Feb. 21, 2017

Ten Steps

We observe that people solve crossword puzzles the quickest and most productive way by first getting the big picture, i.e. working the entire puzzle at the same time and filling in the easiest parts first [See blog, Getting Started With Writing, Part XVIII].
This seems to work better than by starting in one corner of the puzzle and working laboriously across to the other side one tedious square at a time, disregarding any clues the surrounding parts of the puzzle might lend.
In like manner, the quickest and most productive stance to take for solving the puzzle of writing a fugue is to adopt the same approach by working the whole score at the same time rather than starting with the 1st measure of music and finishing with the last one [See blog, Getting Started With Writing, Part IX].
The metaphor of comparing fugue writing to working a crossword puzzle is an entirely valid one; working the squares across is akin to developing horizontal melodic lines within a given harmonic framework; working the squares up and down is akin to the vertical harmonies created by the horizontal moving lines as they intersect each other in time.
Zooming out a little bit from there, the various "chunks" of the crossword puzzle also are akin to the various entries in the fugue; the squares in the puzzle where these chunks join with each other are akin to the material which connects the fugal entries.
The subject is the melodic statement from which the whole fugue is developed, and is therefore its most important feature; just like a seed, it contains within itself an invisible instruction on what to become.
Not every interesting melody makes a good fugue subject.
Read that again.
Every well written fugue will have a good subject; no good fugue with a poor subject was ever written, nor shall be; it's no accident that the glorious organ fugues of J.S. Bach all have well thought out subjects.
A shorter subject in terms of length may present a single figure; a longer one always subdivides into members which are duplicated by sequence [See blog, Sequencing] or by repetition, either simply or with variation.
Tonally speaking, variety and contrast are desirable in a fugue; Bach preferred non-modulating subjects for a very good reason, viz., to confine the exposition to tonic/dominant keys, giving a sense of harmonic repose; any new keys he introduced after that provided the contrast which would be lost if there had already been much modulation, or change of tonality, in the subject itself; he knew very well that if the available tonal forces for variety and contrast are brought out too soon in a fugue subject they would lose their effect in later developments.
The exception to this is the fugue which starts on scale degree 3; in this case the "tail" of the subject (i.e., its final note, couple of notes, or last few notes) MUST point strongly to the dominant key.
Those theorists who teach and maintain that fugues do not start on scale degree 3 are promoting something factually inaccurate and are laboring under a serious misconception (for proof of this, see the Fugues in the scores of Op. 19, 27, and 29).
Concerning rhythm (note values), a good fugue subject could have uniform rhythm throughout, slight rhythmic changes, or several different rhythmic groupings, but the combination of outline and rhythm are what give to a melody its identity.
Rising and falling curves are found in endless variety in music, and rhythmic patterns have innumerable possibilities; with the 2 working together, the melodic interest culminates.
Therefore, IF we've got a fugue subject that's good in terms of length, tonality (key), rhythm, and melodic curve -- those qualities which lend it character and make it capable of contrapuntal elaboration -- and IF we know in the exposition where the answer should follow (See blog, Getting Started With Writing, Part XX, there are rules for this] -- and IF we've got a logical plan in mind for the voice combinations in the various entries ... THEN we've got a fugue.
Technically, a fugue doesn't HAVE to have a countersubject, but the majority of fugues do; this is another moving line which, in combination with the subject, complements it tonally and rhythmically and makes a satisfying melody all by itself.
We prepare ourselves for this by studying some of the best examples that have been left to us, beginning with the strongest fugue writer in history; the fugues from the "the 48" (Well-Tempered Clavier, Parts I and II) of J.S. Bach and all of his glorious organ fugues should be consulted; we should also get ourselves well informed in harmony, counterpoint, the rules of voice leading, the general rules of fugue writing, along with reading Steven Pressfield's book, "The War of Art" [See blog, The Book, Parts I].
ALL of this is important.
Critically important.
The process of fugue writing for the organ successfully practiced by this author can be summarized in Ten Steps (photo) which, as they're carried out, may be permitted to overlap to some extent.
We need to get for ourselves a notebook PC and either download some music writing software to it (such as Finale or Sibelius) or sign up with an on line music writing application (such as Noteflight) if we haven't already, make sure we're set up to write with a blank score [See blog, Getting Started With Writing, Part V], click as many measures as we think we'll need, add an upper and lower voice to the upper staff, then we're ready to begin the exposition.
This is how it's done:
STEP ONE: The first move we make in writing a fugue is to invent a subject (theme) in the tonic (home) key; in general, the longer the subject is, and the more varied it may be rhythmically, the more its material can be worked later on, in the episodes.
