Thursday, November 10, 2011

Exemplar 6: Doctor of Able Polyphonists

You have to read this blog from the beginning to have any hope of, "getting it."

The highest level within the guild as I currently have it laid out is Doctor of Able Polyphonists, though a level of Professor between Honorable Grandmaster and Doctor is a possible addition. Whereas the three Master levels are of peers and there is no huge barrier to advance from Master to Esteemed Master and then Honorable Grandmaster, advancing to Doctor is different: Nothing but an epic contrapuntal work will do, it has to demonstrate profound mastery, and it has to have at least one unique aspect - preferably more.

The exemplar for this level is a Ricercare for solo guitar that has a lengthy story behind it. Back in 2005 I decided to transcribe the D Minor Organ Fugue that is usually attributed to J.S. Bach for solo guitar. In E Minor, it worked perfectly with the subject and answer using the open B and E strings as the played zero axes. Where I ran out of room was in the bass, as a seven string guitar with a low B would be needed to pull off the transcription really well. That's when it hit me: The D Minor Organ Fugue was originally a work for baroque lute - which had more courses than the guitar has strings - and Bach did not compose it. This is obvious to me because, 1) there is a parallel perfect fifth in the exposition and, 2) the countersubject - such as it is - just makes parallel thirds or sixths with the subject and answer: IOW, there is no counterpoint. I don't believe Bach would have done anything like this, but it is exactly what you would expect from a lute virtuoso with a shaky understanding of counterpoint.

In any event, the idea is a good one, but the execution was lame, so I decided to improve upon it. As I was thinking about how to do that, I noticed that an old Schillinger-inspired open-string study I had written back around 1987 had a melody and counterpoint that contained nothing but contrary and oblique motion: If there is nothing but contrary and oblique motion in a contrapuntal combination, then both voices can be doubled in parallel thirds or sixths, and all six resulting combinations will be technically correct (This is something I got from studying Sergi Taneiev's Convertible Counterpoint). So, this piece is the culmination of twenty years of working with Schillinger's axes of melody concepts, and Taneiev's vertical-shifting counterpoint techniques.

The answer and counter-answer in this piece are note-for-note exactly like the A section of that old study, with the exception of the sixteenth-note ornaments, so I actually added the subject statement before it to get the fugal part of the exposition. As for the version with both parts doubled in thirds, that full combination is saved for the recapitulation, and it only works in A major. This set the piece up as an epic struggle between minor and major with major winning out at the end.

Formally, the piece is a combination of both the fugal and the sonata processes: Basically, a monothematic sonata with a fugato as the opening theme.

There are also some unique modifications of the theme that owe their existence to the idiom of solo guitar: In order to modulate with relative freedom, I had to maintain the use of open strings, so the zero-axis of the subject and countersubject - the repeated notes - had to change function from perfect fifth to major or minor third and also the root of whatever the key of the moment was. This technique enabled me to create a gigantic piece of musical architecture, as you shall see, with constant variation of aspects of the thematic material, while keeping it all idiomatic to the guitar.

Here is the sound file:

Ricercare in E Minor

And the score with the required structural and thematic analysis, and commentary:

The subject is 7.25 measures in length, and the first zero-axis is the fifth of the key of the moment, so the open B string is employed. The answer is at the fourth above, and the zero-axis is still the fifth, so the open E string is employed there. Since the subject and answer create an antecedent-consequent phrase group that does not return to the original tonic, a release episode was needed. This first one stays in the secondary key of A minor. The first middle entries at 10, then, are still on the subdominant level, with the parts inverted, and the zero axis is still the fifth (And not an open string, so this is pretty difficult to execute). The final measure of the subject provides the motif for the sequential episodes, and the first one beginning at 27 modulates the piece to C major.

So then, for this C major statement, the open E string is employed as the zero-axis again, but now it is functioning as the major third of the key of the moment, versus the previous fifth. The resulting sequential episode is different, and this one does not modulate, it just shifts genders to C minor when I introduce E-flat in the last measure. This sets up an inverted statement in C minor in which the zero-axis is the fifth again, and the open G string is used for the first time. At 55 the sonata exposition is concluded with a different kind of episode that is heard only before fugal expositions: We'll hear a different version of it before the recapitulation. The counter-exposition at 61 is the first time since the beginning that the home key of E minor has appeared. This time the subject is as it was in the beginning, but there is a countersubject below and a drone on the open E string above.

