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.

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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.

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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

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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.

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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.

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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.

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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.

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