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Intelligent Musical Instrument Systems

Dr. Peter W. Farrett

Introduction

This article examines two important areas in the computer music research literature concerning Intelligent Musical Instruments (IMI): knowledge-based systems (KB), and knowledge representation issues that surround those systems. My article will focus on a knowledge-base design with respect to musical systems; a survey, which examines some of the components that are "core technologies" of IMI research; a critical assessment of important principles for the Knowledge Engineer regarding IMI. This article is directed at the computer music specialist, and assumes some familiarity with music composition and theory, and artificial intelligence. However, general readers should be able to understand the overall discussion. A glossary of terms is also provided so that unfamiliar terms can be understood.

IMI Schema

Because the field of music KB systems is small compared with its academic/industrial counterpart (implying a less well-defined methodology), IMI specification should model perhaps the more traditional KB approach. KB systems are a sub-discipline of artificial intelligence (AI), and an amalgam of database technology, formal logic, expert systems work, and natural language processing {Frost,1986}. This synthesis is easily grasped when one considers the simple dichotomy of a KB system:

Definition 1: "An information system consists of two parts: a knowledge base, which contains information about a universe of discourse, and an information processor (inference engine), which can manipulate, in well-defined ways, the contents of the knowledge base" {Jardine,1987}. This can be translated into a definition for an IMI: Definition 1': An IMI is the knowledge representation of musical concepts and the (logical) manipulation of those concepts. Paraphrasing Max Mathews {Roads & Strawn,1985}, a further definition may help (with notes):

Definition 2: The nature of an intelligent instrument:

  1. It can synthesize sounds and sense the intent of the musician (interpreting creative performance).
  2. It can remember and execute a program (knowledge base/data base technology).
  3. It can act as a Composer's tool (score I/O, natural language processing, etc.).
  4. It is a computer. The program computes aspects of the music using its own rules, reads other aspects from a score the composer has put into memory, senses still other aspects from the performer, and combines all of this information in limitless ways to create music (a mixture of formal logic, cognitive modelling, and knowledge acquisition).

Applying definitions 1, 1', and 2 to a final definition for a IMI/KB system, the salient features are:

Definition 2': An IMI/KB system consists of:

  1. A quasi natural language front-end (or language handler) whose main function is to process musical expressions.
  2. A knowledge base, which consists of musical facts (static or dynamic).
  3. A logical inference mechanism that allows for some kind of reasoning about musical facts, events, processes, etc. (i.e., a deductive system).
  4. Although there are differing opinions concerning intelligent instruments systems, the above definitions illustrate a particular viewpoint: the components resemble knowledge base concepts and techniques. If one accepts this translation, then it seems desirable that a schema for such systems consider issues within the framework of knowledge engineering principles. I will approach my paper from this perspective.

Components of IMI: A Survey

Knowledge Representation

Some of the general choices and considerations when defining a representation for a musical system involve views, perspective, and classification of musical objects. Facts, properties, and events are commonly viewed as musical abstractions that often depict diverse relationships. These abstractions, in particular, have been popularized by two views: the hierarchical and the relational model. The hierarchical view (structure), has been discussed at length in the computer music literature {Buxton,1978}, {Tenney & Polansky,1980},{Balaban,1988}. Typically, the structure is viewed as a hierarchical scheme where one composes music in a tree-structured format. As a representational scheme this seems to have merit, but possibly lacks an intuitive appeal since a rigid approach to composition seems to be enforced; this suggests that a dynamic taxonomy of objects would be a more flexible alternative. Relational views have been mentioned in {Roads & Strawn,1985},{Laske,1981},{Rubenstein,1987}. Musical entities and their attributes are defined by a set of relations. The is-a and frame relations view the musical process as a decomposition of musical activity into modular components. This perspective has been a prominent representational idea in the literature, particularly semantic-like networks {Laske,1981},{Roads & Strawn,1985}. Perspective and classification of musical objects, however, is more opaque with respect to representation. While music theorists and composers belabor musical significance, the representational issue is mainly one of choosing an abstract level: What is the desired level of representation for (conceptual) musical facts, events, and processes? Is the representational view contingent upon domain-specific descriptions? Balaban {Balaban,1984} refers to this problematic area as "the common denominator type", and suggests that the desired level of representation is dependent on common terminology found in musical text books (i.e., as a form of vocabulary representing theoretical Western tonal music). Indeed, as Balaban points out, a musical object that seemingly appears naively simple from an intuitive viewpoint often is quite problematic concerning categorization. For example, consider the following staff with the information illustrated in figure 1:

Figure 1

What is the correct interpretation? Seven notes? Two groups of (quintal) chords? Screen coordinate x-y values?

