Saturday, July 26, 2008

How to Compose Counterpoint (Imitation and Modulation 2)

This is part six in a series, following Where to Begin, How to Progress, Using Larger Forms, Using Three Voices, and Imitation and Modulation 1.

In part one of Imitation and Modulation we looked at a strict fugue, which is technically limited to modulations to the close keys - those differing from the tonic by one accidental in either the sharp or the flat direction. In that fugue were examples of normal modulations achieved by introducing a new dominant harmony, modulations achieved by deceptive motions from a dominant, and a modulation achieved through a sequential homophonic episode.

Today we will look at a ricercare, which is a looser fugal idiom that is not limited as to which regions it can modulate to. While the previous Fugue was the finale of Sonata Zero, this Ricercare is the middle movement (of five).

The key is C major and the subject is just an ascending form of the same subject used for the fugue. This creates a very interesting exposition, as the subject begins on the subdominant degree, and while it is at the very bottom of the guitar's range, it is actually the middle voice that speaks first. The answer, then, is a perfect fifth higher than the previous statement of the subject, even though it is now the lowest voice that states the thematic element.

Since the subject started out on the subdominant and its tail figure tonicized the tonic, the answer starts on the tonic and tonicizes the dominant. This allows the final statement of the subject to be presented over a vi triad, and then all three voices can move in parallel into the vii(d5) due to the unequal fifths involved. Note that the last statement of the subject is a full two octaves higher than the original statement. The original entering middle voice also has the range of a full two octaves in the exposition. These features are so unusual that they very well may be unique.

At the end of the exposition the harmony arrives at the tonic in thirteen. This modulatory episode is yet a third variation on the two heard in the fugue, and it brings the piece to a D(m7) chord, which will take the piece to the dominant region.

The incongruous first system is actually a major key restatement of the exposition of the first movement Extempore in A Minor (I composed this piece last of the imitative trio), and it ends on an implied I(6/3) of the new dominant level major key at measure twenty. I did this so that I could actually start out with the answer in this new key area - which presents an ascending series of 4-3 suspensions - and that leads to a tonicization of "the dominant of the dominant" at twenty-four, where an inverted form of the subject (the actual original fugue answer, to be precise) - along with another 4-3 suspension chain - brings the piece back to the dominant of the key of G at the end of twenty-seven.

Into the second modulatory episode I use a deceptive motion to an E minor chord, the vi of the key here, and this is yet a fourth variation on that original episode I came up with for the fugue. Notice how this time the sequence returns to the tonic of the moment, G major, at the beginning of measure thirty, and ends with an F#(m7) at the end: We're going to the key of B minor, which is the leading tone minor of the original key of C major. This is something you wouldn't want to do in a strict fugue, but in a ricercare just about anything goes.

Now in B minor, we get the answer along with 2-3 suspension resolutions, and it is the answer, so into thirty-five, F-sharp minor appears to be tonicized. However, since I use the answer form of the original fugue subject there, this is actually a modulation: We are now three sharps away from where we started - quite remote! The rest of this set stays in F-sharp minor to present the rectus and inversus forms of the 7-6 and 2-3 suspension-resolution chains. In fact, the last three systems here are just a half step lower and in the minor modal gender compared to the corresponding section of the fugue! That means, of course, that the final sonority at the end of measure forty-six is a C-sharp dominant chord. What to do with this?! What to do, what to do...

Hey, I got an idea: Why not treat that C-sharp overtone sonority as a so-called German Augmented Sixth chord (A subV7/I in jazz-speak, and a V(d5m7m9/0)/I in my modern terminology)? Then, we can just arrive at the original tonic! So, that's just what I did.

The sequential harmonic episode is the ricercare's subject (answer, actually) in augmentation, and therefore it arrives at a dominant-level triad.

Any time you want to modulate and you arrive an a dominant, there are eight resolutional possibilities: 1) Treat it as a dominant and resolve to normally to a new major tonic, 2) Treat it as a dominant and resolve it normally to a new minor tonic, 3) Treat it as a dominant and resolve it deceptively up by semitone to a major tonic, 4) Treat it as a dominant and resolve it deceptively up by whole tone to a new minor tonic, 5) Treat it as a dominant and resolve it deceptively up by semitone to a new minor tonic, 6) Treat it as a dominant and resolve it deceptively up by whole tone to a new major tonic, 7) Treat it as a German Augmented Sixth/subV7/V(d5/m7/m9/0) and resolve it down by semitone to a new major tonic, or, 8) Treat it as a German Augmented Sixth/subV7/V(d5/m7/m9/0) and resolve it down by semitone to a new minor tonic.

Likewise, arriving at a fully diminished seventh chord yields eight possible modulations treating each tone as a possible leading tone into a major or minor chord, and arriving at an augmented triad yields six possibilities through the same means. Knowing these possibilities and being aware of them is the major part of the process of learning to structure effective and varied modulations.

Now, the recapitulation is an inversion of the exposition, right down to mode gender, and I was able to accomplish this using harmonics for the first statement of the theme. I ornamented it with 4-3's where the answer comes in, and again over the last subject statement. I also modified the inversion step by step so that the last statement is the subject of the final fugue. At the ending I worked in some humorous chromaticism, and the ending to a C major chord comes as a funny surprise. Ricercares are inherently fun.

Thursday, July 24, 2008

How to Compose Counterpoint (Imitation and Modulation 1)

This is part five of a series that progresses from Where to Begin through How to Progress, Using Larger Forms, and Using Three Voices. All of the examples so far have been non-imitative and none of them have had any modulations, however, so now we are ready for those subjects.

