Happy Holidays

I had hoped to get a post together on how I am creating virtual guitar parts with my notation program - notating on six staves, one for each string, so you can notate precisely what is happening on each string - but I have a new computer. The problem is, I can't remember how to log into my Lunar Pages account! lol.

Anyway, I have gotten back into Smugmug, so I'm half way there.

Hope Santa was good to you.

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Recording!

After two years of prep work - TWO YEARS! - the easiest pieces in my set are now absolutely perfect and ready to record. As I present the recordings, I'll explain how I practiced them into such a state of perfection.

First ones up will be my twelve figuration preludes, and then I'll move on to the axial studies, &c.

By the end of next year, I should have all of my repertoire recorded. All 70 pieces.

I'm recording a guitar synth track, a stereo guitar track, and finally a hexaphonic guitar track for each piece, though I may not use all three tracks for every one (It will depend on the piece, of course). And, there are a few that will have no synth track from the beginning - I'm thinking of the tap technique pieces and some of the more rubato stuff.

First piece should be the day after tomorrow, so stay tuned.

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Sonata Two: II - Scherzo in D-flat Major

Yes, you read that right, D-flat major. There's a reason for that: It's the only key in which the piece will fit on the guitars. Guitar I has a high B, and Guitar II has a low E during the course of the festivities. Uh huh, naturals, not flats... because there is only one modulation, and it's a tritone to G major. Cool, huh?

This jazz swing tune began as an assignment my second semester at Berklee: The assignment was to write a jazz piece with only one modulation (The first semester it was a non-modulating jazz tune, and I wrote a Bossa Nova for that). I was around a lot of horn players then, and they were always going on about Giant Steps, which I never cared for. To clarify, Coltrane's improvisations are fantastic, but the tune itself is kind of trite. So, I wanted to make only One Giant Leap and a prettier song. I think I succeeded.

I was also very much into the music of Larry Carlton back then, and I had learned two of his pieces: Room 335 and Mulberry Street. So, it is in that style, and it was originally for steel string guitar, and it had string bends in it as well.

Years later, two of my students wanted to play it as a duet for their jazz duo, so I did a second version with accompaniment and without the string bends. Finally, after writing the jazz counterpoint scherzo for Sonata One (Links in the sidebar), I decided to make it a, "classical" piece with the song - or menuetto - in two-part counterpoint, and the improvised section - or trio - with the accompaniment I wrote for the jazz duo. Of course, I also wrote out the pure swing as being in 12/8.

I have not written out the improvisation yet, so the trio is just the accompaniment, and I want you to hear that isolated so that I can make a few points.

Here is the MIDI to AAC version I did in iTunes: Scherzo in D-flat Major

This is a I, vi, ii, V tune, and it modulates at the end of the second cycle of that continuity. I'm using the duo as one big virtual guitar here, so it's what I would play solo if that were possible. The melody is just as I originally wrote it, sans string bends, and the bass line is a modified version of what was in the original accompaniment I wrote (Which we'll cover in a moment). I had to make some changes so as not to violate any contrapuntal laws, and I made the bass part more melodic and interesting in the process. Note how smooth and natural the tritone modulations are. They are not jarring in the least.

The form is A, A', B, A", and when that is trrough, the trio starts.

This accompaniment style is called, "guide tone comping," and it's what the old school guys like Herb Ellis and Joe Pass would do when the situation was right. You improvise the bass part using chromatic approaches to the roots, and in the upper part you have the guide tones, which are the third and seventh of the chord of the moment (Usually, but not always: Sometimes you might want the fifth if it is diminished, &c). Very cool and economical. I was never a great jazz improviser, but I got really good at this kind of accompaniment because it was fun to me.

The way I plan to compose the solo is to make it so that the melody and bass part make correct counterpoint with each other, and disregard the guide tones in those calculations. There are already a lot of parallel fifths among the guide tones - it's a major aspect of the jazz style, after all - but the bass line will be perfect to write counterpoint over. I think this hybridized approach will work well. When? I don't know. Things like this tend to sit percolating in the old bean until they finally manifest themselves.

The trio gets the full A, A', B, A" treatment, and then we are back to the top.

Since the finale is going to be the same fugue that is the finale of Sonata One arranged for two guitars - an arrangement I will be able to actually learn and record - Sonata Two will be done whenever the solo comes to me.

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Sonata Zero: III - Fugue in A Minor

Finally!

Eighteen years after coming up with this fugue subject, I've, at long last, arrived at the perfect two-voice arrangement. If you remember the Fugal Science posts, I started out with this subject in a two-part invention format - I just call them octave fugues, or subject-only fugues, since there is no answer (Or, the subject is the answer) - and went on to develop it through a two-voce fugue with the answer at the fifth above, and finally a three-voice fugue. Well, by taking it back to the beginning and using the octave fugue exposition and some of the material discovered and developed in the two and three-voice versions, I got it all to make absolutely perfect sense. This is what a composer strives for: Beautiful music that makes perfect sense.

The key, remember, was the two-voice fugal texture for solo guitar I invented with Imitation Study #1, and I've continued that here.

Here's the MIDI to AAC audio: Fugue in A Minor

The five-measure subject starts out in the bass, and is answered at the octave above in two-part invention fashion. This really is the best solution for two-voice fugues with these types of subjects, as the addition of an answer begs for a third statement with the subject: Tonal answers really belong in fugues of three or more voices.

