Research Proposal on "Numerology in Music"

Research Proposal 7 pages (2281 words) Sources: 3

[EXCERPT] . . . .

Numerology in Baroque and Classical Music

The idea that music is related to mathematics goes back to ancient times. In his Dialogues, Plato agreed with Pythagoras's assertion that harmonics and astronomy are sister sciences of mathematics.

The connection to astronomy, in particular, reveals Pythagoras' mystical bent. Much as the Ancients saw the stars and planets as controlling the workings of the natural world, so too did they note a relationship between mathematical principles and the movements of the celestial bodies. Music, too, depends on specific measurable relationships between quantities of sound. The movements of the stars and planets can be precisely measured and plotted. In a similar way, musical notes correspond to specific positions on an overall scale. Harmonies are created by varying the length of these notes, and also by combining two notes that are fixed distances from each other on the overall scale. In this way, music can be seen as a kind of code that guides cosmic processes. Pythagoras was both a mystic, and a mathematician. Like many other Classical philosophers, he did not separate the invisible world from the material world as do modern scientists. Music possessed mystic properties that made its study and cultivation essential components of understanding the larger Divine Plan. In the Ancient World, and also later, in Medieval Europe, music was linked with arithmetic, geometry, and astronomy in the quadrivium, the set of four mathematical sciences that, together with the trivium of grammar, rhetoric, and logic, comprised the Seven Sciences. Music, thus, was one of the foundational principles of the Cosmos.

So it was only natural that, many centuries later, Baroque composers, like Bach, and Classical composers, like Mozart, turned to the numerological ideal as a source of inspiration for their work. For these composers, music was transcendent. It spoke to the very rhythms of creation. It did not matter whether the music was sacred or secular, for in the purity of mathematics, all was united. Numerology was the invisible force behind the manifest form of the music. As early as the Ninth and Tenth Centuries, the composer and musical theorist Hucbald, made use of the idea that the mathematic arrangements of music derived from the musica mundane, the Music of the Spheres. This Music of the Spheres was none other than the World Soul, the creative and motive force behind the cosmos, its actions represented in the tones of the musical scale. Hucbald composed sacred music including,

Offices for St. Andrew, St. Theoderic, and St. Peter. The structure of the last-mentioned anticipates the baroque practice of writing sets of preludes in all possible keys: Hucbald sets the antiphons for matins to each of the eight modes in turn, coming back to the first mode at the ninth and last antiphon

By writing music in each of the possible modes, or keys, the composer was setting forth all the possibilities of Creation. Plato described a cosmos that acted as a gigantic monochord, a one-stringed instrument that could be set to vibrate at various frequencies. These frequencies corresponded to the Pythagorean numerological ratios of 2:1, 3:2, 4:3, and 9:8. Everything from the planets to the individual human soul vibrated according to these ratios. Music was, quite literally, the sound of the cosmos.

But these Pythagorean rations were not the only possibilities in a mathematical universe. The Golden Ratio and the Fibonacci sequence also represent attempts to tap into the powers of the Divine. The Golden Ratio, or Golden Proportion, is an infinite number, like the better known pi. The Golden ratio is, in fact, called phi. A fundamental unit of calculation, the Golden Ratio can be represented in music as the ratio 12:9=8:6 which represents the division of the octave by the arithmetic mean of 9, and the harmonic mean of 8.

Legend had long held that Pythagoras had discovered the ratio in the sounds of four hammers that together banged out the cosmic harmony of 12:9:8:6.

The Fibonacci sequence, too, is a numerological building block that consists of a sequence of numbers, each succeeding member of which is composed of the sum of the two preceding numbers. The Baroque scores of Johann Sebastian Bach are filled with numerological notation, though these examples are rarely straightforward. Numbers can be obtained by counting up the notes in almost any musical section, from a simple line to a short score. Alternatively, the number of bars, movements, repetitions of phrase, and so forth, can be considered significant. The numbers obtained are then subjected to further mathematical calculations; multiplied, divided, or squared by yet other mystical numbers, such as 3, 7, or 10.