The subject should be examined carefully with an eye for this, and for contrapuntal elaboration, including stretto (overlapping of entries before the first entry finishes).
One of the best ways to engineer a stretto into a subject is to shape it so that it follows an implied tonic-dominant harmony with every other bar (or half bar).
In other words, in the 1st bar (or half bar) we make the first few notes outline or follow a imagined tonic harmony, then in the 2nd bar (or half bar) we shape its outline to follow an imagined dominant harmony, then in the 3rd bar (or half bar) we make the notes different but able to blend harmonically with the notes in the 1st bar, then in the 4th bar we make the notes different again but able to blend harmonically with the notes in the 2nd bar, and so on.
This method leads to a possible stretto (which is nothing more than an octave canon) at a distance of one bar (or half bar).
By the time we get done with this "sculpting" of the subject, we might think the pile was scraped off the velvet and leaves us with a subject that's a bit drab, maybe even mundane, and might be boring for the listener to endure, but this is precisely what makes it workable.
The subject for Bach's Art of Fugue [See blog, Getting Started With Writing, Part XIX] is short, little more than a bare outline of the tonic chord in slow notes, with a little tail in quicker notes attached; it's without color, without light, and anything but striking, but, just like the most common lump of clay, he knew that such a substance could be molded and worked in every possible contrapuntal direction; the result, at his hand, was an hour and 10 minutes of some of the most beautifully intricate music ever written.
Taking a page from this, composers have created some of the best fugue subjects by making its "head" (first few notes) begin in slower note values or maybe a dotted rhythm, then having it pick up speed with shorter note values in its middle and tail.
The subject is then repeated, usually in the dominant key (or, sometimes, in the tonic or subdominant), which is called the "answer" and is subject to certain "rules" with which we should be familiar before proceeding any further [See blog, Getting Started With Writing, Part XX].
The chief secret to getting a solid toe hold to begin writing a 4 voice fugue, once we've settled on a workable subject, is to examine its tessitura (range) and bear in mind the highest and lowest scale degrees of its melodic curve; we then compare that with the 4 normal voice ranges (soprano, alto, tenor, bass) and imagine placing the subject as close to the middle of these voice ranges as possible during the various entries in the exposition (usually the bass is last to enter, but not always, not 100 per cent of the time); once we determine what the best starting note would be, in order that the entering subject will not exceed any normal voice range as it plays out, then we'll have a good tonic note in view.
All that remains then is to decide major or minor to determine the key signature, we can mark our blank score accordingly, and then get busy filling in the subject in each voice where it is to enter.
We cannot simply pick a key signature out of thin air and begin writing the exposition without giving some thought to the subject's range and how it dovetails with the ordering of entries being planned for the exposition or we risk having to start all over again.
By following this method, since the normal voice ranges are fixed, the melodic curve of the subject and its range will suggest a good, if not the best, tonic note and key, whether major or minor.
STEP TWO: is to write a contrapuntal line which sounds in harmony with the answer; when this line is reproduced against the subject and answer at many, if not all, of its subsequent appearances in the course of the fugue, it's called a countersubject.
This countersubject should generally move in contrary motion to the answer and in faster notes whenever the notes in the answer are slower or stationary; it may (but doesn't have to) have slower notes against faster notes in the subject.
When the answer and countersubject are put together, the result should be good implied harmony in mostly contrary or oblique motion and perpetual 8th note or 16th note motion (there are exceptions to this, for good and sufficient reason, where both subject and countersubject may move briefly in quicker notes in similar motion, usually to create a sense of excitement).
If either of these 2 moving lines (subject and countersubject) can serve as a bass for the other, then the music is being written in double (invertible) counterpoint.
This is crucial, to have these 2 lines well thought out, but, we sometimes have to come back later on, after we've worked an entry or two, and "tweak" (change a note or two) something in the answer or countersubject(s).
Why is this? ... there can be many reasons, one of which is that the music needs to remain within one key and not wander away from it.
One of the principle rules of harmony forbids consecutive perfect 5ths, octaves, or unisons in similar motion, but sometimes we find them cropping up unintentionally right in the middle of our writing which wasn't noticed earlier; we're human; things like this can be overlooked; this necessitates fixing that passage to eliminate the mistake and then going back through all preceding passages and making the same change in the subject or countersubject all the way through, for the sake of consistency.
If in the construction of a certain entry we're finding that one of the lines can't be squeezed into the space planned for it, then we put it in a different voice and move the displaced voice somewhere else; it doesn't mean that there's something wrong with our subject or countersubject(s), that they need to be resculpted or, worse, the entire piece abandoned; it means nothing of the kind; we just fix it and move on, easy peasy neat 'n squeezy.
