Sonata One in E Minor IV: Axial Fugue in E Minor

This is the final of four posts in this series on Sonata One in E Minor for solo guitar. The first three movements are here: Toccata in E Minor, Sonata in A Minor, and Scherzo in G Major.

If I was to go strictly by the fugal categorizations as I learned them from analyzing J.S. Bach's music, this movement would have to be called a ricercare if for no other reason than the number and remoteness of the key regions it traverses. But there is much more that is unique to this piece, as it is a combination of fugal and sonata processes, it uses vertical-shifting counterpoint a la Sergi Taneiev, and the subject-answer theme appears in several modified forms. No other composer has ever used this subject modification scheme before, though Palestrina did present modal variants of some of his thematic material in a more casual way. I chose to call it a fugue because the constructivist approach I took to it is so rigorous.

Since the subject uses a zero axis that is played - and that zero axis can be the root, third, or fifth of a tonic major or minor triad - there are six rectus forms available for each open string of the guitar that is used as a zero axis: The high E, the B, and the G strings, respectively. The inversus forms only work with the root as the zero axis, so the low E and A strings offer an additional four possibilities. That makes for a total of twenty-two (!) possible permutations of the subject/answer theme. Obviously, presenting all of these would lead to a gargantuan and unwieldy work, so I had to come up with an organizational strategy that would present only the best possibilities in a logical order.

Obviously, the subject here bears more than a passing resemblance to the subject from the Organ Fugue in D Minor from the Toccata and Fugue in D Minor which has long been attributed to Bach, but which I'm 100% certain Bach did not compose. The Wikipedia entry on that work is a good place to start, if you want to research this for yourself. As for myself, I transcribed that fugue for the guitar, and I was amazed by how well it sits on the instrument in E minor: The answer at the fourth above uses the open B and E strings, just as I do here. The only problem is that of range in the bass, as a seventh string would be necessary - a low B - to get the organ transcription onto the guitar. I say "organ transcription" because I'm also 100% certain that the D Minor Organ Fugue was originally a piece for Baroque lute, which had many more courses than the guitar has strings. Not only that, but there is no counterpoint in the organ fugue, as the counter-subject, such as it is, merely doubles the melodic trajectory of the subject or answer in thirds or sixths. bach would never have done that, but this is exactly the sort of thing you'd expect of a lute virtuoso who had a shaky understanding of counterpoint, and who wanted to simply indulge in idiomatic fugue-like playing. As for the episodic material, I'm not sure: The provenance of the piece is via one of Bach's students who had a less than honorable reputation, so almost anything is possible.

In any event, doing that transcription exercise gave me the idea for this piece, as the idea is a good one, but the execution of that idea was very ham-fisted and lame. Yet another reason I'm sure Bach is not the author of that "fugue." Convinced I could do much, much better justice to the zero axis fugue theme concept, I looked through the Six Studies on an E Axis that I wrote back in 1987 to get some ideas. While doing that, I noticed that the melody and bass line of E-Axis Study No. 2 in A Minor contained nothing but contrary and oblique motion: If there is nothing but contrary and oblique motion between a melody and it's counterpoint, then both trajectories can be inverted at the octave, and they can be doubled in thirds or sixths! This is Sergi Taneiev's Convertible Counterpoint. So I was in business.

Here is an MP3 of me playing the E-Axis Study in A Minor.

The score is below.



As you can see, the zero axis E here is functioning as the fifth of the tonic minor triad, and there is nothing but contrary and oblique motion between the trajectory of the melody and the trajectory of the bass line, so either can be doubled in thirds and all resulting contrapuntal relationships will be technically correct. This is exactly what became the answer and counter-answer in the final fugal exposition, as you'll see. The problem is, using those doublings is not technically executable on the guitar in the key of A minor, but it is in the key of A major! This set up the fugue as a battle between minor and major, with major winning out at the end.

Here's page two of the study so you can follow the whole thing as you listen if you wish.



What was the melody and bass line of the study became the answer and counter-answer of the fugue, as I said.

Here is a MIDI to MP3 conversion I made in iTunes of the Axial Fugue in E Minor that you can play while reading the score.



So, the subject starts out using the open B string as the fifth of the tonic E minor triad on the top system - I used a system for a solo guitar piece because the music is far to much for a single stave, obviously - and that subject is 7.25 measures in length. As I've said before, odd and fractional bar lengths for fugue subjects are highly desirable.

The answer then comes in on the last eighth of measure seven over the desirable "dissonant fourth," and notice how the sixteenth ornamentation makes the previous zero axis on B "disappear" into the new melodic trajectory: I am very scrupulous and exacting in how I handle the axes and melodic trajectories in this fugue. Likewise, the melodic trajectory of the subject goes smoothly into the counter-answer from measure seven to measure eight.

On the third system down is a brief episode that I call a "release area" that sets up an inverted statement, still in A minor, on the fourth system down. Note how the melodic trajectory on the top staff in the release area and the bass line converge on the note A in measure nineteen, and the zero axis of E falls smoothly into the counter-answer of the inverted statement as well: No loose ends.

This inverted statement is one of the most difficult sections to perform in the fugue, because the E axis here is not an open string on the guitar. I toyed with the idea of using a scordatura tuning with the D raised to E, but that screws up some of the following material, so I'll just have to grin and bear it. In any case, this statement is positively required to get the structural architecture of the piece off the ground.

Starting in measure 27 there is the first of many sequential episodes that modulates the piece to C major.



Now, the open E string zero axis is functioning as the major third of the tonic C major triad: See how cool this device is? I'm able to get many modulations and still use the open strings of the guitar, which is the only thing that makes this fugue possible: It is quite idiomatic, for the most part. This is the subject form of the theme, by the way: The subject's trajectory descends at the end, while the counter-subject's trajectory rises at the end (The opposite is the case with the counter-subject and counter-answer, obviously). Again, there are no loose ends with the trajectories: The G above and the E below in measure forty converge on F-natural in forty-one, and this continues throughout the episode's sequences.

The second system, then, is another sequential episode that is organically spun out from the tail of the subject/counter-subject combination. This one doesn't modulate, however, it only changes mode genders by introducing the E-flat in measure forty-seven.

