Godfried-Willem Raes

"A Book of Fugues"


It may have to do with some historical mythology pertaining to the Flemish and polyphony, but I have had an ongoing interest in counterpoint and polyphony since my earliest occupations into the realms of musics. Part of my activity in musical improvisation -a musical genre were polyphony is at the very essence of the form- may reflect this very same interest. However, after long thoughts about the subject, I finally decided in january 1991 - just after finishing my Tetrahedron-concerthall building-project, to undertake a major and abstract composition project, wherefore I choose the fugue -always considered as the culmination point of the art of counterpoint- as a starting point. My aim was to write a full book of different fugues, wherefore the compositoric rules would have to be entirely dependent on the aesthetical and analytical characteristics of a given dux ( the subject). It should be well understood that it certainly has not been my idea, to implement the full classical counterpoint/harmony after Fux or any other classic or academic, in this project! Contrariwise, the project - apart from some esoteric and personal aesthetic rules of my own, had to have barely any a priori rules and ought to derive almost everything from the sole and given dux. Thus a fugue would only have tonal characteristics, if this were formally clear from the dux and only in as far as it would be entailed by tonal hierarchies in this dux. The basic harmony system I wanted to implement is in fact very minimalistic: In as far as tonality is concerned - only the following distinctions would have to be made: 

First Principle: tonal tension

  • Tonal music can be fully described using no more then three intervals and chords:
  • All tonal modulation has to be prepared by adding the subtonic of the new tonality. The new tonality has to be confirmed by adding its fundamental and its dominant.
  • In order to realize this project, I started writing a rather large and complex computer program, which eventually became what is technically known as an expert system. This composition program consisted of four modules:

    • 1.: Analyzer
    • 2.: Fugue-writer
    • 3.: Fugue-player
    • 4.: Fugue-notator

    The first module -the analyzer- as the name implies, analyzes the given dux. It calculates Markov-chains for the probability of the note order, figures out some of the aesthetics of the dux (tonal, modal, atonal, serial..., metrum, - binary, ternary, quinternary, mixed -, rhythmical structure, articulation...) and tries to figure out a set of rules appropriate to handle the dux in counterpoint and throughout as fugue. Also, this program module calculates a suitable comes (the counter-subject) and some variations on both dux and comes. It proposes these to the composer who can accept or reject them. From these acceptations and/or refusals, the program takes lessons for any further proposals with regard to this same dux. The second module attempts to apply the formal structure of the classical fugue to the given and calculated or derived material. This form is constant and cannot freely be changed by the user (composer). However, the form is defined in it's most maximalistic appearance and thus comprises:

    • exposition of the dux
    • exposition of the comes
    • divertimento: motivic work and variation on dux and comes
    • counterpoint / choral
    • metrical and tonal variations on dux and comes
    • stretto
    • finale with reexposition of the augmented dux in the bass (pedal) and counterpoint in other voices.

    Depending of the intrinsic properties of the given material, the program will decide which sections to work out, and which ones to leave out entirely: For instance, not all duxes allow for an elaborate stretto, nor for a choral section. This way, the final structure of every composed fugue will and can be quite different. After having written the first sketch of the fugue, the program plays it to the composer, who can -again- be the expert to the program and teach it certain of his own and extra preferences or avoidances. After an unlimited amount of run -throughs, the program writes to fugue in binary format to disk, and the fugue is considered to be finished. A third program module allows the composer a minimal form of interpretation of the thus composed fugue. It is just a bit more than a simple juke-box program since it allows the composer to instantly change tempo, dynamics and some of the instrumentation. Also it can transpose and interchange voices in real-time. I wrote this module basically to be able to give audiences some idea of what these compositions sound like, in my own concerts with the Logos-Duo. (Being only a duo, clarinet and violin, we cannot play 4-voice fugues live in concerts of course). Also, the fugues can - using this program - be played on midi- player pianos (Trimpin machines for instance), if organizers have such instruments available The fourth and last program-modules I wrote in collaboration with my friend and colleague Geert Logghe, because it is a more universal kind of program that allows translations of the binary files generated and used by the previous modules, into DARMS-code. This DARMS-code can then be fed to standard music notation software. This way the fugues can be made available to musicians in the form of traditionally notated scores.

    In total, the program took me about four months of quasi continuous work to write, and it comprises about 600 rules pertaining to my idea of fugue composition. The code came out to be just about twice as long, as the totality of all the fugues I wrote using it. (About 500 pages of code).

