Imitation Study Number 3 in F-sharp Minor

Here's the third entry in the series, but I must mention that the sequence of these in the final set of pieces will surely change. That will depend on the keys, time signatures, and types of pieces these end up being. This one happens to be an actual two-voice fugue with a tonal answer at the fifth, as opposed to the previous two, which were two-part inventions, per Bach's definition, with real answers at the octave.

Number three here also ended up in the tres cool key of F-sharp minor, whereas the previous two were in the boring and overworked key of A minor. This being a collection for solo guitar, at this point I'm thinking that A minor pieces will probably end up alternating with those in other keys... if I end up with enough pieces in other keys. lol.

Since these are solo guitar pieces written in open score, they can also function as duets for students too, which is a nice feature.

The subject of today's fugue was created one day while I was driving from San Antonio to San Marcos when I was a masters student at Texas State. I'm not positive anymore, but I think it was 1989 or 1990. It just came to me while I was daydreaming on the drive, and I sang it out in solfeggio.

First it became a rather lengthy and undisciplined string trio piece, but later it became a very tight fugato for chamber orchestra. I'm sure I'll still use that fugato in a larger piece at some point, but it's nice to have a solo - and duet - guitar version of it.

This is not simply a transcription of the fugato, though: I had to do quite a bit of re-composing to get this guitar version... or perhaps rearranging would be more accurate: The orchestral interjections are gone, naturally, but some of the episodes are redone as well.

Here's today's MIDI to AAC conversion:

Imitation Study Number 3 in F-sharp Minor



As you can see if you read the previous posts in this series, this isn't the stately Musical Offering/Art of Fugue type of subject I used for those pieces. This is a sprightly type of subject with lots of leaps and tied notes that nonetheless gradually accelerates to become a head/tail type of deal.

One of the coolest things about the answer is the counter-answer that works with it: There's a descending chromatic tetrachord at the beginning, and the ascending version at the end. I remember being amazed when I discovered this... and, well, it is kind of amazing. There's an eighth rest at the beginning of the last beat of measure 6 to avoid the unison on G-sharp, but it remains implied and a duet performance could actually execute it. Oh, and I have the high notes in the head of the subject and answer notated as harmonics, but it is technically possible to execute them as normally attacked notes.

If you are writing a two-part fugue, many times - but not always - the exposition will work out better with a third statement so you end up with the subject twice: That's the case here.

Note also the even more amazing feature of the countersubject's beginning: It's yet another ascending chromatic tetrachord!



The first episode, such as it is, is just a single measure spin-out of the subject's tail. One of the things I got better at here was register shifting: To get this kind of music to work on the guitar, it's necessary to shift registers to keep the music within the guitar's quite limited contrapuntal range. The descending minor seventh from F-sharp to G-sharp makes the required adjustment smoothly.

By not chromatically inflecting the sixteenths on the final beat as la and ti, they become fa and sol to effect the modulation to the relative key of A major. The low E's in this section are why the piece ended up in F-sharp minor.

I needed a new version of the countersubject at 11 because the descending chromatic tetrachord wouldn't work there, so it's a simple diatonic accompaniment. Same deal at 14, as an ascending chromatic tetrachord wouldn't work there either, so I used another diatonic version of the countersubject. I had to make another range concession at 15, but it sounds very natural; as if it's a natural part of the piece. Bach was a genius at this, but I'm just now getting really good with it.

Note that these are both subject statements and not answers.

Measure 17 is another single measure episode, and I used another octave displacement to set up the final statement in the relative...



... which is finally the answer, complete with descending and ascending chromatic tetrachords in the counter-answer. This sounds really awesome in the major mode, as you usually don't get this sort of thing in that context. I like it a lot. Love it, even.

The episode at 21 is now two measures: 21 modulates back to the tonic minor with the introduction of the raised submediant and leading tone in the final four sixteenths - a new figure for the fugue - and then 22 allows for the required register adjustment. Note that measure 22 is just like the first episode that modulated the piece to the relative, except that the raised sixth and seventh degrees are retained on the last beat, so there is no modulation.