On the third system is another inverted statement, only this one is is the key of C minor, the G axis is an open string, and it is functioning as the fifth of the tonic triad again. In 55 is a new kind of episode, which leads to the counter-exposition. So, we've already been through the keys of E minor, A minor, C major, and C minor, and we're just getting out of the exposition (Remember, this is a mono-thematic sonata process exposition, and not a strictly fugal one). Note that this episode's ending sounds rather "incomplete" ending on the C in the bass as it does: This is intended, and I'll "fix it" next time we hear this episode, which will be leading into the recapitulation.

OUr counter-exposition begins in measure sixty-one, and we're back in E minor. The subject is exactly like it was at the beginning, but now the main counter-subject is below it, and it has a drone above. Since both the zero axis B and the drone E are open strings, this is not overly difficult.



Whereas the exposition's answer was two voices, here in the counter-exposition it is three voices. Though counter-answer two, the new element, crosses the melodic trajectory of the answer, it effectively doubles it in thirds, which is part of the progressive uncovering of the "original combination" which will appear in the recap.

The 'release area" episode is the same as before, only now I introduce a C-sharp at the end to make the next inverted statement in A major, versus the previous A minor. These sharps will help to affect the next modulation to C-sharp minor, as you can see in the sequential episode that begins at measure eighty-seven.

So the bottom system here is exactly the same as the C major statement in the same place from the exposition, but now we're in C-sharp minor with the zero axis open E string functioning as the minor third of the tonic triad. This is really, really cool, if I do say so myself.



This means that the following sequential episode has a sharp to shed, and so it is more interesting as well. At the end of this episode, I use some chromatic motion in the bass to lead into an entirely new element, which is a longer episode based upon an ascending chromatic bass line. The C-sharp in measure 107 appears to be "left hanging" - the first instance of this in the fugue - but it is all part of the plan of the episode. That C-sharp finds it's home as the D descends to C natural at the very end of the section in measures 124 and 125.

On the bottom system is the inverted statement in C again, but this time it's in C major instead of C minor, and the counter-answer is doubled in thirds for the first time.



That then leads to a gnarly episode with thirds in the lead, and that returns us to A major for the answer section in the major mode with the counter-answer below doubled in thirds. I needed a quarter rest in 143 because a unison is not physically possible there: I needed to re-attack the same E as is in the bass part. By the way, this is hard as hell to play.

At 147 the release area reappears, only this time in the major mode, and that leads to the first of the inversus statements, and it is also the first time that the zero axis open A is functioning as the root of the tonic triad, while the inverted counter-subject is doubled in thirds. This isn't exactly easy to execute either, but you ain't seen nothin' yet.

The inverted sequential episode is really weird and wonderful: The converging trajectories make it triad, diad, monad every iteration, and the whole of the thing modulates us back to E minor for the development sections. Yeah, it's a bitch to play.



Here in the development we start out with an answer-form variant on the original pitch level of E with the countersubject in the lead and a pedal point below. The only things that make this possible are all of the open strings involved.

At 173 is a new form of the release area, and 177 is the answer and counter-answer two over an alternating pedal point. Both the A and E are open strings, so this isn't that difficult to play, actually.

This leads to what at first sounds like the original release area episode, but this modulates to G major at the end in a startling way. Note the chromatic line from F-natural to E, and then D-sharp on the top staff which becomes D-natural on the bottom staff. I'll reverse the D-natural and D-sharp to get to G-sharp minor next time. Don't remember how I thought of this, but it's a nice effect.

The statement in G major is pretty tricky, but is is possible to keep the high G drone going with some fancy finger-work. note here that the open B zero axis is functioning as the major third of the tonic triad.



This sequential episode - notice how they are all the same and yet different: I like fractal self-similarity principles, and use them to get unity in variety throughout this piece - leads us back to E minor, and the first of two episodes based upon an ascending chromatic line in the bass that are the central pillars that this piece balances on.

The end of that episode introduces a sixteenth note run that is ridiculously difficult to execute with all of the other stuff going on, and we are back in E minor. I'll change that sixteenth note figure to lead into E-flat major next time.

From 216 into 217 is the only illegal intervallic sequence in the piece. Between the F-sharp in the bass and the G-natural above it in 216 is a minor ninth. That moves in stepwise parallel motion into a major ninth between the low E and F-sharp above in 217. Since the parallel ninths are unequal and the G is the beginning of the establishment of a new zero axis, I decided to allow myself this license. Plus, it doesn't sound in any way bad or wrong. It's one of those things that works, despite being technically illegal.

Our E minor statement at 217 is new, as the open G is functioning as the minor third of the tonic here, the open B above that is a drone, and the counter-subject is in the lead. All of that over the open low E string's pedal point. Yeah, it's a nightmare, and using the c finger of the right hand is positively required.

As a result, final sequential episode on the page is the most vigorous one yet, and this leads to the exuberance climax on the next page.



The second half of the development starts in the major mode, and now counter-answer two is added. Then, the newer release area episode is just a major mode variant.

OK, now for the third system. Stay with me here. We're in A major now, and we have the answer, counter-answer one as the top line of the lower stave, counter-answer two adding the thirds to the answer's trajectory, and a syncopated E pedal point in the bass. This is not impossible, but it is very difficult, and I actually anticipate using the bass player's technique of thumb slaps on that low E. If I can ever pull it off, it will be totally awesome, dude. LOL!

At 249 is the modulatory release area again, and as promised, I reverse the D-sharp and D-natural from before to modulate to G-sharp minor here.

Holding the G-sharp as a drone is at the edge of impossibility, so I made them eighth notes this time. I may do that with the earlier G's as well; we'll see when I start learning it... if that day ever comes. ;^)



We have a bunch of sharps to shed in this sequential episode to get us back to E minor for the upcoming chromatic bass line episode, so this one is more interesting, as it should be later in the work, and notice the F-natural at the very end of it in 265: This was an F-sharp last time, so now we have an augmented sixth with the D-sharp above. This is a setup for the modulation to E-flat major at the end of this next episode.

The second of our "pillars" is then exactly the same until the last measure where I change the sixteenth note run by introducing F-natural, A-flat, and B-flat in the run-up to E-flat in the lead, and the F-natural in the bass again. Since the guitar doesn't go down to E-flat, I was able to avoid the parallel ninths this time by simply having the bass drop out. LOL! That F-natural finally finds a home on the next page, however, when the low E picks it back up.

