Cowell's New Musical Resources

I read Cowell's "New Musical Resources" a while ago and thought that it might be nice to cover a topic or two of it since maybe not everyone has access to it.  We just recently read an article that gave is explanation for a new system where note values are assigned by the shape of their head and not using just the common quarter- and eight-note systems we currently use, placing brackets with numbers to designate the length of that note.  Cowell came up with a great system, if anyone hasn't seen Brian Ferneyhough's "Bone Alphabet" (which is a contemporary percussion solo), you should check it out.  It is riddled with a mass of bracketed rhythms within bracket rhythms (as some refer to them as "nested rhythms").  If we were fluent in Cowell's rhythmic notation, it would make pieces like "Bone Alphabet" a lot easier to read (theoretically...).  All of this is located in the first section of the chapter entitled "Rhythm" in the subsection labeled "Time," but beyond this he starts to utilize the theory that meter can be treated the same way a harmony is by using math to figure out how many beats per minute a meter will create, which will determine a given pitch.  Because, after all, pitch is made up of beats per minutes, we just think of these as waves instead of individual beats with space in between.  He goes on and uses things like dynamics, forms, and a whole slew of other things to try and give composers a library of new resources to be able to develop throughout a piece.

The most interesting part of the book for me is in the first chapter "Tone Combinations" where he explores the idea of overtones and undertones.  An undertone is similar to an overtone in that it is has a mathematical relation a the fundamental note.  So in the overtones series, if C = 16 vibrations, then an octave above that is C = 32 (16x2), then an octave and a fifth above is 48 (16x3), and so on and so on.  Undertones are related in the same way, except they go down.  So, if you have a C = 256 vibraphones, then an octave below that will sound at C = 128 (256/2), then a octave and perfect sixth below that will be F = 85.333 (256/3), and so on and so on.  Cowell proved this by making chambers/rooms that were the exact size to contain a certain volume of air that would resonate at certain low frequencies, and then all he would have to do is play a pure sound that would resonate with an undertone at the pitch of the room and you would be able to hear a tone that was not a part of the overtone series.

Long story short, he basically attributes undertones as a new way to view harmony.  So now we are not confined to traditional thinking of the overtone series where the G above C is considered harmonious, but now we should feel more free to explore tones that we wouldn't normally associate with a certain note because the undertone series will make most notes that we do not commonly think of as sonorous as actually having a high harmonic connection to its root note.  Now we are free to harmonize C with D and Ab.

I think this gives insight to why he used his tone-clusters, because in the long run, pretty much every note in the 12 note scale is closely related to the rest, so why not play them all at once!