Friday, June 03, 2005

Summary One

While studying my way through Riemann's "History of Music Theory", I managed to distill a few principles and crystalize them into a very reduced form that I'll be able to build upon. The first principles concern the Natural Harmonic Overtone Series.

1) The ideal for tonal perfection is embodied in the Natural Harmonic Overtone Series.

2) This ideal is impossible to achieve in a twelve pitch-level reality because all intervals cannot be arranged to be Justly Intonated (To the point of beatlessness) in such a system.

3) Nevertheless, the Natural Harmonic Overtone Series explains perfect versus imperfect consonances by:

a) Showing that perfect consonances maintain superparticular ratios when inverted at the octave, and...

b) Showing that imperfect consonances are only superparticular in one of the two possible octave exchange positions.

Applying the octave exchange principle to the rules of counterpoint - meaning, taking as a point of principle that correctly written counterpoint is invertible at the octave - we find that:

1) No parallel perfect consonances may be allowed, and...

2) Parallel imperfect consonances need no restrictions other than those imposed by taste.

It is important to realize here that I am going after the laws that govern musical motion in counterpoint completely independently from the laws that govern musical motion in harmonic progressions. In fact, I am trying with my utmost effort to expunge all harmonic considerations from the laws that govern contrapuntal motion. Such a rule of law has never existed in theory, and certainly not in practice, for when the ancient masters first stumbled upon the 6/4 arrangement, they excluded it for its harmonic "instability". Thus, the laws that govern musical motion in counterpoint have always been "polluted" by harmonic considerations. Conversely, the rules of harmonic motion taught via voice leading precepts have always been similarly "polluted" by contrapuntal considerations. As we shall se later when we address harmonic motion, that type of musical motion is actually governed by circular permutations of the chord's member tones, and has nothing to do with vioce leading per se.

I take as a given that these two subjects can be logically untangled, and as we go through Gioseffo Zarlino's "The Art of Counterpoint" - which is Part Three of his Le Istitutioni Harmoniche of 1558 - I will attempt to logically formulate the basic laws that govern musical motion in counterpoint, and seperate them as completely as possible from any and all harmonic considerations. The reason for this is to arrive at a set of laws that will apply no mater how diatonic or chromatic the composer whishes to make the contrapuntal idiom, and in this type of an approach, all vertical sonorities will properly speaking be the result of voice leading independent of any harmonic progression paradigms. It is noted that harmonic incursions may appear due to instinctive impulses on the part of the composer, but they will be only that: Artifacts of previous conditioning not directly related to the laws of counterpoint.


Anonymous Jack S. said...

Hey Monk,
Have you gotten into Jeppesen yet?
He has a great overview of all the Renaissance period theorists and his own exposition after Fux of species counterpoint "in the style of Palestrina". Knud Jeppesen, Danish guy wrote in the 1920s and '30s. A book I haven't gotten tired of. Same didactic material essentially as Fux, with modern commentary and perspective. Here's the link:

3:30 PM  
Blogger Hucbald said...

Hi Jack,

Yes, I've had Jeppesen since the 80's. One of the best modern books about modal counterpoint, the historical overview being particularly worthwhile.

3:37 PM  

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