Progress Report

Here are some of the preliminary formatting decisions I've made for the music we'll be analyzing:

1] I am putting in every single note that Liszt transcribed from Beethoven's score of the Ninth.

The idea here is that I obviously don't want to second guess one who forgot more about this symphony than I'll ever know. Liszt has some alternative ossia passages notated that I am going to omit, however. I'll just comment on them with a gloss as we get to them.

2] Stem lengths and beam groupings I'm being flexible with.

Since I'm going to be taking screen captures of the music I'm entering into Encore, I have made all of the beams level to avoid zig-zag lines: Encore is not 100% WYSIWYG, unfortunately. There is also the fact that I want to keep enough space between staves to comfortably add the analysis, yet wind up with few enough total pages so that the posts won't contain too many of them.

3] I am not going to be using engraver's spacing.

I have decided to keep the number of measures per system at four, unless the phrasing varies from that number, and also keep the size of the actual measures equal within each system. This makes the phrasing more readily apparent, and also gives a better visual representation of the temporal duration of each phrase and the piece as a whole.

4] No piano fingerings or other idiomatic piano indicators will be used.

That includes pedal indications as well as fingerings. I want to keep this score as clean as possible, and considering the mind-numbing nature of entering just the music, I want to save myself a little bit of effort as well. The placement of those indicators would also often be competing for space with the analysis.

5] No dynamics or tempo change indicators will be used.

Again, cleanliness is a goal here, and I'm assuming anyone interested in following this project along will be familiar enough with the music to be generally aware of the phrasing and dynamics. Of course, I will comment on a lot of this stuff as we progress along. Again, dynamic and tempo indications are often placed where I want to have the analysis.

6] No 8va/8vb indicators will be used.

Wanting to actually visualize the piece, I decided against using these. I will, however, use most of Liszt's clef changes in the left hand part.

There are some other minor things, like the presence of rests in secondary voices within a texture, which you will notice if you have Liszt's piano score handy, but since this is an analysis of the music, and not a performance score, I have decided to concentrate on getting the actual notes right while making room for the analysis. The end result of these decisions is that the music looks... well, clinical is the only word that comes quickly to mind. Peculiar would be another befitting term, I guess. In any case, I'm pleased with how it's coming along and actually like the way it looks.

I may be one of the last people to learn actual music calligraphy from Bill Brinckley when I was an undergraduate at Berklee, as the Synclavier's Music Printing Option was being developed at about that time, and I aquired a Synclavier in 1984. By the time I got to graduate school in the late 80's, Finale had appeared (Though I refused to use it because it was even MORE user-hostile and anti-intuitive than the Synclavier was (And it still is, amazingly enough)), and by the time I was a doctoral candidate, Encore - the first intuitively usable music printing program - had appeared and I made the switch to that. By the time the Mac OS X-native version of Encore came out, it was slick enough that I rarely picked up a sketch pad anymore. While Finale seems to still be mired in decisions the early programmers made when they wrote it (Like having to define repeats and having those idiotic Layers: Why not have the music play back by default as if someone was actually reading and playing it?), I have heard that Sibelius is quite good and has a great artist interface. Unfortunately, having ported my completed compositions across three platforms and two programs, I simply don't have the stomach to take another few months off to re-enter everything (Guitar music has a gazillion idiomatic performance indicators which are lost in MIDI exports/imports). This is just a long winded appology for being stuck with Encore, which has it's shortcomings, but I am so familiar with it that it's just an extension of my creative process anymore. "Well, there you have it. There it is." as the King in Amadeus said.

I have still not gotten a shipping confirmation from Apple on the Mini yet, which is starting to chap my butt a tad as I'm anxious to get this project off the launching pad, but the keyboard, mouse, ADC/DVI converter and, of course, my magnificent monitor are all in place now. I'll just keep entering the music as well as posting various inanities until that day arrives.

Rambling Ruminations

This is the most interesting analysis project I've ever taken on. Just the preperatory work is staggering in it's magnitude. Since I haven't listened to the Ninth for about three years - intentionally - and I only ever listened to the Liszt transcription of it a couple of times before last week, I'm listening to it with fresh ears. As fresh as can be expected, anyway, since I'm sure that even with the extended layoff, I've still listened to the Ninth more than any other single piece of music.

My history with this symphony goes back, literally, to the very first memory that I have. Back in the very early sixties, the Huntley/Brinckley Report news program used the Scherzo of the Ninth as it's opening theme music. My father was a news junkie, and so it was on in our home every night. I never stayed around to listen to the news, but I vividly recall standing spellbound in the den listening to the opening music. I mean, like it happened five minutes ago. I was just barely walking at the time. The opening timpanic assaults followed by the fugatto simply captivated me. I wish I knew for sure which recording that the network used for the Huntley/Brinckley Report (I can't even remember if it was NBC, ABC, or CBS), because I would sure like to know and aquire it. I'm betting it was Toscanini's version, but I'm just not sure.

Years later, in 1983, I took a job as a roadie for a rock band that was doing a European tour just as I graduated from Berklee. Since I was going to be gone for at least nine months, I bought a Sony Pro Walkman (Very high tech for that time), and the cassette collection of Solti's Ninth that was available then on DG. That was actually quite an outlay of cash for me at the time. I can still remember going to a little hi-fi joint near Harvard to get the Walkman and a great record store nearby to buy the cassettes. I had a lot of other music with me for that year in Europe, but I listened to the Ninth an awful lot. When we were based out of Paris, I quickly learned that the Louvre had no admission on Wednesdays, so every Wednesday that we werent on some leg of the tour or other, I was there or at Jeau de Palme (sp?), which had all my favorite Impressionist stuff and was just down the mall. Walking through the Louvre with Beethoven as a soundtrack wasn't the highlight of my Parisian experience with the Ninth, however: One day I walked from Notre Dame to the Eiffel Tower listening to the Ninth, and when I got to the tower, the elevators were shut down for maintenance. One of the last things I did before I left Boston was to run in the Boston Marathon, so I was twenty-something and in excellent shape: I walked up the stairs all the way to the top deck listening to Beethoven. That was an amazing day. When I got to the top, there were only young people there, for obvious reasons, and adventurous ones at that. There must have been ten different nationalities represented, and fortunately for me, English was the common language, so we had a blast. I'm wasn't into the whole European "mixing hash with tobacco in a cigarette" thing though. I much preferred a pipe at the time.

Back in the states during my R&R guitarist days, I was one of the first kids on the block with a Discman, and the first CD's I bought were? Solti's 1985 recording of the Ninth, and Von Karajan's DG recording of Mozart's No. 41 and Haydn's No. 104 (That's a fabulous CD and the recordings actually date from 1978). I wish Solti's earlier recording was available on CD, because I preferred it to the latter one, but "oh well". I worked at Manny's Music on 48th Street in those days, and lived 'cross the river in Hoboken. I took the PATH train to 34th Street every morning and walked the rest of the way. Walking midtown Manhattan listening to the Ninth was sublime. This symphony is so universal that it really does fit in anywhere.

