During the last" eight or nine years of his life, Bach devoted himself more and more to complicated contrapunctal works; the Goldberg Variations 1742, the Musical Offering 1747, canonical variations on "Vom Himmel hoch" 1747; and in 1748 he conceived the idea of composing a great work cycle "in which every kind of contrapunct and canon should be contained in one main theme" (obituary from Mizler’s Mus. Bibl. VII, I 1754). The work should have then been printed. Bach did not live to see its appearance.
The sources are as follows:
a) The autograph copy contains fifteen pieces and there are some loose sheets with three further pieces (Cp 14 in final form, the mirror fugue 18 and unfinished Fugue 19). Cp 4 is missing, so are the canons 16 and 17. Cp 10 appears in the earlier shorter setting; there are two different versions of canon 14. The manuscript is clearly allready a fair copy in score form, countless improvements were then entered. Some canons are noted down with each voice separate, the unifinished fugue in two not four systems.
In spite of the many corrections, the musical text often deviates strongly from the printed version - with the exception of Cp 10 (variation) 14 (final version), 18 and 19.
b) The original printed version (1751 or even 1750 - second empression 1752, with introduction by Marpurg), presents the work in full score notation, the canons with each part separate. It was probably a mistake that the variations from Cp 10 were printed. The chorale "Wenn wir in höchsten Nöthen" was added as the final piece, also in the full score notation, in order to "keep friends of his Muse without loss" (Marpurg) as regards the torso of Cp 19.
The first twelve pieces are numbered. Compared with the Autograph version, the musical text offers appreciably better versions, so that it must be assumed that a further Autograph copy was available after the existing one. In spite of this, the persons in charge of the typesetting after Bach’s death seem not to have been familiar with his intentions, and helplessly viewed the many posthumous manuscripts. Only in this way is it possible to explain the fact that the variation to Cp 10 was printed between pieces 13 and 14. Also the great number of inaccuracies can be attributed to the inept supervision of the printing. As justifiable doubts exist concerning the absolute validity of the printed version, we may here try to pursue certain trains of thought, which even though they strive to be logical, must only be taken hypothetically.

First question:
Is the work really unfinished?
Although one may agree that the work really is unfinished, different oppinions about this appear shortly after publishing.
In 1752 (introduction to the second edition) Marpurg wrote; "Nothing is more regrettable than the fact that Bach, through his eye illness and subsequent death, was prevented from finishing his work himself and making it available to all. He was surprised by his own death which overtook him while he was in the middle of completting his last fugue, which was fashioned around his own name in the adding of the third part". But in 1754, Bach’s obituary (compiled by Agricola and C. P. E. Bach) in Milzer’s "Musikalischer Bibliothek," VI, 1 makes the following observation:
"His last illness interrupted his plan to complete the last but one fugue entirely, and to finish the last fugue, which contains four themes and should have been inverted in all four voices note for note." I would like to question these reports from people who were not resident in Leipzig during the last two years of Bach’s life, and who received this information from second or third hand authorities after his death."
Firstly it seems illogical to me that a great work - and Bach certainly didn’t leap off into the unknown when he started to write it - should have been written out twice in full score (the second score includes the setting that we know from the published version), when one piece (according to the obituary 3 pieces) was not even composed.
Should Bach have not been able to write the 19th Fugue (in the printed version Fuga a 3 soggetti, not contrapunctus) - even the notation using two systems points to a first outline - we may assume that he was working on it before and until his loss of sight. It should be added to this suggestion that the Art of Fugue theme does not appear in this piece, (all three so-called Soggetti are newly invented themes. It is entirely possible that the fact discovered in the 19th century, that the main theme of the Art of Fugue fits in with the three new themes, can be attributed to mere coincidence), and that the form of a possible quadruple fugue following the three previous expositions, each one 38 bars shorter than the preceeding one, and following the Stretto of the three themes is absolutely unthinkable - in spite of Tovey, Martin and others - so that it appears that one must a least doubt the relationship of the 19th fugue to the Art of Fugue.
The observation in the Obituary however, cannot be entirely dismissed. It could be that Bach had three new compositions in mind, a triple-fugue and quadruple mirror fugue after the completion of the Art of Fugue, and from these, only parts of the third can be considered for performance. This can also be surmised from the handwritten - not in author’s hand - remark at the back of the last manuscript sheet of this fugue; "and another layout". Lastly, one can resort to the symbolism of numbers; it would lead us too far afield to embark on this most important but ticklish territory, which would take us to wholly convincing results if we regard this work as completed. It cannot be mere coincidence that both the Wtk II as well as the Art of Fugue (without the uncompleted fugue, but with repititions in both works) contain 2, 135 bars.

