As organists we learn many things by example, both at the keys and away from the instrument.
This is especially true with writing for the organ, and with improvising.
The world renowned French organist, composer, and pedagogue Louis Vierne (1870-1937) had a method of teaching improvisation on a single free theme to his numerous pupils from around the world who came to Paris to study with him [See menu bar, Photos II].
Fortunately, even though he himself has left this world, the details of this method of his has survived through his numerous pupils, and their pupils, etc.
This approach of his was a 6-part form which could be used as is or modified (truncated) as needed to accommodate the nature of the theme at hand; this represented the formal basis for many of his written compositions as well, notably his famous collection of Twenty-Four Pieces in Free Style for organ, 2 staff, Op. 31.
It would be most instructive to take a single free theme, either by inventing one of our own or deriving it from some previous theme by rhythmic transformation (same pitches in succession, different note values) and try to build a composition in this same style.
Giving it this 6-part improvisational treatment "a la Vierne" will help anchor in the mind this very useful and highly effective form for working a single free theme.
The Bb Major Op. 5 Prelude Internationale (photo) is an example of this kind of written exemplification and it will help to download and print a hard copy of it as this narrative is followed [See menu bar, Photos 2, 6-Part Improvisation].
This is a dreamy piece and, as a tribute to the memory of Vierne, I decided to include in this work some of the things for which he was noted -- such things as irregular phrase length, triplet rhythms within a constant duple time -- 3 against 4, inverting the theme, preference for the mediant key with the 2nd entry, frequent and unexpected modulations wandering through remote and distant keys far away on the Circle during development, the deliberate inclusion of consecutive 5ths woven into the harmony but never between outer voices, the final reentry of the theme employing a 2-part canon at the octave, a coda with chromatic inflections -- ALL of which are very reminiscent of Vierne's methods and vocabulary.
In this form, as taught by Vierne, there are 6 parts, or sections, as follows:
1) 1st exposition of theme (16-20 bars consisting of theme harmonized diatonically, commentary, return of theme, & concluding commentary in home key),
2) Bridge (12 bars formed of 3 modulating phrases, separated by breaks, based upon one bar of the theme),
3) 2nd Exposition of theme (12-16 bars in new key, consisting of theme, commentary, theme, and brief conclusion in key of 2nd exposition),
4) Development (24-32 bars based upon a rhythmic element and a melodic element of the theme, modulating through 3 or 4 more keys),
5) Preparation for the reentry (4 bars consisting of 2 times 2 bars on the "head" of the theme, separated by a break, and
6) Reentry (final exposition, or return) of theme (24-28 bars consisting of theme (harmonized chromatically?), commentary (canon), brief reference to bridge, (theme inverted?), commentary on the pedal of the home key, and conclusion).
This general outline is not set in stone, and Vierne reshaped it in various insundry ways to suit the character of his themes; it can be modified, for example, by prefacing the 1st exposition with a short introduction of 2 bars, compressing or shortening entire sections, animating the 2nd section using canons or quicker note values, making excursions into additional keys in the development, or even omitting entire sections.
The theme for Prelude Internationale was derived by rhythmic transformation (same pitches in succession, different note values) of the main theme from the C Major Op. 4 Variations, deliberately and irregularly reshaped as 2 phrases of 4 bars each, with a third phrase of only 3 bars long attached; triplets in every other measure of the theme were also included.
The 1st exposition of the theme is worked in 3 voice parts rather than 4, simply for the sake of variety.
The 2nd exposition which is to follow typically presents the theme in a different key (often the dominant), but before that happens there will be a modulating bridge section (Fr. "pont") usually built upon the first few notes of the theme in imitation which will connect the 1st exposition with the 2nd exposition.
This bridge section will also succeed in its purpose if it is only 6 bars long and consists of 2 phrases each 3 bars long, with a break between.
Here, to create this bridge, the notes of the 1st phrase of the theme were worked in imitation, still in 3 voices, both upright and in inverse movement.
As a tribute to Vierne, instead of moving to the dominant key in the 2nd exposition, the theme was presented in inverse movement and in the mediant key of D Major, as Vierne had a predilection for mediant relationships in his own writing; this was accompanied by a move to a richer 4 voice texture.
The development section was built upon fragments of the theme in imitation; considerable freedom may be exercised in working this section, and it doesn't have to be extremely long; it was determined that 20 bars would suffice here.
In this work this development begins in the key of b minor (the relative of the mediant) and modulates to G Major, Eb major, and E Major before landing in B major, all unrelated keys.
Here, in the course of this development, fragments of the theme are subjected to imitation and 3 against 4 rhythms; this section begins in a 3 voice texture and moves to 4 voices as it progresses, which is then retained through the close of the work.
This development section is worth a close look in terms of how it was constructed.
The function of the preparation for the reentry is to connect the development, which may wander far away on the Circle, with the reentry of the theme and to bring about a smooth return to the home key.
In this case the preparation for the reentry leads from B Major back to Bb Major via the key of A Major, which is another unexpected turn.
Finally comes the reentry of the theme in the home key harmonized in a different way than earlier, which, in this case, incorporates a 2 voice canon at the octave with 3 against 4 rhythms; this ends gently with chromatic inflections.
In quiet pieces like this one, very often an 8-foot string Celeste stop is reserved for this reentry along with a slight reduction in tempo and expressive slowing through the final measures.
NOTE: The use of forbidden consecutives (perfect 5ths and octaves) was something in which, believe it or not, even J.S. Bach, for one reason or another, employed in his Chorales (but never between outer voices); Vierne was one of many late 19th and early 20th century composers influenced by new textures and a new perception of part-writing which relaxed the rule about consecutive 5ths; this is plainly evident in pieces like Berceuse from Vierne's 24 Pieces in Free Style for 2 hands Op. 31, a beautiful work which no one can label "poorly written music" -- and, since this little Prelude pays homage to Vierne's memory by incorporating many of his methods and vocabulary, consecutive 5ths have been deliberately woven into the harmony of this work in no less than 4 places (bars 8, 30, 39-40, 47) never involving, of course, the outer voices.
Four more Preludes from Op. 25-28, all of which are paired with related Fugues, employ the same 6-part improvisational form [See blog, Getting Started With Writing, Parts XXXI, XXXII, XXXIII, XXXV]; these scores may also be consulted for examples of how this type of treatment may be employed successfully in working a single free theme.