We have no way of knowing what Bach’s exact tuning preferences were, but we can at least assess likelihoods. There are a few general points about which we can be reasonably certain:
(1) His views changed and developed during the course of his career: he began in the context of the late seventeenth century and lived on into the age of Empfindsamkeit. Ideas of temperament, tonality, style, and keyboard technique are in reality inseparable aspects of a single development. (2) Tuning was an important issue to him, as were all other aspects of music. C.P.E. Bach reports: ‘The exact tuning of his instruments as well as of the whole orchestra had his greatest attention. No one could tune and quill his instruments to please him. He did everything himself . . . .’26 (3) His approach was practical and intuitive; it is most unlikely that he engaged in mathematical computa- tions, or worked out temperaments with a monochord. He did not ‘occupy himself with deep theoretical speculations on music, but was all the stronger in the practice of the art’;27‘in these questions [tuning] he went by the light of nature, and not according to rule’.28(4) His views and practice were in general accord with the tradition of his time and place, and probably at the advanced end of the spectrum. Had he had some highly personal and idiosyncratic views they would surely be reflected somewhere in the literature.29
Bach’s early years were spent in an environment of transition where there was much experimentation, but where there were three main types of tuning in practice: 1⁄
4-comma meantone, something like Werckmeister III, and something like equal temperament.30Of these the Werckmeister III type was used not only in and around Thuringia, but also in some parts of north Germany. It seems likely that Buxtehude had the organs of the Marienkirche, Lübeck, retuned to it in 1683.31 After Bach had returned from this three- month visit to Lübeck in 1705–6 he confounded the Arnstadt congregation by mixing strange notes with the chorales. Buxtehude was known for his richly harmonised improvisations on chorales, and if Bach used the same vein on an organ nearer 1⁄
4-comma meantone the result would have been indeed strange. It was perhaps to facilitate this that he arranged two years later for the Blasiuskirche organ at Mühlhausen to be completely retuned, possibly in a temperament à la Lübeck.32
Apart from the organs at Lübeck, there were organs nearer home in the Harz area, just north of Thuringia, using Werckmeister temperaments. Works of Werckmeister’s were in the library of the Michaelisschule at Lüneburg, where Bach could have got to know them.33Peter Williams has noted strik- ingly similar formulations to Werckmeister’s in Bach’s reports on organs.34 Bach’s relative and organ colleague at Weimar, Johann Gottfried Walther, went to Halberstadt and Magdeburg in 1704 to get to know Werckmeister, for whom he had a high regard. He remained in correspondence with him and obtained from him copies of many organ works of Buxtehude.35The article ‘Temperamento’ in Walther’s Lexicon (1732) cites Werckmeister 1691. Whether or not Bach ever used straight Werckmeister III tuning is open to question. As it stands it is obviously designed for ease of tuning, and to be acceptable to conservative-minded organ builders in its very straightforward tempering of the 5ths. Sophisticated musicians must have used something more subtle.36But a highly coloured tuning of that sort does suit Bach’s earlier clavier works, such as the F sharp minor Toccata (BWV 910), with its very long sequences, and the D minor Toccata (BWV 913), whose third, improvisatory, section uses a repeated rhythmic figure to explore remote sonorities such as A flat major and E flat minor. This section loses much of its sense of adventure in an equal tuning.37
It is likely that the development of Bach’s style in his later Weimar days, which entailed not only changing concepts of structure and tonality under Italian, particularly Vivaldi’s, influence, but a development of keyboard technique as well, was accompanied by a change of tuning along the lines of the later works of Werckmeister, and of Neidhardt. A work of Werckmeister’s which is particularly intriguing from the point of view of The Well-tempered
Clavier is the thoroughbass tutor of 1698. This had a certain popularity, being
reprinted in 1715, and reissued in 1737 by Bach’s friend and pupil the theorist Lorenz Mizler. It ends with a short lesson, ‘Wie man ein Clavier stimmen und wohl temperiren könne’, which is as straightforward and practical an instruction as one is likely to find in print. After an explanation of beats and of the intervals that have to be divided to make a temperament, he gives, without any quantities, a recipe for tuning a sort of equal temperament by 5ths up from c, all very slightly narrow except for the last few (from e
♭
) which may be very slightly wide or, in the case of f–c, pure, depending on how one wants the 3rds on b, e♭
, e, a♭
, and f to be. He then gives recipes for tuning triple-fretted and double-fretted clavichords into some semblance of a circulating temperament. All this is pitched at a fairly homely level, but it does correspond to two remarks from the Bach tuning lore: (l) that he tuned all major 3rds wide;38and (2) C.P.E. Bach’s statement that almost all 5ths should be tuned narrow.39Bach himself assuredly did not need this sort of low-level instruction, and these two points could apply to a number of tunings, but he may have recommended thislittle treatise to Mizler, who says it is the best instruction before Neidhardt.40It is tempting to think that Bach may have used it to recommend to pupils who asked for something straightforward and concise to read about tuning, in the same way that he apparently used F.E. Niedt’s Musicalische Handleitung for instruction in thoroughbass and improvisation.