    Using this first version of the software, I wrote a first book of no less then sixteen fugues -in total good for some 3 hours of music and more than 300 pages of full score. The idea was to present these fugues as strictly abstract music in the sense as generally J.S.Bach's 'Kunst der Fuge' is taken. As a consequence, instrumentation is left intentionally open and up to the performers, just as well as indications with regard to tempos (although here I have some suggestions in the following notes), dynamics and most elements of traditional music interpretation. Also, performers are invited to try out any orchestrations- even varying ones throughout the fugue, as well as meter changes in any of these the pieces. Also, transpositions can freely be made with maybe one restriction: the bass part should remain the lowest part, and the soprano (but this is less stringent) the highest in the fugue. Should performers want to get transposed parts of any voice in any key or clef, they are welcomed to ask me.

    One last general remark: in all the fugues as written in this first book, accidentals only apply to the note they precede!!! Accidentals were not used in any tonally logical way anyhow. This is merely attributable to some deficiency of my software so far. Sorry. 


    program notes and performance comments on the individual fugues.

    FUGUE 1: " A Fugue for Irma "

    This fugue was originally written to be used in an anti-opera production I was working on with my students, based on the 'Irma' score by Tom Phillips. Only the four notes A-C-C-B are derived from the original score. The fugue is written in a hypothetical baroque style.

    Tempo should be quite majestic in the exposition (MM60), but should be taken faster in the choral section (MM90-120) where it may be given the character of a dance. In the finale a poco a poco ritenuto can be performed.

    An fully orchestrated version of this fugue is available, scored for brass-band. There are parts for the following instruments: piccolo, flute, Bb trumpet, 1th, 2nd and thd clarinets (Bb), Eb clarinet, altoclarinet (Eb), bassclarinet (Bb), altosaxophone (Eb), tenorsax (Bb), euphonium (Bb), trombone, tuba (C), horn (F), bassoon, contrabassoon, double bass. Individual transposed parts are available.

    This fugue was premiered on 26.06.1991 by the Ensemble for Experimental Music of the Ghent Royal Conservatory, conducted by Geert Logghe.

    An orchestrated version was realised by Sebastian Bradt, in a setting for the M&M robot orchestra. Premiered on january 11th 2006.


     FUGUE 2: " Fug' A Due"

    The dux for this fugue I wrote with the purpose to tease my own program, and particularly its analyzer: on the bases of the used notes the dux could easily be taken as being atonal, but from its intervallic structure it is a clearly tonal -late romantic- melody. The program proposed me this fugue which really has two faces.

    theme for fug' a due



    The tempo should be taken quite fast. A performance for two pianos sounds very interesting here, although a version for clarinet-quartet (with transposed parts) is available as well. This version - called 'Fug' A Due per Arundo' - is scored for Eb-clarinet, 2 Bb clarinets and bass-clarinet.

    This fugue was premiered by the Arrundo clarinet Quartet, composed of Geert DHONT, Henk SOENEN, Stefaan CORNELUS and Harry BLOMMAERT in 1993.


     FUGUE 3: " Triple Triplet Fugue "

    A very flexible and melodic fugue written in 27/32 (this is in fact 3 times 9/16). The metric structure is purely ternary in all its divisions. The notation looks a bit weird, but this is due to the fact that this version of my program didn't know how to do triplets.

    This fugue was orchestrated for the Logos Robot Orchestra in 2018 by Lara Van Wynsberghe and premiered on the concert of may 17th in the Logos Tetrahedron.


     FUGUE 4: " A Fugue 4 Mi "

    This fugue, as happened for fugue 2, was a challenge for the program. The first seven notes of the dux are a whole tone series, but the aftersentence contradicts this. In fact the algorithm behind its tonal structure is: an octave divided in 6 equal parts (whole tone scale), in 4 equal parts (C -Es-Fis-A - diminished seventh chord), and then in 3 equal parts. ( C-E-Gis - augmented fifth chord)

    PLAY MIDI FILE (raw file)

    Download MP3-recording for the robot orchestra, 2016

    Midi file used for this recording with the Logos Robotorchestra ( Note that midi-files made for the robotorchestra cannot be played on sound cards or synths.)

     FUGUE 5: " Fuga Cinque "

    In this fugue, the dux is a simple converging series. Therefore it would be good to give it altogether a clear decrescendo wherever it appears.

    The time signature is a bit strange at first sight probably: 60/32. As a matter of fact, one should consider it to be a normal 5/4 with both binary and ternary subdivisions. Again, this notation was the result of my programs' inability to deal with triplets.


     FUGUE 6: " A minimal Fugue "

    A fast and short fugue that should be played quite mechanically. The subject is treated as modal, but as the redundancy became to high for the standards I've set in the program, this modal character was contrasted with some tonal and even atonal eruptions.

