My previous posts introduced Music and Multiple Intelligence. Given that my last post on Music and Mathematics caused some discussion, I’ll give the background to my thoughts, beginning with a simple summary of music education in Ancient Greece.
The Ancient Greeks believed that one must study and understand those subjects that involve abstractions. While these subjects have practical applications, their real worth was seen in leading the soul out of the ephemeral world of the senses and into the unchanging world of the mind. Thus, as Plato said “we pass from darkness into light and come to understand the idea of the Good”. In what must be the fairest system of education yet proposed, all children in ancient Greece received the same schooling to the age of twenty. Early education began with physical education—gymnastics, and so on, followed by six years of training in music, so that the soul may learn harmony, rhythm and grace. Note that Plato believed that music should precede and dominate gymnastics for the soul should form the body, not vice versa.
During the Middle Ages of Ancient Greece -as defined in the 5th century AD by Martianus Capella, the seven liberal arts were divided into an advanced division –the quadrivium, and a lower division –the trivium. Here, the word ‘arts’ is not as the word is understood today. In classical antiquity, the liberal arts denoted the education ‘proper’ to a free person (as opposed to a slave), a curriculum that imparts general knowledge and develops the student’s rational thought and intellectual capabilities, unlike the professional, vocational and technical curricula emphasizing specialization.
It was the Greeks who considered music as one of the four branches of mathematics. In classical Greece a master’s degree required completion of the quadrivium. The quadrivium included arithmetic, geometry, music and astronomy, and these subjects were seen as wholly mathematical in so much that maths is concerned with quantity (for which we have arithmetic) and magnitude at rest (for which we have geometry), and magnitude moving (for which we have spherics as evident in astronomy). Music was included because it considered the relations between quantities, that is, it dealt with the ratios inherent in melody and harmony. Music was considered a mathematical science, so the quadrivium therefore was all mathematical science. Incidentally, the lower ‘trivium’ preceded study of the quadrivium, and consisted of grammar, rhetoric and logic (or dialectic as it was called at the time and some would say –sadly missing from decision making and thought clarification today).
That music concerns itself with ratio occurs on more than one level. The ancient Greeks were referring to ratio within the construction of harmony. But in melody too, it is ratio rather than static frequency that is important. What creates melody is not the frequency of the notes, but the relationship between them. This is why you can recognise a melody played in any key, but most of us cannot recognise a single note –unless you have perfect pitch. Hence, it is always the next note that counts, and puts the former note into a perspective. A note without context is essentially meaningless. In fact, a jazz musician would argue that there is no such thing as a wrong note until the next note is played. This provides a kind of retrospective context, or hindsight.
No civilization held music in as high esteem as classical Greece. Music dominated religious, aesthetic, moral and scientific life. To be called unmusical was to be labelled ‘brutish’. The primary role of music in Greece was to build character and health. Greeks believed that music puts us in touch with the vibrations of the universe. I’ll continue this theme in my next post, eventually arriving at Pythagoras.
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Also by Michael Griffin
Music and Keyboard in the Classroom: Fundamentals of Notation is a unit of work for general music middle school classes. Designed around the mastering of practical skills, it integrates theory, aural and history, and allows students to progress at their own rate. View Table of Contents. “This has been a great buy; the books are just superb! Interesting topics with a wide range of pieces. Great content with clear progression of learning. Fascinating teaching philosophy! BRAVO!” -The Grieg Academy, London. Available at Amazon.com
Music and Keyboard in the Classroom: Let’s Get Creative! is the fun and creative extension to ‘Fundamentals of Notation’.
View Table of Contents. “We have been using your keyboard course and the results have been amazing!” – St George College, Australia
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Modern Harmony Method: Fundamentals of Jazz and Popular Harmony (Third Edition, 2013) is a clear and well organised text suitable for students of arranging and composition, and for classically trained musicians wishing to grasp the beautiful logic of jazz harmony. Essential understandings include chord selection, voicing, symbols, circle of 4th progressions, extensions, suspensions and alterations. Included in the 107 pages are explanations, examples, exercises and solutions. The course can be started with students in year 9 and worked through to year 12 musicianship, composing and arranging. Available at Amazon.com