The ability to view musical objects from multiple perspectives is also tantamount to the representational issue. For example, Roads {Roads,1985} suggests that an inversion or transposition for a chord represents a different perspective on that same musical object. What is at issue here is extension vs. intension. A chord's properties (intervalic content) represents extensional values while an inversion denotes intensional meaning. A two-tier approach to any representation-level emerges: an intensional one (the meaning or interpretation of an object) and an extensional one (specific values). The lowest level of representation would perhaps imply an extensional one, while higher symbolic abstractions would imply a musical intension.

The use of knowledge engineering methods help to explicate musical facts, processes, and events. Recently, Laske {Laske,1988} has emphasize the importance of this discipline for problems in knowledge acquisition. Knowledge engineering is, perhaps, one of the best ways to help codify musical primitives because the expert's knowledge can be organized and transcribed directly. This has been severely neglected in the literature, as Laske points out.

Declarative vs. procedural knowledge representation is represented in the literature by numerous examples. Although Minsky {Minsky,1981} and Laske {Laske,1981} have elegantly argued for procedural representations as a means for understanding task-dependent musical activities, and few have disagreed, implementations abound that seem to suggest otherwise {Levitt,1985},{Tobias,1988}; the implication is that procedural representations are not necessarily the best approach concerning modelling. This general issue, whether knowledge should be contained in procedures or facts (programs vs. databases), however, is considered by Roads {Roads,1990} as a distinction that is not significant: "The declarative/procedural debate comes about with the traditional dichotomy between a passive database and application programs that extract information from the database. Object-oriented programming disposes of this dilemma; in fact, data are active objects, the database is a program. The distinction between data and procedure is not significant".

Developmental Theories of Knowledge Processing

Minsky's work {Minsky,1981} attempts to examine musical understanding from the mind's rationalistic point of view. He considers music as a psychological vehicle in order to determine how people process musical phenomena. Minsky's speculative theory views the sonata-allegro form as a demonstrable structure with respect to a trichotomy of cognitive functions:
  1. Exposition as an introduction to atomic understanding in the sense that basic musical units serve as an explanation of some idea.
  2. Development used to construct compound information from lower-level atomic material which can clash or merge, contrast or join.
  3. Recapitulation to review in the mind what has consciously been stated.

Minsky views this analogy as a way to describe musical semantics: "A thing or idea seems meaningful only when we have several different ways to represent it - different perspectives and different associations" {p.29}. This idea of meaning as defined by several perspectives is important. This would imply that in order to gain a musical "awareness", different instantiations of a problem could serve to understand a musical context. (See {Riecken,1989},{Smoliar,1989} for more recent work that incorporates Minsky's theories about computer music applications.)

Otto Laske has pioneered the field of AI and music since 1968 {Laske,1972},{Laske,1973} and has been one of its chief architects. His work on formalizing musical knowledge {Laske,1981} has influenced numerous practitioners. Laske views (musical) knowledge engineering as a methodology that includes an orderly sequence of steps:

  1. The elicitation and analysis of knowledge.
  2. Modelling in some implementation-independent form.
  3. System design.
  4. Implementation in the form of a knowledge base.
Laske acknowledges that this approach to knowledge engineering is fundamentally a two-phase process: knowledge modelling and knowledge implementation. He further states that an intelligent computer music system should be able to serve both as a knowledge acquisition device, and a compositional assistant for a particular type of composition. For further discussion of knowledge processing concepts related to musical activities, see {Leman,1986},{Bharucha,1988}, {Vercoe,1988},{Albright,1988},{Kugel,1988},{Laske,1988,1991,1977}.