Second question:
Is the order of the pieces in the printed version Bach's intention?
The order of the pieces in the autograph is essentially different from the printed version, and this makes it difficult to assume that it was Bach himself who abandoned the established layout of the extant autograph and produced another conception as a foundation of his work. The autograph is after all certainly in Bach’s handwriting and the printed version only supposedly. Firstly the detailed readings of the printed version in comparison with the autograph are always better corrections, secondly some pieces of the highest quality appear for the first time (Cp 4, 16, 17), thirdly the numbering of the first twelve pieces indicates an intended order, fourthly the ordering of the canons form an "ending" only in tone quality, but in no sense in artistic perfection. The counterpoint of the canons is much more complicated than in the fugues. These considerations may lead one to accept a change in the original layout by Bach in the lost "second autograph"; whereby one also accepts the validity of the printed version, which must have been - at least in the first twelve numbers which are faultlessly engraved - based on that autograph. The printed version places the mirror fugue 13 (Cp 18) at the end as an appendix - not illogically. Interpreting it, one would play it instead of No 13 (see later remarks about this, III, 5.)
In my opinion, further evidence of musical consideration is the fact that in the last numbered mirror fugue 12., the Inversus is printed followed first by the Rectus; because the second version forms a better end affect. On the other hand, the order of printing the other mirror fugues that are not numbered is inconsequential; Cp 13 first rectus, then inversus, Cp 18 first inversus, and then rectus. The first order is musically clearer. The order of the canons in the printed version does not require a change in my opinion.
The reason for changing, perhaps unjustifiably, the order of the original edition in the placing of the fourth fugue in this recording, is based on the assumption that the smoothly flowing first fugue is better followed by an equally flowing fugue in inversion, instead of by a dotted, lively charactered fugue also on the rectus-theme, which would be followed by a light dramatic chromatic inverted fugue, which would again be followed by a brighter inverted fugue. In the autograph, the first fugue is followed straight away by the inverted fugue 3 (in our recording the inverted fugue 4, which does not appear in the autograph). This diange of order could also be supported by considering the symbolism of numbers.
To sum up I should like to express my opinion that the Art of Fugue was completed by Bach; that the Fuga a 3 soggetti (Cp 19) and the Chorale which he composed later have nothing to do with this work; that the printed version comes very near Bach’s intentions in the text as well as in the order of pieces.
The Art of the Fugue - ("...a practical and magnificent work" - Mattheson 1752 - "... I am sure that he will need his own soul, in order to observe all the beauty contained therein, not mentioning the occasion when he will be wanting to play it himself." - J. M. Schmidt, 1754; "...the most accomphished practical work on fugues" - C. P. E. Bach, 1756) was appreciated until our century as a practical keyboard work by Czerny, Storck and Spitta. But during the last’ fifty years a veil of mystery has been drawn over the work: the - wrongly - interpreted notation in the score without an indication of instruments to be used gave rise to the indulgence in "abstract and dematerialized qualities" in this last work of the "lonely" Bach. The fact that the Art of Fugue still continues its existence in our musical life as a work not instrumentated by the composer (this is born out by the many transcriptions and instrumentations), in spite of a number of articles in specialized publications by musicologists as Handschin, Husmann, Kinsky, Müller, Rietsch, Steglich, and Tovey, gives us the reason to approach the work from the point of view of musical appreciation in the 18th century particularly as regards the tonal structure, with the following considerations.