Philosophically, I simply do not think that small pieces have to modulate, and for the idiom of the guitar, specifically, modulations tend to complicate things significantly. As a result, I write a lot of miniatures that don't contain any modulations at all, though they may be quite chromatic, as you will have seen if you have followed this series of posts. Another issue I have with Baroque and Classical miniatures is that the modulations are so formulaic and predictable that they border on the manneristic: "Oh, it's a major key: We're going to modulate to the dominant," or, "Oh, it's a minor key: We're going to modulate to the relative."

I knew from my years of writing popular styles and jazz that modulations weren't required to write effective music, so I didn't want to get caught on that particular strip of flypaper. However, some idiomatic pieces do actually require modulations - fugues, sonatas, preludes &c. - so I saved those things for last in my musical evolution, at least in the area of contrapuntal guitar music.

Between the E-Axis Studies and the B-Axis Studies I found another vehicle that allowed me to create a large series of pieces that did modulate, and that vehicle was the figuration prelude. I've written fourteen out of the twenty-four so far, but since they are homophonic versus polyphonic, they don't fit in this particular series as examples. So, we are going to go forward to fugue today, and speak of the modulations as they arise. Since imitation and modulation are such deep subjects, I anticipate three installments on this topic.

A distinction should be made here between the idea of modulation and tonicization: A true modulation changes key for a section of the piece, while a tonicization just targets a secondary chord within a key for a fleeting moment. Therefore, almost any employment of a secondary dominant can be considered a tonicization, while a modulation is going to present some new material in a different key region, or previously heard material on a new level, and perhaps in a different modal gender. In really sophisticated music, like the songs of Schubert, for instance, the dividing line between what constitutes a modulation and what is merely a tonicization can become quite blurred, if I may be allowed the understatement.

A good composer doesn't just throw modulations into a piece willy nilly, but rather plans them out according to some logical formula of his own devising. Strict fugues actually make this process easier, as there are only the close keys - those differing by one accidental in the sharp or flat direction - to work with. Some fugues never modulate at all, in fact, as is the case with Contrapunctus I in Bach's Die Kunst Der Fuge. I dare you to call that a boring piece because it doesn't modulate. Some fugues do go to more remote keys, of course, but many of them I think ought to be strictly referred to as ricercares. Beethoven's Grosse Fugue for string quartet, for example. He subtitled it, "Sometimes researched, sometimes free," which would not have been necessary if he had just gone ahead and called it a ricercare, which implies much more freedom in that regard.

So, today's example is going to be a strict fugue I wrote for the guitar. This is far from the first fugue I ever composed, as I believe no less than five fugues preceded this one, as well as several canons and other imitative pieces. The problem I had was that I wanted to write a stately Art of Fugue kind of piece for the guitar - in miniature, of course - but there were no models for me. The kinds of subjects Bach used were fine for the keyboard, and I wrote a lot of subjects similar to his for organ and ensembles, but for the much more restrictive idiom of the guitar the were unwieldy, to say the least. Then, the subjects he used for lute and violin were too - there's no tactful way to say this - trivial, which is why his fugues for those instruments are so highly episodic. I was left then to come up with a new kind of subject that would work for the guitar, and that would have some weight to it that allowed for some interesting contrapuntal devices. I finally got the subject back in 1999, but it took seven years before the piece reached its final form. It's written on two staves, but this is a solo.

As you can see, the fugue is in A minor and the subject is 3.5 measures in length. There are no leaps in it at all, and after tonicizing the dominant degree, it just descends the scale to the tonic, where there is a brief tail figure that likewise tonicizes the tonic. The range of the subject is a minor sixth, and this is important: Subjects with wide ranges suck for the guitar. An octave is pretty much the outer limit, and that is really, really stretching it.

The answer starts in measure five, it is tonal, and it begins by tonicizing the tonic and then descends the scale. You'll note all the parallel thirds: This is idiomatic for the guitar. Because the answer starts on the tonic, it ends in a half-cadence to an implied V(6/3) in nine, which allows the final entry of the subject to begin on a highly desirable I(6/4) sonority, and the D-sharp actually momentarily creates a diminished triad sound. Looking for cool harmonic juxtapositions like this is a big part of the job of writing counterpoint, and total awareness of these details adds an element of craftsmanship to the work. Bach and Beethoven both filled their music with nifty minutiae like this, and I picked this stuff up by analyzing in detail every momentary vertical sonority in some of their works. It was a serious chore, but it was well worth it.

You'll notice that the parallel thirds are between the lower two voices this time. This is not particularly idiomatic, but as you can tell from the fingering, it isn't overly daunting to execute either.

At thirteen the first modulatory episode starts, and I just used a modified retrograde of the subject's tail figure to achieve it. Note the idiomatic parallel thirds in the top two voices. The harmony in thirteen is i, of course, and thirteen has an implied ii(d5). Then, I just modified the sequence in the bass to get the, la, ti, do, sol of the upcoming dominant region with, me, re, do, ti in the lead and the new, fa in the middle voice. This gives the V(m7) of the new key on the final eighth note, and we're there in three measures flat.

Bach was fond of lengthy episodes - especially in his younger days - and his episodes are sublimely beautiful, but my approach is far more minimalist. It's a shame the term "minimalist" has been used to describe the repetitive music of Philip Glass et al because it is really fitting of my approach. I'm interested in economy of means and expression, not lengthy perorations, and if you look at Bach's last works, he cut down on the episodic material there as well. Beethoven became almost ascetic in his spareness in some of the movements of the late string quartets, and it is from there that I take my queues.