Of course, being an Apple guy, I had one of the first 5GB iPods ever made (Still have it and use it to this day, in fact). One of the first things I turned into MP3's and downloaded to it was that Solti CD of the Ninth I had bought all those years before. Also a motorcyclist (As opposed to a "biker": I have a pair of Beemers, no Harleys for moi), I got the iPod set up with a pair of Etymotic ER-4P insert-earphones that work like earplugs in eliminating external sound, while at the same time providing amazing fidelity, so that I can put them in under my helmet, and be in my iPod coccoon while I ride (Don't give me that "it's illegal!" nonesense: I'm a ruthlessly purist libertarian. Those laws are BS and have no place in a society of free men who are responsible for their own actions). I usually take at least one motorcycling vacation every year that is 4K miles or more, so I've listened to the Ninth in more than half of the States, I'm guessing.

Now that I live in one of the most remote areas in the lower 48, I do a lot of driving. The nearest towns to me are 25 miles east, 30 miles west, and 26 miles north. The nearest Wal-Mart is 68 miles away. I had to go there Friday because I was out of fingernails. Yes, fingernails: I use fake ones on my p, , a, and c fingers to play guitar, and I needed a new batch. My place to Fort Stockton was just enough time to listen to the Allegro, Scherzo, and the Adagio. On the way home I listened to the Finale, and then Pat Metheny's "One Quiet Night" to decompress.

I really can't stand the Finale. In fact, I pretty much hate it. Over 95% of the time I listen to the Ninth, I skip the finale. Since the Adagio leaves off at a very pleasant place, I never miss it in the least. The problem for me is primarily classical vocal technique: The tastelessly over-the-top vibratos literally hurt my ears. I'd rather listen to Megadeath or Metallica any day than to any classically trained singer. Are those idiots even capable of singling without vibrato?! In any event, I simply am forced to go to the Liszt transcription to even be able to tolerate the Finale. Asside from one of the most kick-ass fugattos ever written, in my opinion the Finale of the Ninth is one of the poorest of all of Beethoven's creations. When you get past the bombast, there is really very little "there" there. Or at least that's my current impression. We'll see what I discover when I analyze it.

I may hate the Finale of the Ninth, but I love living out here.

Miscelaneous Musings

It's a lot of work being Abbot of one's own Monastary. Don't worry, the analysis of Beethoven's Ninth is proceeding apace, but there are many decisions concerning the details of the settup for it that I had to make before it could actually be started. Since those formatting decisions are now in the bag, I have entered the music up to the first statement of the main theme for the Allegro, and I should have the entire exposition ready by the end of the day tomorrow.

Add to that monumental project the fact that 1] One of my Lexicon MPX-G2's needs repair, and I'm communicating with Lexicon about that, 2] One of my sets of PA speakers requires the same, and that's looking like a DIY type of deal, 3] My new Mac Mini hasn't shipped yet (But the wireless keyboard and mouse are on the way: Bluetooth rocks) [I simply must have access to my 23" Cinema HD Display to get screen captures of entire pages for this project] and add to these gems the Mother of all Distractions, 4] I got a new Godin Multiac Grand Concert SA electric nylon string guitar Thursday, which has captured quite a bit of my attention. So, as you can see, I have a lot on my plate right at the moment, figuring in my busy gigging schedule on top of it all. Good thing I'm a "no wife, no kids, no pets, no girlfriends" kind of guy, or my life would really be impossible!

Oh yeah; I have a new BMW on the way too. No, not an automobile (Never had one of those: I'm a full-sized, four-door, 4x4, four-inch lift, 33" AT tires, V-8, American pickup truck kind of guy, since I live in the most remote high mountain desert region of Far West Texas and enjoy outdoor sports). No, not a motorcycle (I already have two of those: K1200LT and R1100RS). A bicycle. Mountain Bike, speciffically. I'm sure I'll have to make some time to ride that when it arrives as well. Hey: All work and no play...

I have been listening to the Ninth in both the solo piano versions and the orchestral versions a lot since I made the decision to analyze it (It will be the soundtrack for my life for the forseeable future, though I'm swapping between it and Pat Metheny's "One Quiet Night" and "Beyond the Missouri Sky" for a break in the drama and some perspective-adding relief), and it is amazing the different prism you can view that symphony through simply by listening to Liszt's transcription. A large part of the formidable nature of that symphony for me from a listener's standpoint is definately Beethoven's scoring. The piano transcription makes the actual music much more transparent since I'm not being constantly carried away and distracted by all the fine details of the orchestration. It's looking more and more likely that I'll have to do an orchestral analysis after the harmonic/thematic/formal one.

Quite often I feel like I'm not "relatable" to very many other musicians. I say that because when the subject of listening experiences comes up, I feel like what I experience and what others experience are quite different things the vast majority of the time. At least, judging from what others describe to me. One outcome of this is that I am constantly amused by what others tell me about the music that I compose. Since I make my living as a guitarist who gigs at least three days of every week, and over 60% of my set consists of my own material, I get a lot of feedback. Anecdote in point: I was performing at a very small and laid back Art Opening a few months back, and it was one of the few gigs where I didn't bother with any amplification. I just brought one of my 1979 Anthony Murray classicals, set up in a corner, and enjoyed myself while the Marfa/Alpine/Fort Davis/Marathon artistic hoi palloy hob-nobbed (I love playing art openings: The artists are as interesting as the art, and people watching during gigs is a fun sideline). Anyway, near the end of the night, a very attractive young lady came up to me, and in a delicious French-Canadian accent said, "Your music is so peaceful." Of course, I had just finished playing a Prelude of mine that was full of harmonic "storm and stress" from my perspective - one that I wrote at the sad conclusion of my pursuance of the lady who was doubtless the love of my life - and so I just smiled and said thanks: I have to admit not understanding reactions like that to my music.

The reason I bring this up is because as I go through this symphony of Beethoven's, I will be describing in unabashed terms some of the emotional and spiritual effects this music has on me. You may not relate. In fact, Beethoven probably wouldn't relate. I suppose that's OK: One of the coolest things about music is that the same work can mean very different things to different listeners. Beethoven's Ninth, as I've said before and will say again, is my favorite of all compositions and it is constantly taking me into new and uncharted realms of spiritual and emotional awareness. Even with the score in hand as I listen, these effects are not diminished for me (And in at least one classical music community I'm part of, there is almost universal agreement that reading a score while listening diminishes the listening/relating part of the experience: I cannot relate to that in any way, as reading the score while listening actually enhances the experience for me). Anyway...

Apple said "seven to ten days" on the Mini, so I'm hopeful that I'll have the first analysis post ready by the end of next week.

Analysis: Beethoven's Ninth, Prolog

This is something I've wanted to do for years: Analyze the entire Ninth Symphony of Ludwig van Beethoven. If you want to follow along, the materials I'm going to use are Franz Liszt's Piano Transcription of the symphony, along with Cyprien Katsaris' recording of the transcription.