Sometimes we have to change a note or two in the answer to get it to work in the home key; if something in the answer is changed tonally to keep it in the home key, it's called a "tonal" answer and the fugue is a "tonal fugue"; if the answer is an exact transposition of the subject in the dominant (or subdominant) key, note for note, then it's called a "real" answer and the fugue is a "real fugue."
This is why working from a notebook PC with online music writing software can be such a time saver; changes like this can be made quickly and easily without crossing things out or maybe trashing the entire copy and starting over.
STEP THREE: is to write a 3rd line; this must return to the home key and blend in harmony with the subject and countersubject; if this 3rd line can be maintained throughout each successive entry of the subject, then it becomes a 2nd countersubject, the original one becomes the 1st countersubject; if any of these 3 moving lines can serve as a bass for the other 2, then the music is being worked in triple counterpoint.
As the voices of our fugue enter, one by one, it's easy to see that our mind can quickly get boggled trying to coordinate all this complexity unless we work from a predetermined written plan.
We can keep things straight here by working the whole exposition at the same time, like a "chunk" of a crossword puzzle, by first placing the subject in whatever voice we want it to enter in the exposition; we can then come back and enter the countersubject(s), one at a time.
After deciding on the order of voices in the exposition, the expected plan would be for each voice to commence immediately after the conclusion of its statement by its predecessor; but here were very often find that, instead of this arrangement, there is inserted an additional passage (called a codetta, interlude, link, or bridge).
This bridge could be merely one or more measures used as a connection, or it could be extended into a significant statement; this is very commonly encountered after the 2nd voice has given the answer, and its function is to bring about a smooth return to the home key for the 3rd entry.
STEP FOUR: is to write the entrance of the subject again in the remaining 4th line of the exposition; if the fugue is in 4 voices, then this line will enter after the 3rd line while the other 3 lines go one to play the 1st and 2nd countersubjects and a free voice.
If this 4th free voice can be maintained throughout each successive entry, then it becomes a 3rd countersubject, and the music is being written in quadruple counterpoint.
It isn't always necessary to insert another codetta to link the 3rd and 4th entries, although composers sometimes do.
Don't be surprised if, while you're building the 3rd or 4th entries in the exposition, that you encounter something that isn't making good vertical harmony; this situation crops up all the time, and it may require you to go back and change something in the subject or 1st countersubject to get everything to sound in consonant harmony; it may even be necessary to completely rewrite one of the lines.
Whenever making these changes, the end product should be a moving line that makes a good melody all by itself, times four; this is the secret, if "secret" it may be called, to getting the entire exposition to sound well.
If we're writing in triple or quadruple counterpoint, it will help to keep the range of each voice within the span of a 6th or 7th, if possible; the more narrow the range between highest and lowest note, the better chance we have of avoiding voice collisions and crossings when the lines are brought together in their various combinations.
Expecting (and having) to edit and adjust the exposition when constructing it, where it doesn't come out perfectly on the first try, does not mean the writing is defective; on the contrary, it simply goes with the territory, and ALL who write fugues are subject to it.
This exposition will then typically end with a full cadence in a related key, usually the relative.
One way to construct a smooth pedal line to transition from the 4th entry to the relative key is to have a look at what's going on in the bass a couple of measures before that, invert that figure, and finish it with an octave leap on the dominant note of the relative key using whatever accidentals are necessary to land on the new tonic.
At this point it helps, and is in fact necessary, to print a hard copy of this 4th entry in the exposition, where all 4 lines sound together; we will refer back to it when it comes time to enter the subject and countersubjects in the remaining entries and to figure the inverse of the subject and countersubjects for possible use in the episodes or coda.
STEP FIVE: is to work out on a separate sheet of paper how many additional entries there will be, in which keys, and the order of voice leading for each (the positions of the subject, countersubjects, and free voice) so that duplications might be strictly limited, if not avoided; this sheet of paper will be consulted frequently as work progresses.
We do this by listing the entries by name (1st entry, 2nd entry, 3rd entry) in a vertical column on the left margin of the page, top to bottom, spaced a little apart; we then move to the right of each and list another vertical column for each with the letters "S, A, T, B" for the 4 voices, with each letter followed by a dash.
If we're writing in triple counterpoint we then abbreviate the subject (theme), countersubjects, and free voice with "Th, 1CS, 2CS, F" and add them after the dashes in the order we'd like to arrange them in the various entries.
