The genesis of mathematical/musical connection is often attributed to Pythagoras born 570BC, a scientist-mystical polymath and possibly the first Greek to be given the title ‘philosopher’. He was one of the greatest thinkers of ideas and believed in the mystical significance of numbers. He held the view that creation itself is essentially a harmonic and mathematically undertaking.
Pythagoras had an insatiable thirst for knowledge . He had an excellent education, studying with Thales of Miletus, and then abroad in Egypt, Phoenicia, Babylonia, Chaldea, Persia and possibly India, before settling in Crotona, Italy. He believed that if he took the truest points of each of the doctrines –however diverse, and combined them together, he could create the ultimate philosophy. Ultimately, he was in search of spiritual peace. He was probably not an innovator, as much of what is now attributed to him and his ‘Pythagoreans’ probably originated elsewhere. For example, the harmonic scale was a restatement of the Chaldean (Babylonia) discovery of the harmonic series. Chaldeans also believed that the harmony of the spheres could be expressed in numbers. They came up with the harmonic series, and even related certain intervals to the four seasons of the year. Pythagoras searched for trans-disciplinary connections between natural properties in order to unlock the secrets of the world. It intrigued him that mathematical equations could explain everything we know about the physical world. Pythagoras expected to find these connections and his underlying philosophy and key to reality was based on this divinity of the number. The inspiration of Pythagoras ignited a flame, where 100 years later in Athens did occur the greatest assemblage of geniuses that history has ever witnessed: Socrates, Plato and Aristotle.
Pythagoras’ great contribution to music was in the formation of the diatonic scale. Pythagoras believed that musical chords are harmonious because we ourselves are constituted in such a way to resonate with concord and to revile against discord. Consonance matches up with something in the soul that resonates. Discord -such as a tritone, was seen as a violation, and as sinful right up until the Middle Ages. Consonance is both a psychological and a physical criterion. Two notes are psychologically consonant if they sound pleasing to the ear. What Pythagoras found was that this occurs when the physical frequency ratio of the two notes is a ratio of low integers. And further, the simpler the ratio, the more consonant are the 2 notes.
Pythagoras believed the effect of harmony on the soul is not a coincidence but an ultimate truth. Beauty and truth are combined in music. How does one distinguish the true from the false, the beautiful from the ugly in life? Poetry and music would purify the immortal soul. Music could quell the lawless desires of the flesh! For Pythagoras, medicine and therapy used music centrally. He called the medicine obtained through music ‘purification’. This is not so different from within the Old Testament, in which the healing properties of music are themed throughout.
Music played an important part of Pythagorean education. Manners and lives could be refined though music. Those who committed crime were prescribed “pipe and harmony” to shape the mind so that it becomes capable of culture. Music was used to care for both physical and moral ills, and to control the emotions. Music was used at night by the Pythagoreans to produce tranquil sleep and sweet dreams through singing certain odes and hymns. Again in the morning different hymns were sung to liberate from slumber. Sometimes the music was played on the lyre alone, deliberately without words. Perhaps Pythagoras had an instinctive understanding of the power of non-lyric music, something only proven quite recently. Recent studies have found that the emotional valence of happy music is not enhanced with lyrics, but the emotional valence of angry music is.
For Pythagoras, the study of geometry, music and astronomy was considered essential to a rational understanding of God and nature. I’ll discuss this in my next post.
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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