Wednesday, March 03, 2010

Joseph Schillinger Inspired Guitar Pieces

One of the Facebook groups I belong to holds online classes about aspects of The Schillinger System of Musical Composition, and since I have studied Schillinger on and off for over twenty years now, I thought I'd share some of the solo guitar pieces I've written that Schillinger inspired.

I put a page together with PDF files of the scores and MPEG4 streaming audio - my usual MIDI to AAC conversions - so that my Facebook Friends could peruse them at their leisure, and that open directory is here, but I'm going to list them all below, with an example fully analyzed.

The way this twenty year journey started was - back in 1986 when I was still a rock guitarist living and working in NYC - I was visiting a musician friend and noticed a copy of The System on a bookshelf in his studio. Being a Berklee alum, I had heard of it - Berklee was originally called Schillinger House - but I'd never actually seen a copy. Long story short, I borrowed it, and ended up making so many notes in the margins that I kept that copy and ordered my pal a brand new one. Not cheap!

These three sets began when Schillinger used the fugue subject from the Toccata and Fugue in D Minor as an example of a melody in which the zero axis was played, rather than simply implied. I realized that this played zero axis device would lend itself to a series of idiomatic studies for solo guitar, and so I was off and running.

Since the played zero axis could be the root, third, or fifth of a tonic major or minor triad ,that meant that each set would have six pieces in it. For the high E string then, the keys would be E major, A minor, C major, C-sharp minor, A major, and E minor if organized in a quasi-symmetrical way, which is what I ended up doing. I started composing these in 1986 or 1987 - I really don't remember exactly anymore - and I distinctly remember hearing about Segovia's death when I was working on learning one of them.

So, here are the Six Studies on an E-Axis:

E-Axis Study Number 1 in E Major - m4a

E-Axis Study Number 1 in E Major - PDF

E-Axis Study Number 2 in A Minor - m4a

E-Axis Study Number 2 in A Minor - PDF

E-Axis Study Number 3 in C Major - m4a

E-Axis Study Number 3 in C Major - PDF

E-Axis Study Number 4 in C-sharp Minor - m4a

E-Axis Study Number 4 in C-sharp Minor - PDF

E-Axis Study Number 5 in A Major - m4a

E-Axis Study Number 5 in A Major - PDF

E-Axis Study Number 6 in E Minor - m4a

E-Axis Study Number 6 in E Major - PDF

NOTE: For some reason, PDF files often don't render properly for me from in Safari. If you end up with bizarre figurations instead of music, just hit the BACK button on your browser, then FORWARD. This always clears them up for me, though I may have to also scroll down to the bottom to make all of the text elements show up.

Since I was just starting out with classical music back then - I was 29 when I wrote these - they range from completely diatonic to major, as Number 1 in E Major, through diatonic to melodic minor, as Number 6 in E Minor, to having only one implied secondary dominant, as in the remaining four. These are excellent technical studies, and they are accessible to any intermediate level student of classical guitar. They are also fun to play and pleasant to listen to. I still perform all of these in my set to this day.


Once I had completed these six pieces and a few others not related to them, I decided to give up the rock lifestyle and go back to school for a Master of Music in traditional theory and composition. Since I was still working on aspects of Joseph Schillinger's work, it was only natural that my final project was, Aspects of Joseph Schillinger's System of Musical Composition as Applied to Composing for Solo Guitar. I presented this as a lecture recital in which I performed the following pieces and explained how I used Schillinger's techniques in creating them.

These studies are on a B-Axis - the open B string of the guitar - and the melodic trajectories are above the zero axis, instead of below them as in the E-Axis studies. As a result, the melodies have larger ranges and the pieces are far more difficult to execute.

