Introduction

    The purpose of this study was to examine the opinions of experts regarding the relationship between logical/mathematical intelligence and musical intelligence and how these intelligences are represented in music technology. Specifically, there was a curiosity about the following questions:

• 1. What are the different approaches that experts in the area of music technology adopt?
• 2. How do logical/mathematical and musical intelligence contribute to success in music technology?
• 3. Are there inherent biases toward logical/mathematical reasoning in music technology software?
• 4. How is programming like/unlike musical processes?

    People such as Thorndyke, Gilford, and Sternberg have advocated for an idea of domain specific intelligence. With his book, Frames of Mind, Howard Gardner has continued this trend with his theory of multiple intelligences. Gardner describes intelligence as the possession of potential. Basic "core" operations define an intelligence. In each domain, basic information is dealt with and processed in different ways. Gardner rejects the idea that there are a set of broad mental functions that operate across domains, regardless of the content. Sets of know-how's and specific procedures for doing things are native to each type of intelligence. (Gardner, 1983)
    Gardner (1983) goes on to characterize logical/mathematical intelligence as being pure abstraction in contrast with sensory/motor "knowings". This type of intelligence deals with abstract, nonlinguistic entities. There is a type of linear chain of reasoning that is employed in order to problem solve. Recognition of patterns is considered at the center of logical/mathematical intelligence. Western societies often claim that math and science are basic types of logic that can be generalized to other domains. There is a sense that these types of logics have an intrinsic superiority for many in the West . there is indeed a logic to language
and a logic to music; but, these logics operate according to their own rules, and even the strongest dosage of mathematical logic into these areas will not change the ways in which their endogenous "logics" work." (Gardner, 1983, p. 168)

    There is a resultant overemphasis of linguistic and logical/mathematical intelligence in our society. "The end result is a society that cares deeply about the logical, scientific, and mathematical concerns ... at the expense of some of the more aesthetic or personal forms of    intelligence... "(Gardner, 1983, p. 164)
    Musical intelligence also has specific "cores" (pitch, rhythm, timbre) according to Gardner. The perceptual, auditory sense and the emotional/affective aspects are crucial components of what music is. It is possible to analyze music in terms of numbers, patterns and structure. Those who wish to reinforce the rationality of music use these types of techniques to underscore their purpose. However, it is impossible to reduce music to an entirely "objective" form and deny its affective power. "... none of the claims with respect to musical breakdown suggest any systematic connection with other faculties (such as linguistic, numerical, or spatial processing): music seems, in this regard, sui generis, just like natural language." (Gardner, 1983, p. 120)
    Having defined the two types of intelligence, an effort was made to find studies that examined at correlations between the two, specifically involving mathematics, computers, and music. Chesson (199 1) studied the characteristics of musical ability and information processing among music and computer science students. Music students employed more integrated modes of processing while computer students were more analytical, sequential, and logical in their processing. Piro (1986) compared hemispheric processing among students gifted in mathematics, music, and dance. The processing in these three domain areas was very distinct and unrelated.
    Logical/mathematical intelligence and musical intelligence seem autonomous, distinct types of intelligence. Mathematical principles, while being complementary to music, are not rudimentary. "...although mathematical skill is desirable for a theoretical comprehension and appreciation of musical form and its workings, its actual operational efficacy may be quite restricted." (Piro, 1986, p. 150) Piro quotes Gardner as saying "In my own view, the task in which musicians are engaged differs fundamentally from that which preoccupies the pure mathematician. The mathematician is interested in forms for their own sake, in their own implications, apart from any realization in a particular medium from any particular communicative purpose. He [the mathematician] may choose to analyze music and even have the gift for doing so; but from a mathematical point of view, music is just another pattern." (Piro, 1986, pp. 126-127)

Methodology
    A qualitative design was chosen to address the complex, multidimensional types of questions. There was not an interest in discovering a "right answer" but rather exploring the possibilities in a holistic way. The design allowed the possibility of looking at emergent issues arising from the study.
A lengthy, semi-structured interview was used to engage four individuals noted for their music technology achievements. The interviews were a forum to probe the duality of the two intelligences by talking to people fluent with music technology and a uniqueness of personal understanding and experience. Expert opinions were gained through guided questions.

Interview Questions
1. Describe how you are involved in both music and technology in your work and in your life.
2. What is your background as it relates to music and to technology?
3. How has technology changed you as a musician and as an educator?
4. How has music influenced the way you interact with the technology?
5. Do you feel that the intelligence required in the area of music and the intelligence required in the area of technology are related in any way? How do the two overlap and how do the two differ? Has involvement in one of these areas changed your perception of the other area?
6. Describe to me, to the best of your ability, how the information processing is different in each of these areas.
7. How does your background in the areas of music and technology impact your teaching?
8. What would you say are the most important issues surrounding the areas of music and technology?
9. What are your biggest concerns related to the pedagogy of music technology?
10. Are there any really important issues that you would like to elaborate on relating to the topic that have not been raised with these questions?