Formal Logic

Intelligent computer music system design usually involves formal logic; therefore, the study and application of formal logics is important. This is also important in the area of music knowledge representation where logic formally represents underlying musical structures. Xenakis {Xenakis,1970} has defined the role of a logic for symbolic music as sonic events (sounds are statements or propositions), which can be inter-related by algebraic laws and relations among events. He describes "laws" for sonic events, and also defines mathematical relations. A structure for a sonic event (pitches) consists of:
  1. Structure outside-time (pitch, intensity, and duration without context).
  2. Temporal structure (a correspondence between events and non-events).
  3. Structure in-time (the relationship between 1 and 2).
Xenakis states axioms for pitch (describing the origin, note, and successor) influenced by logical axioms for arithmetic. He concludes with a brief discussion on the logic of classes with respect to music composition.

Charles Seeger's Music Logic {Seeger,1981} is a synthesis of aesthetic aspects of musical order coupled with mathematical rigor. Laws of musical thought (also known as a Speech Logic) are based on an Aristotelian viewpoint, and comprise various notions found in Seeger's discussion for a logic. Seeger derives various types of musical expressions from the logic, which are "moods" that depict a musical context. The music logic, it should be noted, is more a formal representation of a musical environment, and less of a logical system. (See {Blevis,1990} for a more detailed analysis.)

The relation of logic and set theory with respect to music theory is explored further by Rahn {Rahn,1979}. He views formal logic, a calculus of intelligible declarative statements, as a means in which to communicate a tonal music theory. Rahn discusses a tentative foundation of a music theory, and suggests that such a theory should be a construction of axiomatic set theory, predicate calculus, a minimum of a few musical primitives, and the addition of two predicates that denote the properties of pitch and time. Rhan does not attempt to put this in a deductive system, but maps musical definitions into their formalized counterparts.

Mira Balaban {Balaban,1988} has developed a calculus for describing a hierarchical view of music called music structures. A logic is used to represent and to reason with temporal knowledge. The logic (time-structures) {Balaban,1987} views a musical score as a timed collection of sonic events along a time scale (i.e., a music piece is time-stamped). It is developed further to incorporate the TTS language, a formal language for music description, and includes specialized time functions that compute temporal properties of music structures. Balaban developed music-structures to account for the structural view of music and its independent subparts. The logic of time-structures constructs hierarchical expressions that combine musical statements with respect to time intervals.

Another theoretical application of mathematical logic, in the modal and temporal domain, is discussed further in {Kunst,1976}. Kunst describes the notion of musical well-formedness (in the abstract) as a musical law with the following property: "a music's behavior is law-like iff it behaves as it always did in the past" {pp.9-13}. Kunst describes a fundamental property of music in accord with an elementary model that can be interpreted as a branching time; a musical formula, given some time-line, has a past and an implied future. Preliminary musical axioms are postulated in accord with the usual definitions for modal operators. Kunst gives a possible worlds example in which worlds are traversed, and success is obtained if a path leads to a musical solution. Since a musical listener travels through worlds past and future, a revision of ideas can occur. This suggests an intensional property, since meaning is based on the listener's reflection, and is interesting with respect to the notion of capturing dynamically changing musical information. Kunst's application of a logical system is successful; this is a good example of the synthesis of mathematical logic and music. Kunst was the first to apply (modal) logic to musical knowledge representation. (See {Laske,1981} for further analysis.)

Systems

Expert Environments

Expert System (ES) engineering, in the current computer music literature, investigates the role of the composer's assistant. In music tutoring systems or aids for musical interaction, it can be argued that many of these systems perform a similar function in the sense that they act as an assistant. Roads {Roads,1985}, Scheidt {Scheidt,1985}, and Loy {Loy,1987} (among many others) have discussed such a concept, and examples can be found in {Pope,1986},{Roads,1981;1983}, and {Scheidt,1985}. Several systems that also act as a musical assistant include {Sorisio,1987}, {Tobias,1988},{Fugere et al,1988}. In this section, I concentrate on systems that perform expert-like decision making mindful of Roads' {Roads,1985} remark: "the capacity for inference would lead to a truly powerful composer's assistant" {p.173}.