The Liszt transcriptions of Beethoven's nine symphonies are a musical monument in their own right, and are no mere collection of piano reductions, but are rather scholarly works of supreme transcendency by arguably the greatest piano virtuoso/composer of all time. Liszt's own introduction to the transcriptions is as follows:

"The name of Beethoven is sacred in art.  His symphonies are at present universally acknowledged to be master-pieces; whoever seriously wishes to extend his knowledge or new works can never devote too much reflection and study upon them.  For this reason every way or manner of making them accessible and popular has a certain merit, nor are the rather numerous arrangements published so far without relative merit, though, for the most part, they seem to be of little intrinsic value for deeper research.  The poorest lithograph, the most faulty translation always gives an idea, indefinite though it be, of the genius of Michel Angelo, of Shakespeare, in the most incomplete piano-arrangement we recognise here and there the perhaps half effaced traces of the master's inspiration.  By the development in technique and mechanism which the piano has gained of late, it is possible now to attain more and better results than have been atained so far.  With the immense development of its harmonic power the piano seeks to appropriate more and more all orchestral compositions.  In the compass of its seven octaves it can, with but a few exceptions, reproduce all traits, all combinations, all figurations of the most learned, of the deepest tone-creations, and leaves to the orchestra no other advantages, than those of the variety of tone colors and massive effects---immense advantages, to be sure
 
Such has been my aim in the work I have undertaken and now lay before the musical world.  I confess that I should have to consider it a rather useless employment of my time, if I had but added one more to the numerous hitherto published piano-arrangements, following in their rut; but I consider my time well employed if I have succeeded in transferring to the piano not only the grand outlines of Beethoven's compositions but also those numerous fine details, and smaller traits that so powerfully contribute to the completion of the ensemble.  My aim has been attained if I stand on a level with the intelligent engraver, the conscious translator, who comprehend the spirit of a work and thus contribute to the knowledge of the great masters and to the formation of the sense for the beautiful."
 
Rome, 1865                               FRANZ LISZT

From the reverent tone of Liszt's dedacatory introduction to these transcriptions, it is evident that one of the main reasons he undertook this monumental and worthy task was to provide these nine musical epics of Beethoven in a form that could be studied, which is the task at hand. For years the musical language of Beethoven - hands-down my favorite composer of all time by many lightyears of distance beyond Bach, who is my second - was an impenetrable fortress of sublimnity that I simply stood in pious awe of. Lately, however, I have began to comprehend "one thing and another" about his music while perusing the Liszt transcriptions, and so the time has come for me to analyze the entire corpus of my favorite of all symphonies. Before I was successful at writing an Art of Fugue-style string quartet piece, I analyzed every intervallic relationship between every voice in Bach's Contrapunctus I, and so here I wish to finally, at long last, penetrate the mature musical language of Beethoven, just as I have done with Bach.

I will be entering the Liszt transcription into my music printing/sequencing software as I go, adding the thematic and harmonic analysis to it, and providing commentary throughout the process. For a listening reference, I will be using Katsaris' amazing recording of the solo piano transcription, which I actually prefer to most symphonic performances due to the "issues" I have with the finale: I'm one of those old school guys that does not care to hear vocal soloists and vocal choirs in a symphony.

I will be recieving a new computer and an enhanced package from a new ISP in the next few weeks, and so I am hopeful that I will be able to learn how to link to MIDI files of the musical examples I present before too awfully long that will be extremely tiny file sizes that will play via QuickTime readily, even if you have dialup internet access (If anyone is familiar with the details of how to do this - I already have the hosting part figured out, it's the linking details I'm not positive about yet - please do share).

Obviously, the orchestration will probably not be analyzed in any great detail here. I must admit to being diffident about that particular subject, as I already have very definite ideas about orchestration that are nothing like Beethoven's. I reserve the right to "revise and extend", of course, so don't be too surprised if I eventually drag the full score into this at some point. It would be untruthful of me to say that I am jumping into this with supreme confidence: while I'm certain it will be a very profitable enterprise, at the same time I must admit to having some trepidation... ah... like... permiating every cell of my entire being.

"Completed" Climax and Fugatto Sketches

As promised, I am going to present the completed initial version of the climax phrase I was working on earlier for my sonata-process movement in today's post, but I have also done a lot of polishing up on the fugatto as well, and it's now reached the same initial stage of completion, so I will present that today too.





The only change to the first two phrases of the climax episode is in the pitch level: This movement has now found its home in the key of D minor (Scads of monumental symphonic movements are in the key of D minor: No pressure ;^)). Raising the pitch level a wholetone from C to D brightens it up a tad, and as you will see, allows for a low C-sharp in the contrabasses near the end (I always assume five string basses, or basses with low C extensions, will be available. Since the only place this will probably ever be played is in my Virtuoso 2000 sound module, it's not really a consideration in any case).



In the completion above you can see that I have written a six-voice canon that dissolves back to a singularity on the bottom line B-flat of the contrabass staff. The six-voice simultaneous diatonic mirror climax itself actually wrote most of the canon for me as you can see: Using the me, re, do figure that violin one has in the following voices made it work out effertlessly, and as a result it sounds very organic. Repeating the concluding eighth note figure violin two has at the end of the climax in successively lower octaves releases the tension inherant in the climax quite effectively. This passage may seem overly brief, but I have programmed in a retardando along with a diminuendo to stretch it out so that the climax is still near the Lagrange Point of the Golden Mean in terms of temporal duration. Using the decending augmented triad for the dissolve was really the only thing "I" had to come up with. I piddled around with the mirror of this canon, and it had some interesting effects, but it was nowhere near as nice as this rectus version.

Note that I have a feint to D major in the middle of the first measure of the canon: Since this is shaping up as a battle between the major and minor modes, this is a cool little point of doubt about exactly where the phrase is headed. Also, at the very end the leading tone is abandoned for the natural seventh degree to allow the phrase to end with the deceptive movement to B-flat, which is the major key of the submediant degree. Combined with the keys explored or implied by the fugatto, I am beginning to get my first ideas about which regions of the home key will be explored in this piece.

Since the buildup phrase exists in both major and minor versions, the climax exists in minor and major/minor hybrid versions, and this deceptive movement at the end here can also retain the leading tone and end on B-natural, there are eight possible permutations of this phrase. If you'll remember, I eliminated the mirror with the diatonic bass line due to a parallel fifth (Twelfth, actually) that resulted from the combination, not to mention the vioce crossing that resulted. Had I not made this decision, I would be faced with a harrowing sixteen choices here: When you develop well organized sketching proceedures that exhaustively enumerate all the arithmetical possibilities, you will never be faced with a derth of material from which to choose; rather, the problem you'll face will be concerning what to winnow out from the embarrassment of riches you will have come up with. That is why it is important, in my opinion, to allow your taste and intuition to function in these instances: The parallel twelfth bothered me, so I eliminated those two combinations. Here, I like the gravity of the deceptive movement to the B-flat, along with the jaw-rattling effect of the super-low minor third that preceeds it, better than the possible movement to B-natural, so I am back down to four possible variations of this climactic phrase. The version that has the buildup to the climax in D major, the climax itself in D minor, and this very same dissolving canon is without doubt my favorite of the four: The brief feint back toward D major in that version is particularly poignant.

On to the revised fugatto.