The results of these calculations yield numbers deemed to be of mystical significance in Bach's works. 10, for example, can stand for the Ten Commandments, 12 for the Apostles, and 27 for the number of books in the New Testament.

Possibly even more productive is the assigning of a letter of the alphabet to each number. Using this scheme, musical notes, phrases, numbers of movements, and so forth can be seen to spell out significant words, such as the reference to Jesus Christ as a Fish, as in Fish = 153.

The workings of the process can be shown through an analysis of the first two movements of the Symbolum Nicenum in the B minor Mass where,

Together these have 129 bars (enumeration), which can be read as 43 + 43 + 43, or 43 x 3, hence C (3) + R (7) + E (5) + D (4) + O (14) = 43 (operation), which translates into 'Credo, Credo, Credo' or 'Credo' multiplied by the triune God.

The above method clearly represents the system of counting up musical elements and converting them into meaningful numeric segments that can then be subjected to further mathematical calculations that are then linked to alphanumeric values.

The use of such numerological values lends to Bach's work, a transcendent significance. The score is transcendent, encompassing the varied aspects of cosmic truth and wholeness. The composer is become creator. Every note and phrase vibrates with the vital energies of the universe. The sound of the piece is quite literally the sound of an ever-continuing rebirth, and also a cyclical return to the point of Divine Origin. Bach's work endlessly reaffirms scared truths, endows them with life, and permits them to work in real time, within the frame of mortal existence. Bach was a devout Lutheran, and a firm believer in the doctrine of musica theorica, a system of belief that held that a "perfect cosmos, [was] rationally ordered by God according to measure and number."

Indeed, the notion of rationality, of a fine-tuned mathematic universe, appears to foreshadow the more highly rationalistic and abstract outlook of the Enlightenment. Bach's numerous explicitly sacred works, together with his polyphony, speak to a world that requires a clear, and visible, guiding hand. Though that guiding hand might act according to predetermined mathematical formulas, it is nevertheless the source of the formulas, and works constantly to maintain the visible order of the cosmos. Bach's polyphonic compositions appear to suggest the blending together of varied elements of Creation. God strives to keep His universe in tune.

In contrast, the increasing rationalism of Composers, such as Haydn and Mozart, even when working within the sacred tradition, brings to mind a different kind of cosmos. Here, God is more distant, and humankind more to the fore. The Deists of the era saw God as a Divine Watchmaker, setting in motion the natural processes at the beginning of time. To human beings is left the task of preserving and perpetuating order and meaning within the already created world. The early Classical composers worked toward a new kind of music, "That expressed and indeed embodied the noblest sentiments and aspirations of humanity -- humankind in a state of perfect harmony…. Specific examples might include Haydn Creation (a sacred work), or Mozart Magic Flute (a secular work)."

In their search for the deeper, and unchanging, secrets of the universe, many in the Eighteenth Century gravitated toward Freemasonry. The Freemasons believed themselves heirs to a mystical tradition that stretched back the days of Ancient Egypt and which combined various aspects of perceived Egyptian mysticism with Biblical mysticism and numerology. Mozart himself was heavily exposed to Masonic ideas. Mozart himself assigned mystical numbers to parts of The Magic Flute, intending to call the Introduction "2" and the Overture "1" because that was the order in which he intended to compose them, while at the same time listing a total of 22 pieces, or stucken, in his own catalog. 22 is the number of the major arcane cards in the tarot deck.

It is a symbol of completeness, each card of the major arcane representing one stage in humankind's journey from that of unenlightened Fool, to that of a complete being in perfect harmony with the World or Universe, the twenty-second card.

In fact, the overall organization of The Magic Flute recalls once more the ancient numerological system, cosmic order represented in… READ MORE

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