1. The score notation.
The score notation of polyphonic keyboard music (organ, harpsichord etc) was traditional. The following list of works in print (only Froberger and Poglietti are hand written, nevertheless as official ornamental writings with dedications) gives evidence of this practice, which was more a rule than an exception:

Valente 1580
Mayone 1603, 1609
Trabaci 1603, 1615
Frescobaldi 1608, 1615, 1624, 1628, 1635, 1645
Guillet 1610
Coelho 1620
Titelouze 1623
Scheidt 1624, 1650
Cavaccio 1626
Steigleder 1627
Klemme 1631
del Buono 1641
Salvatore 1641
Froberger 1649-1656
Scipione 1652
Roberday 1660
Scherer 1664
Battiferri 1669
Buxtehude 1674
Fontana 1677
Poglietti 1677
Kerll 1686
Strozzi 1687
Casini 1714
della Ciaja (1671-1755), opus 4

Bach joins this international tradition by using in the printed version the fourth variation of the canon-variations on the Chorale "Vom Himmel hoch" (for organ), 1747 or 48, four part score notation. This variation appears in the autograph on three staves. A similiar contrast between practical notation for playing purposes and an official score notation appears in both versions of Bach’s six-part Ricercar in the Musical Offering, 1747, a work composed in the old classical style, allready marked as a keyboard composition by reason of its origin (even Nicolai’s "Allgemeine deutsche Bibliothek" 1788, classifies the work "for six voices manualiter"). W. F. Marpurg’s introduction to the second edition of the Art of Fugue (1752, a second edition following shortly after the first indicates a success in my opinion, and not a sad case of lack of recognition, a state reserved by the romantics for their heroes), emphasizes the fact that; "it is a particular advantage of this work that all it contains is written in full score". If this remark referred to an ensemble work, it would be superfluous. The remark makes sense only if we take into consideration that most keyboard works around 1750 are not polyphonic and notated on two staves, but that the Art of Fugue continues in the old tradition of keyboard polyphony and presents itself to the student of counterpoint polyphony in a clear fashion.
Mattheson writes in 1752.: "J. S. Bach’s so called Art of the Fugue ... will surprise all French and Italian fugue composers; even if they will be able to follow and understand, it does not mean that they will be able to play it". Now, every Frenchman or Italian is capable of playing a single voice of the Art of Fugue; for Mattheson it is apparently only doubtful because of the difficulties facing a single player.

2. Bar 77 in Cp 6
The fourth beat of this bar is unplayable for two hands. The same difficulty - also a case of pedal point in the base - can be found for example in the keyboard works Wtk 1, A Minor fugue, conclusion; cadenza of the 5th Brandenburg concerto, bar 192.

3. The instances of Cp 4 bar 35, Cp ; bars 41 and 60, Cp 9 bar 94
Two voices meet on one note, where one voice, forming the end of a phrase, has a shorter duration than the identical note of the other voice. This notation does not make sense on a keyboard instrument. Nevertheless this does not constitute a reason against a keyboard instrument, because Bach uses the same notation in keyboard works, for example Wtk I, C Major fugue bar 11, C Sharp Minor fugue bar 38, F Minor Praeludium bar 3, Orgelbüchlein, "Christe Du Lamm Gottes" bar 4, Cl. Üb. III, large "Vater Unser" bar 13.

1. The compass of single voices
One glance at the compass of the alto voice (down to b, second octave below middle c) in the first twelve fugues suffices to make sure that none of Bach’s nevertheless richly varied ensemble groups can be used for the Art of the Fugue. Every instrumentation must resort to a completely anachronistic group of instruments. Furthermore no single voice has a specific instrumental character. This lack of instrumental characterisation may account for the great variety of instrumental attempts.
Just how freely Bach uses the compass of the voices in his keyboard fugues can be seen, among many other examples, from the F Minor fugue of Wtk I. The compass of the voices in the canons entirely surpasses the compass of every melodic of Bach’s period; for example Cp 15, upper voice D below middle C to B"; Cp 16, lower voice D below middle C to B'; Cp 14, lower voice B three octaves below middle C to C".