If the free voice is maintained throughout, where it could also serve as a bass for the others, then we're writing in quadruple counterpoint with a 3rd countersubject which may be abbreviated "3CS."
Now we have a specification on paper of where we're wanting to go with this fugue of ours, and it will keep things straight as we proceed.
As soon as we have this figured out we expand our working screen to accommodate the number of measures it will take, then mark off with double bar lines the various entries and episodes which separate them; this is so we can find them quickly while scrolling down (these double bar lines are changed back to single bar lines during the final editing).
Now then, by labeling these blank segments with the words "1st entry D Major, episode, 2nd entry b minor, episode, 3rd entry A Major, episode" etc., these segments may be easily located when scrolling up or down the screen; these labels are deleted upon final editing.
There's no rule which prohibits interpolating another bridge, more or less prolonged, in the exposition between the entrance of the 3rd and 4th voices (Op. 10 is an example);
There's no rule which prohibits interpolating a redundant (5th) entry in the exposition (Op. 18 is an example);
There's no rule which prohibits building an entry on the inversion of the subject and countersubjects, simultaneously (Op. 13 is an example);
There's no rule which prohibits the last voice in the exposition from entering in the relative key (Op. 11 is an example);
There's no rule which prohibits 2 or more consecutive entries in an exposition from entering one by one in the home key (Op. 11 is an example);
There's no rule which prohibits starting the subject on scale degree 3 provided the tail of the subject points strongly to the dominant key (Op. 19, 27, 29, and 30 are examples);
There's no rule which prohibits building an exposition by means of these or any other bold moves, as long as they're made with good reason, the general rules of part writing are observed, and the result sounds smooth to the ear [See menu bar, Free Stuff].
Doing what's unexpected like this changes the musical landscape from common to uncommon and is the way the boundaries of art have been extended and music has been permitted to grow and develop for thousands of years [See blog, Do The Unexpected, Poetic License].
From here on the remaining steps may overlap some, depending on what captures our working attention at the moment.
STEP SIX: is to fill in the subject and countersubject lines in all the remaining entries, leaving the 4th free voice blank for now; this work proceeds quickly.
Before moving to the next step this would be the time to carefully check the score for voice crossings or consecutive 5ths or octaves between the moving lines in their various configurations and make the necessary corrections; this may require the tweaking of a note or two in the subject itself, which will then make it necessary to backtrack and do the same for each entry, to get the outline of the subject consistent.
When we take an entry into the minor key the lines always move with the melodic minor scale, i.e. the 6th scale degree is raised a half step when ascending and follows the key signature when descending; not observing this will result in some ugly harmonies on playback and serve as a reminder.
If it happens, according to the plan on paper, that 2 of the lines in a certain entry which start on the same scale degree will have to start on the very same note, then they cannot be adjacent voices (collisions and voice crossings will result); in this situation they will have to be separated so they start an octave apart, OR (more likely) all the lines in this entry will need to be reshuffled; while this is a relatively common occurrence, it is however easily fixed.
STEP SEVEN: if we're writing in triple counterpoint we now go back and fill in all the free (4th) voices in the various entries; we don't just pick notes out of thin air to make a 4-note chord with each moving note; instead we make this 4th line just as singable as the other 3 lines; this is the "secret," if there is one, to get the music to sound with an easy, flowing beauty.
If there isn't sufficient space at some point to squeeze another note between 2 others, we adopt one of the notes already on the page as the note for the free voice and resume the line a beat or 2 later when there's enough room; 2 different lines may share the same note momentarily, if necessary.
If we're writing in quadruple counterpoint we've already filled in the 3rd countersubjects in each entry, and this step will be skipped.
STEP EIGHT: is to create a stretto, if there is one, immediately following the last entry by starting the subject in one voice then starting it again in another before the first voice can finish; we start it again at the same distance so that the voices create some excitement as they accumulate and "pile up."
If we find, after we begin what looks like a promising stretto, that after the 3rd or 4th bar the harmony isn't working, we don't have to throw it away; we can still continue the passage in imitation which will lend a certain excitement leading into the coda (Op. 29 is an example).
There should be no falling off of energy level in this stretto section by allowing the polyphony to suddenly dwindle down to one voice; it's better, when the subject first enters in stretto, to have 2 more moving lines moving with it in trio texture; these 2 additional lines can be freely invented or countersubjects can be used, which we already know will blend well in combination; when the moment comes these countersubjects can then cease as they take over the subject.