Since the B-flat drone is not an open string, obviously, I made the upper voices eighth notes for the E-flat major statement. Between this and the radically fast modulation down a semitone, this sounds "wicked pissah," as we used to say in Boston.

Finally, we get the second appearance of the episode that ended the exposition, but now it's completed and makes a proper modulation at the end. The high C-sharp in measure 294 is also the pitch climax of the piece: That's at the 73% point, which is virtually perfect for a piece based on the answering interval of a perfect fourth (a ratio of 4:3, i.e. 3÷4= .75).



So, here's our recapitulation, and now we are in E major. On the top system we have, top to bottom, a drone on the open high E string, the major mode variant of the subject with the open B zero axis functioning as the fifth of the tonic major triad, counter-subject two doubling the trajectory of the subject in thirds, and counter-subject one in the bass.

Then, the second system has the "original combination" in all of its glory: The answer using the open high E as the zero axis, which is the fifth of the tonic, of course, then counter-answer two doubling the answer's trajectory in thirds, and finally counter-answer one doubled in thirds. This is what I wrote first, and it's only executable in A major: The entire fugue is based on the possibilities of this combination. This is so highly virtuosic, I don't know if I'll live long enough to learn it. I'm not kidding. It would take someone like Kazuhito Yamashita to pull this off with the bravura I envision.

I then use the release area, which is stupid-simple after what just went before, to turn around to E minor again and the first of the inversus statements using the open low E string as the zero axis. It is again the root, of course.

At 320 is and inverted from of the release area episode, and that leads to...



... the first statement of the rectus form of the subject that uses the high E zero axis as the root of the tonic triad: Saving the best for last, as usual. A variant of counter-subject two is also present, but without the thirds in the bass this is much, much easier to play.

At 331 I introduce the ending episode, and it sounds like the minor mode is going to hijack the piece and end it early, but E major interrupts at the last possible moment in 342, and we get the major mode version of the inversus and its inverted release area episode.



As I said, save the best for last: These major mode variants using the zero axis as root work much better than their minor mode counterparts, which is the whole point.

At 361 the final episode based on a chromatic bass line interrupts the action, but this one is based upon a descending chromatic bass line, as is apropos nearing the end of the piece, and it balances out the one in the counter-exposition perfectly. Notice that I let placement of the sixteenth note ornaments from the subject clash with those in the episode this time: I've scrupulously avoided that up to now, because it is a really wild effect I wanted to save for the end.

The ending episode then returns at 373, but this time the bass gives mi, re, do after the descending chromatic tetrachord. Since the chromatic tetrachord implies minor and the bass lick implies major, this is the final clash of wills between minor and major.



After the point where major interrupted previously, minor finally surrenders as the chromatic line becomes diatonic and doubled in thirds on the second system. The final triumphant statement is the trajectory of the subject and the counter-subject in augmentation harmonized using all the strings of the guitar possible: Six voices except for measures 393 and 394, which are five voices. Ta da!

Probably needless to say, this piece is at the very bottom of my to-do list. LOL!

Of course, the series must end with a redhead.



That's a mirror, she's not twins. Otherwise, yeah, twin redheads would pretty much be my ultimate fantasy. LOL!

Sonata One in E Minor III: Scherzo in G Major

The first two posts in this series are here and here respectively.

This is the third of four movements, which are Toccata, Sonata, Scherzo, and Fugue. The order of composition for these pieces, as far as completing them is concerned, was however, the Sonata first, the Fugue second, then the Scherzo, and finally the Toccata.

As for the beginnings of the pieces though, this Scherzo has by far the earliest point of origin. I actually wrote the melody of this tune back when I was twenty-one years old, which would have been sometime in 1979 (!). It was an assignment given to me by Jackie King when I was studying with him at The Guitar Institute of the Southwest - later the Southwest Guitar Conservatory - in San Antonio. This was the year before I started at Berklee in the fall of 1980. The assignment was to write a swing tune to a pre-existing chord progression from a jazz standard, and what I came up with totally knocked Jackie and my classmates out, so I kept it around. BTW, I cannot for the life of me remember what the standard was, but it was something out of the old, and illegal, Real Book.

Fast forward twenty-six years (!) to 2005, and I dragged the piece out of my archives to make an arrangement of it for two of my students, who had a jazz guitar duo. While working on that project, I noticed that the compass of the melody would allow for a single guitar to play the melody along with a contrapuntal bass line. I had the idea to write counterpoint in a legit, straight ahead jazz swing style for many years, but I was thinking about using a Charlie Parker tune like Donna Lee for the project. Needless to say, this was an exciting discovery for me, and a very fortuitous event, so I first wrote a contrapuntal bass line to the melody in late 2005, and then the "trio" section, which is like a jazz soloist improvising for a chorus, sometime in 2006. I didn't even have to change the original key, and it fit into the key plan for the sonata perfectly!

So, this piece only took me 27 years to compose. LOL!

Here is the MIDI to MP3 conversion of the piece I made in iTunes: Scherzo in G Major.

As usual, clicking on the blue playTagger icon will allow you to listen to the MP3 in this window, while clicking on the link will play the MP3 in a new window or tab, depending on your prefs.

The word scherzo translates into English as jest or joke, so a scherzo is supposed to be a humorous piece: What could possibly be a better or cooler joke for a multi-movement sonata than to have the scherzo be a swing tune written in two-part counterpoint?! Yes, I love this little piece, and it's all the way up to #3 on my to-do list now, so I ought to be performing it by next year at this time. Technically, it's really not that virtuosic. Not any more than one of the more challenging Bach Lute Suite pieces, anyway, and Bach was actually the inspiration for this piece: I just asked myself, "What would Bach be writing if he were alive today." A highly speculative question, to be sure, but I reckon he'd be doing exactly the same thing today as he did then: Writing highly sophisticated pieces in popular styles - Bourrees and Sarabandes were the pop tunes of his day, just like swing tunes are in the jazz world.

I actually did a technical analysis of this piece for a much earlier post on this blog, so I won't have to offer a blow-by-blow description today. Here is just the original tune and counterpoint, with the chord progression I wrote it to above the staves, and the resulting progressions that the contrapuntal bass line created below:



The chords indicated above the staves are exactly what I had on the ancient manuscript I pulled out of my archives, as is the melody, so it was originally just a jazz lead sheet. I did change the time signature from 4/4 to 12/8, however, so that the swing would be correctly written out and properly played back via MIDI.

