Stravinsky's Prediction

With an extensive history of music already in place, one might wonder, what more could possibly be accomplished? Are there really any musical components left for radical exploration? Here is how Igor Stravinsky, one of music's most historically celebrated composers, decisively answered a similarly posed question:

“Yes, pitch. I even risk a prediction that pitch will comprise the main difference between the “music of the future” and our music.”

— Igor Stravinsky, Memories and Commentaries

Why would Stravinsky say that the transformation of pitch is the future of music?

If we look at the components of a single musical tone, whether it be from the voice or any instrument in the world, we see an endless series of pitches, many of which have still never been heard consciously in isolation, let alone heard in a musical or harmonic context. These sounds within one sound, or pitches inside one tone, which I will now refer to as partials, could be the music of the future that Stravinsky predicted. Partials work with largely different rules and principles than those that have already been established.

One reason for the discovery of additional partials, along with the expansion of what pitches are deemed acceptable, is modern technology. In Stravinsky's time, along with all the ages before, there was not an efficient way of isolating, and thereby hearing and discovering, complex partials. Only with relatively recent advancements in science and technology are we able to bring the more complex and higher partials into our listening experience.

With further advancements in technology, modern instruments can play nearly any combination of tones and partials that can be conceived. As in many areas of life, the modern era is a unique time for musicians to be alive due to the contemporary opportunities and changes that only this period has yet been able to provide. Certainly, a number of musical creators from the past would be envious of our current circumstances, for many of those prominent composers and players felt limited by the constraints of their generation. Even Arnold Schoenberg, a true innovator in his time, articulated:

“We ought never to forget that the tempered system was only a truce, which should not last any longer than the imperfection of our instruments requires. I think, then, contrary to the point of view of those who take indolent pride in the attainments of others and hold our system to be the ultimate, the definitive musical system—contrary to that point of view, I think we stand only at the Beginning. We must go ahead!”

— Arnold Schoenberg, Theory of Harmony

Perhaps we are entering that age where imperfection need not last any longer.

Going Around in Circles (Of Fifths)

www.MusicCrashCourses.com

     Many ideas in the world are superficial constructions created to simplify and avoid the complexities of life. What's more, some of these ideas go largely unexplored and unquestioned. A concept in music known as the circle of fifths (COF) could qualify as one of these ideas. Indeed, a number of musical theorists elegantly simplify music into this single circle, and it has become a foundational symbol of most modern music and theory. While the COF has been useful to a degree, like most complexity-simplifying concepts, might it stifle deeper understanding?

      First off, what is the circle of fifths? It is a repeated cycle of one of the most, or if not the most, important musical intervals known as the "perfect fifth." Musicians throughout history have analyzed where, and how, fifths shed light on music. In modern music theory, when the fifth of every tone is taken consecutively, it circles back around to the same tone. At least, it seems that way. Curiously, it takes twelve successive fifths to complete a circle. Hence, the result is the twelve-tone scale found in most modern music. This, in theory, makes music more understandable and practical, because any musical pattern or song can then be taken through only twelve permutations (keys) before returning to square one.

      While the COF makes sense conceptually, the subject in question is this: does a consecutive series of fifths actually make a perfect circle? Surprisingly, mathematics shows otherwise. A true fifth originates from the third harmonic of a tone, which is measured at 702 cents. If a cycle of twelve true fifths is taken when measured at 702 cents, it very nearly shuts into a circle. The key word in the last immediate sentence is: nearly. When fully calculated, it is off from a perfect circle by a mere 23.46 cents, an interval that baffled Greek musicians over two thousand years ago. This seemingly minute difference is so important that the infamous circle symbol associated with the fifth completely depends on it.

       Consequently, if the math doesn't hold up to support the circle of fifths theory, then what symbol might best represent the concept of a series of fifths? If a closer look into nature is taken, one eventually finds a perfect fit: the spiral. A spiral always remains open, as do successive fifths. A spiral can expand or contract, as can successive fifths. A spiral can theoretically extend indefinitely, as can successive fifths. The parallels are clear.

       Symbols are powerful due to humanity living largely visual-based lives. With a simple change of musical imagery, the very nature of music becomes dramatically more mysterious and complex. When the spiral starts to symbolize the musical fifth, society may begin to visualize music in its true, boundless form. Indeed, the spiral can lead musicians away from circles, and straight into the unknown, spiraling as deep as the imagination allows.

Spiral of Fifths