Predicting the Unpredictable The Unpredictable in Music The Meaning of Music What is Music For? Ask a group of people the above question and the most likely result will be a look of bafflement. What does the question mean? Why ask it? Isn't it obvious? Press the matter further and obviously the result will depend to some extent on the people you ask. Music as a Product of Culture Conventions in Music Music is more like the law than a science One thing that Hofstadter tries to do is to make direct links between, for instance, the way we see a paradoxical Escher etching, how we respond to mathematical paradoxes, how these illusions illuminate elements of how we think, and how we can map thoughts into language and so on. His references to music - specifically the music of Bach are not of principal importance in the book. Indeed, from Ultimately, of course, no matter how some people would have it, music is not a science in any way shape or form. Cf Lewis Wolpert Like the law, most of musicology would suggest that rules change as do laws, according to fashion and common opinion, as well as, perhaps, a few general precepts that are generally accepted. As people behave, so is their behaviour reflected in law and so, for instance, there is the principle that only those laws that are practically enforceable are reasonable (in the sense that should a law be introduced that the majority of a population were not prepared to obey, it would be virtually impossible to enforce). Similarly, music must abide by certain conventions in order that it should be understood by an audience, but those conventions are liable to change and development according to the audience involved as well as the function of the music. In this way, it could be seen that western 'popular' music changes and develops according to the audience (large and not necessarily musically sophisticated) in conjunction with its function(s) - variously and arguably, to make money, to communicate day-to-day and straightforward social and personal information, to provide social cohesion to various (and usually young people's) sub-cultures, to provide an escape from life's mundaneness. Because of these factors, 'popular' music changes relatively slowly in terms of its use of musical language, but quickly in terms of its perceived 'fashionability'. Alternatively, music of the Western European Establishment with a relatively small audience and functions that are generally less practical than those of popular music, has the ability to change slowly but radically and to cover within a relatively short space of time, a wide range of musical 'dialects'. (The above comparison is made assuming that we may include what we currently call broadly 'popular' music is a continuation and development of what has been called 'folk music' - if this is not included, then if 'popular' music needs some additional definition...) If music is a set of conventions rather than a set of rules, as in mathematics and logic, and if the rules governing mathematics and logic have been found to be, at least potentially liable to fault, (admittedly under the extreme circumstances predicated by ...Godel under Typographical Number Theory), then how much more vague and undefinable must be the voluntary conventions used by musicians motivated by such varied and scientifically rather irrelevant desires? Music of the Tradition of the Western European Tradition What is it? What differentiates it from other types of music? Notation Performance Money Notation of the Music of the Tradition of the Western European Establishment According to many, usually rather unformed, opinions, music - or at least 'serious' music (why haven't these terms been properly defined yet?) -or at least, the Music of the Tradition of the Western European Establishment, is and has always been inherently 'pre-defined', or notated at least to some extent. Indeed, this is what has often been thought of as one of its major distinguishing features. Unlike many, and probably the majority of other sorts of music throughout the world, whether belonging to a classical/establishment tradition or not, that of Western Europe has shown particular distinction in the quality and precision of its notation. Students of this tradition spend many years, should they wish (and all too often should they not wish), learning its details, precisions, imprecisions, probabilities, fashions, its strange, illogical and often contradictory 'rules'. The balance of these will have depended on their circumstances and time of birth within the past thousand or so years of this tradition's notational development, in much the same way as a young English lawyers(and, I imagine, young lawyers of most nationalities) have to learn the intricacies of Jurisprudence which have developed and matured over many years of testing experience. (This may well be especially the case in those nations who have no written constitution or bill of rights - these latter acting as a more strict set of rules which do not change for as long as they remain valid -although even here, these strict rules are often so vague as to be easily argued over and severally interpreted.) When attempting to answer a particularly obscure question concerning notation I often find myself pausing thoughtfully before commenting that, well, x would have probably done so and so, but this isn't really considered proper any more. Now, we'd be more likely to do it in this way, like y. Ultimately, as we have no courts of law, our opinions are neither confirmed nor denied by the comments of judges officially appointed for this duty, but we can, should we wish, nod our heads to the twin Magistratesof practicality and legibility. This, certainly, is my general opinion, although it can mean creating a notational compromise between exactitude, fashion and intention. This is not in itself a particularly serious situation - just one of many in music (and life) where a number of factors have to be born in mind and where there are no precise rules. However, it is an example of the fact that the system involved here is subject to imprecision and interpretation. The Relationships between Music and other Media As musicians, or as students of music, we often either praise or slander ourselves or others by equating music to other media - languages, mathematics, logic, geometry, literature, the graphic arts, even, as above, the law. This, I suppose, is because music is inherently abstract and so inherently liable to interpretation through metaphor. Indeed, it is in the nature of abstraction that it may well be impossible to interpret or even discuss music without the use of such metaphors at some level or