One of the earliest programmed environment for knowledge acquisition was OBSERVER {Laske,1991},{Laske,1979}. Laske and Truax's motivation is predicated on a problem-space for melody in which one can discern strategies of compositional thinking. Their goal is a performance model of melody composition by children. OBSERVER was highly successful at the attempt to monitor, by a computer, a subject's problem-solving tasks

A different approach for ES exploration is taken by {Camurri et al,1988} in their prototype of an AI tool for music knowledge representation and music composition. Key-Music, an expert system for music composition, is based on a knowledge representation scheme of inheritance networks, which are semantic frames that store definitions about musical timed processes. Key-Music can be considered as as composition tool. An example of a fugue that demonstrates this approach is given; their representation of the fugal process is correct since they hardwire the fugal exposition, but leave out the more nebulous development and recapitulation sections. (If one takes the Bachian style as the model, then one cannot successfully model other sections since there is no specific schema.)

Another ES environment is examined by Ebcioglu, and discussed in {Ebcioglu,1986}, and further extended in {Ebcioglu,1987b}. Ebcioglu describes the chorale via 270 rules, represented in the form of a mathematical calculus, and his application of musical heuristics produces better musical solutions. (See, for example, his motivation for constraints and heuristics {pp.128-130}.) Ebcioglu's theoretical contributions can be summarized as follows: The formal investigation of intelligent backtracking, which includes a new and efficient logic programming language (BSL or Backtracking Specification Language), and multiple viewpoints of the Chorale. Briefly, intelligent backtracking is a mechanism that was developed for the multiple views of the Chorale model. For example, when a step of the chord skeleton view fails, it must backtrack to the previous step of the chord skeleton view, which may not be the immediately preceding step. Ebcioglu describes this as an "intelligent backtracking heuristic", and incorporates this in the design for BSL. Ebcioglu's work is one of the most successful attempts at the non-trivial problem of music generation in the Schenkerian/Bach style. (See {Ebcioglu,1987b} for analytical details, and {Lischka,1986},{Thomas,1985} for other approaches and comparisons.)

Laske's KEITH {Laske,1984} is the design of a rule system for music analysis tasks. It is based on empirical evidence deriving from a talking-aloud protocol of student experts in music analysis. (Keith is the name of a brilliant student analyst.) Laske takes Debussy's composition Syrinx as the material for protocol analysis. The protocol comprises a notation-based as well auditory analysis of Syrinx. The user is instructed to verbalize their reasoning efforts: "Tell me what you are doing, doubts, etc., not only your results!" {p.506}, in the form of a running dialogue, locksteped with simultaneous musical actions. The user is also asked to provide the experimenters with notational sketches that describe the parametric development and structure of Syrinx, for the purpose of comparing them with verbal traces and notational annotations. What emerges is the control structure of an intelligent music analyzer. Although KEITH is highly exploratory in nature, Laske has envisioned a system that is the very essence of the Composer's Amanuensis. Other recent ES work can be found in {Maxwell,1988},{Ames,1987}.

A successful approach that incorporates a grammar historically used in natural language parsing systems is David Cope's {Cope,1988} EMI system; Experiments in Music Intelligence (EMI) is an interesting expert system. Cope uses an Augmented Transition Network (ATN) for parsing, based on an earlier syntactic formalism of Woods {Woods,1971}. The ATN formalism, in turn, is decomposed into a system that is based on a Schenkerian model where rules produce elements of "style syntax" or a particular compositional palette. However, at no time is the composer constrained with a certain style syntax. Thus, rulebase, dictionary components, and Lisp definitions (the language chosen) can all change. Cope's application of ATNs is an effective generative mechanism for producing music of many diverse styles. Cope lists numerous examples of particular composer genera including Mozart, Bach, and Bartok in {Cope,1987},{Cope,88}.

An area that applies case-based reasoning {Riesbeck & Schank,1989},{Hammond,1989} to music composition is Blevis' work {Blevis,1990}. Blevis incorporates this AI technology by investigating a system in which a composer's knowledge, in the form of examples, is used to guide choices made in forming a composition. An interactive prototype implementation demonstrates how Blevis' approach supports the composition process.

Finally, my recent approach {Farrett,1992} to IMI research involves notions about time and space (temporal/modal) within a logic- object-oriented paradigm (i.e., parallel distributed processing). My work incorporates AI and software engineering techniques with music composition as the "test-bed". The intent is a creative reasoning system, which captures the composer's "creative" actions.