    An orchestrated version was realised by Sebastian Bradt, in a setting for the M&M robot orchestra. Premiered on january 11th 2006.


     FUGUE 7: " Fugue Septique "

    This fugue in 7/8 was thought with string quartet in mind, although of course it may very well be played in other instrumentations. The dux is edgy and fragmented. The tempo should be taken quite fast (MM120 per quaver sounds like a good starting point).

    An preliminary orchestrated version was realised by Sebastian Bradt, in a setting for the M&M robot orchestra. Premiered on january 11th 2006.

    A new version of this fugue, orchestrated for the Logos Robot Orchestra, with assistence from Kristof Lauwers and Lara Van Wynsberghe, was realized july 2017 for performance in Liepaja (Latvija) on august 3th 2017. Here is a link to the midi-file for this orchestration, using player piano, Hybr, Vibi, Korn, Ob, Heli, Fa, So, Xy and Klar.

    PLAY MIDI FILE (midi synth version, for documentation only, not suitable for performances)

     FUGUE 8: " Fuga Otto Nove " ( new car fugue)

    This very plaintive fugue starts from a dux written in the whole-tone scale. The harmony is quasi without any direction. The metrum is 9/8, although quite a few metrical modulations were applied throughout this fugue. The atmosphere is meditational. The tempo could be taken between 90 and 120 per quaver.

    A version for piano-4-hands and synthesizer was premiered on january 3th of 1992 by Marc Maes and Karin Defleyt. A version for harpsichord was premiered by Marc Maes in 1992 as well.

  • This fugue can be heard on the CD 'Logos-Works' (XI-117, New York, 1995)

  •  FUGUE 9: " Fugue NEIN !"

    A peaceful fugue with a dux based on one single diminished seventh chord. Such a dux is treated by the program as being modal in nature. Hence the treatment it received in the fugue. This fugue sounds particularly interesting when played used a tuning system wherein the different minor thirds used sound individually different. Most non-tempered tunings will do.


    A first orchestration for the M&M robot orchestra was written by Sebastian Bradt in 2004. A later revision was performed with the robot orchestra, april 2012.

     FUGUE 10: " Fuga Deca(pant)"

    The oddest characteristic of this fugue is that its dux has many more rests than notes. The notes have a simple arithmetic relation, that the program tries to continue - mostly in vain though. The metrum is 5/4 and a tempo of MM90 is suitable. After the analyzer, this dux ought to be considered as written in C#-major, using a ten-note scale. This led the program to inventing a bizarre ad hoc harmony system. Because of its fragmented character this fugue leans itself particularly well to coloristic orchestrations.

    If limited to only four instruments however, the following combinations seem to work out well:

    • Soprano-part: violin, flute or oboe.
    • Alto-part : violin, viola, altoflute, clarinet or cor anglais.
    • Tenor part : cello, viola, tenorsax, trombone or bassoon.
    • Bass-part : cello, bass, bassclarinet, trombone or bassoon.

    Transpozed parts for transpozing instruments can be obtained on request from the author.


     FUGUE 11: " El'Fuga"

    This fugue got a purely tonal dux, but... lacks any kind of periodicity in its metrum. Hence it is treated as tonal but a-metric. The notation in 2/2 is completely arbitrary.

    The fugue lends itself particularly well for performance on one or two keyboard instruments. Four-hands piano is possible as well. The soprano part may in this case be played an octave higher. The tempo can be taken around MM60.

    An orchestrated version was realised by Sebastian Bradt, in a setting for the Logos robot orchestra. Premiered on january 11th 2006.


     FUGUE 12: " Dodecafuga"

    This fugue is dodecaphonic and a-metric as well. Also here, the notation in 4/4 is arbitrary and irrelevant. The tempo should be taken rather fast (MM120 or faster) and should be maintained constant throughout the entire fugue, since the metrum has been calculated according to strict serial principles. As to the dynamics, it is advisable to take a different dynamic for every single note.


     FUGUE 13: " Fugalitania"

    a very contemplative fugue written in a fast 13/8 metrum. The dux is based on an extremely simple kind of counting-down algorithm. Due to the lenght of the dux, the voices start even before the full exposition.

  • This fugue was premiered in a version for player piano by the author, on june 6th 1995.
  • A version for the Logos robotorchestra was prepared in 2014. Here is the link to the midi-file for this version. Note that midi-files made for the robotorchestra cannot be played on sound cards or synths.