Since the melody is in a legit straight ahead jazz swing style, I wanted the bass line to be as well. I've heard some other composers attempt things they call jazz counterpoint, but none of them sounded legit to me: This does, since the bass line is exactly like something Ray Brown might come up with. As you can see from the analysis, that bass line implies much more interesting harmonies than the original lead sheet had.

This has lead to a much more high tech method of writing for me: I can compose a pure harmonic continuity now with well ordered root progressions that has all of the structural modulations worked out within, then I can write a very colorful melody over that chord progression, and finally, I can compose a contrapuntal bass line that raises the musical interest level even more.

As I've written about before, the traditional way of teaching counterpoint is quite tiresome and inefficient. Basically, the rule sets that are taught as seventeenth and eighteenth century counterpoint are burdened with rules that basically describe the styles of Palestrina and Bach respectively, but the underlying fundamental laws are never given.

There is only one prescriptive law of pure counterpoint:

1) Only imperfect consonances may move together in parallel stepwise motion.

From this, we can deduce the two proscriptive laws of counterpoint:

2) Perfect consonances may not move together in parallel stepwise motion.

3) Dissonances may not move together in parallel stepwise motion.

Then, from these three fundamental laws of contrapuntal motion, we can deduce the three exceptive laws:

4) Imperfect consonances may move in parallel stepwise motion into perfect consonances or dissonances.

5) Perfect consonances may move in parallel stepwise motion into imperfect consonances or dissonances.

6) Dissonances may move in parallel stepwise motion into perfect or imperfect consonances.

Finally, the true law concerning the "emancipation of the dissonance":

7) Dissonances require no preparation or resolution.

So far as the issue of parallel perfect fourths being allowed in so-called "simple counterpoint" is concerned, simple counterpoint is not pure counterpoint: All pure counterpoint is invertible at the octave, so parallel perfect fourths - since they invert to perfect fifths - are not allowed.

When you purge the teaching of counterpoint of all of the niggling rules which just describe stylistic aspects of Palestrina's and Bach's compositional practices, this is what you get. Counterpoint is much simpler than harmony - which is why it appeared first in western musical evolution - it's just that it is not taught properly because the simple underlying laws were not distilled out until, well, I did it.

So, though I treat dissonance quite freely in this piece - dissonances require no preparation or resolution (!) - there is only one parallel stepwise dissonance here - into the second beat of measure six, which I corrected in the final version - or perfect consonances (in the final version), so this is perfectly pure counterpoint, it's just in the jazz style of swing.

Here's the final version of the "menuetto" with that single correction:



As you can see, by simply changing the B-flat to D-flat in measure six, I got rid of the illegal parallel dissonance. This is one of only two changes I made to the melody that I wrote back when I was twenty-one; the other is the note G on the third eighth of measure nineteen, which was an E-flat previously. I made that change simply so that the figure wouldn't be an exact repeat of the previous one just heard.

For the "trio" section, I wanted to have an analog to the jazz practice of having a soloist improvise for a chorus. It took me a while to come up with the approach for this, but I finally decided to keep the original bass line as a cantus firmus, and just progressively elaborate on the original melody until I worked up to constant eighth notes for the internal repeat - which is here written out, of course. Since jazz improvisation actually began with soloists ornamenting the original melody, this is actually seriously old school. LOL!



For the return of the "menuetto" section, I just used the repeat, which gives the whole piece a nice proportionality to it.



I end the piece with a stylistically apropos 6/9 chord, which is a nice parting shot for this particular musical joke.

So, as you can see, counterpoint can be written perfectly well and legitimately in styles quite distantly departed from anything resembling Baroque or classical music... if you understand what the fundamental laws actually are, and are not hung up on a bunch of arbitrary rules that just pertain to to the expressive stylizations of Palestrina or Bach.



Beautiful face, natural blond, no makeup: A perfect ten (She'd "go up to eleven" if her hair was naturally red. LOL!).

Sonata One in E Minor II: Sonata in A Minor

This is the second of the four movements of Sonata One in E Minor for solo guitar. The first post in the series is here.

To review, the four movements of Sonata One are, Toccata, Sonata, Scherzo, and Fugue. In the first piece, I slightly extended the tap techniques that rock guitarists developed - Eddie Van Halen, Joe Satriani, Steve Vai, et al - and brought a traditional composer's sensibilities to their application. In this Sonata, however, I wanted to combine traditional sonata process - and, sonata is a process, not a form - with the harmonic concepts I've picked up through my studies and writing of contemporary jazz as well as classical music. In a nutshell, I'm using all of the colorfully dissonant harmonies I love, and combining that with more traditional voice leading.

One of my main beefs with the music of Claude Debussy and other Impressionist composers is that, while the harmonies are strikingly beautiful, the overall vigor of the music suffers from lackadaisical voice leading. Part of this was a reactionary movement against the perceived confines of traditional technique, of course - and so it was a natural and inevitable occurrence - but some of the reaction lead to music that was, well, a bit flaccid in its drive and organizational aspects.

Now, this is, strictly speaking, free composition, so I'm not afraid to employ some parallelisms, but I'm aware of them and am employing them to effect. In any event, the voice leading is far more "normal" than that which the impressionists allowed for.

Here is the MIDI to MP3 conversion of the score: Sonata in A Minor

As usual, clicking on the blue playTagger icon will allow you to listen while following the score, while the link will open up the MP3 in another window.

The piece begins with an introduction.



Keeping in mind that the listener doesn't know where he or she is at this point, the beginning harmony on the top staff is a v(sus4). The chromatically rising bass line begins redefining this on the second staff, first to a bVI(M7/addA11) and then to a vi(m7/add11). At measure seven the upper harmony begins to transform against the chromatically rising bass, which first creates a bVII(6/9), and then that becomes a bVII(m7), which makes the listener expect a modulation to C major. This is thwarted at the time signature change, however, where we get a V(6/3) into a vii(d5). After that, in measure eleven, there is a secondary subdominant, which is functioning as a traditionally so-called Neapolitan Sixth to the vii(d4/3)/iv, which resolves into a iv(6/3) at thirteen. Then we get a bVII in fourteen, a i(6/4) in fifteen, and finally, the tritone gives us the V(m7) in the final measure.



