About Schillinger Works:
Nevertheless, I asked Marteen if I could borrow it, and so I took it back to my apartment in Hoboken and began to read it. It was so dense with material and unfamiliar terminology that I quickly decided that IÕd just read through it once Š cover-to-cover-to-cover-to-cover Š like it was a novel, to just familiarize myself with the terminology. That was the best decision I made in that endeavor.
Frankly, the system is a mess. It didnÕt take me long to figure that out, but I wondered why: There were nuggets of incredible insight buried within acres of jumbled up presentations, and the musical examples Š those not by great composers of history - were impossibly lame. A little research lead me to the discovery that The System was put together after SchillingerÕs sudden and untimely death by some of his students. Once you realize that the System was not put together under SchillingerÕs supervision, and is certainly not anything like how he would have presented it, it actually becomes easier to deal with: The shortcomings are understandable.
Another hurdle many musicians face with the system is that most of us have asymmetrical intellectual abilities biased towards abstract and mechanical reasoning, and away from numerical abilities. IÕm a pluperfect example of this, as I have top 1% abstract reasoning scores and am below the 50th percentile in numerical. This means that the systematic and formulaic core of The System is simply not of any use to many of us, and realizing this also makes Schillinger more approachable: Just skip all of the formulas, like I do, and pretend they arenÕt even there. What is important to those of us with natural musical intuition Š but lacking mathematical minds - is internalizing the concepts. If you are a musician like I am, your mind works in terms of sight and sound: If you can see it and/or hear it in your noggin, you can manipulate it. Numbers look and sound like nothing to me, so I simply canÕt process them. I stopped worrying about this decades ago. Fortunately, The System has lots of diagrams: Concentrate on those if youÕre mathematically disinclined. ItÕs no moral failure if you canÕt do numbers, itÕs simple genetically defined aptitude.
There is no doubt but that SchillingerÕs greatest contribution for most of us is his Theory of Melody, which is the only rational theory of melody extant. Schillinger defines a melody as a trajectory of pitch through time. With my students I use a football analogy: The composer is the quarterback, the football is the melody, and the listener is the receiver. When the QB throws the ball, he imparts spin to it so that it is stabilized in flight. Likewise, the composer imparts spin to a melody to make its trajectory logical. During flight, the football encounters forces of resistance in the form of gravity and atmospheric friction. Likewise a melody, as it rises away from its zero axis, encounters musical gravity and resistance to increasing velocity. So, if the football only encountered gravity, the peak of its flight would be somewhere just past the halfway point, but the wind resistance makes the peak closer to the 2/3rds point: This is the most common placement of a melodic peak as well. In other words, a natural melodic trajectory mimics other natural phenomena with which we are all intuitively familiar.
To extend the analogy, the QB may throw the ball over the receiverÕs head, forcing him to leap to catch it. Likewise, the composer may stretch the integrity of the melody, forcing the listener to work for the understanding of it. Or, alternately, the QB may put the ball right on the receiverÕs numbers, just as a composer may satisfy the listener in a simple way: As long as the ball is caught/the melody is perceived, the reception is a thing of beauty. Failure to connect is a lost down/poor melody though.
The other major breakthrough that Schillinger enabled for me was in the area of counterpoint. I was given the counterpoint virus by Chris Frigon when I was at Berklee, but I had never created anything that I thought was particularly sublime until Schillinger pointed out that the main feature of great counterpoint was that it was a combination of two Š or more Š complementary melodic trajectories, and not simply a succession of intervallic relationships at various ratios (1:1, 2:1, 3:1, &c.). Looking at CP this way gave me a meta view of the process, and I was creating pleasing, if simple, counterpoint pieces within a few months of figuring this out.
Finally, Schillinger says his Theory of Rhythm is the foundation of The System, and that everything else depends on the understanding of it. Well, perhaps if you want to do The System proper, but if you just want to inform your preexisting musical intuition, bunk. I never understood how to apply anything from Theory of Rhythm. Sure, I understand how the resultants work, but they are exceedingly boring as surface rhythms, and The System flatly states things like, Ņresultants can be used to distribute parts within a scoreÓ without actually explaining how to do it, much less providing any examples. IÕd suggest reading it though, because you may have a more fertile mind than mine in that area. To me, Theory of Rhythm is a mildly interesting book of no practical worth, and until I meet somebody who can say, ŅhereÕs how you use it,Ó IÕll continue to ignore it.
So, I donÕt use The System proper, just concepts from it, and in an ordered but intuitive way. I really think this approach will work for a higher percentage of musicians.