Now that we have reached the dominant level and the key of E minor, you can see here in the first middle entries the contrapuntal device this subject is set up to exploit: Suspension chains (Or, syncopation chains, if you prefer). I modified the first counter-subject so that instead of parallel thirds, we now have a series of 4-3 suspension resolutions in measure seventeen into eighteen. I repeat this 4-3 device at twenty into twenty-one under the answer (Now on the original tonic level: Tres cool, non?), and the lowest voice on the second system is free.

In the third system I inverted the subject in the bass and have the syncopations in the lead, so we get a rising chain of 11-10's at twenty-five into twenty-six. The inverted subject leads into a half cadence in twenty-eight, so the second modulatory episode has an extra measure in it to turn us around to the tonic. Aside from a slight elaboration in the lead, this episode is the same as the previous one, so it seems to be taking us to, "the dominant of the dominant," but that would be out of bounds for a strict fugue. So...

I used the traditional deceptive motion to "modulate" to the relative of the dominant, which is perfectly legit, even in the most rigorous of fugues. See how looking for the most economical means can lead to some great ideas? I could have composed an entirely new episode and just modulated in the same old boring way, but this arrival comes as a surprise after hearing just a mildly varied form of the first episode.

Since suspension chains are this subject's raison d'etre this set of middle entries starts off with a 2-3 chain. I'm adding some sixteenth note action to build up to the third episode in the final measures, as you can see, and the second system presents the 7-6 posibilities. I present the 7-6's again over an inverted form of the subject in the third system, and the 2-3's again in inversion in the bottom system. Finally, I give a run of four sixteenths to lead to the final episode at the end of the page, and it appears from the V(m7)/I that we are going to stay in the key of G major.

Wrong! The previous D(m7) allows for another deceptive motion, this time by whole step instead of half step, and to E minor this time versus G major previously: We're back in E minor... or so it appears.

Believe it, or not, this episode is actually the original subject in augmentation. If you look at the first and last notes of every measure, you can see this clearly: I've just ornamented it with harmonic figuration and put it all over a dominant pedal, the open low E string of the guitar. As my mom would say, "That's the bee's knees!" LOL! Notice that I don't shed the F-sharp until measure fifty-three, at which point the modulation to A minor becomes apparent.

The recapitulation is a stretto, of course, but a unique one: Every voice starts out on the same pitch, which is the open high E string of the guitar, and then descends to take its place in turn.

None of this is overly difficult to play, and I ought to be performing it within the next year or so, but I just have so many pieces on the to do list. At least I can see light at the end of the tunnel now. Coming up on four years ago I was looking at a list of nearly eighty pieces and saying... well... you know. LOL! Now I have less than ten left.

Monday, July 21, 2008

How to Compose Counterpoint (Using Three Voices)

I briefly considered re-titling this series, "How to Compose Counterpoint for Guitar," but the examples thus far will work for keyboard as well, so I decided against it. I'm sure guitarists will find these posts if they search that term anyway.

We started with Where to Begin using a microscopically small ternary miniature in two voices as an example, then we learned How to Progress through a series of small pieces adding implied secondary dominants, augmented sixths, and whatnot, next came Using Larger Forms, in which I gave an example of a compound ternary Scherzo, but everything thus far has been in two voices, so now we're ready for three.

One of the fortunate things about being a composer of counterpoint for the guitar is that two-voice counterpoint is completely idiomatic for the instrument. On the keyboard, two-part polyphony sounds rather naked and spare - incomplete even - but on the guitar it is completely full and satisfying. Unfortunately, however, three contrapuntal voices on the guitar compounds the technical execution significantly, and restrictive idiomatic concerns can become nightmarish. As a result, I was writing my first three-voice pieces for organ and trio ensembles long before I tried it on the guitar.

In order to crack that particular cosmic egg, I had to come up with at least a quasi-idiomatic approach to three voices on the guitar, and it finally happened with one of the last G-Axis Studies that I wrote, G-Axis Study No. 3 in E-flat Major. While any of the eighteen Axial Studies could be considered incipient three-part counterpoint due to the repeated zero axes, for the sake of this series of posts, we'll leave the repeated notes out of our calculations in that regard.

This then, is the first fruits of three-voice polyphony that I came up with for the guitar.

Obviously, three flats is a very, very uncommon key for guitar music, and I learned something valuable about that issue as well: The zero axis of G is the major third of the tonic E-flat major triad here, so this really shouldn't be such a daunting key. I also ended up with pieces in C minor and G minor in this series - where the open G string is functioning as the fifth and the tonic of the keys, respectively - so there are a lot more nice possibilities for flat keys than most composers of guitar music have heretofore realized. Guitar recitals get boring to me very fast because the vast preponderance of traditional guitar literature is in the same old, boring, predictable keys.

Next, you'll notice that this particular Axial Study does not have an interlude between the A and B sections - it is the only one of the eighteen so configured - and so the form is a much more normative, A, A', B, A, A', B, A''. This texture is inherently much more interesting, so it just wasn't required to have the interlude.

Since, in these G-Axis Studies, the zero axis is not bound to the melodic trajectories as was the case with the E-Axis Studies and B-Axis Studies - and since there are two strings above the G to work with here - I was able to start the piece off with the simple idea of just doubling the melodic trajectory in thirds. This is quite idiomatic to the guitar.