The exposition begins with a tune in A minor and back in 3/4 time, and the first four measures are a simple, i, iv, V(m7), back to i at measure twenty. At the end of twenty, however, another V(m7) appears, and then the harmonies begin to get more interesting. Twenty-one has a bVI(M7/addA11) which goes to a bVII(m7) in 22. This chord picks up an augmented fifth on the final eighth note of the measure, and then in 23 we get a V(4/3/b)/bVI - the traditional so-called French Augmented Sixth, only targeting a degree other than five - and then this becomes a bII(6/4) in 24 - basically a traditional so-called Neapolitan Sixth, only in second inversion - then this, ultimately, morphs into what us jazzers call a subV(9)/V, which is a so-called German Augmented Sixth in traditional parlance. This gives the V(m9) in 25, which pauses on a sounding second. This sounding second will become a major feature of the sonata's developmental process.

I also injected a measure of 2/4 in at 26, as you can see, and this will lead to many more metric modulations later in the piece. One of the things I am going for here is a very natural, organic plasticity of phrasing. Before the "tyranny of the bar line" and "primacy of four" eras, composers such as Palestrina exhibited a very elastic sense of phraseology, and I think much was lost with the end of that era in the "breathing music" department.

The "tune" resumes at 27, at which time I begin to effect a modulation to the relative of C major. Twenty-seven itself is a V(m7)/iv), which dutifully resolves to iv in 28. The last quarter of 28 introduces a vii(d5)/V, which hits a V(m9) in 29. There is then a deceptive motion to bVI(M7/addA11) at the 4/4 measure of 30. The sounding second again reappears, and the last beat presents a vii(d5)/bVII, which is the V of the new key. The final 5/4 measure then has the V(M9) of the new key of C, and we're ready for the second key/theme area.



The main thrust of the sonata process is that of contrast: Contrast of key, tempo, texture, or any other musical element you chose. So, here we are not only in the key of C major now, but I have gone from a primarily homophonic texture to a contrapuntal one. Nonetheless, I'm using harmono-contrapuntal effects, so there is a chord progression: I, V(6/5), vi, V(m7), into IV(M7/addA11) at the first 4/4 measure 36, and then V(M9) in 37.

Then, the tune relaunches, only this time I used a descending chromatic line to get, I, V(6/5), V(4/3/b)/vi, V(m7)/ii into a ii(d4/3) at 42. The 5/4 measure than has a V(m9) which appears to signal C minor, but that becomes a V(6/3) of the original key of A minor at the last beat.



A minor isn't the key I give, however, as the counter-exposition starts off in A major. This is the same tune as was in the exposition, only now in the major mode, so the harmonic progression is what you'd expect of a major key variant.

Since the idiom of the guitar is so restrictive, composing a sonata process piece for it is several orders of magnitude more difficult than composing one for a keyboard instrument: There are many things that will only work in one key - or at only one pitch level - on the guitar. My solution for this piece - the first sonata I've written for the guitar - was to simply reverse the mode genders for the counter-exposition.

Measure 51 is a new element - I needed it to deal with the F-sharp in the bass - and I'll use this measure more in the coming sections. Harmonically, it's just a vi(m7). After the "Neapolitan" and "German" sonorities in 52, the sounding second on the old V(m9) reappears, only this time it launches into the second theme, but in the key of A major at a much higher pitch level. It was a major breakthrough coming up with this idea: I had the exposition done as far back as 1996 and the idea to reverse the mode genders as for the counter-exposition by Y2K, but this idea didn't hit me like a ton of bricks until 2005! That was a very, very good day. Talent is great to have - I'm glad to have been blessed with some - but there is simply no substitute for pig-headed stubbornness and a refusal to quit. LOL!

Having the second theme at this higher pitch level allowed me to get a new IV(M7/addA11) at 59, which goes through a vii(d5d7)/V to become a regular V(m7) at the final measure of the page, but I managed to work in the sounding second element in both sonorities.



The second part of the second theme then appears - the part over the descending bass line - and because of the higher pitch level, I had to add a new measure at 66 to bring the melody back down to restart the first theme tune in A major. I'll use this again, too. Right after that, in 67, I use the previously added measure to set up the relaunch. I give the V(m9) witha sounding second in 69, and then the tune restarts in 70 and begins the modulation to the upcoming key of C minor. Tthe 5/4 measure at 75 gives the V(m9) to finish the setup.



Now we have the second theme at the original pitch level, but now in the minor mode. Again, this is primarily a contrapuntal section, and the harmono-contrapuntal details differ from the previous appearance of the them as you'd expect a minor mode variant to do. Measure 80, the one in 3/4, introduces a #iv(m7/add11), however, and I take advantage of the minor mode to get more "beautifully dissonant" harmonies whenever I can.

By the end of the page I present the V(m9) of C minor, and I make the key change "official" with a change of signature leading into the development area.



As I mentioned previously, the fingerboard is such a restrictive idiom that you just can't toss tunes and themes around at will on it, like you can on a keyboard. So, the solution for the development didn't come to me for a long, long time, either. What I finally came up with was a six measure chord progression - related to the progression for the first theme/key area, but extended - and i set it up as a variation set: I'm using the previous textures, not the tunes.

The first variation is the original texture of the first theme - but in C minor - and the progression is, i(add9), iv, BVII(add9), bIII, bVI(addA11) - which becomes a "French" chord at the end of 93 - and finally a v(m7) in 94. Then, the second variation introduces the sounding second element, and it metrically modulates to 4/4 in the last two measures, where we get some more "French" action leading into the V(m7) of measure 100.

I then use a deceptive motion from that dominant to return to the home key of A minor for the third variation. Tres cool, non? This variation uses the texture first heard way back in the introduction!



The end of this variation leads to the pitch climax of the piece, and I move to 2/4 to double the speed of the harmonic progression here: This is the texture of the second theme/key area, obviously. At the end of this variation, I modualte back to C minor for the fifth and final variation, which again uses the texture of the second theme.

I then restate the second half of the introduction to lead the piece back for the recapitulation.