Other concepts that I got from Schillinger that have been of great use to me are, 1] The idea of mechanical efficiency in music, 2] The concept of asymmetrical phraseology (Phrases of odd measure lengths) and, 3] The effectiveness of employing symmetrical musical structures (Diminished and whole tone scales, and diminished an augmented triads mostly).
As for mechanical efficiency, I use another analogy with my students, and that is a comparison of modes of transportation. When Bach traveled, it was in a coach drawn by a team of horses. The coach was ornate, had lanterns for light, a top speed of just a few miles per hour, and was the last thing youÕd call aerodynamic. My favorite conveyance is my BMW motorcycle, which is powered by an internal combustion engine, has electric lighting, tops out over 120 MPH, and is very sleek and aerodynamic. Likewise, BachÕs music was a reflection of his lower tech and slower paced era: There are lots of pretty but mechanically inefficient noodlings, and ornamentations that slow or even interrupt the pace. Modern music Š even tonal music Š ought to be streamlined like my Beemer, and not ornate like BachÕs coach (And clothing!).
Asymmetrical phraseology surprises the listener. I got this idea from where Schillinger explains that the most desirable fugue subjects are odd and fractional measure lengths, as this keeps the flow going forward better than square four-measure phrases, which can actually ruin a fugue. Simply put, I decided to apply that to non-immitative counterpoint pieces, and I think the effect achieved is a highly desirable one.
As for symmetrical structures in melodic trajectories, they serve two purposes: They suspend the feeling of tonality, and they can increase the rate of balance or imbalance depending on whether they are leaving or approaching the melodic axis. Bach used diminished seventh arpeggios a lot, but not augmented triads. I love augmented triads and use them often to get quickly from point A to point B while maintaining a level of tension, even if the trajectory is approaching balance. This is particularly effective at cadential points.
Before I got, ŅThe Big IdeaÓ for the Axial Studies in this series, I had composed a few small pieces in two-part CP for solo guitar, but when Schillinger used the subject from the D Minor Organ Fugue Š usually attributed to Bach, but I wrote an article demonstrating that Bach didnÕt compose it and that it was originally a work for Baroque LuteÉ but I digress Š is when I got the idea for these pieces.
I realized that the played zero axis could lead to a series of idiomatic guitar studies if the open strings were employed, and since that played zero axis could be the root, third, or fifth of a tonic major or minor triad, there would be six pieces for the high E string: E major, A minor, C major, C-sharp minor, A major, and E minor. So, thatÕs the key plan for the Six Studies on an E-Axis.
01_01: E-Axis Study No. 1 in E Major
01_02: E-Axis Study No. 2 in A Minor
01_03: E-Axis Study No. 3 in C Major
01_04: E-Axis Study No. 4 in C-sharp Minor
01_05: E-Axis Study No. 5 in A Major
01_06: E-Axis Study No. 6 in E Minor
I started these in late 1986 or early 1987, I forget which, but I do remember hearing about Andres SegoviaÕs death when I was working on one of them, and that was in 1987. Since the zero axis here is the high open E string, the melodic trajectory is projected below it, just as in the fugue subject from the D minor organ fugue. This creates an effect of musical anti-gravity, as the lower the trajectory gets, the further from balance it is. The anti-gravity effect is weaker than musical gravity, however, so itÕs not analogous in a symmetrical way. ItÕs an interesting effect though.
These pieces range from completely diatonic to major, as in No. 1, completely diatonic to minor, as in No. 6, to having only one implied secondary dominant function harmony, as the rest of them have.
Because the texture got tedious, I inserted an interlude between the A and B sections, so the forms are like this: A, AÕ, I, B, A, AÕ, I, B, AÓ. By reducing the number of variables, I was able to concentrate on becoming more facile with the melodic and contrapuntal concepts. Also, since I was trying to break my old jazz, pop, and rock rhythmic paradigms, I had to rely on the constant eighth note motoric rhythm: Back then, as soon as I tried to get rhythmic, it started to sound like jazz.
I mentioned that I used asymmetrical phrases: Nos. 1 and 6 have 13.25 measure A sections, counting the pickup notes; Nos. 2, 3 and 5 have 11.25 measure AÕs; and No. 4 has a 9.25 measure A. The interludes are all square by contrast, as are most of the B sections, but the A minor and A major studies have two measures of 2/4 alternating with two measures of 3/4 in the B sections. Originally I had this notated as five measures of 2/4 each phrase Š a hemiola, in other words Š but I found that young students balked at that, so I changed it to make it easier to read.
These pieces are so simple that the melodies donÕt even have to be graphed in order to be analyzed: The notation makes everything clear enough.