    The MicNotePad (http://moof.com/nirvana/) was used to gather the data. 'There are several advantages to using this system over a traditional tape recorder: (1) data is stored in digital form and does not lose quality over time; (2) built-in microphone or sound input may be used along with a hard drive; (3) traditional navigation controls; (4) freeware; (5) random positioning for playback (browsing or markers); and (6) operates in the background if a word processor is running up front.

    The data were analyzed by examining case uniqueness as well as cross-case patterns that emerged. Biographies and unique qualities of the four participants will be described and a discussion of cross-case categories will follow.

Mr. Ed
    Mr. Ed has a Bachelors, Masters, and PhD degree in music education and is currently a college music educator. His primary area of research is creativity, including computers. He spoke extensively on how the role of talent is perceived in logical/mathematical domains as compared to music. Giftedness is often thought of as being inbom in music at a very young age while mathematics intelligence tends to manifest itself later. He describes the relationship between technology and music in the following way: "...and Boulez speaks elegantly in his writings and also personally when you interview him about the synergy between technology and music and it being a natural kind of development all through the history of the art form and so my greatest concern would be that people lose sight of the fact that the technology is just an interesting way to make music."

MultiMax
    MultiMax is a visual artist, multimedia expert, composer, performer, programmer, and mathematician. He learned the "New Math" at a very young age and is fascinated by patterns found within and across the different domains. He is interested in the collaboration that can bring people back in to the process of art through technology. He believes that it is more likely that problems will be solved by chance operations or the randomizing of elements in math as compared to music. He emphasizes that it is necessary to understand the underlying technology to conceptualize what is happening on top in a computer application. Technology has allowed him new creative avenues with music. "Well, technology has made it possible for me to do some things as musician that I could never do without having to get in contact with several people - a way of realizing composition."

Toolman
    Toolman is a bass guitar player who teachers theory and cognition at a university. He is interested in measuring precisely the nature of musical performance. He has been involved extensively with artificial intelligence work, programming, and modeling of musical behaviors. His distant relationship with technology, given his background, was surprising. He believes that machines do not help people to learn better and that musical intelligence has more to do with listening than with performing. "Is the music we make with these machines better or more powerful than Schubert ... [or what] Bobby McFerrin can do standing alone on stage with only his body? ... Is it worse? No - maybe because the tools are so crude ... no digital instrument that approaches the flexibility of the human voice or a cello."

C-Man
    This person has been involved with math, science, engineering, music, theory, and composition. All these interests come together in electronic music, programming, and the teaching of music technology. Sound processing and software writing are additional areas of interest. He believes that technology should be put in people's hands and they should be empowered to succeed. He does not believe that music technology is dominated by logical/mathematical intelligence. Technology is viewed as changing learning and transforming thinking. "...there's this side of music which is descriptive and logical and seems math like ... my actual experience of this ... is that it isn't really useful to think about what you think is typical or normative in people - that individuals are so uniquely constructed ... there is a variety of different types of intelligence ... the kind of thinking that people use in music and the kind of thinking people use in technology is a very complex mix and I don't accept immediately the notion that there is an immediate or obvious analogy between the two."

Cross-Case Regularities

    Most participants were highly concerned about the affective domain and that technology should be used to express feelings in sound. Aesthetics and emotion were also important issues. One person spoke of peak moments experienced in life through technology. Mathematics was thought to be characterized by linear, elegant theories and the type of problem solving involved in this domain may leave the world of affect. The participants agreed that rigorously working through material by experimental means and connected events were important components of logical/mathematical reasoning. Programming was described as being paradigmatic of technology in some instances. Convergent thinking was equated more closely with programming while a process such as composition was described as involving more divergent types of thinking. It was stressed that not all musicians work through a process of problem decomposition. There were comparisons made between intuitive/creative approaches versus logical approaches. Some participants felt that technology was a tool while others were convinced that it changes the paradigm of learning. There seemed to be some difference of opinion concerning the role of the teacher, some believing that the students should become autonomous with the technology while others felt strongly that teacher presence is vital to the learning experience. All participants articulated the hope that technology would serve the music and that expressive, sensitive, musical tools would be developed in the future. The Internet was viewed as a forum for human involvement in the arts and a way to bring people back in to the process. While pattern recognition is a part of the musical process, it is also a robust human cognitive behavior found in many other domains. The Internet is changing the way that music and art are produced and there may be possibilities for interesting collaborative works in the future.
    There were several questions that emerged from the study. Do we learn better because of machines? Does music software assume capacity in certain knowledge domains? Are there options in programs for students who do not think in a linear fashion but rather work more intuitively/creatively? Is technology only a tool to be used in the service of some "other" or is it transforming the paradigms of teaching and learning?
    There are several implications for further research. The questionnaire should be refined to specifically focus on the areas of intelligence apart from the technology questions. There is a need for case studies of people who program/design notation software. Software could be evaluated looking for underlying assumptions about intelligence, learning, style, etc.

References
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