The three measures of the top system create a simple, I, vii(d5), vi(m7) progression that is really just the result of contrary contrapuntal motion, but in measure four we arrive at a ii chord with M9 and P11 suspensions, which gave me the opportunity to create a V(m7)/V in the second half of that measure. After the V triad at the beginning of measure five, then, I was able to create a V(m7) targeting the tonic using a major ninth as a lower neighbor to the third, and then after the tonic triad (diad, actually) I was able to create a V(m7)/IV at the ned of measure six using the same major ninth as lower neighbor device, only this time in the top voice.

At the beginning of the third system, the IV chord is also a diad, and it becomes a V(4/2)/I in the second half of measure seven, which then "resolves" to a I(6/4) sonority before I introduce the tritone to make it the V(m7)/I which leads to the repeat of the A section. The second ending just creates a triad on the dominant degree to lead into B.

You'll notice I had to let the bass rest in measures five and seven. This is simply the result of it being physically impossible to hold them there due to the idiom: The bass notes remain implied. This is a very pretty A section, and it has a logical inevitability to it that suggests that it has existed forever; it was just left to me to discover it.

I reduced the number of essential voices to two for the first measure of the B section, so this piece has an element of "free-voiced-ness" to it: Later I'll use four essential voices for the climax. Measure eleven begins with a ii(6/4) sonority which becomes the traditional French Augmented Sixth in the second half. I call this chord a V(4/3/b)/V, of course. measure twelve gives us the major triad on the dominant degree, and then I sequentially repeat the formula starting on a iii(6/4) triad in measure thirteen. The resulting "French Sounding" sonority is this time a V(4/3/b)/vi, which gives an indication of how ridiculous the traditional nomenclature for these chords is: They are just altered secondary dominants.

After the measure of vi in fourteen, I repeat the sequence yet a third time, only now, since it is the third time, I vary the formula: The bass rises a third this time, and the chromatic alteration of the A from A-flat to A-natural makes the chord a II, which you can think of as a modal interchange from the Lydian mode. As for myself, I was just shooting for the V(4/3/b)/I that appears in the second half of the measure (Or, the French Augmented Sixth of One, if you still need to think of it that way).

At sixteen we get the expected measure of the tonic triad, and then I retain the E-flat as a pedal point for the next two measures, which are the climax of the piece. The sonority at the beginning of measure seventeen is actually a ii(4/2) in fully open position. What does fully open mean? The chord spelling reads precisely from top to bottom: F, A-flat, C, and E-flat. This is way gnarly! In the second half of seventeen, that sonority becomes a doubly-augmented fourth augmented sixth, which is a V(A4/3/b)/I (Over a tonic pedal) in my modern terminology, and that resolves to a root position tonic triad. This would have been a I(6/4) chord, as expected, if not for the tonic pedal point: See why I used that device? I didn't want to have to "resolve" a 6/4 sonority into a dominant harmony here, I wanted the tonic to be a fully resolved arrival. I wonder if any other composer has ever done this. I can't recall ever seeing it before, but the literature is vast.

Measure nineteen has a m6-d5 over the A-natural for a V(6/5)/V effect - and I again reduce to two voices - then, measure twenty consists of a V to vi deceptive motion, which leads to the fully diminished vii in second inversion (vii(6/d5)), which functions as a ii(d5) in the second half of that measure, and then we get the V(m7)/I in twenty-two to return us to the A section.

There is no variation in the repeats, and the A'' prime section just has a new and final ending where the zero axis G raises to A-flat to make the final dominant seventh resolution to a close position E-flat triad possible.

The climax of this piece is very, very difficult to execute. In fact, it is nearly impossible on a standard non-cutaway classical guitar, but it is manageable for a virtuoso... which I'm not. LOL! This is one of the reasons I don't play non-cutaway guitars anymore. So much of what I write is real, actual guitar music versus lute (or whatever) transcriptions, so I use the entire range of the thing. This was one of the last pieces that I re-memorized, so it's not quite in my set yet - I've been working on it for about a year - but it is close. One thing for sure, and that is that this is quite an interesting guitar piece.

Saturday, July 19, 2008

How to Compose Counterpoint (Using Larger Forms)

Well, it's official: This is now a series. In the first post I gave an example of a simple diatonic ternary form piece as a starting point for composing counterpoint pieces from scratch, then in the second post I gave three examples from a series of pieces I wrote that show how to make progress, and in this post I'll give an example of a larger form work in two-voice counterpoint that I had as my first major goal.

As you begin to master counterpoint, you'll want to set goals for yourself that will allow you to progressively grow. You may wish to write some two-part inventions if you want to progress to fugue, for example, but early on I realized that imitative counterpoint wasn't really idiomatic for the guitar (Or rather, it was too complicated for me to tackle as an early goal), so my first major goal was to compose a compound ternary form Scherzo.

Back in that first post the example was a simple ternary form piece in B minor and 6/8 time that I call a Menuetto. As I said, my favorite single piece in the entire symphonic literature is the Scherzo from Beethoven's Ninth, and I wanted to write something of a similar character on a smaller scale for the guitar. I didn't use imitation as Beethoven did, obviously, and I changed the anachronistic super-fast 3/4 time to a more modern and manageable 6/8. From that first simple A, A, B, A, B, A' ternary form it was a small conceptual step to progress to a compound ternary form, because it just amounts to a ternary form within a ternary form.

So, today's example is the Scherzo I ended up writing between the E-Axis Studies and the B-Axis Studies, and the form is, Intro, A, A', B, A', C, C', D, C, C'', A', B, A'', Codetta. It is also in B minor and 6/8 time, as the first example in this series was, but the form is expanded - compounded, actually - and I made my first successful attempts at the kind of motivic development that one uses in sonata process pieces here.