Under the subject is a countersubject that is every bit as perfect as the subject. In fact, it could be a subject.

Starting at 11 is the episode, and I mean THE episode: It is used, in different forms, for all of the episodes. Here, it does not modulate.

At the top here are the first middle entries, and the subject makes a stretto with itself with one measure of overlap. This stretto would be trivial except for the fact that it is a perfect dovetail between the subject and countersubject, which is here modified with an ascending diminished scale lick in the second measure. I did this because it sounds cool and it makes the dovetail easier to perceive when that lick appears in the bass at 22.

From 23 on, everything is as it was in the original exposition, and that leads to a seeming repeat of the first episode. That repeat is cut short by a measure as the music modulates dramatically to the dominant region, however.

Note the seemingly minor rhythmic variation in the bass at 29-30: This makes the descent more adamant, and it syncs up with the sextuplet better. There is still a tasty - but hard to pull off - cross rhythm with the triplet, though. This is also a preparation for the third and final time you'll hear this episode on the tonic level before the recapitulation.

That spicy little cross-rhythm comes upon an augmented sixth, which makes the modulation to the dominant particularly dramatic. Then, the soaring variant of the countersubject ads to that, and at 33 a closer stretto with two measures of overlap appears (I composed this subject as a four-part canon, so it is really destined for a string quartet or a symphony).

The third episode must be different, so I present the subject over the bass line of the episode. This hilariously comes to a dramatic pause on a diminished twelfth in 42, at which point everything suddenly modulates to the relative region.

The subject sounds beautiful in the major mode, and here we get another closer stretto with three measures of overlap. The original episode formula then reappears, but this time coming out of the major, it has a very different effect. The B-flat introduced in the bass at 53 was hinting all this time at a modulation to the subdominant, but I didn't see it until I got way, way into the Fugal Science series of posts. Well, it ended up being THE THING that makes this piece not just good, but a real work of art: The first episode was six measures, the second was five, the third was the bridge, so this is the true third episode, and it's now whittled down to four. Concurrently, the ever close stretti have been shortening the middle entries as well, so the pace is ever quickening. This creates a subtle but awesome effect.

With the subdominant begins another dovetail section, but this one modulates back to the tonic by using the answer form of the head - relative to the subdominant - in 59. Since it's another dovetail, I bring the diminished scale lick back to bring it out again.

This is great, and the listener isn't positive the piece has modulated until the confirmation into 64, where the original episode formula appears in the tonic for the third time. This time, however, it isn't shortened, it is lengthened with the addition of a pedal section. here is where that subtle rhythmic variation in the bass gets its full say, and to great effect.

The recapitulation is the closest stretto, a canon at one measure of delay.

By splicing the final measure of the countersubject onto the subject, I was able to extend the canon slightly to 6.5 measures. When that concludes in a false and unsatisfying ending, the coda is then introduced. This is a two-part hyper-stretto wherein the subject and the subject in augmentation start simultaneously. Yes, it's epic.

So, if you set out to master fugue writing, plan on working for years and years to get to perfect arrangements of your materials. When you end up with something like this, it's all worth it.

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Sonata Two: I - Sonata in E Minor

After taking some needed time off from thinking about compositions, I quite suddenly have had a nearly complete sonata for two guitars appear in my head. As of now, it is a three movement sonata da chiesa - or Church Sonata (As opposed to the four movement sonata da camera - or Chamber Sonata) - with the movements being Sonata, Scherzo and Ricercare. Three movement sonatas are common in chamber music and especially concertos. The Ricercare here is exactly the same piece as the finale of Sonata One for Solo Guitar (Links in the right sidebar), but arranged for two (The solo guitar version is an epic virtuoso piece, but for two guitars it will be pretty easy). So, Sonata One for Solo Guitar and Sonata Two for Guitar Duo: I like the symmetry of that. A lot.

Today's post is about the first movement, which is a sonata with Mozartian and Beethovian overtones.

Here is the MIDI to AAC conversion I made in iTunes using the Realfont 2.1 guitar soundfont: Sonata Two: I - Sonata in E Minor

I usually create a separate tab to listen and read the score.

This sonata uses an unusual rhythmic augmentation curiosity: If you augment a theme - in this case, a fugato subject - that is in 6/8 time, it comes out in 3/4 time, with a constant eighth note. So, the modulation here is going to be both harmonic and metric.

As you can see, the fugato subject is a model of simplicity, but it has a very bouncy and infectious rhythmic aspect to it. Guitar I starts out with the subject and answer, and then Guitar II takes the subject in the lower octave, but the answer is on the same level as before: This was the only way to fit it on two guitars, and it worked out pluperfectly.

During the second statement of the answer, the texture transforms from polyphonic to homophonic, and the modulatory episode begins at measure nine. It is just a vii(d7) in the 4/2 inversion to V(m7) cycle, which has connotations of turmoil.

At measure thirteen, I start the metric modulation by putting the acCENT on the wrong syllABLE, so to speak, and it takes two full measures to get the effect to work out perfectly. Probably needless to say, this looks simple now, but it took a LOT of experimentation to get to it.