    FUGUE 14: " James Ensor Fuga "

    This fugue starts from a strictly pentatonic dux. However, the redundancy check-rules in the program made sure, there would be some interesting exceptions in the course of the piece to watch out for. As one may know, the flemish painter James Ensor also wrote some musical pieces and liked to play the piano himself very much. However, he never understood why pianos had white keys, since he could never discover any musical usage for them. He thought they were there only to confuse him. As a result, all of his music came out strictly pentatonic.

  • This fugue was premiered by a quartet composed of Johan Vercruysse (tuba), Jurgen Deschepper (clarinet), Gunther De Backer (saxophone) and Hilde Gyssels (oboe) on januar 3th 1992.

    FUGUE 15: " Circus Fuga"

    This very awkward and hard-to-perform fugue uses a very fast and irregular 5/16 metrum. Hence, it wouldn't be a bad idea to play it on a player-piano or even better, an orchestrion. This fugue was premiered in a version for player piano, on june 7th 1995. (tem po MM130).

    When the tempo isn't taken at its extreme -lets say 1 second per bar- performance becomes perfectly possible either on percussive keyboard instruments (cembalo, piano, celesta) or stave-percussion instruments ( marimba, vibes, xylophone, glockenspiel).

  • Also, performances by recorder quartets have some nice perspectives to offer.

    FUGUE 16: " The missing fugue..."

    This is the fugue as J.S.Bach for sure never wrote it. It uses his very infamous dux from 'The art of the fugue'. The program had quite a few difficulties with this one, because the dux misses an explicit sixth tonal degree (B or Bb).

    An orchestration for the organ-type robots at Logos Foundation was worked out by the author in 2017.

    Gent, april 1991 

    "A Second Book of Fugues"

      After having completed the first Book of Fugues in 1991, I then started changing the software, such as to generalize the concept of the Fugue further and further.

    Thus, in this second book, a specific version of the software was used for every new fugue. Also, the software now started incorporating a gradually increasing set of rules derived from classical rhetoric in music. At one hand, some formal fugue rules became vaguer, but a fifth section in the expert- software was written to add rhetoric ornamentation to the pieces.

     FUGUE 17: " Ango Laina "

    In Fugue 17 ( Ango Laina Fugue), the concept of Fugue was broadened to incorporate the spoken voice. This fugue was scored for voice, cello and piano, on a request from Jaap Blonk. The phonemes as used in the vocal part are to be pronounced as one would do in dutch language. They are:

    • aaa iii uuu eu oe ooo o(h) a(h)
    • Haa He Hij Hee Hie Huu Heu Hoe Hoo Hoh Hah
    • Zaa Ze Zij Zee Zie Zuu Zeu Zoe Zoo Zoh Zah
    • njaa njui njei njee njie njuu njeu njoe njoo njo nja
    • maa mui mij mee mie muu mjeu moe moo mo mja
    • djaa djui djei djee djie djuu djeu djoe djoo djo dja
    • kaa ke kei kee kie ku keu koe koo ko ka
    • ta tu ty te ti tu tu toe to to ta

    These phonemes are treated as musical material, and become even subject to modulations throughout the fugue. For instance, the vocal theme is:

    • Djuukoo kiekeuzaanja hoe
    • nja djoedjag kikukoeko
    • zi djeikaa kakaakoekie hoo

    ,but this same theme a 'triton' lower, sounds like this:

    • Djaakee kokuizuunjm hij
    • njm djeidjm kokaakeikie
    • zo djeikuu rkuukeiko hee

    Tempo, for performance of this fugue, should be relatively fast (MM120). Accidentals apply only to the notes within the same bar. The vocal part is written on a single line and only roughly depicts some sort of melody flow. However, it is not meant to be sung. This fugue was premiered by the Ango Laina trio, Dublin, 1994.

     [more extensive notes in dutch text version]

    Organ triptique:

     FUGUE 20: "Fuga Memento"

    Fugue 20, was written on april 4th of 1992, for flute and keyboard (piano, tangentenfluegel, harpsichord, clavichord ...). It was written shortly after the sudden death of a flutist friend of mine, Eric De Quecker. This explains why it stresses the fragility of the flute-sound and why the thematic material of dux and comes, as well as the general form of the fugue as such, are so fragmented.

    The tempo should be rather slow and elegic. In the score, no dynamics, articulations, phrasing... are given. By ommiting systematically all those elements I wanted to connect with the preromantic music tradition, where all those elements belonged to the interpretative field of the performer. So, it should not be misunderstood as being music failing dynamic variation, affects, phrasing and such more! It should contrarywise never be played in a merely mechanical way. This compositional attitude as a matter of fact was inspired by my abdication of ego-expressive romanticism and a will to re-evaluate the performer as a complete artist in his own right. The performer is asked to consider the given score as a fundamental musical material, which he should not neglect but to which he can add articulation, decoration and affects in any way leading to reveal the elegic character of the piece.