The answer and counter-answer are also the same as before, but now there is a second counter-answer that effectively doubles the melodic trajectory of the answer in thirds. This is part of the progressive unveiling of the full combination. Release episode two is exactly the same as before, but it changes gender to A major at the end. The inverted statement at 80 is also the same with the exception of being now in the major mode. These additional sharps enable the following sequential episode to modulate to C-sharp minor, versus the previous C major. That means the final statement on the page at 94 is in C-sharp minor, with the open E string now functioning as the minor third of the key of the moment.

Sequential episode four then modulates to A major. Up to this point, everything in the counter-exposition has had a parallel precursor in the exposition, but at 107 a new element is introduced with the first of four interludes. This one is based on a rising chromatic line in the bass, and it is unique to the counter-exposition. After this much needed nineteen measure break from the primary thematic material, and inverted statement in C major appears at 126. This is like the previous statement in this configuration that was in C minor, but now the counter-answer is doubled in thirds.

These thirds lead to another unique version of the sequential episode that modulates to A major for a statement of the answer with the counter-answer again doubled in thirds, but this time in the original orientation. Release episode three is then like the previous two, but now it is in the major mode, and it turns around in the last measure to introduce the first of the melodic inversions of the subject at 152. When an inverted form is used in the bass, only the root will work as the zero axis, which is the open A string here. This results in a particularly gnarly sequential episode that modulates to E minor for the start of the development.

I begin the development section with an E minor statement of the answer for the first time - which is over an open low E-string pedal point - and this leads to a new inverted form of the release episode that modulates to A minor. That A minor statement of the answer has the melodic trajectory doubled in thirds by counter-answer two, and it is over an alternating tonic-dominant pedal which leads to what seems like it should be a regular release episode: That doesn't come to pass. Instead, there is a very surprising modulation to G major at the end. The G major statement is therefore an entirely new key, and having the open B string as the major third of the momentary key is therefore also a first.

Sequential episode seven - related to the rest, but unique, as they all are - then modulates to E minor for the second interlude. The interlude is marked 2A because there is a counter-development in this piece, and so there is a second version of this later. At 217 the answer statement in E minor uses the open G string as the minor third zero axis for the first time: In the counter-development, this will be in E-flat major. Sequential episode eight is very dramatic, and it moves the piece to E major for the counter-development.

The counter-development begins in the parallel mode of E major, and it contains counter-answer two as well this time. The answer at 242 is very ballsy, with the answer, counter-answer one, counter-answer two, and an alternating pedal in the bass. Release episode seven is like the corresponding previous version, but the surprise modulation is now to G-sharp minor. At G-sharp minor, the open B-string is now the minor third of the momentary key.

Sequential episode nine is a parallel to its antecedent, but with many more sharps to shed on the way to E minor, it is much more interesting. Interlude 2B is the same as the previous version until the last measure, where I use the sixteenth-note run to make a very fast and cool modulation to E-flat major. With the E-flat major statement, all parallels have been worked through, and the counter-development then concludes with the second of the sectional conclusion episodes. This one modulates to E major for the recapitulation.

This recapitulation is what I composed first. The subject statement has - top to bottom - a drone on the high E-string, the subject in E major, counter-subject two doubling the melodic trajectory in thirds, and then counter-subject one in the bass. Then the answer statement has - again, top to bottom - the answer in A major, counter-answer two doubling the trajectory of the answer in thirds, and then counter-answer one doubled in thirds in the bass. Release episode eight then modulates the piece to E minor for the melodically inverted statement with the low E-string as the zero-axis root. Basically, the major modes have just demonstrated their superiority by playing the full contrapuntal combinations, and E minor has a tantrum over it. The inverted release episode nine, then, does not modulate.

The subject statement in E major now has the zero axis as the root - the first time for that in a rectus statement - and that unique arrangement leads to a concluding episode at 331. In the drama that is unfolding, E minor is attempting to hijack the piece and end it early. E major interjects at the last possible eighth-note with an inverted statement of its own, proving again that the major mode handles the thematic material in a superior way. Release episode ten is a parallel with the previous version, but now in major.