The second theme, which, as I mentioned, is the fugato subject in augmentation, starts at fifteen, and I varied the rhythm of the tail section a bit to make it more effective. The modulation, such as it is, is just a regular deceptive movement, but I accented the humorousness of the move by making the major triad on V move in parallel up a minor second to the bVI. Mozart used this fairly often, both up and down. They are usually called side slips, and parallel fifths and octaves are fine in this instance.

I would describe the effect here as slightly jarring and even humorous: Here you are, all dressed up for a serious minor key statement, and it all goes sideways - literally - to a happy sounding major statement in a different time signature. It is a sonata process piece, but it still has many elements of a scherzo.

While it took two full measures to introduce 3/4 from the native 6/8, to get back only requires a single measure - twenty-two - and really, only the second half of that, even.

Putting the second theme in C major versus E minor digs the piece into a hole, so to speak, so to get out of it, I used a series of parallel first inversion triads adorned with linear passages. Beethoven used this to good effect several times, most notably for the closing theme of the first movement of The Ninth Symphony. I needed six full measures, which seems like too much and overly dramatic, but the effect of over-the-top tension is quite beautiful and funny; a tough combination to pull off. Once it gets to the i(6/4) to V(m7) half-cadence, everything is back to, "normal" and the final flourish sets up the repeat.

I would note that the MIDI to AAC conversion does not bring out the fact that the two guitars are trading off, which is a pity, because this back and forth will be awesome in live stereo.

Simple and direct is good, and I guess I'd cite Haydn as a proponent for this kind of tightness in a sonata exposition. Many of his sonata process pieces were just a few minutes in duration.

To get the piece to the relative of G major, I used another octave lick at thirty-three, and then the development starts off with a fugato of the augmented version of the theme. Cool, huh?

Obviously, this is a broader and more stately fugal exposition.

Here too the texture transforms from contrapuntal to chordal, and I again used the major key version of the vii(d5) to V(m7) oscillation for the modulatory episode.

Here, though, I don't actually modulate - key or time - but simply change modes for the second theme, which is presented as a canon. It's an amazing effect, I think.

As the canon concludes in sixty-four, I introduce a written-out trill, which metrically modulates the piece to 9/8 for the new version of the closing theme. I was on a roll by this point, and that is when composing is fun.

The half cadence reverts us back to the major mode, and here there will be an interjection of some type - a bridge, episode or something - in 9/8 and G major. I'm thinking of a Gigue-like feel, but I haven't come up with anything yet. As a result, this is sort of a de minimus version, with the crowning section yet to come.

It works perfectly as-is, however, and if I didn't tell you I was planning a climactic 9/8 section, you wouldn't miss it. Here is the final four-part canon, which is three subjects and an answer of the second theme in 9/8. See how cool this is?

At eighty-three we get the half-cadence back in the home key, and after the concluding lick, everything is set up for the recap.

Everything is unchanged here from the original exposition.

And so it continues unchanged until the second theme appears - the fugato subject in augmentation, remember - now properly in the home key, but still metrically modulated to 3/4. It sounds positively triumphant.

Now that the piece is coming out of E minor instead of C major, the closing theme only needs the proper four reps to reach the half-cadence, and I was able to eschew the overly-dark natural and flat inflections.

The final topper is the linking lick from before the development, now to reaffirm the home key for The End.

I love this little ditty. It's a model of perfection, and the device of having the 6/8 theme transmogrify into 3/4 through augmentation is a tasty one. I've never seen this done before either, so it's at least rare, if not unique.

Next time I show you the Scherzo, which is a swing tune in two part counterpoint, like in Sonata One, but even cooler.

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Back to the Synclavier

I've decided to get another Synclavier. Even after all these years, nothing can touch the Synclavier's voice architecture of additive synthesis with frequency modulation. Fortunately, I know a guy who configures and sells refurbished Synclavier systems. Now I'll be able to record my traditional music as I've always wanted to: With a digital orchestra entirely of my own creation.

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The Hooktheory Article

Several people have brought this article, "I analyzed the chords of 1300 popular songs for patterns. This is what I found." to my attention.

While the methodology is well thought out, I don't think simple frequency statistics with regard to key and chord occurrence will tell anything particularly meaningful about composing popular songs with effective hooks.

Keeping in mind that this is only the first post in a promised series, there are several further avenues of inquiry that the author may intend. So, perhaps he will do more than simply scratch the surface.

With regard to proceeding, an additional level of frequency statistics could be applied to the present data by simply labeling the chords already ID'd with their Roman Numeral degree symbols: I, ii, iii, IV, V, vi, vii(d).

That metric would allow the research to proceed to identifying harmonic succession patterns, and their frequency, which would begin to hone in on what an effective pop song hook looks like in terms of harmonic structure. Here's where details begin to become important: The root motions have to be labelled first in order to get a handle on recognizing the harmonic succession patterns. I have no time to get into that in detail, but what I call Progressive (+4th), Regressive (-4th), Half-Progressive (-3rd), Half-Regressive (+3rd), Super-Progressive (+2nd), Super-Regressive (-2nd), and Tri-Tone motions have to be labelled and added to the database.

The next step would be identifying all of the groups of two types of root motion, then three types, &c. THEN, and only then, could the composer begin to draw some concrete conclusions about what kinds of root progression patterns create harmonic continuities that are catchy.