In the brief two-measure introduction is the ti, la, ti, do, me, sol motif that I use for all of the developmental episodes (It is the only rhythmicized element in the piece, as well) and then the piece launches into an eight measure A section, but this time there are first and second endings. At measure nine in the first ending I use an augmented triad that turns around to a diminished triad to lead into the motif at measure ten, but this time the motif has contrapuntal accompaniment, and that leads to the repeat of A. The second ending at eleven and twelve launches into a diminished seventh arpeggio, which leads to the pitch climax for the A section at B in measure twelve. Ever higher pitch climaxes are one of the features of the organizational scheme of this piece.

The B section begins at fourteen, and the previous pitch climax of B is almost immediately exceeded by C-sharp in sixteen, which is reached via another arpeggiated diminished seventh trajectory. I use a lot of these symmetrical structures in my music - diminished seventh and augmented triad arpeggios - as they are dominant in function, and they are also mechanically efficient, being as they are a straight line between to pitch points. Probably needless to say, I got this idea from Joseph Schillinger.

Through the obvious sequential figure, the next high note reached is B at eighteen, and then a new pitch climax of D is reached at twenty. I rhythmacized this because it is nearly an inversion of the motif.

At twenty-two the second part of the B section begins, and this is a descending sequential harmonic episode that leads to a repeat of the last two measures of the A section in twenty-five and twenty-six. Twenty-six and twenty-seven are the original motif of the introduction, only an octave higher and with contrapuntal accompaniment. This leads to the pitch climax of the B section: The G at the beginning of measure twenty-eight. You may be thinking that this piece is rather virtuosic for the guitar, and you'd be right: When I wrote it, I never thought I'd ever be able to play it, but after many years, I am actually performing this now.

The final two measures of the page bring the piece quickly and efficiently back to the next statement of the A section.

I mentioned back in the first post that the rule of thumb for A sections is that if there are both first and second endings present, you'll probably want to play both between statements of B. I also mentioned that rare exceptions pop up, and this is one of them: The rule of thumb is basically out the window when you compound the ternary form because what is coming up is not another statement of B, but rather the Trio, which amounts to a C section. So, only A' is played here.

In contrast to the eight measure A sections, the C's are four measures, also with first and second endings. These shorter sections combined with an absence of the repeated note figures quickens up the pace and increases the intensity considerably, as is appropriate. Note how I worked the motif into the second measure of these C sections, and note also how much these sections sound like my model, the Scherzo of Beethoven's Ninth.

The second ending of C' leads to D, which begins at measure fourty-three. This sequentially descending figure has it's own internal repeat, which I added mostly to keep the piece on three pages: The second ending does not constitute the beginning of an E section.

That second ending does begin a development of the motif, however. After being repeated on the same pitch level with the countrapuntal accompaniment of the previos version leading to the pitch climax of B, I expand the motif with each successive iteration. Forty-nine and fifty amount to a primary diminished seventh arpeggio, fifty-one and fifty-two delineate the half-diminished chord that resides in the raised sixth degree, fifty-three and fifty-four are again the primary diminished seventh, this time chromatically ornamented, fifty-five and fifty-six are a diminised seventh on the raised sixth degree, also ornamented with passing tones, and then fifty-seven is the primary dominant minor ninth leading to the next area of B. That ending double bar line should just be a regular double bar: I'll have to fix that. Note that as the expanding motif works its way up, the counterpoint works its way down: The low E in fifty-six is the lowest note on the guitar.

This area, also with an internal repeat, is a further development of the sequential figure that started the B section, as you can see. The first ending presents an arpeggiated augmented triad through two octaves for the first time, and the second ending leads to the main climax of the piece. Measures sixty-five and sixty six are exactly the same as the corresponding climax lead-in back in twenty-six and twenty-seven of the B section, but at sixty-seven I compress the ti, la, ti, do, me, sol figure, which is diatonic to the melodic minor idiom, into a completely chromatic version: le, sol, le, la, te, ti. This leads to the high B in measure sixty-eight, which is the highest note on the standard nineteen fret classical guitar: This piece uses the entire range of the instrument.

A two octave descending tonic triad ends the D section, and then C reappears, again with two endings, but the second ending here is new, making the repeat a C''.

Since the piece never modulates, despite all of the chromatic shenanigans, I truncate the repeat of the Menuatto as much as possible: Only the A' is restated, then the entirety of B, and finally the A'' is simply the last four measures of the original A' with a little codetta added. The last super-high notes are harmonics, obviously, and the ending B is actually another octave higher than the previous pitch climax. Since scherzo ranslates to "jest," there is more than just a little humor throughout the piece, and this is the parting "joke."

I must admit that I hit the ball way out of the park with this piece: This is the single largest compositional stride I made on the guitar until I completed the Sonata of Sonata One, so it would be several years before I topped this. I only remember that I was super-highly motivated and intensely focused on this piece for several weeks. I wish I had kept a journal!

Monday, July 14, 2008

How to Compose Counterpoint (How to Progress)

In my first post in this series, I gave an example of where to begin composing counterpoint from scratch after you have learned the basic rules in the classroom (Or in an autodidactic manner, as I did it). This time I'll be giving examples that show the progress I made in composing two-voice counterpoint for solo guitar in the seven year period from 1987 to 1994.