Some Technical Points and Observations about Intelligent Instruments

This section is a critique about intelligent instruments, and addresses the feasibility of such systems. Several important areas and directions are suggested.

Knowledge Engineering

This approach is vital to computer music systems, although it currently lags behind its industrial counterpart as a serious engineering science for music applications {Laske,1988}.

The Need for Formalism

The need for a formal representation that allows reasoning across multiple domains of musical knowledge is important. Specifically, IMI engineering should encompass (in order of precedence):
  1. Interdisciplinary Research: music/computer science primary, mathematical psychology/philosophy secondary.
  2. Behavioral/Enterprise Modeling: the composer/developer knows the domain the best; cognitive/data modeling may not be able to capture< intelligence or creativity in a finite manner.
  3. Logic as a specification tool: a precise mathematical language that is a useful descriptive tool.
  4. Empirical Observation: interpreting one's domain of discourse.

Successes

Those that synthesize computer science principles will be successful (e.g., AI-Music and traditional engineering). While it is extremely important that the earlier AI speculation of the '60s and early '70s continue, it is equally important that AI concepts merge with engineering. This has certainly occurred in the private sector. Since AI has been in existence since the development of computer technology itself, it seems only natural that IMI researchers would want to incorporate both disciplines. (E.g., logic programming was spawned by AI exploration, and benefited greatly by software engineering methodology.)

Defeats

Because AI is an interdisciplinary field, researchers often view a problem from different perspectives. This has lead to Proceduralists assailing Declarists, Formalists impugning Psychologists, Computer Scientists vs. Mathematicians, etc. An amalgam of all areas is necessary if one is to attempt IMI research.

Cautions

The issue of "intelligent behavior" vs. mimicking is important. Researchers, such as Sowa and McDermott {Sowa,1984}, have strongly objected to the misuse of "intelligence": "For AI systems today, a casual use of terms like thinking or understanding is a sloppy and misleading practice. Those terms may have a dramatic effect, but they lead to confusion, especially for novices and people who are outside the AI field. McDermott maintained that they even have a mind-numbing effect on experts within the field" {p.358}. Sowa further contends: "Whether such systems will ever be possible is still an open question, but no such system will appear within the 20th century" {p.363}. To date, mimicking or simulation have been very successful. For example, IBM researchers have been working on problems associated with automatic recognition of speech for well over a decade only to find that no one really understands how people recognize sentences. {Farrett,1987}. Instead, they have produced a highly accurate model with a 20,000-word vocabulary and with 95% or better accuracy of isolated words, which is based on statistical modelling of all speech processes involved. In other words, with educated conjecture and probability, they mimic what we humans do. I believe the successful mechanisms of Ebcioglu and Cope follow this basic strategy.

Not all Musical Problems are AI

Why is a problem AI? Can it be solved using traditional approaches? A computer scientist, critical of AI claims and achievements, has theorized that many AI problems can be solved using more traditional engineering methodologies. However, since music draws on so many convergent disciplines, AI seems to be one of the best candidates for IMI exploration. Does, for example, a music interface need to incorporate AI techniques into its design? No, of course not. Yet, inference-based techniques have been applied to the user interface yielding expressive human-computer communication.

Synthetic vs. Logical Reasoning

Marvin Minsky, one of the founding fathers of AI, argued in earlier writings {Minsky,1981} that symbolic logic is not necessarily a good mechanism for human inferencing, and the more recent work of Johnson-Laird {Johnson-Laird,1983} seems to support his theory. (Earlier, Minsky also argued in favor of information theory as a viable alternative for information processing.) However, for well over a decade, knowledge-based systems have incorporated formal (logical) systems; the results have been successful {Frost,1986}. Perhaps IMI research is a hybrid logic (i.e., musical expressions controlled by a formal system)?

Intelligence vs. Creativity

IMI research investigates the area of intelligence. However, creativity is a "by-product" of this research as well. Researchers such as {Winner,1982} and Sowa {Sowa,1984} have examined the correlation between intelligence and creativity and suggest that while a certain degree of intelligence is necessary for creativity, there is no relationship between the degree of the two {Winner,1982;p.31}. Sowa contends further that creativity and intelligence are possibly unrelated mental aptitudes that are not necessarily correlated with each other {Sowa,1984;p.352}. However, the more recent work of Sternberg {Sternberg,1988;p.132} suggests a direct parallel concerning the intellectual facet of creativity. IMI research should carefully scrutinize this dichotomy.