I'm not going to pursue that myself, as I'm simply not personally interested, but it could be a genuinely scholarly inquiry if it is followed as I suggest.

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Went to New Mexico to View the Eclipse

I'm actually ramping up my practice routine, believe it or not, but I thought the annular eclipse of May the 20th would be a great reason to take my f-car on an overnighter.

The best place in the US to view the eclipse was Roswell, New Mexico: The weather was to be perfect and the maximum coverage of the sun by the moon would happen near sunset, when the sun was low.

Well, it was spectacular.

The Ferrari looks underexposed because the sun was about 80% covered by the moon when I snapped the shot. It was a very eerie atmosphere. The folks in the background were at the rest area west of Roswell with a telescope to view the eclipse. The scope was only a 6" reflector, but the sun looked the size of a pie plate through the eyepiece. Sunspots were easily visible, as was the jagged edge of the moon.

I took this with my camera through the eyepiece. It is very slightly clipped on the left, but pretty amazing nonetheless. This was about 10 minutes before the, "ring of fire" effect, which was goosebump inducing.

All in all, a great trip and the Ferrari is amazing for touring like that.

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Decompressing Nicely

Still have my practice routine going, but I'm otherwise taking some time off from music, and especially composing.

Drove the Ferrari out to the Texas Hill Country a couple of weeks ago, and the wildflowers were amazing.

Spent a week detailing the car for a show - detailing is a zen-like therapeutic endeavor for me - and a friend got a good pic he sent me.

There were some truly amazing cars there, like this Ford GT.

Not sure when I'll get back to music blogging, but I must say my mood is improving every time I take this car out... so it might be a while.

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I Needed a Hobby

While I was looking after my mother for the past three-plus years, I had a Ferrari as my wallpaper on my Mac's desktop. So, I bought one.



It's not a new Ferrari, it's a 2001 456M GT, but it is wicked fast and super-fun to drive. It's not my first Italian car though.



That's me as a sophomore in college, but I got the Fiat X-1/9 when I was in high school. It was super-fun to drive too, but not wicked fast.

Weekends driving in the Texas Hill Country and going to Exotic Auto Shows will be my R&R from music now.

Zoom!

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Mary Barbara Pepper: 01/01/1929 - 02/15/2012

My mother died this morning after a very long illness. She was an awesome woman, and I loved her deeply. Born Mary Barbara Daugherty on New Year's Day in 1929, she grew up during the Great Depression on a farm in northern Indiana. She was ahead of her time in many respects, and wanted to go to college from a very early age. So, she applied herself, worked hard, and was accepted to George Washington University in Washington, D.C. in 1947. It was there that she met my father, Hobart Garrett Pepper Jr., who was a World War II veteran and a pilot in the Army Air Corps. They were married after graduation in 1950.

Dad was recalled to the service because of the Korean Conflict, and mustered into the newly-formed United States Air Force as a first lieutenant. After their first duty station in Waco, Texas, they were transferred to Pepperell AFB in Gander, Newfoundland, Canada in 1956. I was born December fifteenth of 1957 in St. Johns, and since mom had found out she couldn't have children, they adopted me in 1958. I only ever needed one miracle in life, and I got it at the very beginning: Being adopted by Hobart and Mary.

Dad didn't want me to ever know I was adopted, so I grew up completely convinced that I was their natural born son (Dad and I had the same steel-blue eyes, so I even looked the part). It wasn't until mom started suffering from dementia back in 2010 that I found out: I was 52 years old by then. What an awesome gift they gave me.

Mom was a traditional housewife and mother - since dad was off flying so much, there was no way she could work - and our home life was much like the, "idealized" fifties and sixties households you see in old TV shows like Leave it to Beaver and My Three Sons. The main difference was we were stationed in a series of wonderful places as I grew up: Denver, Colorado; Fort Walton Beach, Florida; the Panama Canal Zone; Tacoma, Washington; and Tokyo, Japan: I had a magical childhood.

When dad retired in 1972, we moved to San Antonio, where mom ended up spending the rest of her life. Now freed up, mom became a very successful real estate agent, and also a breeder of champion lhasa apso show dogs. In fact, her dog Lulu won Best in Breed at Westminster the day before she died. Anything mom put her mind to, she got good at: She was a golfer, and hit three holes-in-one in her career, two of them on the same hole of the country club that is in the neighborhood I now live in.

I will miss her, and I will love her forever.

Here are some of my favorite photos of her.



At the top is mom and dad shortly after they were married. Lower left is mom's high school graduation photo, and lower right is mom as a little girl. She was such a happy little girl that everyone called her Mary Sunshine.

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And, the Hits Just Keep On Coming /sarc

Yes, I have gotten sidetracked from the Freestyle Convertible Counterpoint series, but composition is little else than side tracks; some of which lead to completed compositions, but most of which don't. So, when I get into a groove of completing pieces I've thought on for a long time, I go with it until I reach some sort of conclusion.

Today we have yet another Imitation Study - as J.M. pointed out in comments, I should write real studies instead of just imitation studies (lol) - which are what Bach called two-part inventions, and this is the fourth in the series. This is also one of my all-time favorite fugue subjects, as it is a twelve-tone row, albeit one that is easily interpretable as tonal. I came up with this for a graduate level Twentieth Century Counterpoint class when I was a doctoral candidate at UNT, and it became the final project for that class, which was a wind trio. You can see and hear that piece here.