2. Fugues,
- which do not follow an Ouverture - beginning freely in the soprano, alto or tenor voice, are found in Bach’s compositions only in keyboard works. In ensemble fugues there is an accompanying non - thematic continuo voice.

3. Crossing of tenor and bass voices
Such crossings occur frequently in the Art of Fugue: the tenor then becomes bass. Consequently the bass voice cannot be strengthened by the use of a violone; this excludes orchestral instrumentation altogether. It can be mentioned in passing, that the problem of the instrument in ensemble performances is linked to this question and cannot be solved separately, and therefore remains without a solution.

4. The Cleffs
Had Bach intended the Art of Fugue for an ensemble, the score would have been arranged normally and practically. But it is not practical, because Bach never uses the soprano clef for the flute, oboe or violin; the alto clef for the second violin or the tenor clef for the viola, etc. (The unsuitability of the compass of each voice has allready been mentioned). Nevertheless the cleffs he employs have been in use for centuries for the notation of classical polyphony, and last but not least in parts for keyboard instruments. (Viz also Part I, point I.)


1. Playability
The fact alone, that the whole of the Art of the Fugue is written so that everything can be played accurately by two hands (the mirror fugues will be discussed below), should be enough for us to conclude, that whilst composing this work Bach always had a keyboard instrument in mind.
The importance of this will become eminently clear if one tries to play an ensemble work of Bach’s with one’s own two hands correctly on a keyboard instrument: it cannot be done. The possibility of playing this work on a keyboard was also a factor that Bach respected during its composition; he took on this disagreeable limitation consciously, at the cost of being illogical sometimes!

2. Abbreviations of last notes of phrases in order to make them playable
Examples: Cp 4 bar 88, alto (compare bars 90 and 93). Bars 94 and 96, bass voice, (compare the figure ending with half the value of the note with the previous bars); bar 116, bass voice (crotchet instead of minim). The only reason for these inconsequences: playability or avoidance of too great stretches.
Cp 11 bar 18, bass voice; there should normally have been a minim here. Abbreviation in order to make it playable; the alto voice - f-e-f can be played by the left hand, which has to release the bass. Bar 52, tenor voice. The ridiculously short final quaver note can be understood only as a technical difficulty on the keyboard. Similar keyboard practices can be found often in keyboard suites, Wtk and in works for the organ.

3. Addition of further voices in final bars
This concerns the Cp 5, 6, 7 and 11. Bach never takes such liberties in his ensemble composition as these momentary "divisi" or double-stopping practice. In his keyboard compositions this occurs frequently; for example Wtk II, fugues in C Major, D sharp Minor, A flat Major. Compare also the printed edition in score notation of the fourth variation of the Canonic Variations on "Vom Himmel hoch", where the alto part is doubled in the last bar.