The recapitulation at 23 is a super-close stretto between the subject in the bass and the tonal answer above: Only a single beat of delay. This is an extraordinarily difficult thing to pull off, and I really don't know how I make these things happen; I just "notice" them for some reason. Remember, I just sang this subject while on a boring drive up the interstate: I had no idea the chromaticism would work, or that this stretto was possible at the time. I didn't even work out the tonal answer until later.

I've never had a student who could do this, unfortunately, and in fact, I've never met or heard of anyone else who can do it either (Nobody living, anyway). It must be an inexplicable and rare gift, I guess. Too bad it's not worth any money in today's world. lol.

Notice that I had to make a register adjustment even in the subject to get this to work on the guitar there in 25: One hardly notices it. I hadn't acquired this skill when I came up with this subject twenty years ago, and that's part of the development of the craft aspect of contrapuntal writing: It's nice to have the gift of natural talent, but only time and effort can give you mastery of the details of the craftwork.

The final episode beginning at 26 has a gnarly contrary motion dovetail between the tail of the subject and the tail of the answer; it moves into major seconds and out to octaves. In the orchestral version, these are ninths and double-octaves, which are smoother sounding, but his is really excellent on solo guitar (Or, between two guitars playing a duet). the straight sixteenths that originally appeared back in 21 no reappear in 27, and the piece resolves out to a six-note F-sharp minor chord at 28. That's it: 28 measures and about a minute and a half. Very tight and efficient.



I'm sure I've used this image before, but she's just so striking and natural.

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Imitation Study Number 2 in A Minor

Well, this series has found a name now: Imitation Studies. I'm not calling them inventions because, 1] They do not all answer at the octave - some of these are fugues, IOW - and 2] Bach already used that. lol. Believe it or not, I've completed five of them so far, and the previous one was "perfected" by simply changing the dotted-eighth/sixteenth rhythm of the episodes to quarter/eighth triplets. This works better because the triplet feel comes right out of the tail of the subject. Since that was such a minor change, I decided to move on to the next in the series.

With this piece, however, the dotted-eighth/sixteenth rhythm is in the subject, while the written-out trill is in the countersubject: Therefore the episodes sound more natural and organic with the dotted-eighth/sixteenth figuration of the subject. Nice discovery.

I composed this subject back when I was a doctoral candidate at UNT in the early 90's, and it was the final project for the graduate level Invertible Counterpoint and Fugue course I took there. Since I composed it as a four-part canonic stretto with one measure delays, it took the form of an epic string quartet piece (You can also see the score in PDF format if you want).

Well, while writing this guitar invention version, I discovered some new facets of the subject, so that got me to thinking about revising the fugue. I think I'm coming up with a new compositional process here: Guitar invention or two-voice fugue first, then execute the final fugue for whatever ensemble turns out to be most appropriate. Bonus is, I get a bunch of guitar pieces out of all my ensemble fugues. Go me!

Number 2 here also ended up in A minor, but two of the next three are in the "cool" keys of B minor and F-sharp minor (Number 6 I'm working on is in E major).

Here's todays MIDI to M4A conversion:

Imitation Study Number 2 in A Minor



This is a five measure head, body, and tail subject, so we get the desirable odd bar length and an accelerating rhythm until the point of resistance in four and the cadential figure at the end. The countersubject is straight quarters until the final measure, and then there is a dotted-quarter/eighth followed by the written-out trill (I've come up with several of these written-out trills now, and they are becoming a thematic sub-language for me).

For the main episode I chose a descending chromatic line... hey, I like those.



... and this first iteration is non-modulatory.

Since the subject works as a four-part canon, the organizational scheme is of ever closer answers. Starting in 17 we hear the countersubject above the subject for the first time, but this is interrupted in 21 by the subject overlapping itself by one measure. Then, the rest of the countersubject seamlessly continues out of the subject's cadential figure due to the way I constructed it to work like this (I rock).



In 26 the former episode reappears, but this time it's foreshortened by a measure and modulates to the dominant minor region. Sorry I crammed it onto a single system, but it was a matter of keeping the page count down for this post version.

The sweeping rising thirds in the bass starting at 31.5 - me, sol, ti, re, fa, le - sound wicked pisser, as we used to say at Berklee, and then we get another mesure of the countersubject before the next interruption with now two measures of overlap.

