continued…

Another problem area is presented in Slonimsky’s book Thesaurus of Scales and Melodic Patterns. This incredible reference book is both wonderful as well as problematic. The author does not engage in any discussion or justification of his scales and patterns. He simply presents them and leaves us rather bewildered at his achievement. First, the book is wonderful because it shows precisely, logically and systematically how to use the standard 12-note equal temperament chromatic scale to derive scales, chords progressions and voice leading patterns not necessarily based on 18th century Dominant Music Theory. By “splitting the octave” (or in some cases 2, 3, 4, or 5 octaves) into equal musical units he is able to produce astonishing results in a scalar fashion. Unfortunately, he is not as consistent in applying these techniques to his chordal suggestions. He seems to be content to use Dominant Theory to achieve possible harmonies and chord progressions. The very first example in the book starts on C and splits the octave in half at the flat five, F#, then uses a technique he calls “interpolation” to arrive at a pattern that goes: 1, #2, #4, 5, repeat over a few octaves and return to 1. His first two chord choices are then a C major triad and an A major triad. This sounds wonderful and works as an example of proper old school voice leading over his new school scale idea. However, there is no E or A in his scale, so how can these choices be considered valid if he is truly interested in creating a new musical system that is consistent with itself? Of course I am just guessing about his intentions and probably complaining far too much. At least he took the time to write the book (something that no one else did). This is hardly an unfortunate situation, because I can (and I am sure others can also) extrapolate harmonies that are suggested by his scales. There are, to be more than fair, some instances in which he is able to more fully integrate his scale and chord ideas.

A more serious problem with respect to Slonimsky’s book is that he uses octave splitting and inter-, extra-, and infra-polation ideas without respect to the ratios in which these scale patterns result. Remember that “splitting the octave” in half has two contexts. Slonimsky’s half is scale step wise resulting in the flat five being the midpoint, while (as mentioned before) a true mathematical halfway split would be at the fifth note of the scale because that is the ratio of 1.5 (exactly halfway between 1 and 2, the root to octave ratio). Furthermore, the major third note is exactly halfway between the root and the fifth. There are many more interesting ratios that support the idea that Dominant Theory seems to have mathematical (and therefore scientific) value and justification after all. I am sure this is not new information but in this age of multicultural/world music/dissonant noise it is good to reaffirm. Not that the purveyors of irrational nonsense care to acknowledge the value of Western music, much less Western science. My appreciation, gratitude and thanks to Aristotle grow daily, nevertheless. Did you know that even though Pythagoras formulated the intervals, Aristotle was the first to construct a formal Theory of Music?

One more thought on that strange and wonderful interval: flat fifth or sharp fourth. Most of the equal temperament and Dominant Harmony Theory ideas are ultimately derived from the Harmonic overtone series. It is odd to note that the interval of a sharp fourth occurs before a perfect fourth. There is an interval of a fourth that separates the second and third overtone. However, I am thinking about an interval of a fourth from the fundamental note. I am not yet sure what to make of this tidbit. The only possible practical application I can think of so far is that a fourth on a strong beat usually sounds better to me in a minor scale melody than a major scale one. And of course the minor scale intervals are much higher on the overtone series and thus more dissonant. This is a bit of a stretch, I admit.