4. Pecaliarities of the keyboard style
Cp 2 bar 5-6 (many similiar instances follow), bass voice. The ties can be executed only by a player who finds his rhythmical hold in another voice. An ensemble player has a feeling in such places that he has dislocated his foot; we will not be able to find such instances in ensemble works. Further examples of this can be found in the Art of Fuge in Cp 6 bar 11, tenor voice and bars 70-71, also tenor voice. Cp 4, bars 85-86, tenor voice. An absurd musical line, shameful for Bach, had he intended to present such a miserable part to a player. This place is to be understood as a setting for keyboard, where pseudo-polyphony forms a favourite method for achieving a flowing sound: the soprano and alto parts are heard simultaneously in the unsustained sonority of the harpsichord, which becomes a beautiful "echo" effect in bar 86. I would like to select only these from the several hundred similar instances in keyboard literature; French Suite in D Minor 2nd movement, bars 101-102 (compare the original form of this keyboard pseudo-polyphony in the corresponding bar of the A Minor sonata for unaccompanied violin) ; Phantasy and Fugue in A Minor, bar 65: Wtk II, Prelude in E Major bars 39-40 (alto). Cp 6, bars 40, 41 (also 62-63). Long passages in two parts wide apart in a four part piece are a peculiarity of the keyboard style (compare for example Wtk II, A flat Major Fugue, bars 16-18, 46-47). Similiar instances in ensemble performances sound bare.
Cp 7 bar 58, alto and tenor. The ties would seem unnatural to an ensemble player. On the harpsichord the alto part with the joining in of the second soprano form an attractive arpeggio-effect, D, G sharp, B.
Cp 8, bars 16-18, alto voice. Awkward voice leading resulting from unprepared octave transpostion. Musically logical would be:
The reason for this transposition is again playability because the example given above would be unplayable on the keyboard, but certainly playable in an ensemble performance. A similiar case can be found in the "Musical Offerings", where in the bars 53 and 84 (compare bar 69) absurd octave transpositions occur, caused only by aspects of playability. The middle voices would normally read as follows:
The uncompleted fugue which has been added to the printed edition of the Art of Fugue - whether justifiably or not remains uncertain - is also a keyboard work. This is pointed out not only by the notation on two staves in the autograph, but also by the octave transposition in the bars 186-188, tenor. This particular voice would have been more logical in the upper octave, but unfortunately unplayable. Thus Bach changes the logical progress in favour of playability. How important the practical performance is to him, in this case the keyboard performance!
Cp 10, bar 75, bass: octave transposition for the sake of playability. Peculiar short fragments of motives, separated by longer rests - ugly as a single part, but in a keyboard setting which forms a unified sound this occurs frequently, (for example Wkt I, B Major Fugue, bars 13-16 and 32-33, tenor), also found in Cp 2, bars 40-42, bass, Cp 8 bar 43 and bars 49-52, tenor; Cp 9 bar 80, bass; Cp 11, bars 40-43 and 53-55, tenor.
Again the idea of the sound of a "many voiced" instrument stands out in Bach’s mind. In an ensemble setting he never allows himself such weaknesses. In Cp 9, bars 114-118, he seems to have divided a continous long bass line between the bass and the tenor for reasons of visual pleasure. Compare also Cp 7, bars 35-36, tenor and bass; Cp 7, bar 60, bass. The natural bass note would have been the low D (this cadential formula is also confirmed by Bach’s pupil J. P. Kellner; the first dominant note of the bass is always followed by a fall into the lower tonic). But it would be impossible to play this on a keyboard; the lower D is then arrived at together with the final chord. This should be compare with: the English Suite A Major, Prelude, bar 16 and end; Wtk II, G minor Prelude, end. A case in reverse, again dictated by the conditions of the keyboard, can be found in Wtk I, A minor Prelude, the last three bars.
Cp 11, bar 128, soprano. The second half of the bar shows a rhythm foreign to Bach’s style (certainly in this fugue); it reminds us more of the style of the early 16th century than of the middle of the 18th. And again in this instance it is the keyboard performance which presents a different picture: the last beat is heard together with the alto voice as a Schleifer g sharp, a and b covered by "reverberation".

5. The marking of "a 2 Clav." in the original edition in Cp 18
What is above all the reason for the existence of Cp 18, an extended four part version of Cp 13? Why exactly is Cp 18 marked "a 2 Clav."?
If we accept that the Art of the Fugue has been conceived as an ensemble work, why has Cp 18 been written at all? In an ensemble conception, Cp 13 should be played by three melodic instruments. Why then all of a sudden should two harpsichords be brought in for a performance of a piece that does not constitute an improved version of Cp 13 in any way, but is on the contrary a peculiar hybrid piece with a contrapunctally unconnected addition of a fourth voice?
As we are unable to answer these questions, we should ask ourselves if perhaps the entire ensemble thesis should not be abandoned.
Now viewing the Art of the Fugue as a keyboard work, we can explain in the existence of Cp 18. Bach’s intention to demonstrate in the Art of the Fugue a maximum of contrapunctal art, including the mirror fugue. The nature of a mirror fugue implies the impossibility to remain within the limitations of two hands presenting the rectus and inversus at the same time. In all other fugue types Bach could control this limitation, but here it was not possible. In spite of this he wanted to include in the "theoretical Art of the Fugue" a good three part mirror fugue; but he saw the necessity for the "practical Art of the Fugue" to write a special version, which logically brought in another instrument of the same category, and for which he composed a fourth voice, so that the second player does not have to play with one hand in his pocket. (The other mirror fugue, understandably not playable by one player only, did not require a second version because it is in four parts, and both players could divide their parts fairly).
In Cp 18 it is then not a case of a sudden appearance of a strange new instrumentation, but a continuation of the same sound through an addition of a second instrument. Thus the unity of the work is preserved even in the sound aspect. The marking "a 2 Clav." should therefore be read with the accent on "2".