The changes in the exposition and counterexposition are limited to the cadential measures. I have added a decending cadential line and moved the ascending cadential line up an octave to change the former parallel sixths to thirds, like I had in the second phrase previously. I did this retrospectively after I had modified the final cadential episode at the end of the subject/answer canon, as you will see shortly. Now, these cadential lines create incidental parallelisms with the repeated tail figure, some of which are parallel perfect consonances, and some of which are parallel dissonances. Examples of this abound in the classical literature, and the purely contrapuntal passages are perfect in any case. Though I find Shenkerian analysis to be of dubious worth at best, and consider Shenker to be a snake-oil peddler at worst, I do like his concept of Free Composition, and that is what these episodes are: A settup for a larger plan and the coming climactic gesture(s).

That reminds me of a great anecdote. An editor approached Beethoven late in his life, and had to communicate to him with pen and paper due to the advanced stage of B's deafness. He asked, "Her Beethoven, do you allow for parallel fifths in your music?", to which Beethoven wrote back, "What do you mean?". The editor replied, "According to the rules of counterpoint, parallel fifths are not allowed.", and so B replied, "Then I do not allow them." The editor, thinking he had Beethoven cornered, then produced a manuscript that Beethoven had sent him to be published and pointing said, "Well, you've written parallel fifths right here." Beethoven's response was perfect: "Then I allow them." The point of learning to spot parallesims is to develop total awareness. Enough said.

In the second cadential measure the decending line is now just above the bass, where it will be in its final appearance, while in the third, the figures are back to their original positions, only here, they are reinterpreted so that the modulation to the relative major can be made. This improves the effectiveness of these cadential episodes enormously. In the fourth example, the arrangement with the decending line between the two ascending ones is presented, and in the final example above, the original arrangement appears for a third time, but breaks off into a remodulation back to the tonic minor. This level of sweating the details is what seperates the music of a Mozart from a Vivaldi, or similar (Though I certainly don't consider myself to be on the level of a prolific genius like Vivaldi, some of his music nevertheless does show some signs of having been written in haste, which probably has more to do with the pressures and demands of his position than anything else).



At the end of the subject/answer canon, where the two cadential figures dovetail into simultaneous statements in contrary motion, I have added an octave doubling of the descending cadential line to that measure, which adds a very powerful Beethovian effect to this climactic episode. That line continues to take over the ascending line in the following measure, where the octave doublings of all of the voices break off consecutively into individual voices finally "resloving" deceptively to a gargantuan and highly dissonant V7(m9/A11)/bIII, which implies the parallel minor of the relative major is to follow, but yet not, with the augmented eleventh present (You can take the composer out of jazz, but you can't take the jazz out of the composer). I really love this effect, but I'm not sure where I want to go with it yet. As I said earlier, I need a canabile theme for this movement, and that is probably where this should go, but expressive melody writing is definately the biggest of many chinks in my armour. I love counterpoint and voice leading so much that, as a result, most of my melodic ideas are overly linear in conception. As with all of the larger pieces I write, I have reached a point with this where I will now let it germinate in my subconscious for a while so that I can then return to it with a fresh perspective and new ideas.

Since I have mentioned linear cadential formulas, and I want to develop some of those for this piece, that will probably be the subject of the next post. For a long time I wondered how Beethoven got such powerful effects with such seemingly simple opening and closing bi-linear and multi-linear wedge formations. Finally realizing they were cadential pendulums swinging back and fourth between dominant and tonic function harmonies was a revelation.

Composing Fugues and Fugattos

There are as many ways to approach composing fugues and fugattos as there are composers who have worked in those generas, but the basic elements are pretty much constant due to the requirements of the process. I say process and not form because writing fugues and fugattos is not something where you can pour the music into some kind of a mold, like say for instance an A, A', B, A'' standard song form, or something like that. Basically, the subject and the possibilities it has are going to determine the form. Nevertheless, there are certain formal elements present: The required exposition, where the subject, answer, and countersubjects (Or free voices if strict countersubjects are not employed) are first presented, an optional counterexposition, episodes (Either non-modulatory or modulatory), middle entries, some sort of a recapitualtion, and an optional coda or codetta. The possible characteristics that each of these formal elements may take on are literally infinitely varied.

If you followed the link from my previous post to my Fileshare page and took a look at the string quartet fugue I wrote, there is some basic formal analysis there that will give some idea of how I used each of the aforementioned elements in a very strict Art of Fugue-style piece. The piece I wrote for today's post is a fugatto, which is a fugal episode within a larger work; usually a sonata-process piece. Beethoven was very fond of fugattos, and the Scherzo of the Ninth Symphony actually begins with one. There is also a fabulously brilliant fugatto in the finale of the Ninth as well. Beethoven used fugattos to bring a certain level of intensity to an episode within a larger piece, and he used subjects with jagged outlines and great rhythmic vitality to achieve these periods of exuberance. As a result, his fugatto subjects don't lend themselves to very many contrapuntal combinations: Beethoven was not interested in lengthy developments here, but rather brief episodes of great vitality.

My aims are slightly different, as I am interested in writing fugal works that show off the way I can compose subjects and answers that lend themselves to ingenious combinations. For a fugatto I'll have to keep it short and sweet, but I would still rather write it as a complete fugue reduced to it's most essential components than just make it an intense exposition that quickly dissolves into some powerful cadential gesticulations as Beethoven was fond of doing. Of course, it will still have to serve a logical function in the larger context of the piece, which is shaping up as a battle between the minor and major modes in this case.



Since I'm only going to have time to present one contrapuntal "trick", I wanted to make it one of the best ones possible. Above you can see the fugatto's subject underneath it's tonal answer in canon at the extraordinarily close distance of a quarter rest's delay. This is done in exactly the same manner as the canon technique I explained in the last post, but is several orders of magnitude more difficult to pull off: One beat's distance at the octave is not too bad, but this close at intervals other than the octave is quite a formidable challenge. I have never managed to teach any of my students how to do this, because while I can demonstrate the technique, I can't explain in words exactly how I can make something like this "happen". Admittedly, it gets into the area of intuition at this point, and it just takes a lot of practice and determination to master this, as with everything else in music.

Note that the subject is a desireable odd number of measures in length and that it is essentially in a head-and-tail type of configuration. Note also that I have managed to get the rhythms to accelerate into a nice dovetail in the course of the canon. Finally, note that there is quite a bit of rhythmic vigor to the subject and it's answer: Not as much as Beethoven would have used - with all of the insistantly repeated notes and whatnot - but more than the majority of Bach's subjects had. This makes it very suitable for a fugatto.



Above is the first statement of the subject and answer in the exposition of the fugatto. Note that my sonata-process movement has found it's pitch level at D now. After the first statement of the subject, I repeated the cadential tail figure for a measure and let the string choir interrupt the action with some cadential hoopla. In a strict fugue, this would have been left out, and the answer and counteranswer would have started in measure four. This is not just an empty gesture though, as the end of the fugatto will finalize the development of this figure, and this measure also serves the purpose of a modulatory episode in subsequent iterations. A variation of this measure is again present after the first statement of the answer. Again, if this was a fugue for a wind trio or something like that, the second statement of the subject would replace the cadential episode there. Note that I managed to work both decending and ascending chromatic passages into the counteranswer: This relates back to the chromaticism in the six-voice simultaneous diatonic mirror of the first theme that I have already sketched out.