For my esthetic, the third episode has to be different - with Bach everything is beautifully, maddeningly, and organically different - and here I discovered that the subject works over the descending chromatic figure of the episode. This leads to some unusual contrapuntal motions, the coolest of which is the perfect fifth into a diminished fifth from 41 into 42. I need to put this in the string quartet, because it will be even more effective with three or four voices. At the end I modified the tail of the subject and the bass part to set up the modulation to the relative major region. Hot, or not?



We're down to two measures of delay/up to three measures of overlap now, and I changed the second measure of the countersubject in 45 just because it sounds really beautiful this way (Hey, I do have a heart). Same with the bass part in 49 (Mahler said, "Interesting is easy; beautiful is hard"). I thrive on interesting, but I go for beautiful whenever I can.

By the way, the inversion of this stretto would not work, because parallel fifths would be implied. The implied elevenths sound fine (I tried it the other way for grins... but those turned to frowns).

The original episode then reappears at 51, but yet another measure shorter as the piece returns to the tonic for the final stretto... or so it would appear.



The trill figure takes the final canon from five measures to six, and the end is a bit underwhelming, which sets up the hyper-stretto coda: Subject over subject in rhythmic augmentation. This is admittedly a bit weird in two voices, as there is a leapt-into minor ninth at the beginning of 64. Since the implied harmony is so obviously a V(m7m9) though - and this is immediately strengthened by the appearance of the major third - it actually works, IMO. Bach would never have done this (Well, he never did, to my knowledge), but I think it's kind of cool.

I worked up to a nice flourish in 71 and 72 with an implied V(4/2)/iv and then an augmented sixth into the primary dominant. A final - and new - trill figure finishes things off with a final chromatic flourish.

As it stands now, this is a better composition than the original fugue... which is why I have to re-write that puppy.


No doubt about that being hot.

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Invention in A Minor v5.3

This piece is now "finished." I put the quotation marks there because pieces like this tend to get revised over succeeding years - sometimes radically - but it is complete as it is, and I'm quite happy with it. One of the things I like about composing with dispassionate and lifeless notation based MIDI sequencers is that if I like the way it sounds in MIDI, I know a well performed version will be even better.

Here's the m4a sound file:

Invention in A Minor

This is actually version 5.3, as you can see, so it really didn't take all that many versions to get it done.



There are no changes here, so if you want a rundown, see the previous post.



The changes start at the first stretto section in the subdominant minor region. Previously I had both the 2.5 measure delay and the 1.5 measure delay stretti here, but I decided to save the closer one for the upcoming dominant minor. This was the breakthrough idea that allowed me to complete the piece, because I hadn't saved anything for the dominant previously.

There are no changes to the episode starting at 17 or the relative major statement starting at 20 either.



This episode starting at 23, however, is entirely new. The inversion of the major mode statement does not work due to a leapt-into major second - which is an augmented second in the minor version - so this was a natural place to put the harmonized subject in the bass with a melody in the lead. Sounds cool in MIDI, but it would be a PITA to play. Since this is primarily a compositional exercise, though, that's of little practical consequence.

At 27 we get the dominant minor statement with the closer stretto, and this also gives the piece a melodic climax at the C in 28. By saving this for the peak, we get a dramatic pause under it as the next subject statement begins, which sounds nice tres cool. Since the piece is 48 measures long now, 48/28.5= 1.684, which is just about as close as one can get to the Golden Mean of 1.618. Nice, huh?

Saving this stretto for this point also makes it out of kilter vis-a-vis the bar lines, so at the conclusion of the section in 31 I was able to use another nice contrapuntal/rhythmic acceleration lick into the final episode: quarter-eighth, quarter-eighth triplets, and then dotted quarter-sixteenth, dotted quarter-sixteenth. I like this effect, and in performance I'd probably swing the dotted quarter-sixteenth sections anyway - so it doesn't sound so stiff - so the transition is super-smooth.

From the final episode that begins at 32 until the end is the same as the previous version...



... so if you are new to this series and have any questions, check out the previous post.

Now that this has got me exploring some aspects of rhythmic variation in counterpoint - something I'd like to develop more as it's has heretofore been one of my weaker points - I believe I'll write two-voice inventions with all of my previously composed subjects. Series work like this is a great way to develop compositional technique, and after my eighteen axial studies and twenty-four figuration preludes, a series of inventions would be a logical step.