The key of E major is also better with the rectus statement, and that leads to the final interlude. Whereas before all of the interludes had ascending chromatic bass lines in them, this last one has a descending chromatic bass, as is fitting near the conclusion. That final interlude then leads to the concluding episode, which is the same as before, with one exception: The bass notes in the final measures are now mi, re, do instead of the previous me, re, do: This is the final struggle between major and minor.

The minor mode finally gives up for good at 385, where everything becomes diatonic to major. That leads to the final thematic statement in the coda: The trajectory of the subject and primary countersubject in augmentation harmonized for six voices (Five voices in the fifth and sixth measures). An utterly triumphant ending (There will be some sort of finger-strumming figure there to end with dramatic flair).

If this epic fugue does not absolutely rock your world, there is only one explanation: You have no ability to understand the intricacies of fugue or even to properly listen to counterpoint. This is the greatest fugue ever composed for solo guitar, and the most high tech and mechanically efficient fugue ever composed by anybody.

As usual, if you disagree, you are welcome to prove it, but prove it you must.

Monday, November 7, 2011

Exemplar 5: Honorable Grandmaster

As rank increases within the guild structure, so does status: Masters admit apprentices and promote them to journeymen, and esteemed masters promote journeymen to master, while honorable grandmasters promote masters to the esteemed level. Tutoring follows the same pattern, but that starts with journeymen, who tutor apprentices.

Since the three master ranks are not separated by barriers that are too formidable, they are considered peers at different stages of development. In that spirit, the pieces for esteemed master and honorable grandmaster do not have to be so stuffy as the four-voice fugue needed to attain the rank of master. They must display mastery and have a unique or unusual element to them, but submitting pieces on this level is more like a formality than a true barrier: The Best of Ten contest is the motivator toward excellence.

For Honorable Grandmaster then, the entrance fee/first year's dues are $20.00, and the Best of Ten award is $100.00. As with every guild level, there is a one year eligibility requirement: As soon as the second year's worth of dues are paid, the Esteemed Master is then eligible to apply for Honorable Grandmaster. Also per usual, the dues may be paid early if the applicant wishes to advance before the year is up. The point of honor is that everyone pays their dues to advance.

J.S. Bach was addicted to canon - poor schlub - but I had only used canon technique to compose fugue subjects... until this piece "happened." The subtitle could well be, "A Funny Thing Happened on the Way to the Fugue." After composing the string quartet fugue that is Exemplar 3 - it has a five-measure subject that works in four-part canon at the octave - I realized that a five-measure subject that worked in five-part canon at the octave was possible. Even cooler, this would take up all five octaves of the string choir, so my plan was to compose a five-voice fugue for orchestra. I never got that far. What eventually emerged - after working with this subject for a few years - was a five-voice perpetual canon for string choir.

Here is the sound file:

Five-Voice Perpetual Canon

And the score with the required commentary:

I began by composing the opening five-measure fugue subject in five-voice canon back in the early oughts - 2002 or 2003 I think - and that's how it sat for about three years as I tried to get a fugue off the ground, which never happened. Then one evening I was looking at the stretto - because that's all it was to me at the time: A canonic stretto - and I noticed that the first two measures of the subject in augmentation made a dovetail out of it.

That discovery got me to measure 9 of the lead part - violin 1 - but then I was stuck again. What I was attempting then was to continue with the entire subject in augmentation, but that didn't work. What did end up working was to take the third measure of the subject and change it to diatonic notes, and then the fourth measure became... do, ti. What I thought I had done was to take two versions of the subject and combine them into a single stretto - something I call a musical Escher morph. Then I noticed that the original subject would dovetail out of the augmented and modified form, as you see beginning in measure fourteen.

Already having achieved the original dovetail, I had it in the bag at this point, with only a conclusion yet to compose. Note the outrageously dissonant harmonies that occupy the first half of the measures with the augmented form: These are inversions of the major seventh chord on bVI that have the root above the major seventh, creating a minor ninth interval. This is something that really needs five voices to work well, which is why you almost never hear these inversions used. It gives the piece a very sinister air.