Continuing with that idea from the mirrors, I used some chromatic linear motion in the countersubject above the final statement of the subject for the tonic minor region. This time the cadence serves it's purpose as a modulatory episode: By not raising the submediant and leading tone at the end, the figure ends up on sol of the relative major, enabling a modulation with the support of the other voices in the choir. Below the opening statement of the subject in the relative major, I have a diatonic variant of the countersubject, as starting on sol in the bass does not give a pleasing effect to my taste. Note that I have "fattened up" these two cadences with a decending line in the interior to counterbalance the ascending ones and add progressively more "punch". This relative major area could be called either a middle entry or a counterexposition, as the definitions of those two terms have a degree of nebulousness to them, but I consider it a counterexposition since both subject and answer are present.



With the second appearance of the answer in the relative major, all elements of the fugal exposition have been presented: Subject, countersubject one, countersubject two, answer, counteranswer one, and counteranswer two. Since this is a fugatto and bervity is of the essence, the last cadential episode modulates us back to the tonic minor for the presentation of the subject/answer canon. This is an amazing passage, if I do say so myslef, and when the cadential tail figures dovetail into simultaneous statements in contrary motion, a quite powerful effect is achieved. This is the final climactic development of all of those cadential interruptions that came earlier. That the movement slows temporarily at the beginning of the phrase and rebuilds only adds to it's effectiveness. This disolves into an angular cadential gesture, which will be followed by one or two more, and that will lead into a statement of a contrasting theme. Now, all I need to do is compose the lyrical theme, and I'll have all the basic elements to sonata with (Yes, I'm using sonata as a verb).

Composing Fugue Subjects as Canons

I have not gotten the Cube back together yet, but after working with my 15" PowerBook for a few days, I find I can do more with it than I originally thought via some minor work-arounds, so that I can get back to posting.

The phrase for the sonata-process movement that I was working on earlier I have now finished composing by using a four voice canon that dissolves back to a second singularity, and that will be the subject of the next post, but I have decided I want to compose a fugatto for that piece next, so to get my fugue subject compositional juices flowing, I have decided to review for you how I composed the fugue subject for a string quartet I wrote about ten years back.

This fugue was intended to be an homage to J.S. Bach, and in a very close approximation to his late fugal style as exemplified by The Musical Offering and The Art of Fugue. As such, I wanted a subject that was similar to the head-and-tail subjects that those two collections are built around. However, I didn't want anything either so chromatically complex as the Royal Theme nor so spare as the Motto Theme. Rather, I wanted to get elements of both into a subject that would work as a four voice canonic stretto.

I should note that historians seem to have discovered that the Royal Theme was composed by Frederick the Great with the help of Bach's son Carl Phillip Emmanuel in an effort to embarrass the old man, and it was intended to be impossible to work with, or nearly so. There is a new book out about that meeting between Frederick and J.S. Bach entitled Evening in the Palace of Reason, which I have not yet read, but all who have that I have spoken to about it recommend it highly. Briefly, J.S. Bach was an Age of Reason product while C.P.E. and Frederick were Age of Enlightenment proponents: The meeting was supposed to show the superiority of the second philosophy by discrediting Bach the elder, but it ended up turning on the plotters magnificently, as Bach astonished everybody present.

And, concerning the Motto Theme, it was designed to work with the BACH musical anagram, and does not lend itself readily to very many contrapuntal combinations: Bach had an ulterior motive with that theme, and that he could do so much with it and the previously mentioned Royal Theme offers testament to his overwhelming greatness as a contrapuntist.

For my more modest aims, I wanted a subject that would work in stretto at the octave at consecutive measures of overlap: First one, then two, three, and finally at four, where the following voice would be at one measure's distance from the leader. So, the subject would have to be five measures long (Odd numbers of measures of length for fugue subjects is a highly desirable feature, as this more easily creates a freely flowing phraseology without the tyranny of four effect that so much music suffers from, and which is particularly damaging to a fugue), and it would have to be composed using basic canon technique.



In the example above, you can see that I chose the classic do-sol figure for the beginning of the head of the subject, and set it up to be composed as a four voice canonic stretto. One of the nice things about this figure is that it can be harmonized as a full measure of tonic harmony, or as a half measure each of tonic and dominant harmony. For the first measure of overlap, Bach chose me-do due to the BACH anagram he was composing it over, but this would not work well for this application. Instead, I chose the deceptive motion to the submediant degree for the first half of the second measure, which gave me the oportunity to use the le-ti melodic leap of a diminished seventh that is such a dominant feature of the Royal Theme: So I managed to work references to both it and the Motto Theme into the head of my subject, creating a better version of both of those in terms of stretto possibilities as I did so.



As you can see by our second example, the first thing that occured to me for the third measure was the obvious do-re movement in half notes. This worked so readily and obviously, that I stuck with it, and went on to compose the fourth measure, which you can see below. I should point out here that many of the best fugue subjects have a point of restance in them, such as the tied figure I have employed here, which is again directly from the Motto Theme of J.S.Bach.



Bach ended his Motto Theme at the point where the trajectory returns to the tonic for the third time, but I wanted to continue with that eighth note motion and in the process get the five measure subject I wanted, and also to complete the continuity of the surface rhythm of constant eighth notes: Fugue subjects of this type composed in canon and fugue subject/countersubject combinations should always rhythmically compliment one another so that they achieve this kind of an effect of surface continuity.

After finishing this intital version of the subject, I was unhappy with the third measure, as it did not progressively develop any kind of rhythmic acceleration, and it seemed overly abrupt when the eighth notes came in. So, I added the quarter note figure that you can see in the example on the bottom. This is a perfectly acceptable fugue subject in this form, but there are only four different rhythmic values in five measures, while there are eight different notes. This is a little weak on the rhythmic variety side for a subject this long with the range of a minor ninth.



On top above you can see where I have added the dotted-quarter/eighth rhythmic elaboration to the third measure. This gave five different note values for the subject, which is an improvement, but the straight eighth notes now sound a little flat by comparison. So, I took the same rhythmic figure in diminution and applied it to the tail, as you can see in the final example. The complex interaction of the dotted-quarter/eighth rhythm against the dotted-eighth/sixteenth rhythm adds just the right amount of "grease" to the combination, and the end result is quite wonderful, if I do say so myself.

For the fugatto I wish to write, I do not need so many contrapunhtal combinations as this theme offers (Only some of which are evident in this canon), so I won't necessarily compose it as a canon, but will probably go for a more rhythmically vigorous subject instead. Since a fugatto is basically just an exposition and a counterexposition most of the time, I can afford to be more lax in my development of it in this one speciffic way.

If perchance you would like to see the score of the completed fugue and listen to a MIDI file of it, it is posted on my fileshare page here along with a bunch of my early guitar miniatures. The score is posted as a PDF file, and if you have QuickTime, you will get the MIDI file with the string quartet sounds already attached to it.

"We Are Currently Experiencing Technical Difficulties...

...Beyond Our Control. Please stay tuned and we will return to your regularly scheduled programming shortly."