To get this subject onto the guitar in two-part form has been a serious challenge and an amazing learning experience. I first tried it out as a fugue with an answer at the fifth/twelfth, but that lead me to noting but frustration. Then, I did complete a previous octave-answer version back in 2010, but it ended up in B minor, and the material was all drawn from the wind trio, so it really wasn't a very good guitar piece.

There turned out to be three missing elements: I needed a constant quarter-note countersubject to fit into my spartan, objectivist guitar fugue style, I needed an interlude, and I really needed the piece to be in A minor instead of B minor. You'll see why as we go through the piece.

Once I got the interlude, the new countersubject happened almost immediately, and in a single session, the piece was 90% done, with just a few minor tweaks here and there left to do. After struggling with this for years, it was so easy to write that it was almost anticlimactic.

Here is the AAC audio file then: Imitation Study Number 4



This also happens to be only the second fugue subject I've written in 3/4 time, but since you need twelve attacks to get the twelve pitch classes presented, it was a natural thing. The opening interval is also a tritone, which you would never find in a traditional subject.

The breakthrough constant-quarter countersubject is in the bass of the second system, and it outlines the harmonies that the subject implies: i, V/V, V, V/IV, IV, iv, i(6/4), iv, IV, v, V. The second note of measures one and two imply the root, and the final notes imply the seventh, so I got the chromatic notes into the head with secondary dominants. The final measure - the tail - is a chromaticized IV, V, and I was able to get a diminished triad under that in the countersubject.

It should be obvious that a subject that is serial - super serial! - would require chromatic episodes too, and so that's what I created there at the bottom: Both augmented sixths and diminished tenths are in there, but it doesn't modulate.



The first middle entry has a different countersubject over the subject, and it allows the subject to enter under a tied fourth (A re-attacked fourth in this case), which is the traditional slick way to do it. Since I didn't compose this subject as a canon, as I did with the previous three, I don't have a bunch of stretti to work through, so varied accompaniment is the ticket.

The second episode starting in sixteen is a modulating version of the first one, and that takes us to the dominant for another statement with the original countersubject. The third episode needs to be different, of course, and it returns us to the tonic for the next statement.



For the third middle entry, there is a fully developed version of the second countersubject in constant eighth notes over the subject, and then the interlude appears. It is so much easier for me to come up with these homophonic interludes that I usually avoid them until I can use all contrapuntal material for the sections between thematic statements, but this piece really, really called out for a relaxing chordal section. In later versions of these studies - versions that are actual fugues with answers at the fifth/twelfth - I'll introduce some homophonic sections into the previous three as well.

At thirty-six we finally get the contrapuntally inverted version of the original combination, and that leads back to the exact same episode that modulated us to the dominant previously. Obviously, this subject does not yield a major key version, so the relative is out of the question.



One stretto does work, and it's a doozy: One measure of delay/three measures of overlap, and at the twelfth above or eleventh below. Because the subject is completely chromatic, this sounds fantastical in the sense that it is perfectly clear counterpoint, but very, very outside of the diatonic system: Two tone-rows a fifth apart in stretto. Pretty bad ass, IMO, and it sounds awesome.

The lower subject does something else verboten in fugues, and that is it tonicizes the, "dominant of the dominant" that fugue books warn you against. In this case, that's a B minor statement in an A minor fugue. It works fabulously well though, and for a tone-row subject with the opening interval of a tritone, why not?

In the lead voice we also get two consecutive statements of the subject (!) on the dominant, which ameliorates the distant region just touched upon, and it also sets up the return to the tonic. Note how a sequence of the tail makes a nice new countersubject, and hints strongly that, "the end is near."

In forty-nine is the figure I had to transpose up an octave to keep the piece in A minor. There is no doubt but that it sounds better connected to the previous sequences - of which it is an inversion (!) - but the piece won't work in B minor now because of the homophonic interlude. That simple move was actually the toughest nut to crack for this piece to fit on the guitar properly.

At fifty-one is the final episode - filled to the brim with augmented sixths - and then the final statement, which has yet more new material as a countersubject.

I have at least four more subjects I could turn into studies like this, so we'll see where things go from here.

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The Fifth Element

No, not Leeloo, but an interlude.

I enjoy it when a piece takes on a life of its own. It's genuine fun when that happens. Again, just after the previous post - in which the four elements were subject, countersubject, episode, and coda - I came up with the fifth element I was searching for, which ended up taking the form of a six measure interlude.

Fugal terminology can be fuzzy with respect to definitions, and at no place is this more evident than when trying to describe the material that comes between thematic statements. Here, I find it useful to have two broad - and yes, overlapping - categories: Episodes and Interludes. A typical episode will be short - one to four measures, usually - while an interlude can be quite long, so duration has a lot to do with the definition. Also, typical episodes will be based on tight, sequential material that is extracted from, or that is closely related to, the subject and/or countersubject, while an interlude can be composed of highly contrasting or even completely unrelated material. Obviously, there is usually a deft transition into these sections that makes them work, and they virtually always appear when they have to. One of the nice things about these little thumbnail fugues - I may end up calling them that - in the two-part invention format is that they provide clear examples for these definitions.