The stretto, when present, is usually followed by the final entry and a coda employing something original; one way to avoid a mundane or cliche ending is by using the secondary theme or countersubjects as working material, which are unique for each work (this author's Op. 4, 7, and 31 are examples); at other times simply the rhythm of the head of the subject might suffice (this author's Op. 22 is an example); in any case, the coda should connect in some way with what has come before it.
We have it on authority of the strongest fugue writer in history that a good fugue doesn't have to have a stretto -- some of the finest fugues of J.S. Bach have no stretto at all; if a subject doesn't lend itself to stretto, it doesn't mean that it's weak or defective by any means; we just skip this step and move on.
STEP NINE: is to connect all of these separate "chunks" of entries with short modulating episodes; these can be of any length, but 4 or 5 bars is sufficient; they do not each have to be of the same length as the entries, but it sounds smooth when they are, and episodes of uniform length throughout provides for a rapid and weighty development; this length should be considered minimum.
This step is like assembling a string of beads where the individual "beads" are these big entries; when all the beads are connected finally, the fugue is almost finished.
If the episodes are constructed upon fragments of the subject, countersubjects, and their inversions or retrogrades, the notes where the joining occurs on each end of the episode can and should be adjusted so the music sounds seamless.
How this is done: we invert, for example, either the subject or one of the countersubjects and start it on one of the inner voices (alto or bass) when the entry concludes; this will be typically on scale degree 1, 3, or 5; we select the line depending upon where it begins and line it up with the alto or tenor at the conclusion of the entry at hand.
After we have that line outlined in note heads in the alto or tenor, we then adjust the accidentals in the line to take it through a key or two as it modulates to the new key; it sounds seamless when we keep it in the same key for a couple of bars before we start adjusting the accidentals; the idea is to conclude the episode with an implied harmony in 2 voices that "fits" with the new key.
After this line is in place the other inner voice may then be invented to rhythmically complement this line and imply a harmony that's singable; once this is done our 2 voice episode is finished, and we should then listen to it and tweak it, if need be, to get it to sound smooth; by being based upon fragments or inversions of the subject or countersubjects this little episode will have a sense of familiar unfamiliarity and seem to blend right into the next entry.
It's important, during these episodes, to keep the melodic motion going; if one of the countersubjects is in longer note values, and it would cause the energy level to drop if used in a 2 voice texture, then it would be better to use some other line instead.
STEP TEN: now it's time to proofread our work, check it for errors in notation or composition (stems on the top staff up or down, voice lines crossing, notes failing to resolve correctly, consecutive fifths, octaves, or unisons moving in similar motion, awkward leaps in a melodic line, misplaced or missing accidentals or rests, etc.) and make the necessary additions or corrections [See blog, Making Mistakes, A Smooth Sea].
Now is when we add our metronome and tempo marks, dynamic marks, hand divisions, and registration suggestions or changes, if any; here is where we convert our double bar lines to single bar lines and erase any labeling inserted earlier to keep things separated and easier to find on a screen.
This is where we go back and spruce things up, put our work under a microscope, get things as animated as we can and as smooth as we can, so that when we're done we can't imagine a single note following another any other way.
When we can say that, when our score is cleaned up and professional looking, our fugue is finished.
We have a look at it now, and if we see something in it that can be worked as a prelude or other type of free work to be paired with it we create some blank space in the score anterior to it and feel free to have at it again.
Sometimes an idea or two for a prelude occurs to us in the middle of writing our fugue and can/should be notated at that time; it's perfectly okay to postpone work on the fugue today in order to give its matching prelude some attention -- we can always resume work on the fugue tomorrow.
It's better to get the big picture first, to map out the prelude's main sections, theme(s), key changes if any, and creating the framework for the piece, before filling in its smaller details.
By following this process of 10 steps, and without hurrying, a well built fugue can be completed from start to finish in a surprisingly short time; it has been battle tested by this author in the creation of many fugues and is very solid; it makes our time productive over a period of a few days, but it's important to remember not to fly through the work so quickly with such an overambitious timetable and unrealistic expectations that we start flaming out or missing some obvious mistakes.
The best results come by working our projects a little bit at a time, chipping away some of it every day like a sculptor frees the subject slowly from a solid block of marble.
If we aren't careful, we can overdo it; we can get so wrapped up in what we're doing that time gets away on us and our energies get completely spent; we can wear ourselves out -- unless we pace ourselves.
We should stop at the first sign of physical or mental fatigue; as we make progress we learn to develop the ability to recognize that point when it arrives, when the mind starts to get numb, and listen to what our body is telling us, that it's time to call a halt for today.
Composers know to arm themselves with patience; they know, with every day's work, when to say "when," that it isn't a sprint, that it isn't the 60-yard dash.
It's a marathon.