By using the tail of the subject as an ostinato in the bass, I was able to wind the piece down very organically. If you've been paying attention, you will have noticed that the subject contains eleven of the twelve pitch classes. By playfully seeming to end on a tierce de Picardie, I was able to conclude with the final descending chromatic triplet figure, which contains as its penultimate note B-flat, which is the heretofore missing pitch class.

One of the other honors Masters have is that they can chose new exemplars from among the Best of Ten winners for the levels of apprentice and journeyman. Esteemed Masters can chose a new exemplar for Master, and Honorable Grandmasters chose the Esteemed Master exemplar. This amounts to a new contest level, and the composers of newly chosen exemplars will receive an additional award commensurate with the level of the piece ($10.00 for an apprentice exemplar, $25.00 for a journeyman exemplar, &c.).

So, if you think you can improve on my exemplars, prove it.

The highest rank within the guild is Doctor of Able Polyphonists, which will be the next exemplar.

Sunday, November 6, 2011

Exemplar 4: Esteemed Master

Best to read the blog from the beginning, but everybody must start out as an apprentice.

While a Journeyman has the responsibility to make himself available to apprentices for tutoring, the level of Master is the first fully vested level within the guild: Masters vote on selecting apprentices and promoting them to Journeyman. Masters are also the tutors of Journeyman. Yet, to sustain the competition - and therefore promote polyphony - two additional levels within the Master rank exist: Esteemed Master and Honorable Grandmaster.

Getting to Master is passing a huge barrier, as the required masterpiece - a four-part fugue - is a very serious undertaking. Once that leap to Master has been made, the now-fully-vested guild member has standing. This means that there is now a lot of flexibility as to what type of piece is acceptable for the rank of Esteemed Master: There is no requirement for number of voices, the piece does not have to be a fugue, and there is no length requirement either. What the piece does have to demonstrate is mastery, and it should have an aspect of uniqueness too. The entry fee/first year dues for the level of Esteemed Master is $15.00, and the Best of Ten winner will be awarded the usual 50% of entry fees, or $75.00 (The peer pressure involved in the competition is one of the factors driving quality at this level).

Since I love fugue writing more than any other musical endeavor, I chose a three-voice fugue I wrote for wind trio as the exemplar for this level. The unique aspect of this piece is that the four-measure subject is a twelve-tone row. I wrote this for a graduate level Twentieth Century Counterpoint class when I was a doctoral candidate at UNT, so this should be no problem for someone who has mastered four-part fugue to emulate.

Here is the sound file:

Fugue on a Serial Subject

And here is the score with required commentary:

This four-measure fugue subject is a twelve-tone row. To preserve that, the answer at the fifth above is real. Beginning with the third entry, two countersubject/counter-answer lines are revealed. The cumulative rhythm that the parts make is straight eighth-notes on the surface. This makes countersubject two - the flute part - sound like it is in 6/8 instead of 3/4.

The first episode does not modulate, and at the first middle entries starting in measure 16 a constant eighth-note variation of countersubject 1 is revealed. Then, the second episode modulates to the level of the answer, or the dominant region. The completely chromatic nature of the subject/answer lead to some very colorful episodic passages.

Since the subject only makes one real stretto, which will be revealed at the end of the piece, the middle entries are occupied with displaying all of the possible inversions of the subject and countersubjects. The episodes, though all different to a greater or lesser degree, simply modulate back and forth between the tonic and dominant levels while these possibilities are being worked out.

There is an inversion involving countersubject 1a at 37, and then back to the tonic.

At 44 I subjected the theme to intervallic expansion, and then episode six lines everything up for the concluding stretto, which is between the subject and the real answer an eleventh below: Two twelve-tone rows a fifth apart in canon at a single measure of delay. Musically speaking then, this fugue subject is objectively the most superior tone row ever created, as it has intrinsic musical value, unlike the garbage created by Schoenberg et al.

There is one last partial stretto at measure 55, with the head of the subject against the tail of the answer. This creates a nice augmented sixth on the last sixteenth-note, which leads to a sequence of the tail of the answer and another augmented sixth at the last sixteenth-note of measure 56. I then invert the figure in measure 57, and so I end with completely unique accompaniment for the subject. Note also the eight descending chromatic notes in sequence in the clarinet part.