Six Studies on a B-Axis:

B-Axis Study Number 1 in B Major - m4a

B-Axis Study Number 1 in B Major - PDF

B-Axis Study Number 2 in E Minor - m4a

B-Axis Study Number 2 in E Minor - PDF

B-Axis Study Number 3 in G Major - m4a

B-Axis Study Number 3 in G Major - PDF

B-Axis Study Number 4 in G-sharp Minor - m4a

B-Axis Study Number 4 in G-sharp Minor - PDF

B-Axis Study Number 5 in E Major - m4a

B-Axis Study Number 5 in E Major - PDF

B-Axis Study Number 6 in B Minor - m4a

B-Axis Study Number 6 in B Minor - PDF

In these I have a lot more chromatic action going on, and I'd discovered augmented sixth intervals by this time, so those are quite prevalent. Also, whereas in the E-Axis studies the parallel mode versions were mostly gender transpositions - I was still figuring out classical major and minor - here all six are individual compositions. There's also some humor here, especially in Number 4 in G-sharp Minor, where I did some "weird" stuff just because it tickled me. Again, these are excellent technical studies, and audiences seem to enjoy them, but you do have to be a fairly advanced player to pull them off convincingly. I perform all of these in my set as well.


After being awarded a Master of Music in 1991 for the above project, I decided to go for a Doctor of Musical Arts degree at The University of North Texas. While there, I composed the final set of six.

Six Studies on a G-Axis:

G-Axis Study Number 1 in G Major - m4a

G-Axis Study Number 1 in G Major - PDF

G-Axis Study Number 2 in C Minor - m4a

G-Axis Study Number 2 in C Minor - PDF

G-Axis Study Number 3 in E-flat Major - m4a

G-Axis Study Number 3 in E-flat Major - PDF

G-Axis Study Number 4 in E Minor - m4a

G-Axis Study Number 4 in E Minor - PDF

G-Axis Study Number 5 in C Major - m4a

G-Axis Study Number 5 in C Major - PDF

G-Axis Study Number 6 in G Minor - m4a

G-Axis Study Number 6 in G Minor - PDF

Here I began to transcend the original conception I started with: No. 1 has two interludes an octave apart, No. 2 has a melody that breaks away from the axis entirely in a few places, No. 3 is a "free-voiced" piece that ranges from two contrapuntal voices to five and has no interlude, No. 5 requires some extended techniques (Fretting with the right hand i finger), and many of the interludes are in different time signatures. Nos. 1, 3, and 5 go beyond mere guitar studies into being concert etudes, and all of these are wicked difficult. I still don't perform No. 3 in E-flat Major all these years later, but it is coming along.


Here's the analysis I did for my Schillinger cronies of B-Axis Study Number 1 in B major.

This particular Axial Study is a good example of the employment of several Schillinger principles in a simple work that makes the techniques very clear. In this case, the played zero axis of the melody, the open B string of the guitar, is the root of the tonic B major triad, while the texture is two-part counterpoint, not counting the played zero axis as an incipient third voice.

Here, the played zero axis begins as a pickup eighth note, and the genesis of the melodic trajectory is out of that and above the axis. For the construction of the melody, I employed Schillinger’s technique of Quadrant Rotation, which is using an original figure in all four of its possible permutations: Original, Inversion, Retrograde Inversion, and Retrograde in this instance. The simple rotational melodic figure of measures one and two reads, re, mi, fa, mi in the key of B, so that is the original form. Measures three and four answer that with, la, sol, fa, sol, which is a diatonic inversion of the original. Then, in measures five and six, the figure morphs into, do, ti, do, re, which is the retrograde inversion, and finally, the figure appears in seven and eight as, mi, fa, mi, re, which is an exact retrograde of the original an octave higher. Measures nine to eleven simply bring the trajectory back toward balance for the repeat with a stepwise scalar passage.

For the bass melody there are a pair of rough diatonic augmentations of the melodic figure, which you can see just by looking, in measures one through four, and again in five through eight. Even very casual approximations like this lend effectiveness to a piece of music: It is not necessary to strive for formulaic exactitude all the time.

Note another idea that Schillinger made me aware of, and that is asymmetrical phraseology: The A section is 11.25 measures in length, counting the pickup bar. The melodic peak of E in measure seven, then, comes at measure 7.75 out of 11.25, which is at about 69% through the phrase. This is very close to the natural norm, which is 66.6%, or 2/3rds of the way through: This is a “happy” section as a result of this natural melodic form combined with the diatonic major mode.

At the second ending the melody turns around to go into the interlude. Note that this creates an augmented retrograde-inversion of the original melodic germ.