The first thing you need is a vehicle that will allow you to compose several pieces within a relatively short time frame. You may want to take Bach's miniatures as an example and compose suites, for example. As for myself, I knew I didn't want to do that, rather I wanted to write idiomatic pieces for the guitar, because my overarching long term goals were, 1) To develop a personal contrapuntal style of my own on the guitar, 2) to learn how to compose very formal fugues on the guitar (I'm talking stately Art of Fugue type of deals in miniature here), and, 3) to eventually get to the point where I could write a multi-movement sonata for the guitar.

Fortunately, I was studying Schillinger in 1987, and his Theory of Melody book gave me a very wonderful idea for three sets of idiomatic guitar pieces using his concept of the zero axes of melodies. In short - all melodies have a zero axis - or a set of them if the melody modulates - but most of the time these axes are not played and are only detectable through analysis. In some cases, though, the zero axis is played, as is the case with the fugue theme from the Toccata and Fugue in D Minor for organ, which is usually attributed to Bach, but which Bach in fact did not compose (You can start with the Wikipedia entry if you'd like to research this for yourself).

In any event, that fugue subject gave me the idea to write three sets of Axial Studies using the open high E string, B string, and G string of the guitar as every other note in the melody, just like that fugue subject had. Since the zero axis can be the root, third, or fifth of a tonic major or minor triad, this yielded six studies in each set for a total of eighteen: Just the vehicle I needed.

I started composing the E-Axis Studies in 1987 immediately after writing the menuetto that was the example for the previous post. Here's the one in C Major that will demonstrate the first goal you'll want to tackle, and that is implying secondary dominants in your counterpoint.

First, a couple of observations about the form. I am a big fan of odd numbers of measures for sectional pieces, and here the A section is eleven measures in length, and it also has a first and second ending. In contrast to the odd number of measures of A, I have used an even number for what looks like B there at measure thirteen. This is actually an interlude between the A and B, and it also has two endings. The B section proper begins at measure twenty-three, and it is sequential, has four measure phrases, and is sixteen measures in length. I felt the need for the interlude to relieve the texture, which becomes monotonous without this relief.

So, with the repeat scheme the form is, A, A', I, I', B, A, A', I, I', B, A''. Just in terms of formal conception, then, I had already made significant progress.

Here's the second page.

I was still writing the melody out first and then adding the bass line at this time - cantus firmus technique - but I got the idea to imply a V(6/3)/V at the end of B there in measure thirty-seven. It's the only accidental in the entire piece, so it stands out and provides a kind of a climax. Once I had this insight, it was a small step to get the idea to add secondary leading tones in the melody.


I had all six of the E-Axis Studies done before I started working on my master's degree, so for my master's degree lecture recital, which I did in lieu of a thesis, I presented, performed, and discussed the B axis studies. I composed these between 1989 and 1990, and here you can see just how far I advanced in this short time frame.

Here's No. 2 in E minor.

Formally, this is the same as the previous example right down to the eleven measure A sections, but the B sections have odd measure phrases. That's a bit of progress in itself, but notice how chromatic it is?

After the open B pickup note, and the B-axis is the fifth of the tonic triad here, I ascend through the chromatic tetrachord from sol to do. Then, I continue with chromatic figures in measures five and seven: The augmented eleventh created in measure five implies a V(4/2)/iv, measure six has a c-sharp in the bass, so that's an implied V(6/3)/bVII, and the A-sharp in measure seven creates an augmented sixth targeting V. This is a really gnarly sounding A section, so I knew I'd have to pull out all the stops for the B section.

The first ending of A returns home via an arpeggiated primary diminished seventh chord, and the second ending leads into the interlude with another chromatic tetrachord to the tonic an octave higher. In the interlude, I use the descending form of the chromatic tetrachord broadened out, and the do, ti, te, la, le, sol, la, ti line created in the lead is just like the same figure Beethoven uses at the end of the first movement of the Ninth. This interlude is way cool, and it provides a nice and needed lessening of pace and tension between the A and B sections... but not too much.

Here the B section is based on odd five measure phrases, as I said, and I take the ascending chromatic line idea to another level. The G-sharp in twenty-five again implies a V(4/2)/iv and the A-sharp in twenty-six makes an augmented sixth targeting V.

I then sequentially repeated the previous phrase starting on the subdominant level in all details. Here, the C-sharp over G in measure thirty implies a V(4/2)/bVII and the D-sharp over F-sharp in thirty-one creates a V(6/4) targeting the tonic.

The pitch climax in thirty four is the A at the seventeenth fret of the nineteen fret classical guitar, so it is quite high for the instrument, and thirty four and thirty five imply a iv to v progression that arrives at an upper neighbor diminished chord in thirty-six before returning to v, and then a return to the A section, this time via an apreggiated augmented triad. This is really neat, and the resulting final phrase is six measures in length.

The A section and the interlude are repeated, and then we return to the B, but this is a true B' at forty, and now both voices move in contrary chromatic motion! I read in some rather lame counterpoint book or other that this was not good practice, so - of course - I had to do it. LOL! I found that if you present the version with the diatonic bass line first, then the repeat with the chromatic bass is very highly effective, and the intervallic sequences are highly colorful and unusual.

From forty to forty-three the intervals are: 8ve, M9th, d4th, A4th, m6th, A6th, and 8ve: Bad-ass, if I do say so myself. Since forty-five to forty-eight are just a sequential transposition, the interval sequence is the same there, only on a higher level. the final six measures are the same as before, which leads to the ending statement of the A section.

Yeah, I'd gotten a pretty good handle on chromaticism by this point, and it was all because I had a vehicle that allowed me to compose quite a few pieces with limited variables in relatively short order.