The foregoing examinations all point to the result that Bach composed the Art of Fugue, having the practical workability of a keyboard before his eyes. It could be that harpsichord, organ, (in church or room) or clavichord are implied. In principle - also according to tradition in this field of contrapunctal keyboard art - all keyboard instruments of the age must be taken into account. Often the instrument which happened to be available at the time would be used, in order to play part of the Art of Fugue for pleasure. But I still believe that Bach, (although not always), often differentiates between harpsichord and organ, (For example in the titles of the various parts of the Clav. Üb.), and that in the Art of Fugue he had the characteristic unsustained tone of the harpsichord first and foremost in mind.
I would like to put the following points forward for consideration.
a) The compass of the first twelve Contrapuncti remains within the range of the organ C—c”’, in the canons however, the range exceeds that of the organ: HH-d’” (Cp 13 and 18: C-e”’).
b) Cp 18 ("a 2 Clav.") already cuts out the organ as a possible instrument because of its range, quite apart from the fact that it is rather easier to bring two harpsichords together than two organs. (The word "Clavier" as Bach shows in the Cl. Üb. must be understood to embrace all keyboard instruments; it can be then that "Clav." here is a shortening of "Clavizimbel").
c) If the work had been thought of for the organ, then the absence of the pedals (obligato) is rather extraordinary. Bach particularly, to the astonishment of his contemporaries, had cultivated pedal playing to a greater extent than it had ever been presented in any region of Germany before.
d) The rather dense setting of deep tenor and bass parts is unusual writing for organ, quite normal for harpsichord.
e) Unsustained and not static tone seems tobe implied in the parts already discussed as:

Cp 4, bars 84-86, tenor
Cp 7, bar 58
Cp 11, bar 128 soprano

This characteristic keyboard pseudo—polyphony is only effective on the harpsichord (or clavichord).
f) The playing of the music on the organ as well as the harpsichord gives one the feeling that the work is really at home on the harpsichord. This observation is naturally debatable, but I would still like to name examples of pieces (as for example Cp 5 or 10, the B Major Fugue of the 2nd part of Wtk) that demonstrate this to player and listener alike.
g) As it is evident that the clavichord had no place in Bach’s life (in his estate he left 5 harpsichords and no clavichord; it was Forkel who created the clavichord legend about him), I believe, that from the "unsustained" instruments with keyboard range larger than four octaves, the harpsichord claims first place in the Art of Fugue. Organ and clavichord are not however to be totally excluded, especially as a choice for particular pieces.

Conclusions
1. Full score notation does not exclude a keyboard instrument.
2. The unplayable section at the end of Cp 6 does not exclude a keyboard instrument.
3. Sections like Cp 4, bar 45; Cp 5, bars 41-60; Cp 9, bar 94, do not exclude a keyboard instrument.
4. The clefs used exclude an ensemble.
5. The range of the voices exclude an ensemble.
6. This type of fugue is not normally found amongst Bach’s ensemblefugues.
7. The voices have no individual quality that would suggest them for a particular instrument.
8. The crossing of tenor and bass exclude the Violone as a 16 foot fundamental.
9. All is playable by two hands.
10. Pointless musical changes were made to favour playing possibilities.
11. The indication "a 2 Clav." is to be read as "2" in the reprint.
12. The addition of further voices together at the end of some of the fugues is typical keyboard style.
13. Sections of characteristic keyboard pseudo-polyphony will be found.
14. The Art of Fugue was considered to be a keyboard work well into the 20th century.