Musical Implications of the Harmonic Overtone Series: Epilog
The definition of what music is and is not has been disputed for centuries. Meanwhile, sound itself has been quietly knocking on the door and offering to reveal the answer to us.
Many definitions don't even begin with the proper elements: Wikipedia, for example, says, "Music is organized in time and consists of pitch, rhythm, harmony and timbre." Timbre is clearly an extra-musical quality which sound produced by differing means exhibits, and this definition completely ignores formal elements, except by implication from "organized."
The proper five elements of music are harmony, counterpoint, melody, rhythm, and form. Western art music began with monodic plainchant, evolved through the modal counterpoint era, and then to the harmonic system with tonal counterpoint and homophonic music. Rhythmic and formal elements - being simply local and global aspects of the same phenomenon - were mixed in and present from the beginning, and so they evolved concurrently with the other elements. Thus we see that composers intuited music in practice from the simplest melody/rhythm/form-only systems to the most complex harmono-contrapuntal/rhythm/form combinations.
Before the complete harmonic system was ever perfectly codified, however, Western art music jumped the tracks and went off in an anti-musical direction. Even today, there are still some who actually believe that Wagner forshadowed the atonalist movement with his opening to Tristan. Aside from the fact that this famous sonority is just a diminished minor-seventh in sound - in root position, no less - it is obviously just an ancient so-called French Sixth chord with a chromatic lower neighbor to the minor seventh. Hell, the thing even resolves into actually being a classic "French" V(d5m7)/V on the final eighth note of the measure in question before resolving to the primary dominant sonority as expected. Before the resolution it would have been V(4/#2/b)/V. The voice leading is "wrong" from a trasformational logic perspective... because it's a harmono-contrapuntal effect (!), but the chord itself is a simple altered secondary dominant, and not even a remote one at that. Gut-bustingly, even Wagner was ignorant as to what he was intuiting: What he was intuiting was entirely predictable given the implications of the harmonic overtone series, and that was amplification of the leading-tone/leaning-tone properties naturally present in every sound we hear.
That Arnold Schoenberg, the founder of all things "twentieth-century" in music, cited this feeble example from Wagner - and that others like Alban Berg agreed with him - as some sort of premonition of atonality, while a guitar playing cowboy from Texas could even figure out what was really going on... well, let's just say G-d has a great sense of humor... and justice.
Over the course of the past fourteen posts, I have demonstrated how aspects of every musical element - harmony, counterpoint, melody, rhythm, and form - are predicited by implications present in the natural harmony - the overtone chord - that nature bashes us in the eardrums with in every pitch we hear. This overtone chord, which has become known to music theorists as a dominant seventh chord, has desires present in it which wish to proceed: The leading-tone and leaning-tone tendencies, which are contained in the diminished fifth between the major third and minor seventh of this sonority.
If we simply stand back and let this dominant seventh chord do its thing, it works out for us the entire integrated tonality system - all of the secondary dominants and secondary subdominants - as well as the entire integrated modality system - all twenty-four possible tonics and all twelve possible overtone sonorities.
All we have to do is decide between the two possibilities the series implies - resolution to a major target or resolution to a minor target - and then decide if we wish to end up with a diatonic system (Ionian, or one of the viable modes of Ionian), a nona-tonic system ("Melodic" minor, Blues tonality, Flamenco tonality, and the like), or if we wish to operate within the complete dodecaphonic integrated tonal or modal systems: These outcomes depend solely upon how many resolutional cycles we allow, and whether the targets we chose are major, minor, or a combination of both.
What the problem is with a twelve-tone system in which "One tone relates only to another" - Schoenberg's words - is that what he was actually trying to define is a system in which all twelve tones are neutral: This is simply not possible. At all. Ever. No matter how hard you wish it wasn't so, wishing won't make that fact disappear.
In order to discover the truth about a thing, you have to consider every possibility surrounding it, even those you may personally find distasteful, and especially those in which you have a large degree of interest invested. The fact that every pitch in the twelve tone system carries an overtone chord along with it - like so much baggage from past realtionships - and since the relationships between these pitches are actual ratios from the overtone series (Or close enough approximations, regardless of the temperament scheme you chose), there is exactly a zero percent possibility that you can present these twelve pitches in a way that makes them all neutral: The pitches themselves desire to have relationships with each other, and to establish a hierarchy.
