Thursday, June 16, 2005

MM VI: The Mechanics of Melody

This is another concept of Joseph Schillinger's (Who I've linked to before if you look back a few posts) that I find extremely valuable. In fact, in my opinion his "Theory of Melody" is the single best reason for the study of his "System of Musical Composition". The reason for this should be obvious: No other theorist in music history has ever taken a scientific approach to describing this phenomenon, and the art of writing melodies has always remained in the realm of the mysterious or even the supernatural because of this regrettable fact.

Now, it must be admitted that there are many problems one encounters in the study of Schillinger. First of all, the two volume System is a daunting 1,640 pages in total length. Second, Schillinger's prose is very densly abstruse due to the unalloyed mathematical and scientiffic terminology he employs: Terminology that is profoundly alien to the vast majority of musicians. Then there is the fact that Schillinger was a futurist, and so he attempts to present all the possibilities for music of the future along side of explainations of past and present practice. Additionally, the System was compiled by some of his students after his death, if memory serves, and so there is some doubt that he actually would have wanted the materials presented in the form that they are encountered. Finally, there is the fact that the musical examples he presents that are not by other composers are abjectly lame in the extreme. In light of these formidible and compounded difficulties, it is easy to see why the overwhelming majority of traditionally oriented theorists and composers dismiss him out of hand. This is a shame - not to mention that it's usually an intellectually lazy cop out - because, thought flawed in many ways, Schillinger was nevertheless a genius who had many unique and penetrating insights into the nature of music that can be found nowhere else. In lieu of inserting pitch scales into formulas as he suggests in his over-rational methodology, I took the ideas Schillinger presented and made myself aware of them on an intimate enough level that I was able to allow them to function intuitively as a natural - and normal - part of the compositional process. Since the type of personality necessary for a composer is not usually one prone to an overtly scientiffic or mathematical disposition, I believe this is the way that many of his ideas should be employed. Melody is one of the subjects where a looser, more intuitive approach has yeilded better results for me, whereas the harmonic motion mechanics he explains can be used in practice very closely to the way he describes them in his theories.

So, the first step in coming to an understanding of a subject is to define it as precisely as possible.


A melody is a trajectory of pitch through time.


Once this definition is made, an analog can be used to put it into an understanable perspective. I will use the analog of a quarterback on a football team throwing a football to a receiver.


A melody is like the trajectory of a thrown object, such as a football.


Now, in a perfect vacuum with no gravity, if the QB threw the football, it would launch in a straight line and continue off into infinity on that perfectly straight trajectory. If you continue in the vacuum but add gravity to the calculation, the trajectory of the football would peak at the approximate half-way point between the QB and the receiver. Gravity becomes a force of resistance that the football encounters, and so the trajectory has a beginning and an end with the climax of the trajectory at the half-way point. The trajectory under these conditions would describe a part of a circular curve. But, the football game is not played in a vacuum, so there is another form of resistance that the ball encounters: Wind resistance. In an indoor stadium with no additional wind but only still air for the QB and the ball to deal with, the trajectory would now peak approxamately 2/3 from the QB and 1/3 from the receiver. This is in fact the primordial blueprint for a melodic trajectory as presented by the natural order.

Just as the QB imparts rotational spin to the football to stabilize it as it travels along it's trajectory to the receiver, melodies are often adorned with figures that impart rotational spin to them as well. And these rotations often impart increasing degrees of momentum to the melody on the way toward the climax, and then release the momentum after the climax.



Schillinger describes the Axes of Melody as I have labelled them on the top staff in the example above. The Zero Axis can be the pitch axis, or tonic, of the key, or it can be either the third or the fifth of the tonic major or minor triad of that key. The A and D axes go above and below the zero axis respectively, and they are unbalancing axes, meaning they increase tension as they move away from the Zero Axis. The B and C axes travel toward the Zero Axis from above and below respectively, and they are balancing axes, meaning they release tension as they move toward the zero axis.

Since the subjects involved in immitative or fugal composition are often micro-melodies that offer a microcosm of these principles in actual practice, I have taken two of them from Bach to use as examples. The middle example is from the Two Part Invention No. 8. In the first measure Bach establishes a Zero Axis on the tonic degree, and as the A Axis moves away from it and returns to it in successive movements, momentum is increased as an integral part of an increasing scale of tension. This is a broadening rotational structure. After the climax on the upper octave C, this tension is released with a contracted rotational structure in the decending sixteenth note figure that brings the melodic trajectory back into balance at its return to the Zero Axis. In the bottom exampe, which is the fugue subject from the D minor Organ Fugue of Tocatta and Fugue fame, Bach establishes a Zero Axis on the fifth of the tonic triad and spins the subject out below it. Here, the Zero Axis acts as a form of artificial gravity in an inverted musical environment where the B and C axes are employed to give cycles of tension and release through broadening and contracting rotational periods against the established axis.

This subject will come up again and again in various degrees of depth, but an understanding of these basic concepts can be of inestimable value to a composer who is intent on organizing melodies and climaxes to achieve desired effects.

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