Imitation Study Number 4 in A Minor

This is an interesting piece. It's a fugue with the answer on the subdominant and in inversion, and the initial statement of the subject has an accompaniment line. This was necessary because the subject begins on the third degree of the mode, which may very well be unique. I've never encountered another subject like this, anyway.

Interestingly - to me - this is actually the very first fugue subject I ever came up with back in 1986 or 1987. I got the idea while studying through Joseph Schillinger's System of Musical Composition. Historically, fugue subjects have begun on the tonic or dominant degrees - or with approach notes to those degrees - and I wondered why not the mediant, since it is a degree of the tonic triad? So, I came up with this wedge shaped theme with the idea of writing a two-part invention for guitar with it. That idea fizzled because I just had no idea how to proceed.

Later, when I was working on my masters degree, I wrote a three-part invention for string trio with the subject, which I really, really like. In that piece, I came up with the chromatic countersubjects and the solution of having the answer on the subdominant degree and in melodic inversion.

So, here we are 23 years later and I've come full circle back to the idea of writing a two-voice solo guitar piece on the subject; only now I have the compositional technique to make it work.

Here's today's MIDI to M4A conversion:

Imitation Study Number 4 in A Minor



Despite the subject's unusual feature of starting on the mediant degree of the minor mode and having a diverging pair of melodic trajectories, it's actually fairly Bachian (Since Bach was my inspiration here). However, you'll notice the G-sharp a the beginning of measure two is followed by a G-natural one beat later: This is strange, and it sets up a tension that I really like a lot. Furthermore, on the last eighth note of measure two, there is a diminished octave - equalling a major seventh in sound - between the C-sharp in the bass and the C-natural in the subject, and the final sixteenth is a diminished seventh (Which equals a major sixth in sound, of course). These bold cross-relations give the piece the dark feel of a lament: Something is just not right with the universe, and so there is quite a bit of expressive sadness to the piece.

This is only reenforced by the true counter-answer in measure three, which is an ascending chromatic line at the beginning, and a descending chromatic line at the end. Pathos. On the last eighth of measure four, we have a diminished fourth (plus an octave) and then a diminished tenth (Which is the inversion of an augmented sixth). This is another highly unusual feature of the exposition.

As I mentioned in the previous post, many times two voice fugues work out better with a thrid statement of the thematic unit, so that two subjects appear and you can reveal the true countersubject: That's the case here. Just as the answer is inverted from the subject, the counter-answer is inverted for the countersubject. IMO, this is very, very cool.



Most of the time I use tail figures for the episodes in my fugues, but in this case the head works better. Since there are losts of wide leaps, this also allows for range adjustments that keep the elements within an executable range on the guitar. I made that adjustment in measure eight, which set up the upcoming middle entries, which are in the relative major.

The major mode version of the subject and answer worked out better starting off on the tonic degree of the triad, and the countersubject and counter-answer therefore ended up diatonic instead of chromatic. this provides a happy sounding contrast to the dark sounding exposition.

The second episode that starts at fourteen required another range adjustment in fifteen, whereas the string trio version allowed the violin to continue into the stratosphere.



The second middle entries are all about displaying the contrapuntal inversions of the previously revealed material. the original orientation of answer and counter-answer are first stated, only in the dominant level minor of E, and then the countersubject over subject appears starting in nineteen.

Episode three at twenty-one takes the piece to the subdominant minor region, where I present the answer over counter-answer orientation. At the end of this, we get an augmented sixth, of course. Both of these inverted orientations sound very dark. Darker than one might expect just judging from an intervallic analysis. I've never really been able to figure out why this is - even the consonances sound dissonant - but I really like the effect (Even if it was a happy - or sad, I guess - accident).



The final page gets us to the concluding stretto section - also the first stretto I ever composed - and there is no episode needed to get here because the subject to the previous answer is back in A minor. Is that cool, or what?

The first 1.5 beat overlap appears in measure twenty-seven, and then the 2.5 beat dovetail starts in twenty-eight. To get everything back in sync vis-a-vis the bar line, I relax that back to 1.5 beats in the first half of thirty, and then just the head appears in the second half, which sets up the conclusion.


Obviously, it's bedtime.

Read More

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.

Read More

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.

Read More