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Invention in A Minor v4.5

At first I thought I was working on a two-voice fugue with this subject, then it became an invention, and now it's actually almost a piece of music. Previously I had the various statements and stretti linked only by lineal licks, but now I've put some real episodes into it.

Here's today's AAC sound file:

Invention in A Minor v4.5



The exposition hasn't changed any, but beginning in measure seven there is an episode that modulates to the subdominant minor region. This is actually a harmonized version of the subject, which you can see if you look at the first dotted-eighth note of every group: It's the note at the corresponding location in the subject until I prepare to modulate at the end. Since the tonic A minor is the dominant degree of the upcoming D minor region, this was easy to accomplish by using the written-out trill on the proper level and introducing the C-sharp leading tone at the end.

An interesting aspect of working in two voices is that you can't easily just work your rhythmic velocity up to a constant eighth note motoric motion - or alternating dotted-eighths and sixteenths, as the case would be here - so that makes one think about how to make the combined rhythm breathe smoothly. This actually requires a bit of thought. Fortunately, the subject has six different rhythmic values in it and the trill tends to scrub out any buildup and so allows for a new beginning, so to speak. That's why I put the trill figure at the end of the episode: Going back into a constant quarter cumulative rhythm sounds excellent with that trill as a re-transition.

Since I've now established that there will be no perpetual motion cumulative rhythm, the stretti beginning in eleven breathe quite naturally from a rhythmic standpoint.



This culminates in a virtual stop in the rhythm at fifteen, which sounds quite dramatically cool at the new pitch climax of B-flat.

There is another episode based on the harmonized subject beginning at eighteen, but I've modified the counterpoint to facilitate a modulation from the subdominant minor region to the relative major. This took a little more head scratching and chin rubbing than the more obvious and easy previous episode, but the result is more interesting, which is what you want in succeeding versions of a musical idea.

The relative major statement is the last confirmed bit of the piece from the beginning - I'm sure the first 23 measures won't change any - but I had to resort to a lineal link to get to the final episode based on the harmonized subject, which is back in the tonic minor. I'm just not sure what will replace measure 24 at this point, but I'm thinking of statements of some kind on the dominant minor level, which would provide an overall pitch climax on C above the previous high of B-flat. I must admit to being stuck here, but that's usually a good sign, as what comes after much consideration is always - in my experience, at least - the final element that makes the piece perfect (Or pluperfect, if I'm particularly inspired).

For the final version of the harmonized subject episode, I discovered that two consecutive statements of that harmony, with slight variation, would work with a descending chromatic tetrachord as the counterpoint. this is goosebump-inducing cool if the listener is astute enough to follow what's going on, and it's one of those musical effects that can only be perceived with a bit of retrospection. So, 25-27 have the first statement over do, ti, and te...



... while the second statement is over la, le, and sol. It isn't really possible to perceive the new beginning of the subject until half-way through 28, so the effect is quite surprising. Tres cool, non?

There is no change to the closest stretto that begins at 31 - which functions as a recapitulation here - but the hyper-stretto coda that starts at 35 has been improved with some very nifty chromatic, rhythmic, and contrapuntal action.

The last quarter of 38 now has an augmented sixth on it - the only one of those in the piece at this point - and then there is an ascending chromatic tetrachord in 39. Then, the descending quarter triplet that starts in 40 has some cool contrapuntal relationships over the rhythmically augmented trill: m7-M6, m6-P5, and d5-m6 into the m6-m7 and d5 last two-beat triplet. It sounds a bit awkward in the m4a version because MIDI assumes every note is attacked, but when played the trill will be executed with hammer-ons and pull-offs, so it should be very smooth and cool. It's a nice closing contrapuntal device.

Almost more interesting to me though is the cumulative rhythm produced. If you consider a half note as the basic rhythmic unit, starting in 39 the cumulative attacks are 2, 4, 6, 3, 1, which is a very nice accelerating and decelerating rhythmic ratio.

I'm learning some cool things about the musico-psychological effects of rhythm with this piece.


I haven't posted a redhead in a while.