    On some notes, the + sign was written in the score. On these notes, the performer should build up a multiphonic starting from the written fundamental note. However, ad libitum, he may also do so on other suitable held tones in the pieces where it appears appropriate. The flute sound which should be aimed at is not the one used in the symphony orchestra, but rather one where the process of sounding the tube, becomes audible. A sound, that has an acoustical life in itself.

    This fugue was premiered by Karin DEFLEYT and Marc MAES in 1993.


     FUGUE 21:" Tenthousand Years of happiness"

    Fugue 21, was written as an answer to a special request from mr. Wu Xi Ming from the Shangai Centre Theatre, who wanted me to include some Chinese music in the Logos-Duo concert programs we played there on 5 and 6th of august 1992. It is scored for Chinese traditional instruments such as the Er-Hu, the Cheng, the Suona and the Yangqin. Versions for old western instruments are also possible.

    The melodic material for dux and comes was taken from an old Chinese melody from the Kirin province. The tempo should be taken slow (andante grave) and the mood should be peacefull. As a preludium, the choral 'Plum Blossoms' can be performed.


    FUGUE 22: "20 two Cage"

    Fugue 22, was written to the memory of John Cage, who died on august 12th 1992 on a request from the German music journal 'MusikTexte'.







    For the dux of this fugue I took one single note from 6 different compositions by John Cage. The compositions are 'Atlas Eclipticalis', 'Winter Music', 'Ryanghi', 'Cheap Imitation', 'Wonderfull Widow of eighteen springs' and 'Music of Changes'. The dux is only 1 bar long and the comes was derived from it by the computer.

    The resulting scaled down fugue (18-bars only) was written using a version of my fugue-writing software, that I infected -for this Cagean occasion- with a a virus. The virus was designed to work according to I Ching chance operations and it changes chords build with thirds to chords built with fourths. Although the fugue goes through 6 'modulations' (C,G,D,E,B,C), this structure became completely obscured by the effect of this fourth virus.

    The piece can be played on any stringed keyboard instrument.

    An orchestrated version was realised by Sebastian Bradt, in a setting for the M&M robot orchestra. Premiered on january 11th 2006.

     FUGUE 23

    This Fugue is not a stand-alone composition, but the second part in a larger String-Trio, that also uses different versions of my choral-writing programs (Symmetrical Harmony Systems) in its other 3 parts. The Fugue-part is not a complete fugue, but merely a stand-alone inversed stretto per augmentationem in 3 voices.

    A short version of this fufue (Fuga23b) was orchestrated for the M&M robot orchestra by Sebastian Bradt in 2004.

     FUGUE 24: "Berceuse"

    This fugue became the Berceuse in my piccolo composition 'Picco', scored for piccolo (or recorder), cembalo and bass-clarinet or viola da gamba.

    The Fugue, as the previous one, was generated from a very deconstructed version of the software. More extensive comments can be found in the introduction to my piece 'Picco'.

    Fugue 25: "Concise Fugue"

    This extremely miniaturised fugue was composed to be written into a commemorative book at the occasion of the retirement of a colleage at the conservatory who used to be the fugue teacher. It consists of no more than 9 bars. Each voice nevertheless gets to play the dux three times and there is even a real stretto in two steps. We encounter a modulation to the dominant (bar 5) and come back to the original tone at the end. However, the fugue is written in a symmetrical tonal system with a scale of 9 notes. (C-Db-Eb-E-F-G-A-Bb-B-C). The dominant chord in such a system happens to be a dissonant.

    this fugue is playing on the background...
    An orchestrated version was realised by Sebastian Bradt, in a setting for the Logos robot orchestra. Premiered on january 11th 2006.


  • Scores, transposed parts, adapted versions for specific instrumental combinations can be obtained from the publisher:

    logos editions

    Kongostraat 35

    B-9000 GENT



    Note, december 2017:

    All software written for this algoritmic composition program was designed for the QBX-BC7 professional Basic compiler by Microsoft. For the music notation, using DARMS code, the Note Processor software was used. With the advent of Windows, Microsoft dropped all support for the BC7 compiller. For our later work in algoritmic composition we moved to the Power Basic compiler. However, the Fugue software was never rewritten to use this newer compiler and hence, it does not run anymore on modern Windows computers.

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    last updated: 2018-05-16