The interlude starting at ten functions as a respite from the original texture, and here I establish a secondary axis on F-sharp that has 1/3rd the number of attacks as the primary axis. This is obviously the perfect fifth of the tonic major triad. I also made a point to work a version of the original rotational figure into this, though, as in measures nineteen and twenty we get, la, sol, fa, sol, which is exactly the same inverted form heard in measures three and four. Tres cool, non?

Another idea I got from Schillinger that is here applied intentionally, but in a casual non-rigorous way, is the idea of modifying themes by intervallic expansion. I touched on this briefly when I described the bass melody of the A section. Here, in measure twenty-five, the melody starts out as if it is going to make a retrograde statement of the original figure, but the following intervals are expanded to minor thirds, creating a diminished triad as the tail of the motif. This is a prefiguring of what is to come in the B section proper. Note that the F-double-sharp creates a DINO – Dissonance In Name Only – over the E in the bass: A notated augmented ninth is in sound a minor tenth. This allows both voices to proceed up stepwise – a semitone in the lead and a whole tone in the bass, into the true dissonance of a major ninth. Just a little contrapuntal affectation I’m fond of which produces an effect I enjoy.

At twenty-nine then, the proper B section begins, and it starts out as a regular sequential section for the first three phrases. Even the bass melody is perfectly sequential after the initial intervallic adjustment of a falling minor third in measure twenty-nine.

For the climactic phrase I wanted something more dramatic, so I employed a symmetrical structure; an augmented triad in this case. These are highly unusual in early common practice music, which is where most listeners are familiar with two-part counterpoint textures from, so it really is a surprising device, especially in a major key piece like this: Even in early Romantic homophonic music, these are more common in minor keys.

After using the augmented triad to quickly and dramatically increase imbalance with its rapid departure from the melodic axis, I answered it, so to speak, with another symmetric structure, a fully diminished seventh chord, on the descent back to balance in measures forty-five and forty-six.

Again, fully diminished seventh arpeggios are far more common in minor key pieces, so this continues the drama, albeit at a reduced level of intensity, even as the trajectory returns to balance for the next statement of the A section. So, I set this climax up – foreshadowed it, in other words - with the diminished triad I employed back in the interlude: We’ve heard a diminished triad, an augmented triad, and a fully diminished seventh chord in the melodic trajectory in this piece. By employing devices like this strategically and sparingly, very satisfying musical effects can be achieved, even in tiny miniatures of very limited scope, such as this guitar study.

This B section is eighteen measures in length, which, while an even number, is still not divisible by four, so it isn’t exactly square: The first three phrases are four measures each, but the final climax and denouement phrase is six measures, which divides as four plus two. Since the melodic peak is at measure 15.5 out of eighteen, that gives the 86% point, which is much later and more dramatic than the more normative climax back in the A section.

In conclusion, Schillinger has much to offer a composer, whether that composer has a proclivity for the rigorous formulaic aspects of The System or not. By simply internalizing a few of the concepts he presents, and employing these tactical devices in an organic stratagem, anyone can increase the effectiveness of their compositions, regardless of style or scope.


I was editing the G-Axis Studies until 2000, so after six plus years, I returned to the concept for the fugal finale of Sonata One for Solo Guitar.

Axial Fugue in E Minor - m4a

Axial Fugue in E Minor - PDF

I did an epic analysis post of this piece here on MMM back in 2008.

From the first diatonic E-Axis Study to the epic 405 measure Axial Fugue was almost exactly twenty years. When you get a, "Big Idea" like these Axial Studies as a composer - we're lucky if we get a half dozen of these in a lifetime - you want to follow it as far as it takes you. If you listen through all of these, the musical evolution is quite evident, and there would never have been any Axial Fugue without those other eighteen pieces that lead up to it. Also, since I used the E-Axis trajectory-below-axis paradigm for the Axial Fugue in E Minor, I am also aware that the B-Axis trajectory-above-axis paradigm is also a possibility for another epic Axial Fugue in B Minor. Yeah, that's cooking in my noggin right now, but it will probably be a few more years before I commit pencil to paper pixels to screen on it.

The primary reason to study things like The Schillinger System and Convertible Counterpoint (The other book that contributed to the Axial Fugue, but that's a story for another post) isn't to understand music better, that's just a byproduct: The primary aim is to get inspiration for compositions.


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