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Hope all are enjoying good times with family and friends. I'll start a mega-posting series tomorrow.

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Post Haste

v 2.0 of the CD is now recorded, and the edited version of "Implications" is on it's way to me, so regular posting will resume within a few days.

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Two Sample MP3's from my Upcoming CD

If you go to my .Mac Download page here there are two MP3's at the top of the page which are tracks 21 and 23 respectively from the CD. These tracks are raw: I have not scrubbed the noise from the heads and tails yet, but that is all the editing I plan to do. I'm not really a good enough guitarist to worry about getting perfect performances, so I just don't mind if there is a buzz, squeek, or dropped note here or there. You have to pick your fights carefully in music, and I can afford to be a perfectionist about my composing, but not my playing: I simply don't have the time or inclination to be enslaved to scale and metronome work. I'd rather write or study.

The bonus is, this is exactly how I sound live: All I'm doing for this CD is playing the pieces down to half speed with the metronome, and then I record three takes. The take I like the best gets on the CD regardless of whether it is a great performance or not.

These tracks are from the E Major suite, which is quite late in the set, so there a lot of effects. The set starts with a fairly dry sound and builds from there. Track 21 is a Figuration Prelude, and is in a five voice texture and 12/8 time. It's modulatory and structural plan is like so:

A: E Major
B: C-sharp Minor
C & D: E Major
E: Whole Tone/Octatonic Episode

A': E Minor
B': C Major
C' & D': E Minor
E': Whole Tone/Octatonic Episode

Codetta: E Major

The harmony is very dissonant, but in a (hopefully) beautiful or awesome sense. Those harmonies are also extremely difficult to play: I jokingly call these preludes "Hard Chord Music" around my students.

Track 23 is an Axial Study: B-Axis Study in E Major. The device used in this piece is the repeated open B-string of the guitar between the notes of the melody. The texture is basically traditional two part counterpoint, whith the open B added as an incipient third voice (Basically a drone). The form is A, A', B, C, A" with the B section being an interlude, and the C being the traditional sequential section. It goes as high as F-sharp and is quite a challenge to play. None of these axial studies modulate.

Keep in mind that these are pieces I wrote back in the 90's and this project is a warm up to the second CD of new stuff I've written since I did the first demo of this back in 2000.

Enjoy.

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Just a Little Longer

I'm busy recording a CD and my book is with the editor now.

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Musical Implications of the Harmonic Overtone Series: Epilog

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Philosophical Conclusions

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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.

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Musical Implications of the Harmonic Overtone Series: Appendix III

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Melodic Musical Examples

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This appendix example is also harmono-contrapuntal in conception, but I used a combination of large scale strategic and small scale tactical processes to create both the melody and the bass line that lend themselves to clear analysis, which is why I chose it.

Before I studied the Theory of Melody book of The Schillinger System of Musical Composition all of the melodies I wrote were almost completely the product of my intuition. Sure, I thought in terms of outlining the harmonies with melodic elements &c., but I didn't use large or small scale planning to organize them. This has been true for almost all composers of history, so far as the written theoretical record is concerned. If any composers did develop these kinds of tactics and strategies - which I suspect some like Bach and Brahms did - they were never recorded in a pedagogical manner.

Though the inherent genius of a gifted intuition has doubtless lead to some of the most sublime melodies ever written, Schillinger demonstrated that melodic elements could be categorized and analyzed to inform the intuitions and intellects of those of us who are not so trancendentally blessed. I know that my own work improved markedly after my exposure to Schillinger, so I'm sure this will work for others as well.

You'll notice in the analysis line of today's example that I have dispensed with the traditional degree analysis symbols. I believe my previous contrapuntal examples have amply demonstrated the shortcomings of traditional harmonic analysis in a contrapuntal context, so now I present a new alternative for the first time.

There are only five possible functions that harmonies can have: Tonic, subdominant, dominant, secondary dominant, and secondary subdominant. Every harmony on every degree of the intedrated tonal/modal twelve-tone system will fall into one of these categories. Tonic, subdominant, and secondary subdominant harmonies can imply either major or minor base triads, but dominant and secondary dominant harmonies will always imply major base triads because they are overtone chords or altered overtone chords (The real root may simply be absent in some cases).

Therefore, there are eight possible harmono-contrapuntal analysis symbols: T, t, SD, sd, D, SD2, sd2, and D2. These symbols correspond to tonic major, tonic minor, subdominant major, subdominant minor, dominant, secondary subdominant major, secondary subdominant minor, and secondary dominant.

Not only does this make more sense for contrapuntal textures, but it simplifies and streamlines the process as well. There is no substitute for degree analysis in harmonic textures because it is that very degree analysis that allows for root progression patterns to be created (Or detected, if you are analyzing the work of another composer: I use analysis in the compositional process, so that is the perspective I'll usually speak from). Beyond that, however, this functional analysis tells you how any particular harmony is actually working within the system implied by the harmonic overtone series, and so it is even more valuable than degree analysis in some ways.

