COMPUTATIONAL TECHNIQUES IN MUSICAL ANALYSIS
Dr. Jim Kippen
Department of Social Anthropology The Queen's University, Belfast
BICA Issue No. 4: March 1986
Recent ethnomusicological research conducted at The Queen's University by myself and in Aix-en-Provence by the computer scientist Bernard Bel, has focussed on the development of new methods for social anthropological analysis of musical systems. The essential problem concerns the use of computational techniques in discovering the structures of musical systems as they are perceived and interpreted by performers and audiences. Ethnomusicology has opened up alternative methods of analysis that avoid the more ethnocentric approach of conventional musical analysis by attempting to formalise the `folk view'. Yet participant observation and dialogue with informants do not in themselves guarantee that an investigation will be anything other than a personal reconstruction of music and music-making, or that its results will be invested with a scientific or universal applicability. Following Blacking's lead the present research attempts to go beyond the a personal Ethnomusicology towards a scientific dialectical Ethnomusicology whose ultimate aim is to identify the cognitive processes involved in the creation, performance and appreciation of music [(.blacking ellis dialec.)]. Three requirements must be satisfied: experimental situations should be context-sensitive; the experiments themselves should be repeatable and verifiable, so conforming to a rigorous scientific mode of enquiry; and informants should be involved in the research as co-workers and analysts, establishing what Dorothy Emmet has called `a more colleague-like or even apprentice-like relationship' [(.emmet motivation sociol{:\085}.)].
Earlier doctoral research [(.kippen tabla lucknow.)] suggested that an ideal subject for such an investigation was the North Indian tabla
(two-piece, tuned drum-set). Its music is highly structured and is orally transmitted by means of a meta-language: a set of mnemonics both indicating drum strokes and imitating their sounds. The solo repertoire of the instrument comprises several categories of fixed compositions and themes designed for improvisation. The logical starting point for an analysis of tabla music is a category known as qaida
which, musicians believe, constitutes the very basis of composition and improvisation in tabla playing. Qaida means `rules' or `system', and implies that sets of variations on a rhythmic theme (also called qaida) are created spontaneously using systematic methods such as the permutation, substitution and repetition of its component parts. The first qaida studied was a well-known and structurally simple piece whose essence is contained in the musical phrase
dhatetedha tetedhadha tetedhage dhinaghina
The syllables used here (dha, tete, ge etc
) are known as bol
(s) (from the Hindi/Urdu verb bolna
meaning `to speak') and have no semantic meaning.
It is beyond the scope of this short article to attempt to define the complex structure of the theme or the various methods used to create sets of `variations'. A detailed account may be found in {(.kippen dialec tabla.)}. However the gist of the process may be understood (at the risk of gross over-simplification) with the following example. The component parts of the sentence `My name is Jim' may be permutated to form other sentences that are also grammatically correct. These are: Jim is my name.
Is my name Jim?
Is Jim my name?
However, a number of rearrangements result in ungrammatical constructions: My Jim is name
Name is my Jim
and so on. In the same way tabla players differentiate between variations that are grammatically correct and incorrect, often employing the term `grammar' or its Urdu equivalent qavaid
(itself related to the word qaida) in their comments. It is therefore perhaps appropriate to think of tabla music as quite literally a language with its own logical rules of construction.
An outline of the analytical process may be stated quite simply. The researcher builds representational models of musical structure based on available musical and verbal data provided by the informant. To test the validity of these grammatical rules, the researcher generates strings of bol(s), so creating operational models. New strings are then presented to the informant who assesses their correctness and quality, and who advises the researcher when something is not quite right. Haing established the nature of any weaknesses the representational model is revised and the experiment begins again. This dialectical process continues until all the pieces generated by the model are considered to be correct.
For an elementary grammar, simple observation reveals that whilst it is possible to permutate certain components of the original `sentence' of the qaida, such as `dha' and `tete', others must be located at specific points within the rhythmic cycle in which the qaida is performed. This suggests that the structure of the composition may comprise several layers of building blocks, each with its own specific sets of rules. Sentences may therefore be divided into two main building blocks: the first is an apparently free arrangement of the components `dha' and `tete', while the second is a fixed pattern that functions as a kind of cadence `dhagedhinaghina'. However, in some variations the cadence may be truncated or suppressed altogether thus creating additional space for `dhatete' patterns.
At this point it is possible to represent the multi-level structure of any given variation of the original sentence as a directed graph or tree. The `leaves' attached to the terminal branches are the bol(s) themselves. The nodes represent higher-level building-blocks.
Similar derivation trees are commonly used to describe the syntax of sentences in English. As Richard Kain has shown: The meaning of a string can be made more evident by its derivation tree if the grammar is constructed so that each non-terminal symbol represents a `natural unit' of the meaning. In natural English, these units are `noun phrase', `adverbial clause' and so on. In programming languages, the units represent the results of individual sequences of computations.