After finishing this set of pieces, I realized that I enjoyed solo nylon string performing and traditional composing more than being in rock bands Š songs about teen angst started to lose their appeal after thirty Š so I decided to go back to school for an MM in traditional theory and composition. It was only natural, then, that when I had to come up with a final project, I chose, ŅAspects of Joseph SchillingerÕs System of Musical Composition as Applied to Composing for Solo Guitar.Ó Also naturally, since IÕm not a good enough writer for scholarly work, I decided to present the project in the form of a lecture recital. ThatÕs where the genesis of the B-Axis studies originated. I started work on these in 1990 or 1991; again, IÕm not exactly positive any more.
I realized that there were six more possibilities with the open B string, and that with the E above I could have the trajectories above the zero axis: regular musical gravity, in other words, along with many greater possibilities for melodic range. The Six Studies on a B-Axis then, are:
02_01: B-Axis Study No. 1 in B Major
02_02: B-Axis Study No. 2 in E Minor
02_03: B-Axis Study No. 3 in G Major
02_04: B-Axis Study No. 4 in G-sharp Minor
02_05: B-Axis Study No. 5 in E Major
02_06: B-Axis Study No. 6 in B Minor
These follow the same plan as the E-Axis Studies, but are more advanced in conception as well as technically: They are much harder to play. They are also more chromatic, with No. 2 in E minor being particularly adventurous. I had discovered augmented sixths by this point, and was using them every chance I got. Also, I remember reading in some counterpoint book around this time that it was not good practice to have both melodies in a two-part texture moving chromatically simultaneously, so naturally I had to do it.
Most of these have asymmetrical A sections as well, but No. 3 does use an eight bar phrase there, and No. 4 is sixteen. Whereas the parallel major and minor pieces in the E-Axis studies were just gender transpositions for the most part Š I was still trying to figure out trad major/minor then - here they are all six completely individual compositions.
Again, these are so transparent that you donÕt need to graph the melodies to figure out whatÕs going on.
After getting the MM from Texas State, I decided to go to UNT for a DMA in composition, and while there I wrote the third and final set of six Axial Studies, the Six Studies on a G-Axis.
03_01: G-Axis Study No. 1 in G Major
03_02: G-Axis Study No. 2 in C Minor
03_03: G-Axis Study No. 3 in E-flat Major
03_04: G-Axis Study No. 4 in E Minor
03_05: G-Axis Study No. 5 in C Major
03_06: G-Axis Study No. 6 in G Minor
I began work on these in 1993 or 1994, and they are admittedly weird from a Schillinger melodic analysis perspective. Whereas in the E-Axis studies the melodic trajectories were below the zero axis and in the B-Axis studies the melodic trajectories were above the zero axis, in both cases the trajectories were generated out of the zero axis and were attached to it, so to speak. Here, the melodies are separate from the G-axis, so the G is more of an internal drone or pedal point than a true zero axis of the melody. Looking at the pieces will make this clear.
By this point I was also transcending the original conception, as No. 1 in G has two different interludes an octave apart, and No. 3 has no interlude at all, and is in a free-voiced texture that goes from as few as two voices to as many as four at the climax (Not counting the G-axis as an incipient additional voice, of corse). Both of these pieces rise above the level of guitar studies and into being concert etudes: They are technically very demanding, with the G Major study using the entire range of the 19 fret classical guitar. That melodic peak is approached by a doubly-augmented eleventh, by the way, and I even managed a traditional Neapolitan sonority in the second interlude.
Since these are so far more advanced than the earlier two sets, I didnÕt finish with all of the edits to them until 2000.
These Eighteen Axial Studies were my journeyman works, and I learned a ton from writing them. Then, after performing them for several years, I decided to return to the concept for the fugal finale of my first guitar sonata. Believe it, or not, the answer/counter-answer combination for this fugue is the A section of the A minor and A major E-Axis Studies. What happened is this: After Schillinger, I got into studying Sergi TanievÕs Convertible Counterpoint in the Strict Style. This is another book where the mathematical formulas just go in one eye and out the other with me Š I set up vertical and horizontal conversions mechanically on staves to that I can see them Š but there are also many cool insights one can get from Taneiev just by reading him like any old novel. One of those was this: ŅIn any contrapuntal combination in which there is only contrary and oblique motion, either one or both of the melodies can be doubled in thirds or sixths, and all resulting contrapuntal combinations will be technically correct.Ó As soon as I read that, I realized that the A sections of those old E-Axis studies in A minor and A major filled the bill. So, this fugue reveals all of the contrapuntal combinations possible with that concept.
04_01: Axial Fugue in E Minor
For a more thorough analysis of the fugue, you can read this blog post I did about it.
So, from beginning the first E-Axis Study to finishing the Axial Fugue was almost exactly twenty years. It has been an enjoyable journey.