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.

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.

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

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.

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!