Since this piece was my pie-in-the-face tribute to serial composition, I even ended it with a tierce de Picardie.

As usual, if you think you can meet or beat this, well, money talks and BS walks.

Thursday, November 3, 2011

Exemplar 3: The Masterpiece

To enter the guild, everybody must start with an Apprentice Piece, and to reach this level a Journeyman Piece must be accepted. After being a Journeyman for a year, the guild member is then eligible to submit a Masterpiece as soon as the second year's worth of Journeyman dues are paid. If the member wishes to proceed to Master early, that is not a problem: Just submit the second year's worth of dues early: Everybody pays the same dues to advance within the guild.

The application fee for Master is $10.00, and the applicant is expected to get it right on the first try. If accepted, that ten dollars covers the first year of master's dues. All accepted masterpieces are entered into the Best of Ten Masterpieces contest, which pays an award of $50.00 (Half of the total application fees, as with every other level within the guild).

While the apprentice piece and journeyman piece exemplars were of modest dimensions - between thirty and forty measures of music - the masterpiece will have to be a four-voice fugue of significant dimensions - say, between 50 and 100 measures. It may be for solo guitar - that, I would like to see - solo keyboard, vocal choir, string quartet, as this example is, or wind quartet. The reason for limiting the potential ensembles is to facilitate recordings of the Best of Ten winners for guild compilations, which will be one of the primary guild benefits.

I composed this fugue for a graduate level Invertible Counterpoint and Fugue class when I was a doctoral candidate at UNT, so this should be a reasonable model for an advanced polyphonist to emulate. It is an approximation of Bach's late Musical Offering and Art of Fugue style, but earlier styles - even modal - are acceptable (This is why there is no requirement for harmonic analysis). Please note, however, that the submission should be a clean urtext score free of dynamics, fingering indicators, &c. Only the analysis points should be included.

Here is the sound file:

Fugue in F Minor

And here is the score with the required commentary:

The basis of this fugue is a five-measure subject that works as a four-voice canon at the octave and with one measure entrance delays. At measure six the answer begins, and it is tonal. Accompaniment parts are free: There is no countersubject or counter-answer per se, but the motives used reflect my preoccupation with fractal compositional strategies at the time.

Only the original statement of the subject is not in stretto, as one measure dovetails begin at measure ten. The figure labeled as Thematic Trill is an important motif that reaches two different fulfillments during the course of the fugue. At measure 14 the answer begins with its one measure dovetail with the subject.

The first episode begins at 19, it does not modulate, and it is based on a sequence of the thematic trill.

At 23 the first middle entries begin, and they demonstrate a stretto at three measures of delay, or two measures of overlap.

The second episode that begins at 31 modulates the piece to the dominant level.

The middle entries on the dominant (Should be labelled second, not third) display a stretto at two measures of delay, or three measures of overlap, so the main organizational strategy for the fugue is ever closer stretti.

The third episode which begins at 43 is based on a diminished form of the subject with a modified tail over a descending chromatic tetrachord. This modulates the fugue to the relative major. The middle entries there then present a stretto at a single measure of delay, or four measures of overlap.

During this closest two-voice stretto, the pitch climax occurs at the end of measure 48. Then, at 51, the fourth episode begins, which takes the piece to the subdominant region. It is based on a sequence of the thematic trill, as the first episode was.

The fourth middle entries comprise a false recapitulation which has the inverted form of the subject as the answer. Even here I was able to present a single measure dovetail.

The return to the tonic level begins in measure 64, and the episode is built on a rising chromatic line.

The thematic trill reaches the first of its fulfillments above the drawn out half cadence which prepares the true recapitulation.

At 71 the recapitulation begins, which is a four-part canonic stretto at the octave and one measure of delay: This is a true recapitulation because it is every stretto demonstrated previously combined into one. The thematic trill figure reaches its second fulfillment here as a sixth measure to the canon.

Since there is more to come, the four-part canon ends with an unconvincing cadence at 80-81, and then the pickup into the coda. The coda is a three-part hyper-stretto that has the subject, its inversion, and its augmentation beginning simultaneously.