By the time I got to UNT in the fall of 1991, I was ready to tackle the G-Axis Studies. We'll look at No. 1 in G major, which shows several more evolutionary traits.

I wrote this one in 1994, and if I recall correctly, I had all six finished in just a few weeks: My facility was pretty decent by this time, and I was also writing both voices simultaneously.

The A section here is ten measures in length, and the first statement of it is totally diatonic. Notice that the bass line first goes up all seven notes of the scale stepwise, and then goes through all seven again (counting the F-sharp in four twice as the pivot) in alternating descending fifths and ascending fourths.

In the second ending at eleven, however, I introduce an augmented sixth targeting the dominant, and thirteen and fourteen give us a I to V leading into the interlude, which starts on VI via the traditional deceptive motion. Notice that I change time signature to 3/4 for the interlude - more progress - and while the first phrase is four bars, the repeat is five - yet more conceptual growth.

The F-natural in sixteen implies a V(4/3)/IV, the C-sharp in the bass at seventeen implies a V(6/3)/V, and then the interlude repeats. In the second ending at nineteen, I use a double chromatic neighbor pair to target V, and the last C-sharp over E-flat creates an augmented sixth, of course. The descending line in twenty is an augmented triad - rare in a major key - and then the final measure gets us to a V(6/3) to set up the B section.

After all of the histrionics of the interlude, I returned to 2/4 time, four measure sequential phrases, and broadened things out to 4:1 counterpoint to begin the B section.

Here in the third phrase I introduced what should be a V(4/3)/V over the C-sharp in the bass, but this is spectacularly interrupted by the fourth phrase, which starts on an implied tonic - a really, really deceptive motion - and proceeds to the climax of the piece. The interval of A-sharp over E-flat in thirty-five is a doubly-augmented fourth, which I was saving for just this moment, and the B in measure thirty-six is the highest note on the standard nineteen fret classical guitar. Sweet, no? Of course, doubly-augmented fourths resolve most typically to I(6/4) sonorities, which is the case here: That chord then generally resolves its suspensions to a root position V, which is again the case here.

Thirty-eight is actually a deceptive motion to vi, and then a ii, V under a descending diminished seventh leads to the second interlude: Yes, there are two interludes here.

This second interlude is an octave lower, and it starts on I instead of vi. There's the V/IV in forty-three, and then the V/V in forty-four which leads to the repeat, but again, no deceptive motion this trip.

The second ending is further extended this time, making the phrase six measures versus the previous five of the first interlude repeat. In this phrase I managed to work a traditional so-called Neapolitan Sixth in at forty-eight, and I think that's the first, and still the only, time I've ever used that sonority in the traditional manner, but it was a specific goal I had to use it here.

So, you can see that by limiting my variables and writing these eighteen pieces over the course of seven years, I totally mastered two-voice counterpoint and made great overall progress as a composer. There are countless paths you can take, but the steps will be nearly the same on each one, you just need to find a path. Of course, this wasn't all I was writing during this time period - I had gotten pretty good with fugue by the time I wrote the G-Axis Studies - but these pieces allowed me to work out all of the elements for myself in the comfort of my own idiom, the guitar. It was a long time after this before I finally figured out how to write fugue subjects that would work for the guitar, however.

Whew! Long-ass epic post. I'm pooped.

Wednesday, July 09, 2008

How to Compose Counterpoint (Where to Begin)

This is not a post about the rules of counterpoint, rather this will be about where to start once you've learned the basic rules. The title of the post is a Google search term I find in the Sitemeter log fairly frequently, so I thought I'd dedicate a specific post to it. So, I'm assuming here that you have already suffered through all of the tedious classroom type exercises of feces species counterpoint, and are ready to begin composing your own pieces from scratch.

Whether you play the guitar as I do, or a keyboard instrument, the place to start is with simple binary or ternary form miniatures in two voices. One of the biggest mistakes aspiring composers make is getting overly-ambitious. Sure, we'd all like to compose "The Great Symphony," but that is exactly the wrong place to begin.

This is only the second piece in traditional counterpoint that I ever wrote - the first being a set of six variations - and it is a perfect model for what I'm talking about. Now, I had ten years of writing jazz and other popular styles under my belt by this time - I was twenty-nine years old - so it isn't exactly nursery rhyme simple, but it's close.

As you can see, I wrote this over twenty years ago in 1987 (Where does the time go, anyway?), and since I had a decade's worth of popular idiomatic rhythm concepts in my noggin, one of the decisions I had to make was to almost completely eliminate rhythm as a variable: As soon as I tried to get overly rhythmic, it started to sound jazzy. This turned out to be a good decision for me, but you may not have that issue.

What I did here was to take the counterpoint exercises I had done as a point of departure, and I just wrote my own lines. I composed the melody first and then added the bass line, so I was basically still using the good, old fashioned cantus firmus technique I had learned, but I just wrote my own cantus.

As you can see, the piece is in B minor and it is completely diatonic to the melodic minor contextual idiom: No modulations at all. The more variables you can eliminate - the simpler you can make the project - the better your chances of success.

There are only two sections to the form; an eight measure A section and a twelve measure B section. The overall repeat scheme makes the form, A, A, B, A, B, A' where A' (The coda) is just the second four bars of the original A section. The rule of thumb for repeating the A sections is this: If there is a first and second ending, then you will probably want to repeat the A sections in between statements of the B section, but if there is only one ending to the A section, then you won't. Exceptions to this crop up, of course, but I find that they are very infrequent. Shortening the final A section is usually a good idea in a little piece like this that doesn't modulate, because, "brevity is the soul of wit" with tiny works like this.