Articulate vs. Inarticulate Composers

Are composers the best domain experts? Should the elicitation of their musical knowledge be a primary or a secondary consideration? Composers who are articulate about the compositional process have explicit knowledge. Inarticulate composers are those that have implicit knowledge. Inarticulate composers know their domain, but not necessarily how they compose for it. I have witnessed countless diatribes of music theories, yet those that articulate clearly their process either explicitly detail numeric processes or implicitly detail symbolic ones. Several years ago, a Pulitzer-prize award wining composer was asked to explain his compositional palette. He was very successful because he could enumerate compositional tasks that were numeric; an other equally well-established and highly respected composer (also a Pulitzer-prize recipient) was asked to do the same. His description of the compositional tasks were vague and unclear, and could only enumerate the most fundamental notions simply because the reasoning process is symbolic and cognitive.

Musical Forms Used as a Knowledge Source

Are there musical structures that suggest a more suitable knowledge processing strategy? Are there structures or other approaches not suitable or inappropriate concerning knowledge processing for musical applications? I suggest a few:

Is a Hal-like System Possible?

dialogue perspective, and can also be viewed in terms of his "visual sketching" of the users input as well as the more obvious score markup. From current indications, a Hal-like system is already a reality (e.g., the Tsukuba musical robot).

Conclusion

Artificial Intelligence and Music, particularly intelligent systems, is an important area of concern to the computer-music specialist. When one considers various paradigms for music that AI offers, it is not surprising that researchers, who historically intrigued with the idea of an intelligent musical automata, find this branch of computer science appealing. However, the current state-of-the-art is still ambiguous and there are many problems remaining for intelligent computer music engineering.

Acknowledgements

I would like to thank Donald Jardine, Otto Laske, Curtis Roads, Barry Truax, Dorothea Blostein, and Lola Cuddy for their comments and suggestions concerning parts of this article.

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Glossary of Terms

Artificial Intelligence: A branch of computer science that examines human intelligence within the context of computer systems.

Knowledge Base/Data Base: A computer system that consists of facts about a domain of discourse, and rules for using these facts.

Knowledge Engineer: A person that translates knowledge about some domain into "expert" system rules.

Knowledge Representation: The representation of an expert's knowledge in the form of logic, facts, rules, etc.

Formal Logic: A mathematical language for expressing knowledge and rules for the manipulation of "laws" (formulas) that are expressed in that language.

Symbolic Logic: A combination of formal logic and cognitive modelling.

Expert Systems: Systems that "mimic" an expert's knowledge. These systems consist of a Knowledge base, inference engine, and user interface.

Natural Language Processing: A Knowledge base system, which ideally parses the syntax and semantics of a language.

Cognitive Modelling: Hypothetical representations of how the mind understands, organizes, and processes information.

Knowledge Acquisition: The acquisition of one's knowledge, typically an expert in a particular domain. (This is in the area of "Machine Intelligence".)

Deductive (Logical Inference) System: A component of the expert system, which controls the rule-order of execution.

Hierarchical Model: The representation of information in the form of "parent-child" nodes or "tree-structured" relationships.

Relational Model: The representation of information in the form of relational attributes or a set of associations. (Note: the "ISA", "Frame", and "Semantic Network" representations generally fall under this area.)

Extension: The actual "value" of an object or entity.

Intension: The semantics or meaning of an object or entity.

Declarative Knowledge: Knowledge, which can be stated or expressed.

Procedural Knowledge: Knowledge, which is based on responses to stimuli.

Augmented Transition Network (ATN): A system that incorporates a natural language (syntactic) parser.

Forward-Chaining: A rule-driven approach in which a computer system only considers rules that are relevant for solving a problem (e.g., Goal := Rules).

Backward-Chaining: A goal-driven approach in which a computer system only considers goals that are relevant for solving a problem (e.g., Rules := Goal).

Bidirectional-Chaining: A hybrid combination of forward- and backward-chaining.

Case-based Reasoning: Systems that search for knowledge in the form of examples. If a match is deemed suitable, the system provides feedback.