Movement 01: Contrapunctus 1
Movement 01: Contrapunctus I
Movement 02: Contrapunctus 2
Movement 02: Contrapunctus II
Movement 03: Contrapunctus 3
Movement 03: Contrapunctus III
Movement 04: Contrapunctus 4
Movement 04: Contrapunctus IV
Movement 05: Canon in hypodiapason 'Canon alla ottava'
Movement 05: Contrapunctus V
Movement 06: Contrapunctus 5
Movement 06: Contrapunctus VI 'in stylo Francese'
Movement 07: Contrapunctus 6 'per diminutionem' in stylo Francese
Movement 07: Contrapunctus VII 'per augmentationem et diminutionem'
Movement 08: Contrapunctus 7 per augmentationem et diminutionem
Movement 08: Contrapunctus VIII
Movement 09: Canon alla duodecima in contrapunto alla quinta
Movement 09: Contrapunctus IX 'alla duodecima'
Movement 10: Contrapunctus 8
Movement 10: Contrapunctus X 'alla decima'
Movement 11: Contrapunctus 9 alla duodecima
Movement 11: Contrapunctus XI
Movement 12: Contrapunctus 10 alla decima
Movement 12a: Contrapunctus XII Rectus
Movement 12b: Contrapunctus XII Inversus
Movement 13: Contrapunctus 11
Movement 13a: Contrapunctus XIII Rectus
Movement 13b: Contrapunctus XIII Inversus
Movement 14: Canon 'in hypodiatessaron' per augmentationem in contrario motu
Movement 14a: Contrapunctus XIV (Tovey completion)
completion of Contrapunctus XIV
Movement 14b: Contrapunctus XIV (uncompleted)
Movement 15: Canon alla decima 'Contrapunto alla terza'
Movement 16: Contrapunctus 13 'Rectus'
Movement 17: Contrapunctus 13 'Inversus'
Movement 18: Contrapunctus 12 'Rectus'
Movement 19: Contrapunctus 12 'Inversus'
Movement 20: Contrapunctus 14
Contrapuncti V, VI and VII: The first four fugues having exposed the subject with simple treatment, the next three show what can be done with it in combination with itself, inverted and overlapping itself at various intervals. These, naturally enough, are the most involuted fugues, though one would not immediately think so when listening unsuspecting to the beautiful and serene No V. Here the stretti (or overlappings) employ the subject with its inversion. The sixth fugue is ‘in Stylo Francese’, familiar in the French overture of the period, with its pompous dotted rhythms; here the subject is combined with overlappings of its own diminution (itself in shorter notes). No VII is per Augmentationem et Diminutionem, and the combination of the original subject with its own diminution and augmentation (itself in longer notes) results in an astonishing continuous tissue of stretto. Apart from the final cadential bars there are only three subjectless bars in the whole thing.
Contrapunctus VIII: In Contrapuncti VIII, IX, X and XI Bach combines his original subject with new ones. The eighth is one of two three-part fugues in the collection and is a gloriously supple and vigorous example of how to write in three parts (much more difficult than in four). It opens with one of the new subjects, striding downwards and with a touch of chromaticism in it. This is then combined with another new subject, also moving downwards like a stepladder—again with chromatic elements. These two are eventually combined with the original subject in a new rhythm, all three forming a splendid triple counterpoint (that is, three subjects combined, any of them capable of forming top, middle or bass, in any order).
Contrapunctus IX: The second of the four fugues in which Bach combines the original subject with others, No IX is a lively essay in double counterpoint at the twelfth; that simply means that two themes are combined—(1) at the ‘normal’ interval of an octave, and (2) at the twelfth (an octave plus a fourth), with quite different harmonic effect. This brilliant quick fugue is enjoyable whether or not you can follow these matters—which is as Bach wanted it. The new subject in running quavers is heard first, then the original one stretches itself over it in long notes, and the combinations at the different intervals occur periodically, with episodes between.
Contrapunctus X: This is the third of the four fugues that concentrate on the combination of the main subject with others. It is one of the most beautiful in the whole cycle, notable for the serenity of its motion. It opens with the new subject, arching with inimitable grace. No IX had a double counterpoint at the twelfth; this fugue shows one at the tenth (an inverted third, and the calm warmth of the whole is a result of this). The scale-figure in the first theme (the new one) gives rise to some lovely episodes.
Contrapunctus XI: The eleventh is the grandest of the four fugues in which Bach combines the original subject with others; it is the culmination of this group and is certainly the most impressive completed fugue in the entire work, surpassed only by the supreme unfinished Contrapunctus XIV. Its subject-matter is the same as that of VIII, but mostly inverted and much more strongly chromaticised. Unlike the other fugues in this group, it begins with the main ‘Art of Fugue’ subject, but upside-down and in the rhythmic form found in VIII. The second theme is the same as the first in VIII inverted, now climbing and accompanied by a rising chromatic scale. Then we hear also the ‘stepladder’ subject from VIII, this time climbing. But soon it begins to go both up and down, and the triple counterpoint of VIII is inverted, plus the chromatic scale. All this sounds very complicated, but the effect is of teeming music of great intensity.
Contrapuncti XII and XIII: Having written four simple fugues, three stretto fugues, and four in which the main subject is combined with others with various kinds of counterpoint, Bach now turns to the problem of totally invertible fugue—that is to say fugue in which all the parts together can be turned upside-down from start to finish, note for note. This might seem to be an exercise of repellent dryness, but the exercise for Bach consists in doing this and making music at the same time. In Contrapunctus XII we find a straightforward simple fugue in four parts, followed at once by its inversion, but XIII is less obvious. It is a three-part fugue—at least it was so written at first. But Bach was so delighted with it that he arranged it for two claviers and for this purpose added a free fourth part to the whole. This extra part has been used in the string quartet arrangement of the vivacious piece, in which the Rectus is followed immediately by the Inversus.
Contrapunctus XIV completed by Donald Francis Tovey: The last and greatest extant fugue of the cycle was left unfinished by Bach. The main ‘Art of Fugue’ subject does not occur in it so far as it was written, but the three new subjects already used make with it a quadruple counterpoint to convince all but the most obstinate. Accordingly, Sir Donald Francis Tovey (1875–1940) completed the fugue, making use of this quadruple counterpoint (all four themes able to combine with any one of them as bass to the others) and the result is so impressive that it is hard to tell when Bach ends and Tovey begins. It may reasonably be doubted that Bach himself would have ended the fugue very differently, and this magnificent conclusion is at all events preferable to the sentimental practice of allowing the music to trail off into thin air like the spirit of the frustrated composer being dragged off to heaven.
The first subject is like a plainsong, or a chorale. The second is a flowing andamento, and the third is B–A–C–H (B flat, A, C, B natural). Each is developed in turn, and Bach’s manuscript breaks off at the moment when all three are combined. Since the main ‘Art of Fugue’ subject has already been extensively developed in the earlier fugues there would be no point in devoting a fourth section to it alone, and to bring it in as soon as possible with the other themes is artistically wise. This is what Tovey does.
Like the rest of The Art of Fugue, this movement is transposed from the original D minor to G minor to make it practicable for a normal string quartet. This means that, when it first occurs, ‘B–A–C–H’ is E flat, D, F, E natural! Purely musically this has no effect on the coherence of the music, and if anyone wishes to complain we beg them to be content. The answer is BACH.
from notes by Robert Simpson © 1992