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Invention in A Minor v3.7

What I thought was going to be a two voice fugue in D minor just ten days ago has morphed into a two-part invention in A minor now. I'm kind of bummed on one hand, as the last thing the universe needs is another guitar piece in A minor. OTOH though, years ago I had the idea to write a series of two-part inventions for guitar, but my development wasn't far enough along, and my compositional technique was therefore not up to the task. Today it's a different story, so no telling where this will lead: I've come up with no less than ten timeless subjects over the years, and I realize now that any one of them would work in two voices on the guitar with imitation at the octave.

That's the difference between a fugue and an an invention, right there: Imitation is at the fifth - or more rarely the fourth - in a fugue, while inventions answer at the octave.

I'm still just using single line lineal links between statements - no episodic material as of yet - but I now have all three of the traditional stretto possibilities in it, as well as the two-part hyper-stretto as a conclusion. There are also not nearly as many possibilities as I initially thought, as the melodic inversions (or mirrors) of the stretti yield some minor ninths and major sevenths on strong beats. I'm not squeamish about those at all in five voices - in fact I seek them out in that context - but in less than four voices they can sound, well, icky. Two voices especially. Yes, I tried strict intervallic inversion, but that yields a Mixolydian minor-sixth mode, which sounded positively bizarre in this context.

With the contrapuntal possibilities cut by exactly 50%, the task of reaching a final configuration for the piece will be much easier, and the smaller implied dimensions of an invention over a fugue are actually more appropriate.

I can again provide AAC conversions, as I realized I hadn't updated iTunes on my old 1.67GHz G4 PowerBook, so you can open another window or tab to follow along.

Invention in A Minor

The work-around is pretty ponderous though: I have to export the Encore file from my PowerMac G5 to the shared HD plugged into my Airport Extreme, then download it to the G4 PowerBook, import it to the old version of iTunes there, create the AAC conversion, and then do the whole thing in reverse with the M4A file. PITA.

Honestly, I really do hate OS X 10.5.8. For me, OS X 10.4.11 is much better, so I'm thinking of wiping the HD on my G5 and downgrading the OS... lot of work though.

But I digress...



No linking measure needed in the expo anymore, and that makes the desirable odd three-measure length of the subject more apparent.

First modulation is to the subdominant, and you can see the two longer stretto possibilities there: 2.5 measures of delay at measure 10.5, and 1.5 measures of delay at measure 12. Since you have two entries at .5 distances, they mesh back up to be at the beginning of the measure for the third entrance.



Next modulation is to the relative major, and only the subject-above-countersubject orientation works properly here: The inversion produces an attacked major second - which was an augmented second= minor third in the minor - and I decided I didn't really like that either. After that statement I plan an episode over the dominant pedal on the low E string, and I have a very cool harmonized version of the subject in mind for that.

Then at 20 we're back to the tonic minor for the closest stretto of .5 measure of delay, and then the hyper-stretto between the subject and its rhythmically augmented form. The pedal episode harmonized version will also be an augmented form to set this up better.

I really like where this is going, and like i said, this could lead to another series of solo guitar pieces. I love composing series... I just hope they are not all in A minor and C. lol

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Tom Silverman: What's Wrong with the Music Business

Tom Sliverman of Tommy Boy Records - and old acquaintance of mine from my days in NYC - has a very interesting idea about how to change the adversarial relationship between labels and artists: Have record deals work in the form of LLC entities. There is also a lot of depressing stuff if you think the internet is a good way to develop music sales, but you should read the whole thing if you intend to make a career out of music.

The LLC idea isn't for those of us so far out of the commercial main stream though.

Oh well.

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Sketch: Two-Voice Fugue for Guitar

Believe it or not, in about twenty years of fugue writing, I've never composed one in just two voices. There is a good reason for this, as the subjects I have heretofore come up with have lent themselves to expositions, stretti, and other contrapuntal combinations of three voices or more. Well, this cool gem of a subject that came to me a few days ago lends itself to several combinations of only two voices, so naturally I think it might make a nice guitar fugue.

Here's the sketch pad page wherein I composed the subject and its stretto possibilities.



Taking the tenor voice as the prime, you can see that the alto makes a stretto at a half-note of delay with the tenor, and the soprano - written here at the same pitch level as the alto - makes a stretto with the tenor at a measure and a half of delay. Not written out is the additional possibility of a third stretto at two and a half measures of delay. So, a two-voice fugue could be written with this subject with the strategic plan of ever closer stretti.