Since we've already heard the original two theme/key areas in both modes, but not the first two variations from the development in the home key, I decided to ditch all of the original elements but one for the recap. The first twelve measures here are almost exactly like the first two variations of the development, but I put some more (add9) chords in. Where it is supposed to launch into the third variation/texture, however, the second theme in A minor comes in, which is the only element from the counter-exposition we haven't heard in the minor mode. This minor mode variant allows for the introduction of the most colorful harmonies yet - always save the best for last - so in 141 I present a IV(m7/d5) and in 142 I give a V(m7/A9). Neato! Then, we get the second trajectory of the theme with the descending chromatic bass line.



When the second theme ends, I need that extra measure again to bring the pitch level down, only this time I can make it a more interesting V(m7/A9), which I call, "the Jimi Hendrix chord" since he was so fond of using it. It doesn't sound like a rock or a jazz chord here, however, due to the overall context and voice leading.

Finally, I present the first additional measure from the counter-exposition for the third time, and the following "French" action leads back to the first part of the intro, which I use here as a coda also. Instead of the full second half of the introduction, I just present the first two measures of it, which resolves to the tonic, which echos the beginning of the first theme. BAM! as Emeril would say.

Sonata One in E Minor I: Toccata in E Minor

I've posted on this sonata previously, but now that I have added streaming audio to the blog, I wanted to go through it again. Now, readers will be able to read the description/analysis and then play the MP3 and follow the score simply by scrolling down.

Here is the MP3: Sonata One I: Tocatta

Clicking on the blue playTagger icon will play the MP3 in this window, clicking on the link will open up Quicktime, WMP or whatever media player you have set as your default in a new window. Obviously, clicking the player icon will allow you to follow the score. This is a MIDI to MP3 conversion I did in iTunes using the Realfont 2.1 classical guitar soundfont, which isn't too bad, really.

Toccata comes from the Italian root toccare, which is the same root as the English word touch, so a toccata is a "touch piece." Most people think of keyboard works when they hear the term toccata, but it was originally used for lute pieces before keyboardists like Frescobaldi appropriated it. So, I am simply returning the toccata to the fingerboard, where it rightfully belongs.

This Toccata in E Minor is based on the tap techniques that rock stylists like Eddie Van Halen and Joe Satriani developed, which goes along with the "touch" theme. In fact, I learned Eddie's Spanish Fly and Satch's A Day at the Beach to prepare for writing this piece (I've had this idea for years).

I expanded the rock versions of tap tech to take advantage of classical right hand technique: I employ the p finger (thumb) of the right hand to pluck a bass note while simultaneously fretting with the right hand i finger, and plucking the first note of the melody figurations with the m finger. The descending parts of the figurations are then pull-offs, and the ascending parts are hammer-ons. This isn't as difficult as it might sound, but it isn't exactly easy either. I used as many open notes in the bass as possible, but there are some fretted bass notes, which complicates matters significantly.

The form of the piece is, I, A, A', B, B', Cadenza, A, A''. The cadenza, at this point, is just an Alan Holdsworth style legato lick, so it's basically a place-holder until I get around to, you know, actually learning to play the piece. LOL! I believe it's #7 on my to-do list right now.

Here is the introduction, and it uses no extended techniques:



The little opening, me, re, me, do figure prepares a lot of what follows in the piece, as you'll see. The rhythm is echoed in measure two, as an e(Add9) harmony is revealed. Then, at the end of four, le, sol, le, fa introduces the subdominant function harmony, which is an F(6/3)secondary subdominant with an augmented fourth in place of the fifth. Traditionally speaking, this is an altered form of the so-called Neapolitan Sixth harmony, but to me it's just a bII(6/A4).

At the end of seven the figure becomes, do, ti, do, le, and this introduces a dominant function harmony, which in this case is a vii(d5/d7) in third inversion.

The entire figuration formula then repeats an octave higher, but with the harmonic rhythm quickened. The e(add9) reappears in 11-12, and the F(6/A4) 13-14, but this time the dominant harmony is a regular B(m7).

Next, the formula repeats with an even quicker harmonic rhythm in a third octave, which leads to a half-cadence on the bottom staff. Finally, the first figure appears in yet a fourth octave, which leads to an augmented sixth interval plus two octaves in the final measure of the intro. The F-natural in the bass is on the first fret of the low E string, and the D-sharp is on the eleventh fret of the high E string. To play this, the left hand 1 finger frets the F-natural, the right hand p plucks it, the right hand i frets the D-sharp, and the right hand m plucks that. I do this kind of thing for several pieces I play, so it's not that difficult in my view: It seems like a logical extension of traditional classical guitar technique to me.

Here are the first A sections:



This might look nightmarish, but it really isn't: In measure 22, the low E is the open low E string of the guitar, and it is plaucked with the p as per standard practice, while the high E is fingered with the right hand i finger, and is plucked with the m. Then, the B and G of the figuration are pull-offs to the E in that figure, which is the open high E string of the guitar. The ascending notes are then hammer-ons back to the high E, which is tapped: Only at the beginning of the measures is there anything beyond "traditional" rock tap tech.

Harmonically, the A section within the repeats is as simple as it gets: i, iv, V, i and the second ending is just the deceptive motion to bVI. After that, however, there is quite a bit of strangeness that is in large part idiomatically driven by what is and is not possible on the guitar. Measure 27 is a iv(m7) in third inversion, and in the succeeding measures I use all open notes in the bass: From E to A, D, and G. You can analyze the harmonies for yourself, if you wish, but they were largely intuitively and idiomatically driven, so there is a lot of strangeness. Sounds cool, though!

My goal was the F(M7) in 32, which, in a weird way, facilitates the V(add9) to I(Add13) into the key of G in 33-34. Later, I'll make this phrase turn around to E, which will be quite nice. On the bottom staff there is a confirmation cadence that echos the previously heard half-cadence, and we're ready to launch into B. The opening figure from the introduction then returns, but it goes down to E at the end.

And now for the killer B's:



The last open low E of the previous page is plucked with the p, and then the G in 37 here is hammered on with the 1 of the right hand. Then the first notes of the upper sixteenth note groups are hammered on my two of the remaining fingers of the left hand (depending on the figuration), and finally the top two notes are tapped with the right hand i and m. This is just a mild enhancement of Satriani's technique used in A Day at the Beach.

Harmonically, to be consistent, within the repeats is just the relative major echo of the previous section as, I, IV, V, I. Again, you can analyze the following harmonies for yourself if you wish, but there is a lot of intuitive and idiom-driven stuff going on. The goal is, of course, the B(m7) in 63, which brings the piece back to E minor. As I mentioned previously, the place-holder mini-cadenza in 64 is just an Alan Holdsworth kind of legato lick - lots of hammer-ons and pull-offs - in keeping with the "touch piece" theme. I'll probably elaborate on this later... or not.