The photo pretty much sums it up. One of the tribulations involved with using a five year old computer. I hope to be back to posting by the end of the week.

Theme Sketches to Score Sketches

Continuing with the symphonic sonata-process movement I'm working on, I have made enough progress to start a second digital sketchbook for the scoring.



Above is page ten of my theme sketchbook. Here, I took the sequential elaboration and got it to a level where it is beyond the musically trivial versions of my first two attempts. Starting with a musical singularity on the third space C of the treble clef, I have harmonized it over a four octave diatonic decending bass line so that it will lead into the six-voice contrapuntal simultaneous diatonic mirrors that I developed previously. Against this bass line I have used good, old fashioned sixteenth century counterpoint with an additional interior generator voice that is a rhythmic augmentation of the theme's head figure in melodic inversion. Since the original head figure starts out with an eighth rest, this translates to a quarter rest for the augmented inverted figure, and it now takes up an entire measure, plus it dovetails with the regular rectus form of the head figure that is sequencing above it. This makes for an exquisitely delicious effect! I have this augmented inversion entering at the interval of a fourth above the note in the bass - which is a "trick" that I learned from Palestrina (Though many others have used it), and it is sort of a mini-homage to him which I have built into the piece. With each successive entry of this figure, a new interior voice is created in the first four bars of the sequence, and the buildup to the cadential tail figure's appearance is quite sublime.

In the second four bars of the passage, this same figure rises, creating a new octave doubling of the bass line each time after it has entered. This continues to add additional impact and weight to the buildup to the climax. Note that I maintained the head figure's rhythm in an interior voice with the intervallic contraction of it that I worked out for the original three voice contrapuntal version of the theme: This maintains the drive of the phrase to the point that without it, the whole thing collapses and seems to start over, versus continuing to relentlessly build up. The end of the second phrase has the tail figure intervallically expanded to get the do-ti-do into the climactic statement of the theme.

The top three staves present the major mode version of the passage in as diatonically pure a state as possible, while the bottom three staves present the minor mode translation. The major version in this condition has a pastoral quality to it which is quite nice, especially for the first phrase, but could use some spicing up in the second go-round. Note that in the third and seventh measures of the minor mode version I had to introduce the augmented inversion of the head figure with a D-flat to avoid a tritone relationship with the bass line, just as the old masters would have done. This has an awesome effect (As in it inspires a feeling of awe, not in the coloquial slang sense). Note also that I was able to use an E-natural against the second D-flat over an F-natural in the bass moving into an F-sharp vii(d4/2)/V across the barline. This is a very amazing sonic effect, and I must admit that I created this intuitively and analyzed it in retrospect (The ultimate goal of theoretical study for a composer is to go the full circle, where in the end it is as it was in the beginning: 100% intuition). After the second phrase of the buildup, the pure minor six-voice contrapuntal complete diatonic mirror is introduced, replete with all of it's internal chromatisism.

As an asside here, I mentioned in my previous post that this particular minor mode arrangement, with all of it's simultaneous cross relations of raised and lowered scale degrees does not violate any of the laws of counterpoint, and this is true (Which you will only understand if you have read my earlier posts concerning contrapuntal laws versus stylistic rules), but there is certainly no rule-set that theorists have devised to explain the practices of previous composers or compositional schools that would encompass this passage. What makes it work is the clear and purposeful linearity and axial orientation of the individual lines: No matter how dissonant the interior mechanics are, the beginning is definite and the end is never in doubt. And remember, the listener will have heard these two three-voice arrangements in various guizes several times before this point in the piece is reached, so it will make the greatest sense, in a revelatory kind of way.

Now, once I reach the point where I am coming up with close to musically viable passages, I immediately start a second digital sketchbook to begin working on ideas for the orchestration. What I do is I start out by scoring the entire passage, or even the entire piece, for the string choir.



Above is the first page of the score sketchbook showing the major mode version of the passage. At the end of the first phrase I introduced the vii(d4/2)/V from the minor mode version, which adds a profound dimension of additional possibilities to the phrase as a whole. Continuing with the interplay between the F-sharp and F-natural of that bar, I introduced chromatically some secondary leading tones in the second part of the buildup. I experimented with an E-sharp at the end there, but dismissed it because I personally didn't care for the effect it created.

The entrances of the augmented inverted head figure suggest instrumental entrances to me, and after creating the dissolution episode for the post-climax cooldown, I will expand the score to include those. One of the nice things about these digital sketchbooks is the ability to quickly copy and paste the music to create subsequent versions, and expand the score to bring the rest of the orchestra online: This sketch, or one of it's subsequent versions, will actually end up becoming the completed score. This is an enormous time saver. I also have an E-MU Virtuoso 2000 sound module fully loaded with all the alternate orchestral sound sets, so I can get a pretty reasonable approximation of an actual orchestra as I'm sketching, which is quite helpful, to say the least.

As I mentioned previously, the major mode version of the six-voice contrapuntal complete diatonic mirror has a parallel perfect twelvth in it. This gave me the idea that this movement is going to play out a battle between the major and minor modes, with the minor being victorious due to the contrapuntal perfection of it's version of the mirror climax. For this reason, I have decided neither to use this version of the climax, nor it's minor mode variant. The individual three voice versions will instead be used seperately. This leaves the minor mode version with the chromatic bass line, and the hybrid major/minor variant of that for the two climaxes. One might ask, since the major mode variants sound quite excellent, "Who's going to know there is a parallel perfect twelvth in there?", to which I will defer to Michelangelo for the answer: "God will know." It is precisely this minor imperfection in the major mode mirrors that I have decided to capitalize on in this piece, and so the overall plan can begin to take shape.



Here is the second page showing the minor mode variant with some minor alterations (I changed the voice leading slightly from the sketchbook versions of both of these to lead more smoothly into the mirrors), which you can see in the second half of the phrase where I added a single secondary leading tone in the first measure. The resulting melodic diminished third interval is really nice sounding here, but again, an E-sharp in the third measure following did not have an effect that I personally liked.

Since there are now only two versions of the mirror climax, and two versions of the buildup, there are four possible combinations of these. The major buildup modified to have a minor tonic chord on the third quarter note of the penultimate measure to the climax going into the minor version of the mirror above is particularly devastating, since it starts off with such a pastoral mood and ends up with the most macabre version of the mirror, so I will most certainly use it for the main climax. The minor buildup going into the major/minor hybrid of this mirror will be the other climax. I have those scored out in sketch on the pages following these examples. As you can see, getting all of the variables skecthed out to audition (I actually sketched out all eight of the possibilities before deciding to dispose of the "flawed" versions), is an enormous aid, as is the simultaneous working out of everything in both of the modes together: If I had only sketched in the major mode, I never would have had the elements to borrow from the minor and vice versa.