With this system and in this context root progression and transformation indicators are also not needed (Traditional "common practice" composers did not use consistent transformation technology anyway, since it hadn't been figured out back then), which only makes the process less ponderous and frustrating.

There are instances of ambiguity, of course: No system is perfect, but there are certainly less ambiguities with figuring out functional categories than degree orientation in two part counterpoint.

*****

This piece is the thirteenth of the Eighteen Axial Studies I wrote for solo guitar between 1987 and 1997: It dates from 1993. The idea for these came directly from Joseph Schillinger and his concept of the zero-axes of melodies. He used as one of his examples the subject from the D Minor Organ Fugue, which has a zero-axis that is actually played, versus being only implied (This piece is almost universally attributed to J.S. Bach, but I can tell you with 100% certainty after analyzing it and just a ton of Bach's music that he did not compose it. Beyond that, as a guitarist I can tell you with virtual certainty that the original must have been for the lute There is the remote possibility that it could have been for the violin). Modern scholars are now beginning to realize these things).

Anyway, I realized that the played zero-axis concept could lead to a nice series of idiomatic guitar pieces, and since the zero axis could be the root, third, or fifth of a tonic major or minor triad, there were six possibilities for each axis. For the high E string that worked out to E major, E minor, A major, A minor, C major and C-sharp minor. For the B string that lead to B major, B minor, E major, E minor, G major, and G-sharp minor. Finally, the G string lead to G major, G minor, C major, C minor, E-flat major, and E minor. This one, therefore, is the first of the G-Axis Studies in G major.

For this melody's organizational strategy I used two structures: A directional unit and a rotational unit. The directional unit is a series of four notes which all progress in the same direction, while the rotational unit is a series of four notes which make upper and lower neighbor relationships between a repeated pitch.

For the directional units, there are only two possible forms: They either go up, or they go down. The rotational units, however, can appear in four forms: Original, inverted, retrograde, or inverted retrograde.

Both directional and rotational units can appear in conjunct contrapuntal forms or disjunct harmonic forms, though I do not exhaust all of those possibilities in this particular piece.

The directional units are labelled with the letter "A" in the melodic analysis, and the rotational units are labelled with the letter "B." The two possible orientations of the directional unit are labelled A and A', while the four forms of the rotational unit are labelled B, B', B'', and B'''. I have written which orientation is which in the melodic analysis.

The first section of this piece is a ten measure phrase that repeats. The bass line is interesting in that, after a tonic half note, it progresses stepwise up the entire diatonic scale to the seventh degree in a series of quarter notes, and then proceeds in alternating falling fifths and rising fourths through all of the diatonic degrees again, but now in half notes. The phrases turn-around is then an implied four to five. If you sing this bass line, it is actually quite infectiously catchy (I have it as an "earworm" just thinking about it).

Over this bass line, the melody descends through six degrees of the diatonic system before turning around in the second half of the first rotational unit. So, the first two measures are the decending version of the directional unit, and the second two are the original form of the rotational unit.

Though the nature of the directional unit is clear - they always are, by definition - the merge into the first form of the rotational unit makes its nature unclear. So, even though it is a rotation on the subdominant level - fa, mi, fa, sol - I immediately repeat it on the tonic level above in it's original form as do, ti, do, re. These are also intervallically strict in relation to each other.

Now I can use the other orientations of the rotational unit and the mind's ear will follow, at least intuitively. The first variation I present is the inversion labelled B'. Notice that as mi, fa, mi, re it is an intervallically strict inversion as well. Immediately after the inversion, I use the retrograde of the original as do, ti, la, ti to turn the phrase around.

This entire first section is completely diatonic to the major mode, and so it sounds quite happy. In fact, diatonic major sounds happy because it conforms most perfectly with the implications of the series for a diatonic system! I have saved the first appearance of chromaticism and the final form of the rotational unit for the repeat. The other form of the directional unit appears in the repeat as well.

As you can see, I use a D2 in the form of an augmented sixth interval targeting the fifth degree at the beginning of the third system. Along with the resolution to the D this creates a chromatically altered form of the inverted retrograde of the rotational unit, which is highly effective and satisfying.

The dominant targets the tonic as expected, and then another measure of dominant functionality prepares for the next section. The final two measures present the ascending form of the directional unit for the first time, only now it is intervallically expanded to a series of thirds, whic create, en toto a tonic major seventh arpeggio with the fifth and seventh being reinterpreted as the root and fifth of the D-function chord.

After all the sweet happiness of the first section I throw a couple of wrenches into the works. The second section - which has the function of an interlude - metrically modulates to 3/4 time, and the dominant sonority at the end of the previous phrase "resolves deceptively" in traditional parlance to the sixth degree tonic substitute.

The bass part of the first phrase of the interlude allows for a secondary dominant targeting the primary dominant, while the melody above has created a secondary dominant targeting the preceeding subdominant degree. This combination of the broadening out of the pace combined with the more expressive implied harmonies give this interlude a plaintive, yearning quality. That the expected primary major tonic never appears adds significantly to this.

