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.
http://hucbald.blogspot.com/2008/08/sonata-one-in-e-minor-iv-axial-fugue-in.html
So,
from beginning the first E-Axis Study to finishing the Axial Fugue was almost
exactly twenty years. It has been
an enjoyable journey.
George
Pepper