Something of Bach’s attitude to the Werckmeister III-type tuning at this stage may be reflected in the report of the inspection he made in 1716 together with Johann Kuhnau (his predecessor as Thomascantor at Leipzig) and C.F. Rolle (organist at Quedlinburg) of the new organ by Christoph Kuntz (Cuncius) at the Liebfrauenkirche, Halle.41 They had previously found fault with Kuntz’s temperament on certain notes of all three manuals and he had undertaken to retune them in accordance with a ‘noch passablen guten Temperatur’ he had shown them. According to Sinn, Kuntz used the Werck- meister III tuning42 and the ‘passably good temperament’ may have been something that reduced the whole-comma major 3rds of that. Kuhnau himself said in 1717 that he was prepared to accept equal temperament on instruments whose sound dies quickly such as the clavichord and harpsichord, though he had never tried it with the rigorous exactness of the monochord.43
On the face of it, it might seem significant that Bach elected to arrange the key scheme of The Well-tempered Clavier of 1722 to go up the chromatic scale from C, with tonic major and minor alternating, rather than in a scheme going round the circle of 5ths from C, with major keys alternating with their relative minors, as Heinichen had pictured in 1711.44Bach’s ordering, putting C major and C sharp major in close proximity, would seem to be the fulfilment of Werckmeister’s prophecy (1697 p.36) that in the future people would tune all consonances equally and play an air indifferently in C or in C sharp. This assumption holds good, though, only if Bach had conceived the scheme fully formed from the beginning. The early sources for the collection show that the concept only gradually assumed its final shape. The original idea seems to have been to provide pieces for the notes of the hexachord, along the lines of seven- teenth-century verset collections, or perhaps for the complete white-note scale, as with the first seven Praeambula (later called Inventions) in Wilhelm Friedemann Bach’s Clavier-Büchlein. The filling in of chromatic steps was an extension of this essentially conservative plan. Different orderings in two of the early sources of The Well-tempered Clavier are relics of this stage.45
Other features show how Bach evolved towards the final state in the early 1720s. Early versions of some minor-key pieces have ‘Dorian’ key signatures, and some major-key pieces may originally have been notated ‘Mixolydian’. These signatures would be illogical in a fully chromatic context.46 They hark back to styles and a world where unequal temperaments prevailed.
Impressions from the music are dangerously subjective, yet there are striking instances of appropriate colours in an unequal temperament. Taking those
preludes which have early versions in W.F. Bach’s Clavier-Büchlein one could mention the character difference between the Preludes in C and C sharp major; the bleak, wintry character of the E flat minor triad with a wide major 3rd on g; the colours of variable major 3rds and 7ths in the A flat major scale in bars 6–8 of the F minor Prelude; many will have their own observations.47 Yet only if it could be shown that these pieces were composed into the Clavier-
Büchlein could we be sure that they were not transposed from other keys, and
that cannot be certain.48In Book I the D sharp minor fugue, and the G sharp minor prelude and fugue possibly, seem each to have been transposed up a semitone to fill gaps in the chromatic scheme.49
It is instructive to look at the views of another composer with a strong speculative bent who was moving in the same direction, Bach’s near-contem- porary in Hamburg, Johann Mattheson (1681–1764). It is by no means clear what connexions there may have been between Bach and Mattheson, or what Bach thought of him,50 but Mattheson’s publication in 1719 of figured-bass exercises in all 24 major and minor keys, the most significant step in the direction of The Well-tempered Clavier since Fischer’s Ariadne Musica (1702), may have had an influence on Bach’s developing concept. Bach visited Hamburg in 1720 to audition for the post of organist at the Jakobikirche, where Mattheson evidently heard him play but did not meet him.51 Mattheson’s book had been published three months before.
Unlike Bach, Mattheson keeps us copiously informed in theoretical publi- cations about the development of his ideas. Being a contentious spirit he is not above taking sides variously in the same argument, so it is sometimes difficult to tell in what direction, if any, his real opinions lie. In his first publication (1713) he gives his famous list of key characters, but omits C sharp, F sharp, A flat and B majors, and C sharp, E flat, G sharp and B flat minors as being very seldom used (p.252). This recalls Neidhardt’s (1706) remark about such keys being unrefined in unequal tunings, and Werckmeister’s similar remarks that equal temperament is not needed if such keys are rarely used. By 1717 Mattheson was working towards his scheme of providing exercises in all keys, and his views had moved on, in theory at any rate.52 He recommends both Werckmeister and Neidhardt, but says that Neidhardt (1706) has given the best description (1717 p.85). Most organ builders are unable to tune it, but although Mattheson says that it may be done on the harpsichord (p.87), it seems unlikely that he had achieved it himself since he says two years later that he had never found it outside Neidhardt’s book (1719 p.99).
The object of Mattheson’s continuo exercises in all keys is not to demon- strate any particular temperament, but to provide practice for learning the handshapes (‘die Griffe’) for chords in unusual keys so as to have total fluency in continuo playing (1719 Erster Theil pp.56–7). He does nonetheless consid- erably refine on his brief remarks on tuning of 1717. One of his concerns is to
preserve the distinction of key characters. For this he proposes a temperament of his own, based on just intonation, but which he must have regarded as somewhat theoretical in view of his later remarks.53But in order to play in all keys the real issue is whether or not equal temperament is the solution. He finds pure equal temperament, as proposed by mathematicians, musically insensitive. Having all 12 semitones the same size is not the aim of music, but that they should all sound pure and agreeable. If they are all the same size they sound wrong, so why take the trouble?54 The practical temperament of a musician may not agree with mathematical calculations, but it will be better in giving more accurately the pleasurable variety of keys. This does not reduce the diversity of keys, but quadruples them.55
If the exact proportions of equal temperament are one side of the definition, the other is intervals tempered by a whole comma, which are unbearable (p.55), a view shared by many from the 1720s.56This rules out those tempera- ments which have one or more Pythagorean 3rds. The views expressed by Mattheson must have been widespread, since it was precisely to satisfy this definition that Neidhardt, Sorge and Marpurg devised their subtly shaded, non-equal temperaments. As far as Bach’s tuning in 1722 is concerned, it would seem reasonable to suppose that he had something in which every key could be used equally as a tonic (i.e. no Pythagorean 3rds), but at the same time preserved something of the evolutionary nature of the collection in a subtly shaded inequality.