other . (For instance, can we really explain or justify a piece of music on the basis of its form, no matter how precise, complex or convincing our analysis of it? By definition, we must generally use words, symbols or other conventions.) How reasonable is it to equate Music with other media or forms of communication? Is there any reason for doing so, or does it merely reflect a dissatisfaction with Music and its abstractions? Do people other than Musicians make such relationships - they clearly do as poetic, scientific and graphic illusions to music are everywhere - and what do these allusions say about how other s feel music to be, Are there differences between Musicians of what their language/art/craft is about or what it is for? Music and Language Musical Allusions in Literature Is Music a Language The Literature of Musicology Music and Graphics Music in the Visual Arts As notated is graphical, or at least typographical in nature, there are clearly strong links between these two media. However, first it may be worth surveying links the other way - the allusions visual artists have made toward music and what this may say about their attitudes. Notation is a form of Graphics Alternative Notations Mapping Music onto Graphics Music and Science There are many allusions in both directions within this relationship. For instance: Hofstadter Douglas Hofstadter's book Godel, Escher, Bach - An Eternal Golden Braid has proved one of the most influential of recent times and has been one of many attempting to form links between different disciplines and media and attempting through these links to draw conclusions about subjects as vast as the way we think and the nature of reality. This is clearly beyond the scope of this thesis but I would firmly recommend anyone with an interest in these (and virtually any other area) to read it. Wolpert Dawkins Swift (Literature or Science?) Pythagoras The Quadrivium: Geometry, Logic, Arithmetic and Music (From Encarta) Seven Liberal Arts, in education, subjects of the ancient and medieval curriculum; grammar, logic, rhetoric, geometry, arithmetic, astronomy, and music. The distinction between the liberal arts and the practical arts originated in Greece. According to Plato and Aristotle, the liberal arts are those subjects suitable for the development of intellectual and moral excellence, as distinguished from those that are merely useful or practical. The Greeks assigned no definite number to such liberal arts, however. The first encyclopedic discussion of the seven liberal arts was that written in the 1st century BC by the Roman scholar Marcus Terentius Varro; he also wrote books on the more utilitarian arts of medicine and architecture. The seven arts, as studied during the Middle Ages, were known chiefly through writings of the 5th to the 7th century AD, notably the works of the Latin writer Martianus Capella (lived about 400-439), the Roman historian Flavius Magnus Aurelius Cassiodorus, and the Spanish scholar St. Isidore of Seville. The medieval course of study was divided into the elementary trivium and the more advanced quadrivium. The trivium comprised grammar, which included the study of literature; dialectic or logic; and rhetoric, which also covered the study of law. Completion of the trivium entitled the student to a bachelor's degree. The quadrivium comprised arithmetic; geometry, which included geography and natural history; astronomy, to which astrology was often added; and music, chiefly that of the church. Once the quadrivium had been completed, the student was awarded a master of arts. The term liberal arts is now often used for the unspecialized, nonscientific studies pursued in an undergraduate college. Can Other Media Illuminate or Inform Music? Changing the Focus So, when one is challenged with the idea that such and such a music is 'mathematical' one is left feeling rather weak and helpless under the weight of many years of conventional and immature musical opinion. I would now propose to re-focus this discussion specifically on certain issues: I will deal specifically with music from the TWEE (that is, the tradition of the Western European Establishment), because of its principally abstract nature, and because, due to this, at least a part of the art of composing in this tradition has been a typographic one - that is, it is involved with the manipulation of the symbols by which it is itself expressed. This decision is based on the arguments mentioned above, that notation is, arguably, the basis of TWEE music's sophistication and that other forms of Western European musics are not as sophisticated notationally. It is possible to see substantial differences between the notations of TWEE composers of, say, three hundred years ago, and those of, say, ten years ago. We should ask two questions here: 1 How much do differences in notational convention express true differences in musical thought? 2 How substantive are such differences in notation in terms of these potential differences in musical thought? Broadly speaking, there has been an increase in the precision of notation over this period. If one considers some of the earliest examples of musical notation - the 'roots' of this tradition - for instance, Gregorian Chant, one can see that in many respects they are more similar to what we would now consider to be other traditions and cultures. The notation is principally there to communicate enough to enable a group of people to perform essentially the same thing. However, much of the precision that we may now teach as essential in composition appears to be entirely absent, such as precise rhythms, dynamics, etc. However, with regard to our two questions above, how different in musical thought are these chants from our current idea of TWEE music? In one way, of course, they are substantially different, at least by most accounts. We are not including in our theory the part that the church played in the life of those who performed it or those who heard it. Undoubtedly, the fact that these chants were functionally a part of liturgy means that they cannot be compared precisely to more modern TWEE music. Also, it is likely that those lay people who experienced the chants would have had some knowledge of melodies beforehand. Once again, the 'originality' that is so much a part of TWEE music for the past few years is not important. Instead, it may well have been that the chant's unoriginality was a bonus point in drawing the listener (worshipper) into the event, much as nowadays the inclusion of a 'famous' melody in an 'original' piece of music may give the listener a welcome point of reference. Similarly, a few hundred years later, music's