The tree in Fig. 1 represents nothing more than a static description of a single variation. This may have some theoretical value but is useless from a practical point of view. Consequently it is necessary to create a dynamic
operational model that can encompass all possible variations of a given qaida. When this is represented in graph form each branch signifies a possible derivation of a nonterminal symbol placed at the node above. To display a complete dynamic model here would be unnecessarily cumbersome. However, the principle may more easily be explained in a graph restricted to an illustration of decision-making processes relating only to the cadence:
In order to create a variation a path must be followed from the uppermost node downwards towards the leaves of the graph. Nodes encountered en route represent intermediary stages of the computation where decisions must be taken regarding the direction of the next stage of the journey. The total number of possible paths will be the same as the total number of possible variations. A formal representation of a language must not only be able to describe paths which lead to correct sentences but must also be capable of determining whether or not a given sentence is grammatically correct. If the sentence is correct (in other words, if it belongs to the language) then a path may be traced upwards from the leaves to the root node of the graph. This path will be unique if the language is unambiguous.
Naturally, the decision as to whether or not a variation is correct lies ultimately with the musician. The models described above may generate thousands of possible variations but, as with the permutations of `My name is Jim', only some will be grammatically correct. Thus, to avoid literally hundreds of hours of painstaking checking and cross-checking musical data and derivation rules, a method was needed to speed up the process of analysing and generating variations. The success of experiments in the field depended on reducing the calculation time to a matter of a few seconds. Fortunately Bernard Bel pointed out to me that a dynamic model of a language may also be realised as an automaton (or machine) programmed both to generate strings of symbols using sets of derivation rules, as well as to analyse strings in order to test their compatibility with the rules. Automata theory links the concepts of `machine' and `language' in such a way that the former may be seen as an equivalent but dynamic description of the latter. Early in 1984 such a machine was created: a computer system known as the Bol Processor incorporating an elementary grammar for the qaida mentioned above [(.kippen linguist rhythm.)]. The software is designed for use on the Apple II series, the IIc being ideal for transportation during fieldwork.
The Bol Processor makes use of computational techniques which form the kernel of `expert systems'. In brief it is an artificial intelligence system based on a modified form of word-processor. It comprises an editor for entering, correcting and deleting data, and incorporates a sophisticated `find-and-replace' feature. Derivation rules instruct the machine to search for a particular string of symbols and to relace it with another string. For this reason they are also called `rewriting rules'. Controlling the entire process and selecting which rules are to be tested by the machine is a unit called an `inference engine'. More detailed information on the Bol Processor will follow in future publications.
The Bol Processor has two functioning modes: analysis and synthesis. The grammar of the composition is in fact composed of several sub-grammars: that is, sets of rules which effect a series of transformations from the most abstract level to the most concrete, or vice versa. In the analysis mode the bol(s) of a given piece are transformed into `intermediate symbols' which are then reduced to abstract `starting symbols' representing the type of composition or variation to which that piece belongs. In synthesis mode the process is reversed: `starting symbols' are transformed into `intermediate symbols' which are then transformed into tabla bol(s). Each computation takes just two to three seconds.
The techniques used in this research are still at an elementary stage but it is hoped that their further development will facilitate a reconstruction of the symbol system of tabla music. Essentially the Bol Processor is being used like a toy. By simply playing with the automaton it has proved possible to translate intuitive ideas about musical structure into unambiguous formulae. This has already led to a more accurate description of tabla music than has hitherto been achieved, and the implications are that in future it will be possible to make more meaningful comparisons with other tabla `dialects' and related drum and dance languages.
As stated earlier, this research attempts to investigate the cognitive processes used in the creation, performance and appreciation of music. Seymour Papert has explained that machines not only make such an investigation possible but also benefit from the interaction with human beings: `In artificial intelligence, researchers use computational models to gain insight into human psychology as well as [to] reflect on human psychology as a source of ideas about how to make mechanisms emulate human intelligence' [(.papert mindstorms {:\0164}.)]. Such interactions give greater prominence to qualitative judgements rather than to formal descriptions. For example, the researcher builds into the system a formal model in the shape of a grammar. Once the system is in operation the researcher is free to concentrate on observing human decision-making processes and need no longer be concerned with the formal model. Through the wider application of computational techniques in developing the study of human processes, cross-cultural comparisons become possible with other musical systems in which radically different products arise from similar processes (or vice versa).
So far this research has perhaps raised more questions that it has answered. For example, will these analyses really prove to be psychologically as well as structurally valid? Will such techniques be easily adaptable for the analysis of strikingly different musical systems? And will informants in general accept this degree of technological interference in their particular musical domains? If we are to begin to answer these important theoretical, methodological and practical points, much rests on the ensuing stages of this work.
Return to Contents page