UPDATE: Much to my horror, I noticed the parallel octaves from D=C between the bass and an interior voice in measure four of these examples this morning. I changed the interior voice to E or E-flat for the major and minor versions respectively. As with all adjustments of this type, the "repaired" version is superior with respect to it's musical effect than the original "flawed" one. The galling thing is that I got that progression right in measure eight. What was it that I said about 100% intuition? Guess I'm not "there" yet. ;^)

Creating and Developing a Sonata Theme

Please excuse the intermission in posting, but I have been suffering with some computer-realted issues: My trusty Cube has been suffering relatively frequent kernel panics since I upgraded it's OS to 10.3 and my old AirPort Base Station's internal modem has pooped out. As a result, I have had to post from my PowerBook, and am crippled by not having the luxury of my 23" Cinema HD Display. So, I had to get the following nine screen shots on the Cube, transfer them to the PowerBook, and then upload them to my Smugmug account. To call this process tedious or time consuming would be an understatement. But, I did finally get it done, so here we go.

As I was working on the harmonic canons, I came up with a nice theme that will work well for a sonata-form movement, and so I will be pursuing that subject in today's post. The toughest nut to crack for an aspiring composer who is trying to learn to write fugues or sonata-form movements is the question of subject or theme choice. What makes a good fugue theme? What makes a good sonata theme? I bring these up together because they share some common traits, and yet they are different enough that what works for a fugue theme may not work for a sonata theme and vice versa.

Both fugue themes and sonata themes should be flexible. By that I mean first of all that they should lend themselves to quadrant rotation - the primary theme should work in it's original rectus form, in inversus, and in the retrogrades of these two forms also, if at all possible. Not only that, but they should also work in either the major or minor genders, and be amenable to frangibility, or fragmentation into smaller portions. Fugue themes usually have an increasing frequency of attacks, and a decreasing frequency of rests: in other words they have longer notes at the beginning, and shorter ones at the end. These type of subjects are called head and tail subjects, and the Royal Theme that C.P.E. Bach and Frederick the Great created in a vain attempt to befuddle J.S. Bach that is found in the transcendental Musical Offering, and the Motto Theme that works with the BACH musical anagram that Bach used in his other towering monument, The Art of Fugue are the best exemplars of this species of subject. There are a bewilderingly vast variety of fugue subject types in Bach's two Well Tempered Clavier volumes, but if you look at what he was using at the end of his career, he chose the head and tail types almost exclusively for their obvious superiority. Fugue themes also usually lend themselves to canonic interactions for stretto sections, and writing fugue themes as canons is in fact the best of all possible proceedures, which I will cover at some point.

Sonata themes, on the other hand, may have the shorter notes at the beginning and are often followed by a broader figure that lends itself to powerful cadential interpretations. The most startlingly brief of these would be the Fate theme from Beethoven's Fifth Symphony, followed by his overpoweringly strong first theme from the opening movement of the Ninth. Again, Beethoven used a wide variety of sonata theme types, but his most powerful and memorable movements were created with these short and sweet cadential types that lend themselves to frangibility and quadrant rotation: I believe if you are trying to follow the legacy of great composers like Bach and Beethoven, it is most instructive to analyze what they were writing at the end of their careers - when they were at the height of their powers - rather than their earlier more formative works.

It is with that idea in mind that I have been seaching for a sonata theme that has elements in common with that first theme from the Allegro ma non troppo, un poco maestoso of Beethoven's Ninth Symphony. As I was working on ornamenting one of the recent harmonic canons I developed, I stumbled upon a figure that worked with one of the nota cambiata quadrant rotations that was "perfect". The following pages from my sketch book will demonstrate some of the techniques used to develop this theme.

Sketching and sketchbook creation and useage is something that I was never taught in all my years as an undergraduate, nor did I encounter any professors who taught the subject right through my years as a doctoral candidate. This is ridiculous on it's face, since virtually every great composer in history had well developed sketching proceedures that they employed on a constant basis, and since with modern music notation programs with built in sequencers, today's composer has the technology to create sketching proceedures and sketchbooks that a Bach, Mozart, or Beethoven would have died for (Though Beethoven's deafness would have made the sequencer sort-of limited in it's value to him personally). I had the oportunity to look at some facsimilies of the surviving notebooks of Mozart and Beethoven, and the progress of the themes, especially those of Beethoven, from relatively mundane basic figures to well polished utterances of musical magnificence is startling. The theme of the slow movement of Beethoven's Fifth Symphony, which is one of sublime beauty, started out sounding like something a neophite would have written. Noticing this proceedure, which often spanned years, was a seminal moment for me, and so I thought it worthy to share a little of my own sketching techniques.



Above is page one of my sketchbook for this theme, showing first the theme in the major mode harmonized as simply as possible in four voices. Even if the theme is going to be used for a movement in the minor mode, as this one will, I find it advantageous to start out in the major, as translations to the other gender are more readily made than from the minor, which has a lot more gender-specific elements to it. The second stave has the theme with a constant half note bass line, and introduces a vi(m7) on the second half of the first measure, while the third staff has a constant quarter note bass line. Note that the second and third examples also have the traditional deceptive resolutions from V to vi and bVI with the deceptive movement native to the current mode first, and the one from the parallel minor second. It is usefull to not only hear these effects, but also to work out where they are available and where they are not, as we shall see. The bottom three staves show the theme translated to the minor gender with the corresponding natural reversal of the deceptive resolutions' target chords.



Page two of my sketchbook shows how the inversus of the theme works with exactly the same basic harmonization variants, in both the major and minor modes, that the rectus does, so long as the inverted form is diatonically mirrored at the normal fifth degree's tonic level. Note though, that with the doubled fourth degrees in the penultimate dominant seventh harmony the traditional deceptive resolutions are no longer available.



Since both the rectus and inversus forms work with the same harmonizations individually, they obviously will work in simultanaity. This is a very cool effect, if I do say so myself.



Focusing on the minor mode that the sonata-form movement will actually end up being in, we find that the minor gender of the theme will work with an idiomatic descending chromatic bass line, as I have shown in the top example. The A-flat descending to G in the bass presents the oportunity to employ a V(4/2/b)/V at that point, and in the traditional arrangement found with the so-called French Sixth. On the third line I created more minor-idiomatic chromaticism in the interior voices, and developed that into an echo of the theme's rhythmic head figure intervallically contracted penultimate to the resolution. This is a powerful unifying force here. The bottom two staves present this variant reduced to a three voice contrapuntal texture, which will be used in the actual composition, above yet another variant that can be used in a complete simultaneous diatonic mirror, as we will shortly see.



On page five of my digital notebook, I used the same chromaticised minor mode variants with the theme in the major gender. Interesting and seldom-heard sonic effects can be achieved with this technique. Note that I have again been alternately employing deceptive resolutions in these examples, but the only one available is the version native to the major mode because the note B must descend to A instead of G moving to A or A-flat: A melodic augmented second in the bass could be used, but in these sketches I want only the most normal and natural deceptive movements at this point for reasons based purely on personal prefferences.



On page six I have developed these chromaticised interior voices in the minor and major genders over diatonic bass lines. Here, both the native and parallel mode deceptive resolutions are available again.