position in society had once again altered. In the baroque era, the church was less important as a patron of the art as it had been - others, including the aristocracy, civic authorities and academies were substantial contributors to what was still, however, an art that was substantially for the wealthy, educated and privileged. During this era music was notated in a way that was considerably greater in detail than most earlier examples. This would have been due, once again, to a combination of factors - the various reasons for the music's existence, (money, patronage, event, audience) as well as the interests and intentions of the composer. Does the increased use of notation indicate a greater sophistication on the behalf of the baroque composer? Does it indicate merely an increased sophistication in the use of notation? Does sophistication of use of notation on a composer have any effect on the sophistication of their musical thought? The above questions are similar to those arguments suggesting that we cannot imagine what we cannot describe in words and so our ability to imagine is related to the extent of our understanding of language. Leaving these questions aside for the moment, (some of them may be left aside for longer than that!), we may ask, however, in what ways a typical piece of baroque music may be thought of as imprecise in its notation. There are, for instance, many instances in Bach where there is little or no urtext evidence of tempo or dynamics. There are a few practical reasons for some of these deficiencies - there isn't much point in including dynamics on a part of an instrument which cannot play those dynamics, for instance the harpsichord. On the other hand, in a typically musician-like illogicality, Bach would have no problem in writing notes for the harpsichord that would be wholly impractical in terms of their sustainability - they are there for the rather esoteric reason of properly defining a particular part. And what are we to make of lack of tempo indications in so much of Bach, Monteverdi, and many other composers of this time? From our current perspective it seems a rather shockingly negligent approach, even if, as presumably was the case, if was conventional at the time for performers to be able to ascertain from certain features of the music what the most likely tempo was. Once again, what are we seeing - a naiveté, a lack of clarity, a lack of need? Certainly, if the practice of employing editors to 'interpret' Baroque music for us over the last century is anything to go by, if those for whom the music was written had this 'intuition' then in has gone in all but a few specialists. Of course, it could be argued that this was and indeed still is the case, that as long as your performer or director knows the convention, the rest will follow and so it is not necessary to go into greater detail. But it that were the case why is the music much more detailed and precisely notated than any music that went before it? Haydn and Mozart, especially in their later works, were far more likely to included both tempo and dynamic information much more freely. Indeed, although the latter are often rather rudimentary by today's standards, and were sometimes somewhat perfunctorily applied, (once again, the recent editor has made much money out of this), in general this music is now approaching what we would call acceptable in today's precision-aware era. Even so, the markings are sparse and somewhat vague in comparison. For instance, we are commonly faced with an Adagio introduction followed by an Allegro main movement followed by an Andante or Andante Molto slow movement. A last movement might be Presto or in some cases Allegretto. These are clearly not going to be all the same tempo. Indeed, Andante is sometimes used as a tempo considerably faster than Allegretto, sometimes considerably slower. Once again, convention needs to be used to interpret these indications. And now an additional factor comes into play with far more importance. Although it was always present as an anomaly, the use of different sorts of basic pulse to indicate certain conventional tempi comes into its prime in the classical era. Ask an American student of music what a crotchet is and you may well receive a blank stare as a reply. You may well find yourself thinking how quaint the American system of nomenclature for our basic duration units is - or maybe the reverse, how quaint the system that includes crotchets, minims, semi-breves, etc is compared to the New York grid-like logic of half and quarter- notes. However, follow the American logic through and you come across a problem - their whole note is equivalent to our semi-breve, a term which translates into English as 'half-short'. The 'short', upon which this whole system seems to rest is, therefore, the breve, or a note twice as 'long' as a semi-breve, or eight crotchets... or twice a whole-note. This strange anomaly typifies the situation. Rather like inflation which has gone on so long that previous currency denominations are meaningless - for instance the French millime(???), the Italian..., and the English farthing, the breve which was once the shortest note, is now not only the longest but in most cases is so long that outside historical transcriptions and music written to appear in some way archaic, (the ... of Brahms German Requiem) it is almost completely unknown. What, then, are we to make of composers who use these divisions in such completely, apparently, illogical ways - or worse, possibly, to use them conventionally to make a point? What do these conventions mean? Do they indicate a greater level of sophistication, or a greater level of musicianship? Why are such illogicalities used, or in terms of music teaching, allowed or even encouraged? Do they help make the music clearer and more defined, or less so? The answer would appear to be somewhere in the middle. They help to define the music if you happen to be aware of the conventions involved. A problem is, of course, at what level do these conventions have to operate when they become a help to definition. If I decide on a new form of notation which, as far as I am concerned is considerably clearer than any I have previously experienced, this will not help the poor performer, who finds it virtually impossible to read and has neither the time nor the inclination to learn - clumsy and complex thought it may be, but at least the conventional version is known back-to-front and has the ability, although probably rather limited, to expand and develop. Who wants to learn a whole new system for one new piece? The Intention of Composition: Practicality, Legibility, Exactitude and Fashion