Here is the new AAC file: Imitation Study Number 3



Only a format change here: There are now four systems on this page. The elements remain the same: Subject on the top system, subject and countersubject on the second, a four measure episode on the third, and then the contrapuntal inversion of the subject and countersubject at the bottom.

Note how the episode springs organically out of the augmented version of the subject's head, and it is based on a sequential statement of a rising chromatic line. Since there are two complete descending chromatic tetrachords in the subject, this is an effective contrast. Also, the eighth-triplets are obviously from the tail of the subject. Very tight.



The contrapuntally inverted second episode statement on the top system is also unchanged. Now, at this point - the end of measure twenty-three - we have heard ALL of the elements so far presented in both of their orientations, or inversions, and so it is time for a new feature to appear.

As is so often the case, the most obvious solution worked out the best: Since the sequential episode is based on a partial chromatic tetrachord that rises, I made the interlude over a full descending chromatic tetrachord. You can see where the distinction between an episode and an interlude can be unclear: Both the episode and interlude are based on chromatic bass lines, and they are both sequential - and in this case the sequences even share the same rhythm - with the main distinction being one of greater length for the interlude.

I would call the listener's attention to another factor, though, and that is one of attitude: The episode sounds like a brief respite from the thematic material, and it seems anxious to get back to that material, while the interlude seems to be taking its sweet time with no particular urgency for a new thematic statement until the very end.

As for the structure of the interlude itself, I was able to get a lot of nice counterpoint into it. If we isolate the eighth-triplets and just look at them, the end of twenty-four into twenty-five reads, major sixth, minor seventh, octave, minor tenth - very conservative and conventional. The end of twenty-five into twenty-six reads, diminished fifth, minor sixth, diminished seventh, major sixth (plus octaves), which is much more interesting. Then, twenty-six into twenty-seven is, octave, major ninth, major tenth, minor tenth, which is conservative again. Twenty-seven into twenty-eight cements the alternating pattern with a major ninth, major tenth, perfect eleventh into another major tenth, which is quite delicious, and then I've set things up for the climactic penultimate measure. There, from twenty-eight into twenty nine, the counterpoint reads augmented fourth, augmented fifth, and augmented sixth - plus octaves - into the double octave on the dominant degree. This is just a killer little climax, and in a later version of this fugue I'll use this interlude to modulate to the dominant with this device. Oh, and sorry I had to cram all six measures onto one system, but it's a formatting issue: Didn't want to get into a fourth page for this post.

From thirty on then, things are unchanged from the previous version: This is the perfectly dovetailing stretto section with two measures of overlap (The only perfect dovetails I've been able to get to work out perviously had just a single measure of overlap).



The top system here is the sequential episode back in its original orientation, then the canonic stretto recapitulation followed by the concluding coda, which is the augmented subject head with modified tail over an ostinato, which is the full tail of the subject.

This piece is now complete in the octave fugue/two-part invention format. Next I'll turn this into a two-voice fugue with the answer at the fifth/twelfth, which will require at least a modulating version of the interlude, and probably a pedal section as well. I'll have to use a real answer with this subject because of all of the stepwise motion in the head and the chromaticism, but I have discovered a very humorous major key version of it, so that could end up in there too. Time will tell the tale.



I do think I'll snag that DVD next time I'm at Amazon. It's an old favorite I just never got around to picking up.

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And Then There Were Three

When I wrote Imitation Study Number 1 back in 2010, it was the realization of my very first goal when I began learning counterpoint: I naively though writing in the two-part invention format would be a good place to start back in the late 80's, but it wasn't. First of all, I needed to develop basic counterpoint technique back then, secondly, I needed to learn fugue, and finally, I had to figure out a way to put it all on the guitar.

Now, I think I have completely changed my fugue writing technique to start with an octave fugue for the guitar first, and then develop further versions. This one now makes three that have reached states of balance, and I'm currently working on number four. In fact, I'm going back through all of the fugue subjects that I've ever composed, and realizing two-part invention format pieces for the guitar with them. If I can get most of them to work out - some really need answers at the fifth or fourth - that will be a nice collection of some ten odd pieces.

Aside from the fact that this two-part style is too ascetic for most musical tastes, there is also the fact that almost all of these pieces will end up in A minor or A major due to the idiomatic requirements of the guitar, nevertheless, I really like how these are turning out, and hey, that's really all that matters.

So, mere hours after the previous post, I tried the most obvious solution to presenting the second stretto I wanted to display - I just inserted the twelve measures of it - and it worked.

Here's the new ACC audio file: Imitation Study Number 3



No changes here except for formatting: There are now only three systems on this page, which are the exposition and first sequential episode.



The contrapuntal inversion of the subject, countersubject, and sequential episode - which is on the top two systems - is also unchanged. It's at 24 that the incised material begins, and this is a stretto at three measures of delay/two measures of overlap. Not only that, but this is also a perfect dovetail: The countersubject is unmodified until the point of interruption in the lead, and then it continues without modification in the bass at twenty-nine.

The way this works at twenty-six into twenty-seven is interesting: The final interval of twenty-six is B over C-sharp - a minor seventh - and this proceeds in parallel motion into a major sixth at the start of twenty-seven - A over C. Noticing these unequal-parallel opportunities is one of the things one learns in pursuit of contrapuntal understanding.

