instances, that he grasps the abstraction, the real concept expressed through the formula.
Algebraic letters are pure symbols; we see numerical relationships not in them, but through them; they have the highest transparency that language can attain.
Poetry as a kind of measurement of time and rhythm developed its own system of scansion. The famous iambic pentameter was the Greek for a line of verse where the foot (iamb) hit the ground five (penta) times in a rhythm space (metre). The way we transcribe this involves us in various systems of signs. Music has its own varied and variously complicated systems.
If we take a description of music by Robert Schumann as a starting-point, he calls it ‘the spiritual language of emotion’ and ‘the spiritual dissolution of our sensations’ so that ‘whoever possesses tones, does not need tears, both are equivalent – dissolved sensations of the soul’. Music is here presented as a particular translation of experience: sensation and emotion ‘dissolved’ into ‘spiritual language’.
R.D. Laing, who was both psychiatrist and musician, advises that ‘we have to clear a space for the discussion of experience as such, because the methods used to investigate the objective world, applied to us, are blind to our experience, necessarily so, and cannot relate to our experience … Experience is not objective and is not conveyed to objects. The way it is communicated or conveyed is different from the transfer of objective information … experience takes on dramatic forms more akin to music unfolding diachronically through time than a pictorial depiction synchronously present, unchanging through time.’ Music, from this perspective, is the most appropriate way of translating human experience into an ‘objective correlative’, to use T.S. Eliot’s useful phrase. Unlike science which seeks to reduce the world of experience to the most abstract and universally applicable formula, music is a sign language which absorbs, maintains and expresses the particularity and full-bloodedness of sensation and emotion. A melody is a patterned sequence of notes of different pitches. The absolute pitches of the notes are their quantity, their relative positions; and the parts they play in the dramatic dynamic structure of the melody are their qualities. The melody does not consist of the notes separately or alone, but the form generated by the sequence of the ratios of the pitches of the notes. These ratios are not themselves notes. They are the differences between the notes. They do not themselves make a sound. If the music gets to us, there is an instant sympathetic vibration through which we resonate and commune with it. This resonant communion is not the way objective facts are communicated.
Science is the way we have developed for understanding and communicating ‘objective facts’. It doesn’t matter what culture we belong to or where we happen to live in the world, we are all bound to accept that H20 = water. Mathematics underwent an excision of verbal content to attain symbolic exactness. The sentence ‘John is here’ can mean any number of possibilities depending upon which ‘John’ we are talking about and where ‘here’ happens to be situated. It also implies that we speak English. Such an impoverished and imprecise system of understanding and communication became common currency as most civilised societies of the 20th century democratised the languages of reading and writing. Scientists would claim that there is a necessity also to learn to read and write the language of measurement if we are to understand the language of modern science.
However, if we are to comprehend more idiomatically the world of sensation and experience, it is incumbent on us also to learn the languages of music and of art. The transformation of our tears into the language of the spirit is quintessentially the task of music. The difference between so-called ‘classical’ music and other kinds of music is the way in which the ‘tears’ are distilled, the sensation and the emotion ‘translated’.
Music is one of the ways in which imagination tries to sort out and find some kind of order in experience. Melody, as one such pattern, provides a basic dramatic form of music which is more or less akin to experience. Melody follows the contours and, as it were, hugs the coastline of experience. We immediately log into the correspondence and the melody is like the chain to the sprocket of our emotional body language.
But there is a music beyond melody. This constitutes a new freedom which involves a change of existence from one mode to another, as a caterpillar (with all those feet!) changes into a butterfly. Essentially we are talking about persons and the way in which they translate themselves into art. Adam Phillips, in an essay called ‘On Translating a Person’, describes how cultural prejudices can prevent us from adopting one such structural form of art as opposed to another: ‘From the beginning of the formation of the industrial working class novel’, he writes, ‘there were always individuals with the zeal and capacity to write, but their characteristic problem was the relation of their intentions and experience to the dominant literary forms, shaped primarily as these were by another and dominant class.’
In other words, the translation of their experience – their moving it across into the alien form of the English middle-class novel – could feel excessively alienating. As over-accommodation, or submission, or distraction. The form was foreign, and it was the form of a dominant, exploitative class. A welsh miner would not feel at home, as it were, in one of Jane Austen’s drawing rooms. What Williams is alerting us to is that what he calls the emergence of ‘structures of feeling’ depend upon the cultural forms available for use. And each of these forms carries with it a history and a class consciousness. Of course this would be true for the majority of Irish people, even though a considerably talented minority would feel quite at home in the Jane Austen drawing room. However, the algebra of music would, for the most part, have been the preserve of the dominant ascendancy class and so the transition from caterpillar to butterfly could have taken on the trappings of a turncoat.
Harry White in The Keeper’s Recital holds that ‘music in Ireland functioned in a vitally different way to music elsewhere. It functioned primarily as an idea of something other than itself’ (p. 260). This could mean that it behaved mathematically but not algebraically, and the explanations for this reluctance to enter the rarefied autonomy of ‘classical’ music are fairly obvious.
The transition from the local to global in terms of algebra means that it does not matter which particular tube station you use as your entry point as long as you eventually reach the underground system which constitutes its own set of reference points, its own train of thought. The examples of Chopin in Poland, Rimsky-Korsakov in Russia, Kodaly and Bartok in Hungary, Sibelius in Finland prove that traditional or so-called ‘folk’ music is capable of algebraic transposition as much and as readily as any other. The transposition does not make it any better, any more, any less ‘musical’ than its original setting. It makes it different.
1. Suzanne Langer, Philosophy in a new Key (New York, Mentor Omega, 1951), pp. 202-203.
2. Thomas Alan, The Aesthetics of Robert Schumann (London, Peter Owen, 1969), p. 25.
3. R.D. Laing, The Voice of Experience (London, Allen Lane, 1982), p. 11.
4. Adam Phillips, Promises Promises (Faber & Faber)
Published on 1 July 2002
Mark Patrick Hederman is a monk of Glenstal Abbey in Limerick. He was a founding editor of the cultural journal The Crane Bag. His latest book is Anchoring the Altar: Christianity and the Work of Art.