In this repeat as well I have employed some extended harmonic implications of the series: In the first measure of the fifth system I have used a double chromatic approach to the dominant degree, the final of which creates another augmented sixth. It is important to note that the progression from c-sharp to e-flat is a diminished third, and so the ear hears this as a contrapuntal whole step and not a harmonic third. Kind of a nifty effect.

This primary dominant harbors an augmented triad in the melody, which is kind of unusual in a major key piece, and it sets up another measure which makes the repeat a five-measure phrase. You can see from the functional analysis that a momentary tonic inference is made at the beginning of that final measure, and then a dominant series which is simply a degree exchange between the upper and lower voices.

The third section is the "real" second section: The interlude was designed to be a pause in the texture, which would have become oppressive if it had continued unabated. Here, the two directional units are used in a sequential section, with the original stepwise descending version now following the ascending intervallically expanded form.

The bass part has broadened out further into tied half notes. There is a rest in the second measure of this secion because the guitarist must physically release the low G in order to reach the upper notes: It remains implied.

The disjunct motion followed by conjunct motion implies alternating harmonic and contrapuntal effects in the texture, and it is quite sweetly diatonic again for these eight measures. As you can see, the initial ascending tonic triad and the following ascending supertonic tetrad both reach the same G. This is at the fifteenth fret on the guitar, and so is quite high.

Oh yeah: Restrictions on the distances between voices in counterpoint are poppycock for instrumental music. As you were.

The overall harmonic motion is four measures of tonic, two measures of subdominant, and then the dominant for two measures.

*****

The continuation of the second section - now in its third phrase - offers another deceptive motion from the preceeding dominant to the submediant tonic substitute. This is followed by two measures of a secondary dominant function, which leads to the expectation of a resolution to the dominant, but this is spectacularly thwarted.

On the second system down is the climax of the piece. Remember that ascending scale in the bass of the first section? Though it rubbed up against the zero-axis it never actually made it to the tonic degree. That was a setup, and here is the fulfillment. The G in the bass part - as opposed to the G in the zero-axis - is the resolution of that preparation of long ago: It is also the highest note in the bass part, and since the axial G is an open string, this real unison is played on the guitar (Take that, you single-manual keyboard players).

The bass part descends in a chromatically altered form of the original directional unit into a D2-function sonority in the form of a doubly-augmented fourth. This resolves across the barline into the primary dominant, satisfying both the e-flat and the previous c-sharp that was leapt out of. Remember the c-sharp to e-flat bass motion from the first interlude? Another setup for this climactic resolution. The b-natural in the melody, by the way, is at the nineteenth fret on the guitar: That is the highest note on the traditional classical instrument. This climax is only possible because the D in the bass part is an open string.

In the final four measures of this section we have the denouement of the piece, and again, this only works because the E, A, and D in the bass are open strings on the guitar. I remember when I wrote this how amazed I was that it all worked out so perfectly: It's a great combination of pure music and an idiomatic guitar piece.

As I used an augmented triad earlier, I have answered that with a fully diminished descending directional unit to end the section. This gives a whistful end, and the overall effect of the piece is sort of Romantic, even though it's contrapuntal in conception. This diminished tetrad is also the first intervallic expansion of the descending directional unit to appear.

Following this section is a second interlude. This is almost exactly like the earlier one, except for the fact that the melody is an octave lower, and the resolution is as expected to the tonic, versus the sixth degree tonic substitute.

The repeat is quite different, however: Since the peiece will come to an end after the second time through this interlude, I do not want it to set up the leading-tone/leaning-tone dual target to the dominant degree again. For this reason I have allowed the c-sharp to resolve at the end of the first measure of the repeat, but I immediately introduce the sixth degree tonic substute to set up the final element at the ending of the piece.

In the penultimate measure of the second interlude's repeat is the only secondary subdominant in the piece, and it is the traditional so-called Neapolitan Sixth, but instead of preparing the dominant it resolves to the tonic (I could have put a small letter "t" there, but I was factoring in for the G-axis, which I usually ingnore in the functional analysis, naturally).

This sets up the traditional plagel "Amen" in the last three measures of the piece.

*****

This concludes the appendices for the present version. I suppose I ought to have some examples to demonstrate rhythmic and formal aspects of the implications of the series, but to be honest, I don't concieve of pieces from those perspectives. The musical material I develop combined with the local tactics and regional strategies I employ are what determine the rhythmic and formal properties of the pieces I write. I know of composers who say the first decision they make is what the duration of the piece will be, but that is almost impossible for me to imagine. The possibilities of the material I come up with determine the length for me.

I will write a final epilog with some philosophical conclusions, and then I'll be done with this for the time being.



I suppose that is technically possible.

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Intermission

Not bad for an old cowboy in his forty-ninth year.



But then, cute young girls in impossibly embarrassing situations are a dime a dozen.



Right? Riiiiiight.

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