The end of the overlap in twenty-nine puts the music back to measure eight of the exposition...



... complete with the original version of the sequential episode. So, the sequential episode is stated in its original form, then contrapuntally inverted, and then back in the original: Nicely balanced, and it keeps with the extreme economy of expression I strive for in these initial fugal constructs.

From thirty-six on then, the piece is as before.

As I mentioned previously, this subject makes a five-voice canon with itself, but for this guitar version I had to avoid the version with three measures of overlap. The reason is because that version puts the dotted-quarter/eight figures of the third measure against the quarter/eighth-triplets of measure five: Those cross-rhythms are trivial for individual string players to execute, but nightmarish for a solo guitarist.

So, forty-eight measures and no modulations. The elements are subject, countersubject, sequential episode and coda. To make this a fugue with a real answer at the twelfth, I'll need to add an element, which will be a modulating interlude. No joy there yet, but I have other projects demanding attention now.

Before anything else, however, midnight marks Groundhog Day, and every year I watch the old Bill Murray comedy of the same name. It really is a comedic masterpiece, and the beer is chilled.

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Surprise Developments

There are many cool and fun things about the adventure of being a composer, but one of my favorite things is how stubborn thematic material can break at any time, usually out of the blue and for no apparent reason.

Back in about 2003 I came up with an epic five-measure fugue subject that I composed as a five-part canon (This as a logical development of the five-measure subject that works as a four-part canon that the Fugal Science and Freestyle Convertible Counterpoint series are based on). For months, and then years, I tried to write a five-voice fugue out of it, but I could never get it off the ground. Couldn't even get the exposition done.

What did happen, though, is that I discovered a dovetail with an augmented form of the subject that made a five-part perpetual canon happen. You can see and hear that piece, which I realized for string choir, here.

Well, since I came up with the austere two-part style that makes stately subjects work for solo guitar, I decided to see if I could make a two-voice fugue at the octave out of that subject (Two-part invention format). "Viola."

It isn't finished yet - there is one more canonic stretto at two measures of overlap I want to present - but I got the exposition, the conclusion, and a, "magic" sequential episode together, and it makes a very concise piece just like that. That is the criteria I always use, by the way: Is it magical? If you want to be more objectivist about it: Does it seem like more than just the sum of its constituent parts?

So, as a respite from the Freestyle Convertible Counterpoint series, here's this cool little ditty.

MPEG 4 Audio: Imitation Study Number 3



The subject is, as stated, five measures long, and it manages to present eleven of the twelve pitch classes. It works as a five-part canon, but we're only dealing with two here, obviously. The Perpetual Canon uses a dovetail with the augmented head of the subject, and that's what ended up being the breakthrough here: In the lead for voice one in measures six and seven is the head of the subject; do, re, me, fa, sol, ti, le. Then, in the bass starting in measure eight, is the augmented form of the head.

This dovetails marvelously with the rising chromatic sequential episode that begins in eleven. Tres cool, non?

Fifteen through nineteen are just the contrapuntal inversion of the subject and countersubject...



... and then twenty through twenty-three constitute the inversion of the episode. Note how the straight quarter note line is an inverted palindrome from the downbeat of twenty-one to the last quarter of twenty-three: It reads upside-down from back-to-front compared with front-to-back. It is simple, but very elegant. Kind of like some of the simple musical structures that Mozart used so often.

Twenty-four, then, is the concluding stretto. As I said, I have at least one more element to come up with before I can present the intermediate stretto, but this merge works almost too well: I haven't been able to come up with any other continuation after twenty-three yet.

After the recapitulation stretto is the concluding ostinato, which I also used in the five-part canon for string choir, but here it accompanies the complete augmented head/modified tail version of the subject. Also a, "magical" element, IMO: Twice it's interrupted by the sequential episode, and then the third time it is presented in its entirety.

Allright then, back to the Freestyle Convertible Counterpoint project.

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Freestyle Convertible Counterpoint, Part 2

In the first post in this series, I demonstrated a method for finding all possible vertical-only and horizontal-only shifts at the thesis points for a five-measure fugue subject and its tonal answer, and in all four quadrant orientations (Original, inverted, retrograde, and inverted retrograde). As I intimated then, this is much more practical than Taneiev's theoretical treatise, it has the advantage of not relying on mathematical formulas, and it also has applicability beyond the strict style. Additionally, the method takes advantage of the copy-and-paste and playback abilities of Encore, so it's far more useful for the composer. I can't stress too much that this method goes beyond fugal composition to any type of contrapuntal writing: Sonata themes can be subjected to the same treatment.

Today, we will continue the process for combination shifts. This will use the same method as for the horizontal-only shifts, only now at all of the intervals other than unison/octave. Just as I went through the most distant canons to the closest canons previously, I'll do the same thing now working logically through the vertical shifts in order:

V= +2/(-7), H= +4/-1, +3/-2, +2/-3, +1/-4
V= +3/(-6), H= +4/-1, +3/-2, +2/-3, +1/-4
V= +4/(-5), H= +4/-1, +3/-2, +2/-3, +1/-4
V= +5/(-4), H= +4/-1, +3/-2, +2/-3, +1/-4
V= +6/(-3), H= +4/-1, +3/-2, +2/-3, +1/-4
V= +7/(-2), H= +4/-1, +3/-2, +2/-3, +1/-4

The top line would read, then, Vertical shift of a second up, or a seventh down, with Horizontal shifts of plus four/minus one measure, plus three/minus two measures, plus two/minus three measures, and plus one/minus four measures: Simple process of elimination. Repeat this with thirds, fourths, fifths, sixths, and sevenths, and you're done.