The cadenza lick ends into another half-cadence leading back to E minor. Then, the opening figure returns again, this time in its original form, and we're set for the return of the A section.



Everything here is exactly the same as before until measure 78: I changed the D-natural from before to a D-sharp this time, which makes the final resolution to E major instead of the previous G major (And I should point out that the E major here is required: E minor is physically impossible to execute!).

Now, go back up, play the MP3, and follow the score.

Test: New and Improved MMM - Now With Streaming Audio!

This is something I've wanted to do for a long, long time, but I'm just enough of a computer luddite not to have been able to figure it out. Well, by hanging out with some composers who are a lot smarter than I am with computers, I think I have finally figured it out.

Turns out there is a super-simple script available for the del.icio.us playTagger that can be embedded into any weblog template, and that should put a blue and white play icon next to any MP3 links I embed here. I'll soon find out.

This is a MIDI to MP3 conversion that I did in iTunes using the RealFont 2.0 classical guitar soundfont, and it is of the third movement Scherzo from my Sonata One in E Minor for solo guitar.

This is a traditional swing tune with the swing written out in 12/8, but it is in two-part counterpoint. Both the melody and bass line are stylistically correct, and the counterpoint is traditionally strict: No parallel perfect octaves, perfect fifths, or dissonances.

Click on the blue and white player icon, not the file name: Clicking on the file name will give you a Quicktime player in a different window if you're on a Mac, or WMP if you are on Windows (And have WMP as your default).

Enjoy!

Scherzo in G Major for Solo Guitar

Hucbald's Number One!

This was actually the chart from a couple of weeks ago, but I was in the middle of the How to Compose Counterpoint series of posts. This is for the Electronic Classical category, and not guitar (I was number two in guitar that week) which surprised me, but I'm not exactly sure how the MP3.COM.AU charts are calculated. In any event, I also cracked the top ten in the Classical category that week to number nine, but I dropped a full ten spots this week to nineteen. Here's my live mp3.com.au music page, and you can see the current rankings of all forty-five of my tracks. For some reason known only to God, I'm starting to appear in the Jazz Fusion (!) category now. Whatever. LOL!

Here's the screen grab I got to commemorate the event:



I put a sidebar section with links to all of the How to Compose Counterpoint posts under COMPOSING COUNTERPOINT (Since that would fit on one title line), and I also put links to my friends Jim Kozel and Richard McClish in the HUCBALD ENDORSES section, something I've been meaning to do since I got the RMC Polydrive equipped Parker Nylon Fly back last spring.



Adam never really had much of a chance, did he.

How to Compose Counterpoint (Imitation and Modulation 3)

This is the seventh and final installment of a series of posts that began with Where to Begin and progressed through How to Progress, Using Larger Forms, Using Three Voices, Imitation and Modulation 1, and Imitation and Modulation 2.

In this third and final post on Imitation and Modulation we are going to look at a piece I call Extempore in A minor, and with this we will have looked at all five movements of my Sonata Zero in A Minor for solo guitar. This Extempore in A Minor is the first movement, the Menuetto in B Major from the first post in this series is second, the Ricercare in C Major from the post prior to this is the third movement, the Scherzo in B Minor from Using Larger Forms is fourth, and the Fugue in A Minor from Imitation and Modulation 1 is the finale. So, the five movements of Sonata Zero are, Extempore, Menuetto, Ricercare, Scherzo, and Fugue.

The piece is, in reality, an imitative prelude, but I am already over half way through composing twenty-four homophonic preludes in all the keys for the guitar, so to avoid confusion with that Prelude in A Minor, I gave this a different designation. I got the idea from the fact that the compositional process for this piece was quite extemporaneous, and besides, Extempore, Menuetto, Ricercare, Scherzo, and Fugue rolls off the tongue nicely and has a cool ring to it. Hey, this stuff is important! LOL!

In this movement's brief fifty measures, it traverses sixteen - a full two-thirds - of the twenty-four possible major and minor keys, so it is just a riot of modulation. That's why I saved it for last: I came up with a very nice modulation scheme that allowed me to organize the key regions so that every key signature had both its major and minor appear. IOW, sixteen keys are travelled through, but only eight key signatures are used.



The subject, such as it is, is just the do, ti, do head figure from the upcoming ricercare and fugue themes, so this exposition is imitation boiled down to nearly its irreducible essence. At the answer we get the desirable entrance over a "dissonant fourth" and the resolution to a third, and then the final entry of the "subject" also happens as the desireable 6/4 sonority and the G-sharp in the bass gives a momentary diminished triad before the resolution to the tonic at measure four.

In the second half of measure four, a dominant function harmony is created - a vii(d6/3) - and then a i(6/3) is reached at the beginning of five. Note that to this point there have been no leaps at all; the voice leading has been totally smooth and stepwise. This exposition is another one of those things that sounds positively primordial in its logical inevitability.

There is another dominant function harmony in the second half of measure five - a root position vii(d5) this time - and then the development begins. For the development, I used the sixteenth-note diminution of the subject in sequence first to get things started. After tonicizing the tonic, it tonicizes the mediant of C and then the dominant of E. Notice, however, that at the "resolution" to E an augmented triad is created: G-sharp, C, and E. I pull out all of the stops with the dissonant counterpoint tricks in this piece.

Into measure eight the bass tonicizes the tonic again, so we really haven't modulated anywhere yet. The descending sixteenth-note figure in eight then descends to the subdominant note, making this a 2.5 measure phrase. Quite unusual.

The sequence then repeats into measure nine by first tonicizing the subdominant, then the submediant, and finally the tonic again into measure ten. Look at the sonority at the second beat of nine: A, F, B-flat. Since we are, in fact, in the subdominant minor key now, this would have to be an incomplete bVI(M7) in third inversion, and with the resulting minor ninth between the outer voices it is very hotly dissonant. The augmented triad at the beginning of ten sounds quite tame in comparison. At the end of ten, the second descending sixteenth-note run gets us to the subtonic minor of G, so we've accumulated two flats so far.