My model for this, by the way, was the Scherzo of Beethoven's Ninth Symphony, only I wrote it in 6/8 instead of 3/4, and I didn't use imitation. If you know that and you play the tune, the connection becomes obvious.


Now, I was specifically trying to learn the traditional melodic minor idiom at that point - which was new to me as a composer then - and I had already mastered traditional major from my jazz composing days, so an even simpler and better place to start would be the major mode. Here is a major key version of the same piece I rendered last year.

I got the idea to do this when I considered adding a little rhythmic vitality to the minor key version, but I decided against it because I really liked the continuous drive of the perpetual motion version in minor. So, since there are hardly any pieces for classical guitar in five sharps, I decided to transcribe the piece to major and add the lilting rhythm to it. That rhythm sounds much better to me in the major mode anyway.

Looking at it in the major really makes it look absolutely pure, doesn't it? There isn't a single accidental in the entire piece.

The only changes I made to the counterpoint were in the bass line, and one of those was an instance of, "things that work in minor, but not major": The A-natural in the bass of measure 9 in the previous version was a cool modal effect only available in minor (Unless I wanted to get all mixolydian about it, which sounds goofy in a context like this), so I lowered that to G-sharp in the major key version. Then, at measure 11, I lowered the E an octave to use the lowest note on the guitar there. I could have done that in the minor key too, but I just like the respective versions in the respective modes, "just because."

This major key version, by the way, just came up on my, "to do" list, and it sounds excellent. It's kind of an anachronism for me - I don't think I could write a completely diatonic major key piece today if my life depended on it (OK, a slight exaggeration) - but it fits into my set perfectly because, like I said, a guitarist can never have enough pieces in B major (I've only ever composed three pieces in B major, with this being the third). And yes, I've been performing the minor key version on and off for over twenty years now.

The bottom line is, if you have the innate, natural musical intuition to create tiny little gems of absolute perfection like this, you can develop that over time by writing more and more ambitious pieces until you reach the point where you are composing multi-movement sonatas containing large works that are also models of perfection. You just have to start simple and gradually and naturally develop over the course of time.

I never would have been able to master the fugal and sonata processes if I hadn't started simple like this.

Tuesday, July 01, 2008

Heavy Nylon Now on

This will be my last post on the Heavy Nylon Demo 2 project.

I have finally finished up the last chores, which consisted of comparing demo 2 with demo 1 and choosing the best tracks from each for the CD, burning a boatload of CD's for my manager, mom and friends, and uploading all of the MP3's into my account. No doubt this will be the best solution for readers because allows you to just listen to the tracks in your browser via their streaming audio player and download only the tracks you might like to have.

Note that I'm ranked #3 in Guitar, #4 in Electronic Classical, and #27 in Classical there! And that only on the strength of my Fossils CD of last year. I'm hoping I'll be #1 in Guitar after Heavy Nylon starts getting some plays, but the #1 and #2 guitarists are really, really good. I'd also like to be in the top ten in Classical, but there a lot of really good ensembles I'd be competing with. We'll see.

It wasn't until I did the track comparisons that I noticed I failed to rerecord one of the tracks, so the total is now eighteen. Here's the song list again, this time with the demo versions that made the cut.

01] Classical Gas - Mason Williams (A Minor) - Demo 1
02] Desert Song - Eric Johnson (A Minor) - Demo 2
03] G-Axis Study No. 4 - George Pepper (C minor) - Demo 2
04] Ode to Joy - L. van Beethoven (C Major) - Demo 2
05] Spanish Fly - Eddie Van Halen (E Minor) - Demo 1
06] Fighter Pilots - George Pepper (E Major) - Demo 2
07] G-Axis Study No. 1 - George Pepper (G Major) - Demo 2
08] A Day at the Beach - Joe Satriani (G Major) - Demo 2
09] Scherzo - George Pepper (B Minor) - Demo 2
10] B-Axis Study No. 1 - George Pepper (B Major) - Demo 1
11] Prelude No. 23 - George Pepper (D Minor) - Demo 2
12] Eu So Quero Um Xodo - Dominguinhos (D Major) - Demo 2
13] Prelude No. 7 - George Pepper (F# Minor) - Demo 2
14] Heavy Nylon - George Pepper (A Major) - Demo 2
15] Yankee Doodle Dixie - Chet Atkins (A Major) - Demo 2
16] Prelude No. 11 - George Pepper (G# Minor) - Demo 1
17] Tears in the Rain - Joe Satriani (A Minor) - Demo 1
18] Stairway to Heaven - Jimmy Page (A Minor) - Demo 1

The earlier version of Classical Gas was much more up-tempo, which got me thinking about tempi, of course. Spanish Fly is just a major PITA, and it goes in and out of focus constantly. I still have never captured a really good take of it, but I'm going to really hit that one and A Day at the Beach hard this fall and winter, so we'll see how demo 3 comes out.

B-Axis Study No 1 is the track I forgot this pass, so last year's version will have to do. All three of the final tracks are from the first recording, which is a bit disappointing, but again, the tempi were better.

Anyway, I learned a lot more this pass, so that's all the mission called for. I keep having to remind myself that I've only been playing the guitar for just over three years after almost four years of not touching one! Another winter of metronome work ought to pay pretty big dividends, as I'm just on the cusp of getting the slow-play/forte practice regimen completed for most of these tracks.

Stay tuned for next summer's version with the Reynolds Fretted Glissentar. That ought to be fun.