Here's how it worked out with my, "super subject." I chose this subject to develop this process with, by the way, because it is a best-case scenario with respect to all of the combinations it makes (Or, it's a worst-case scenario with respect to the amount of labor involved! lol).



None of the plus second/minus seventh combinations worked in the first subject-subject step, so we start with plus third/minus sixth, and one measure of overlap.



Note first that here in minor, the +3/(-6) shift is to the relative major.



Note secondly that, since the subject makes a four-voice canon at the octave, that these +3/(-6) shifts could be used to double the subject in thirds or tenths above, or sixths or thirteenths below. This will be a nice orchestration possibility when I get to a fugue of that magnitude.



The closest +3/(-6) shift did not work, so we're on to the +4/(-5) shifts.



And that was the only one of those that panned out, so here we are at +5/(-4) shifts.



Note that +5/(-4) shifts are at the answer's level, and we already know that two of them work, so this is really no biggie.



This +6/(-3) shift is to the relative minor from the major mode perspective, so that's kind of interesting.



You'd have to double the leading tone to get this one to work out, but with three or more voices and an irregular resolution, it is possible. In fact, one of the things that makes freestyle counterpoint generate so many more viable possibilities than the strict style, is that you can make a lot of combinations work out with creative use of harmony.



Here we are at +7/(-2) then.



This offers some interesting modal and modulation possibilities, and that finishes up the subject-subject combination shifts.



Since there are really only two intervals different between the subject and answer, this will seem somewhat like a rehash. Again, none of the +2/(-7) shifts work.



These do have a different flavor and function though.



And again, all but the closest possible arsis point works. Oh, by the way: Pay no attention to the page numbers. I had to break the Encore files up into smaller chunks after the fact to get them to convert to PDF reliably. Not sure what that bug is, but beyond about thirty pages the conversions are not sized properly.



The +5/(-4) shifts put the answer form on the tonic level, which is unusual, but only this one measure overlap works.



And on to the +5/(-4) shifts.



And these are quite interesting. A composer would likely never stumble upon all of these through casual experimentation, which is the point of this exercise.



And the +6/(-3) shifts.



From the minor, this combination provides a modulation from the dominant directly to the relative major. Very hip.



Now the +7/(-2) shifts.



The way this has worked out, I'll write modulating thematic phrases with the combination shifts that overlap for two measures. These are to be highly prized because it's much easier to write a modulating episode or interlude than it is to modulate with strictly thematic material.



And now for the subject-answer combinations. Here - and in the upcoming answer-subject combinations - you have to keep in mind that the subject and answer are already shifted in relation to one another, so here the answer is a step higher than it already was, answering on the sixth instead of the fifth.



More unusual modulation possibilities.



Here's the first instance where one measure of overlap doesn't work, but two does. Some remote modulation possibilities here.



These combinations are actually like the original canon, but with the answer form following on the tonic level. No big deal, IOW.







Yadda, yadda, yadda/blah, blah, blah. lol.



A perpetually modulating canon could be made with this type of arrangement: Up a step every iteration.



These are so close to the +3/(-6) subject-subject combinations that the difference is trivial.



Still nice modulation possibilities though, and that ends the subject-answer possibilities.



And the last thing to cover in Part 2 are the answer-subject combinations.



Still, some nice subtle variations on the modulation possibilities.



But plenty of trivialities too.



Obviously, very similar to the same subject-subject and subject-answer combinations. I'll group them and compare them later.



With most subjects and answers - those not composed from the outset as canons, like this one was - the composer is looking for whatever works. With the embarrassment of riches here, I need to figure out what to discard.



I'll trash the single measure overlaps, use the two measure overlaps for modulations, and the three measure overlaps - there are only a couple so far - I'll put in places of special prominence.



This rocking combo enters on a v(m7) sonority in the minor and a V(m7) chord in major. Won't find those in Palestrina. lol.



Obviously, I could have skipped all of these trivial one measure overlaps if I weren't doing this as a demonstration, and just hunted down the best stuff.



This is a cool combination. After the answer on the dominant level, you get the subject on the dominant level, which confirms the modulation. Precede this with a subject statement in the tonic, and you'll have some nice modulating stretto possibilities.



Because I originally wrote this as a canon, this one works too.



This is the only non-original subject-subject combination that works with four measures of overlap, but it's not really a big deal because only the head figures differ between the subject and answer. Still, I'm glad I made myself think of this angle.





Another modulation candidate.



And one last unusual combination with three measures of overlap.

I'm keeping the systems large and not worrying about the clashes because it's easier to enter the notes on the largest size staves. When I get to the audition and construction phase, I'll reduce their size and clean them up.

*****

So then, here are all of the combination shifts at the thesis points to add to the vertical-only and horizontal-only results. Next step is to do the horizontal-only and combination shifts for the arsis points. Off-beat entrances can be very sublime, so I'm hoping a few nice ones turn up, but I'm also hoping for less than forty-four pages of results! lol.

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