In eleven I invert the sequence, but the phrases are an even two measures now, so the dominant level of G minor is tonicized on D, then the mediant on B-flat, and finally the tonic on G. The final resolution is no longer to an augmented triad in this formulation. Notice how I used parallel movement into a DINO (Dissonance In Name Only, and augmented second in this case) at the end of twelve? This gives an incomplete fully diminished seventh on B - in second inversion - that takes the piece all the way back to C major, where the formula is repeated. And, with the appearance of C major, both of the natural keys have now appeared. I change the C major to C minor in fourteen, which allows the parallel movement into another DINO augmented second at the last eighth note. This produces an incomplete fully diminished seventh on E - again in second inversion - and so we're going to F.



With the appearance of F major at fifteen, both mode genders of the one flat key signature have now appeared. Here I speed up the pace another notch by combining the sixteenth-note tonicization figure with the descending sixteenth-note run. The bass line gets a chromatically introduced leading tone, so at sixteen D minor is tonicized. I pass the figures between the voices, as you can see, so at seventeen G minor is tonicized, and then at eighteen we're back to C major. This allows for a varied form of the formula to return us to A minor at the beginning of nineteen, where yet a faster formula with a constant sixteenth surface rhythm begins.

Now, this piece is very much a prototype, or an "Alpha Test Version," so I know that the eighth notes will have to be changed to sixteenths in the middle voice, and the notes in the top voice of measure twenty may have to have their durations shortened as well. I call these versions "idealized" and I set them up this way so I can hear the MIDI playback the way I want it. When I get around to doing the fingering, I'll create a "performance" version. This piece isn't even anywhere near the top of my to do list yet.

The new constant sixteenth note figure modulates up a perfect fourth every iteration, so we arrive at E minor in twenty, and B minor in twenty one. Since the formula continues on the third system, we arrive at F-sharp minor in twenty-two, and C-sharp minor in twenty three. I'm keeping the sixteenths out of the bass for idiomatic reasons, by the way.

When we arrive at G-sharp minor in twenty-four, I use yet another formula that modulates up by semitone every cycle: A minor into twenty-five, B-flat major into twenty-six, and then B minor into twenty-seven. B-flat major completes the two flats pair of keys, as we have heard G minor previously. The variation on the current formula in twenty-seven takes us back to E minor in twenty-eight, and I use twenty-eight to re-launch into the constant sixteenth note formula, only this time we will go through major keys.

Twenty-nine starts out on C major, and since the formula takes us up a perfect fourth every cycle, thirty has the arrival to G major, and thirty-one has the arrival to D major. G major and D major complete the key pairs of one sharp and two sharps respectively.



Since this is the second time we've heard this formula, I shorten the number of iterations, even though we're traversing major keys this time. Thirty-two has the arrival to A major, and that completes the three-sharps key pair. Since this formula takes us up by semitone again, we again traverse B-flat major in thirty-three - a key we've heard before - but this time we hit B major in thirty-four: This completes the five sharps pair. Now, the only incomplete key pair is four sharps: We haven't heard E major yet. The last beat of thirty-four intimates that E minor is coming, what with the C-natural and G-natural, but this is a deception, as the resolution into the sequential homophonic episode at thirty-five arrives at an E major chord.

This episode is again a harmonized augmentation of the subject element, and it is longer than the corresponding episodes in the ricercare and fugue because of this. The extra length is also required to shed all of these accumulated sharps. We get D-natural in thirty-seven, G-natural in thirty-eight, and then C-natural in thirty-nine. I retain the F-sharp until forty-two, however, after I can put the la, ti figure in forty-one (lowest voice on the top system), and so the return to A minor is accomplished.

The recapitulation here is a real one, it being just a restatement of the exposition with a final concluding cadence added to get to the close position A minor in fifty.

So, the appearance of the keys - and yes, deciding between what is a modulation and what is a tonicization here is difficult, to say the least - goes like this:

01) i= Tonic Minor-------------Natural Key-----(m=1)
02) iv= Subdominant Minor------One Flat--------(m=1)
03) bvii= Subtonic Minor--------Two Flats-------(m=1)
04) bIII= Mediant Major (Relative)--Natural Key-----(M=2/Complete)
05) bVI= Submediant Major------One Flat--------(M=2/Complete)

01) i= Tonic Minor-------------Natural Key-----(C)
02) iv= Subdominant Minor------One Flat--------(C)
03) bvii= Subtonic Minor--------Two Flats-------(1)
04) bIII= Mediant Major (Relative)--Natural Key-----(C)

01) i= Tonic Minor-------------Natural Key-----(C)
06) v= Dominant Minor---------One Sharp------(m=1)
07) ii= Supertonic Minor--------Two Sharps------(m=1)
08) vi= Raised Submediant Minor--Three Sharps----(m=1)
09) iii= Raised Mediant Minor-----Four Sharps-----(m=1)
10) vii= Leading Tone Minor------Five Sharps-----(m=1)

01) i= Tonic Minor--------------Natural Key----(C)
11) bII= Leaning Tone Major (N)----Two Flats-----(M=2/Complete)
07) ii= Supertonic Minor----------Two Sharps ---(1)
06) v= Dominant Minor----------One Sharp-----(1)
04) bIII= Mediant Major (Relative)---Natural Key----(C)
12) bVII= Subtonic Major---------One Sharp-----(M=2/Complete)
13) IV= Subdominant Major-------Two Sharps----(M=2/Complete)

14) I= Tonic Major--------------Three Sharps---(M=2/Complete)
11) bII= Leaning Tone Major (N)----Two Flats-----(C)
15) II= Supertonic Major----------Five Sharps----(M=2/Complete)
16) V= Dominant Major----------Four Sharps----(M=2/Complete)
13) IV= Subdominant Major-------Two Sharps----(C)
04) bIII= Mediant Major (Relative)---Natural Key----(C)

The numbers at left are the order of the keys as they appear, then the roman numeral designations for them, and the functional relationship they have to the tonic. The middle column has the key signature, and the right column has the check-off list.

The "(m=1)" for A minor means it is a minor key, and this is the first appearance of a key with that signature. Then, the "(M=2/Complete)" means it is a major key, it is the second appearance for that signature, and so the pair is complete. Subcequent "(1)" entries mean that the key has already appeared, but the pair isn't complete, and subsequent "(C)" entries means the key pair for that signature was completed previously. This is how you organize a modulation scheme.