For page seven I returned to the three voice contrapuntal chromatic variant I developed earlier to create a complete diatonic mirror, which you can see on the second stave. The process for creating a diatonic mirror involves using the third degree of the tonic triad as the point of axial rotation and answering the first degree with the fifth degree. In the seemingly amazing arrangement found on the third stave, these two mirrors work in simultanaity to create a six-voice complete diatonic mirror without any contrapuntal laws being broken. I repeated this process with the major/minor gender hybrid form of the theme on the three lower staves. I had to change the chromatic figure that previously implied a V/V-type harmony in the secong half of the second measure of the theme to get this to work out. These two six-voice mirrors sound quite magnificent, with the pure minor version sounding particularly bizarre, or even macabre, while this effect is slightly attenuated in the hybrid form. Obviously, these will be saved for climactic moments in the final symphonic movement.



I wanted a less severe sounding version of these simultaneous mirror climaxes, so I developed one in the major mode over a diatonic bass line on page eight. Notice I left out the chromatic inner voice as well, but maintained the constant eight note surface rhyhtm by continuing back the alternating C motion of the final figure. This ended up being highly effective and the resulting pure major diatonic mirror sounds quite grand, but there is one parallel fifth. Since this parallel fifth is at the octave double of a twelfth, and since the twelfth is the location of the lower note's harmonic anyway, this neither noticable, nor is it distracting in any way. Having completed initial development of the basic theme, I extracted it's most obvious frangibility-based sequential version on the bottom two staves. The repeat of the sequence has secondary dominant leading tones and the V/V's lowered seventh. This particular episode sounds more than a little Haydn-esque.



This is as far as I have gotten: The final page of the sketchbook so far has two more variants of the sequential elaboration. In the first example on page nine, I have added the inversus of the head figure to the interior voice, which creates a nice dialog between the top two voices, and in the second version I started out in the minor mode. The minor mode version is unusual in that the flatted sixth degree of that scale creates a secondary dominant that tonicises the major chord found on the flatted second degree of the scale. This is the region associated with the so-called Neapolitan Sixth chord - which has nothing to do with the various augmented sixth sonorities - and is quite a remote tonicisation to make so quickly (I will cover the so-called Neapolitan Sixth chord when I address secondary subdominant harmonies). It's a quite interesting effect, and the second phrase's return to the major mode offsets the unusual nature of the first phrase quite effectively. Note that I continue to look for the available deceptive resolutions of the dominant seventh.

So, this is an example of the technique I use to set up a digital sketchbook to develop both fugue subjects and sonata themes. During the process of coming to know a theme on this level of intimacy, elements sugest themselves that will lead to related themes, as well to the archetectural blueprint for the entire resulting piece of music.

Harmonic Canons with Two Root Progression Types

In the course of musical exploration, on occasion one learns from unsuccessful experiments as much, if not more, than from the purely successful ones. Today's example will embody that truism. I had in mind to write triadic and tetradic harmonic canons over a root progression pattern that had two progression types in it. For this exercise I chose a pattern that consisted of a mild decending root motion followed by a progressive root motion. Part of this choice was a result of the fact that the patterns I have employed thus far have had an overall decending trajectory in the constant root bass line, and this combination offered a seemingly refreshing ascending pattern for the lower stratum. There was also the fact that the second progressive motion offered the oportunity to employ some of the secondary dominant sonorities I have described to this point.

Well, once I discovered harmonic canons, I naturally ass-u-me'd that any repeating root progression pattern would offer the oportunity to write them. I was only partly correct in that deduction: In a triadic texture, if the two root progression types alternate between clockwise transformations and counterclockwise transformations, the voices simply cycle back and forth between one chord function and another, and so there is literally no canon, strictly speaking, to be extracted that involves all three of the voices. This was... ah... an eye opener. This most likely also applys to tetradic upper stratum textures, as seems logical in retrospect, but I'll hold my tongue and refrain from commenting difinitively until I have had the oportunity to come to terms with the situation more fully. Fool me once...



On the top staff of the above example, we can see where the "problem" arises. The circular transformation types strictly alternate between clockwise and counterclockwise, so in the lowest triadic voice the 5 becomes 1, then it becomes 5, and then it becomes 1 again: That voice never has the third of any of the triads. The other two voices above rise in a series of parallel sixths exchanging 3 and 5, and 1 and 3 respectively. Now, this means that only two of the voices can really be arranged as canonic (And that in a less than perfectly satisfactory manner), instead of all three. This is a situation similar to the one where the double canon arose in the tetradic texture with all crosswise transformations in association with a constant root bass that only moved progressively, but in this situation one of the voices must be the odd man out, it not being given an echo in the triadic texture. I chose the two upper voices that share the third to make this quasi-canon, but either one of the upper two voices could be used against the lowest voice if so desired. I managed to create a series of chromatically parallel sixths in the upper two voices to work with, so I chose them. I still don't have my brain 100% wrapped around this subject, which is why I will continue to post on it until I'm satisfied that I have it under control.

On the second staff, it can be seen that no similar problem arises in the tetradic texture. Here, all four voices get all four of the canonic elements, so an eight bar canonic voice is created that follows the leader at a two bar distance. Applying intervalic strictness to these diatonic frameworks will take us to some interesting places for both the triadic and the tetradic harmonic canons, as we shall see, but the seventh chords take us all the way around the musical universe.

On the third stave I have made the triadic canon strict and added secondary dominant triads to it, as per previous examples. Here, however, the tonic triad must be changed to the minor gender, and the more remote root progressions must be chromatically altered to keep the pattern going. This creates a very unusual effect where the sense of tonality is lost, but the sense of direction isn't. I like it very much, and without this experiment, I would not have thought of going this route. If we analyze it in detail, we can see that the root progression is a falling minor third followed by a rising perfect fourth. This works fine diatonically from C to A, and from D to B, but from E to C, a chromatic adjustment must be made to avoid the decending major third. If you look at the analysis, I am targeting a diminished triad on F-sharp with a secondary dominant sonority on C-sharp. "You can't do that", except for the fact that it sounds righteous in this context, of course.

I used the syncope device to get a weird canon of alternating major and minor sixths (Or augmented fifths) in the triadic "canon" on the third staff, and with the momentary minor major seventh chords, it sounds highly exotic. Though I failed to create a canon proper as I set out to in this part of this experiment, I sure learned a few things and came up with some completely unique and unexplored sonic effects through it. I don't mind at all when that happens.

The bottom two staves show the extracted tetradic harmonic canon with added secondary dominant sevenths and secondary dominant seventh diminished fifth sonorities. I had to keep the canon going for so long to give the final trailing voice the oportunity to present the entire canonic voice. Note that since all four voices share all four of the canonic elements, diminished tenths occur in between the augmented sixths. This actually sounds fine in this context, which surprised me, as in two voice counterpoint on solo guitar I have been squeemish about employing the diminished tenth octave displacement inversion. This would qualify as one of those things that makes ya go, "hmmmm". Note also that with the chromatic alterations to the constant root bass, it is now a twelve tone row that begins to repeat at the upper octave C before it is interrupted by the final cadential figure. Because of this excursion through all of the most remote regions fo the key, any sense of a tonic center is entirely forgotten, as I mentioned previously concerning the triadic example. Here, though, the listener really ends up lost in the Sahara! Overall, I find it to be a magnificent effect worthy of employment. Finally, I should have given another bar for the final cadence, as it sounds overly abrupt, but I was running out of space on the page, and photo hosting is expensive! (Yeah, that was a hint).