The piece concludes with a perfect authentic cadence and a picardy third.

I don't expect any masterpiece submissions to be, "this good." In fact, I seriously doubt that there is anybody currently living who can best this fugue. Sadly, even ivy league music departments have been so overrun with post-modernist, no-talent, know-nothings, that I don't even think anybody at Harvard or Yale could touch this today. Don't get me started on the conservatories: They just teach kids how to acceptably execute dead-guy music, so conservatories are dead themselves, and have been for decades.

If you think I'm wrong about that, you'll have to belly up to the bar and prove it.

The level of Master is not the end though. It is, however, the end of the beginning of becoming a competent composer with objectively demonstrable technical skills, and it is the beginning of the end of having to justify yourself to other composers or guild members.

In coming posts, I'll provide exemplars for Esteemed Master and Honorable Grandmaster.

Wednesday, November 2, 2011

Exemplar 2: Journeyman Piece

The only way to enter the guild is with an Apprentice Piece, so you'll have to begin there. This exemplar is for the next level of Journeyman.

In order to be eligible for the level of Journeyman, a guild member will have to be accepted as an Apprentice first, and then be an Apprentice for a year. Once the second year's worth of dues are paid, the Apprentice is then eligible to apply for the level of Journeyman. If an Apprentice wishes to progress to this level early, that is fine: The second year's worth of dues - only $2.00 in the case of Apprentices - can be paid early. This guild is a level playing field, and everybody will have to pay the same dues.

The Journeyman Piece shall be a three-voice work of modest dimensions that displays fluency with counterpoint. It may be for solo guitar, solo keyboard, vocal trio, string trio, as this piece is, or wind trio. The application fee will be $5.00, and the applicant has two tries to get it right before another $5.00 will have to be paid. If the applicant is accepted, the $5.00 covers one year's worth of dues. Accepted Journeyman will also have their pieces entered in a Best of Ten contest, which pays an award of $25.00. The reason for limiting instruments and ensembles is to make recording guild compilation albums easier and more efficient.

The application must consist of a PDF file of the score, a MIDI file of the music, and the $5.00 application fee, which must be paid via PayPal. All submitted materials become the property of the guild, which simply means the guild can post them and record them if they become Best of Ten winners. The composer is otherwise free to do with them as he wishes.

This piece is a lament for my late father in the form of a three-part invention that I composed when I was a master's candidate, so it should be no problem for an experienced student of counterpoint to emulate. The Journeyman Piece does not have to be fugal or imitative though.

Here is the sound file:

Three-Part Invention in D minor

And, here is the score with a brief commentary:

This three-part invention is based on a subject that begins on the mediant of the key, instead of the tonic or dominant. That is why it begins with accompaniment: To properly define the key at the beginning. The answer is in inversion and on the subdominant level, with the third entry being the subject again in a higher octave. Note that from the G-natural in the fourth measure of the viola part to the second thirty-second note of measure six, that all twelve notes of the chromatic scale appear in descending order.

The first episode starts at measure seven; it is a sequence of the head of the subject, and it modulates to the relative major.

The first middle entries are in F major, and this variant of the subject starts on the tonic instead of the mediant. The second sequential episode based on the head of the subject begins in measure 14, and it uses the inverted form of the head as well. The dominant level of A minor is reached at 17, and that middle entry demonstrates the invertibility of the counterpoint while reaching the melodic peak of the piece in 18.

Invertibility of the parts is again demonstrated at 19, and the third episode begins at 21. This modulates the piece to the subdominant level of G minor - where another melodic inversion of the parts is presented - and this then allows for a direct modulation back to the tonic at 26, where the stretto section begins.

After the stretti are concluded, there is a short codetta to end the piece.

Unlike with the Apprentice piece, where the music must speak for itself, a brief description of the Journeyman Piece will be required, as I have provided above. Remember that, at first, I will be analyzing and judging these, so the description will aid in that work (Later, when there is a quorum of Masters - three - they will do the judging of Apprentice and Journeyman Pieces).

In the spirit of gentlemanly competition, if you think you can compose counterpoint this well, you'll have to prove it. A guild requires members to put up, or shut up.