Finally, between the tenor and bass there is a two-voice hyper-stretto in which the prime and its augmentation start simultaneously. This is seriously cool, and I went ahead and wrote out the most obvious contrapuntal solution for its conclusion, as you can see.

What's unusual about these stretto possibilities is that the following voice always comes in on the weak beat (The final time signature is going to be 2/2). This produces a surprising out-of-sync effect that is very nice.

As for the subject itself, the intervallic leaps in the head are very interesting due to the minor mode and all the DINOs - Dissonances In Name Only - involved: After the initial minor third you get a diminished fourth (Which equals a major third), and then a diminished seventh (Which equals a major sixth). Obviously, this sequence of DINOs is also reflected in the closest stretto above, which makes that combination work (And only in the minor mode).

Looking closer at that stretto between the tenor and alto voices, the head intervals are; a major sixth, a diminished eleventh, and an augmented second which becomes a major third on the final eighth note of the second measure. this is a very gnarly sounding intervallic succession. In the third measure of that stretto the combination yields a minor tenth which becomes a perfect eleventh, and then a major tenth on the final eighth of that beat, so there is a tiny suspension chain there (Which is how that dotted-quarter/eighth rhythm came to be when I composed the subject).

The written-out trill figure creates an alternating minor tenth/major ninth succession with a perfect eleventh above the final sixteenth. So the final quarter note then, moves into a diminished eleventh/diminished twelfth/diminished eleventh alternation. As you can see then, this would never work in the major mode because parallel perfect fourths would result.

Note here that this subject lends itself perfectly to melodic inversion, which would make the head sol, me, le, ti (And yes, I'm aware that the hyper-stretto could then be three voices if the inversion was added to the mix).

With all of these possibilities, the resulting fugue could be positively epic. It could also take a year or more of work before the final perfect form materializes.

*****

When faced with so many possibilities it is easy to become overwhelmed. The solution to this is to write out the simplest possible sketch first to see - and hear - how the most essential elements work together. This is also the best way to work out the countersubject possibilities.

The Create AAC option is still broken in the latest version of iTunes, so I'm going to have to resort to posting a General MIDI file. If you have the RealFont 2.1 GM soundfont set, you'll hear it with the Nylon Guitar 1 soundfont I use. Otherwise, you'll get whatever nylon string guitar sound you have set as your default.

Guitar Fugue Sketch



As you can see, I decided on D minor and a drop-D tuning for the piece, but I'm not at all positive that this will be the final key yet. At this point, Im just concerned with keeping the melodic peak as low as possible.

Also, I'm using a real answer versus a tonal answer, as I wanted to keep the uber-cool intervallic succession of the head intact: me is tonally answered by ti in minor, which didn't sound right to me at all. This necessitated a one measure link, which I went on to use subsequently to join all succeeding statements. Sure, I have some episodic material in mind, but in this first sketch, that isn't really needed as the primary goal was to start sorting out the key plan and working out the countersubject material.

I'm using straight quarter notes under the head here, but those could end up dotted quarters alternating with eighths in later versions. The countersubject/counter-answers are also just the most obvious solutions at this point.

For the statement beginning at measure nine I decided I wanted to hear how the relative major would sound. This results in a leapt-into major second above the dotted quarter in ten, but I actually love that result. I also had to change the final quarter note of the countersubject to sol from the potential mi to avoid parallel perfect elevenths, which sound particularly gauche to me in two voices.



This top stave statement in C major makes this like a counter-exposition in the relative, except that the thematic statements are a twelfth apart here instead of a fifth: I'm working my way up on the melodic peaks: The previous high was F, and here I'm up to A.

At seventeen we're back to the tonic key, and I'm using a descending chromatic tetrachord in the countersubject now. This is a cool thing to save for near the end. The final statement before the stretto also uses this device, and note that no linking measure is required with this arrangement.

Finally, the closest stretto is presented as the conclusion, but not the hyper-stretto, which will have to await a future version.

So, this is how you begin an epic fugue; by working out the combinations of the subject, and then composing a very basic initial version. In future iterations I'll add episodic material, the additional stretto possibilities, perhaps some of the melodic inversions, and the hyper-stretto as a conclusion.

Like I said, it could be epic.



Happy Independence Day!

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