Every pitch desires to have a relationship with the tone a perfect fifth below it through the inherant resolutional desires present in it's overtone structure. But, before it can do that, it must become one of the two possible tonics - either a major or minor triad - by acquiring a fifth and a third. Though it seems counter-intuitive, the pitch in question becomes a tonic by being targeted by the overtone chord a perfect fifth above it: The integrated modal system is really an endless Mobius Loop of minor tonics becoming major tonics before acquiring a minor seventh in order to become the overtone sonority on that pitch, and then they reasove and are absorbed - literally - into the pitch a perfect fifth below, where the process begins anew.
In actual musical practice, however, a hierarchy must be established which nominates and establishes one of the pitches as supreme - whether it be as a major or a minor triad - in immitation of the most perfect diatonic system that the series implies, which is the major key or Ionian mode. This tonic may be any of the pitches in the chromatic system, but it must be one of the pitches in the chromatic system, and it can be either major or minor, but it must be one or the other (Though major may end in minor and vice versa: In fact minor tonics wish to become major tonics by the end of pieces, to which hundreds of years of the tierce de Picardie practice can attest).
Once this tonic is established, the entire secondary dominant and secondary subdominant solar system orbits around that star. Around the respective secondary dominants and secondary subdominants orbit their moons, which are the various major and minor substitutes for them which are on the degrees a third above and a third below those degrees. And so, the old pissed-upon Musica instrumentalis - the lowliest of the ancient musical divisions - finally reveals itself to be the real and true expression of Musica Universalis or The Music of the Spheres.
In order to accept any form of what has been called atonality as music - serialism, stochastic process, &c. - you would have to expand the definition of music beyond what the harmonic overtone series defines as musical. You may do that for yourself, but I simply shall not allow for it.
You can argue that what Arnold Schoenberg, Alban Berg, Anton Webern, Elliot Carter, and John Cage created (A woefully incomplete list of infamous musical miscreants) was some sort of sonic art - I am personally 100% certain that all of them (And many more) were (And are) mere charlatans - but there is absolutely no way that you can claim that it is music.
It is not I who prevents the above named "composers" - the first set of composers in history who began decomposing before they died - from being classified as creators of music, it is the actual nature of sound itself which prevents it. In other words, it is not I who rebuke you, but G-d.
I don't expect that I will change the minds of those who refuse to change or believe the truth, but neither do I feel any pity for those who choose to remain willfully ignorant of the musical implications of the harmonic overtone series: They have chosen for themselves the obscurity to which they will be relegated.
One thing I have no fear of is human intuition: Those not blinded by the petty conciets of their puny egos will always recognize music when they hear it. Plus, those who truly love music will always learn how to create it. And so, the general populace will continue to eschew all forms of atonality - as they have for over fifthy years now - the pseudo-intellectual class will continue to pretend that they "get it" while clutching desperately at the figleaf that hides the obvious fact that they have absolutely zero inate and intuitive musical talent, and the real composers who do have talent will continue to churn out real, actual music. You know: The kind of stuff people applaud.
I am perfectly certain of this.
"Music must never forget itself..." - Wolfgang Amadeus Mozart
And so ends the first complete rough draft of the musical implications of the harmonic overtone series. I have, for the first time in music history, shown the relationship between all five of the musical elements - Harmony, counterpoint, melody, rhythm, and form - and the harmonic overtone series. No biggie.
I have based my work upon the previous efforts of every music theorist in all of Western music history, plus the more ancient Greek works that they reference: Hucbald, Prosdocimus de Beldemandis, Heironymous de Moravia, Guido of Arezzo, Anecius Boethius, Gioseffo Zarlino, Johann Fux, Jean-Philippe Rameau, Frederich Marpurg, Johann Albrechtsberger, and all of the moderns: There is hardly a muisic theorist in history who has not contributed to my understanding, and for that I thank them. My work is their work.
The last thing I ever intended was to write a philosophical music theory book. This work is simply the result of my love of music, and the insatiable hunger for understanding that love has created and fuelled. I have a collection of music theory books that would put many colleges to shame - and they are not just decorations or status symbols: I've read and studied them all - and this present work is simply the result of thirty years of working to understand everything I can about music.
My understanding is far from perfect, but it's pretty "effing" good.
Just a couple of shelves worth: The top shelves.
It's not like she's going to melt, or anything.