4. Text and audio tracks from all the preludes and fugues performed on a Bach-style harpsichord

Peter Sykes played the following examples in two recording sessions (in September 2010) on an instrument built for him in 2005 by Allan Winkler on the basis of a Fleischer harpsichord of 1716. (The plectra are from condor, vulture and seagull feathers chosen to provide varying amounts of stiffness appropriate to different parts of the tessitura.) Prof. Sykes tuned the instrument (he had studied unequal temperaments in a course taught by me in 1984 at the Boston Museum of Fine Arts), and I checked to ensure that the intervals and the relationships among them were within the limits of my concept of Bach-style unequal temperament suited ideally to this music. The temperament is the same for all the pieces. (The room was so well climate-controlled that little retouching had to be done on the second day.) It was tuned with concert-A at ca. 415 HZ (a semitone lower than 440); its C-major pitches are therefore far closer to the B-major than to the C-major pitches in the piano examples, its C♯-major pitches here are far closer to the C-major than to the C♯-major pitches in the piano examples, etc. The differences in effect between the examples performed (a) in the original keys and (b) in the transpositions are thus clearly due more to the nuanced intervals than to the performance-pitch levels.

(A big difference in performance-pitch levels would of course make a palpable difference in the musical effect. And, in each of the comparisons there is willy-nilly a certain effect due to a latent harmonic relation between two keys that are juxtaposed. The only feasible ways to get around this problem would be by means of elaborate electronic procedures either (a) eliminating human playing altogether (a drastic loss) or (b) costing too much money and maybe entailing too much of a cognitive labyrinth.)

Since the audience for the lecture in 2009 with the Bösendorfer pianos (here is the link) was not advised to bring copies of the score, all the examples for that lecture, including the transposed excerpts, were prepared in musical notation. For the following set, however, please have on hand a copy of WTC I or else use my link to the 19th-century Bach-Gesellschaft edition (old but still quite good).

The C-major prelude

This piece begins and ends in a calm mood that is well suited by the moderately tempered tonic triad and the somewhat “lazy” leading-tone:

Track 01: The first 4 and last 4 bars.

The calmness is compromised when (in this kind of tuning) the music is transposed to D♭-major:

Track 02: The last 3 bars to D♭.

Notice how, in the following complete performance, the tuning-nuances enhance the expressiveness of the C♯’s in Bar 7 and of the A♭’s in Bars 9 and 22:

Track 03: The whole piece.

The C-major fugue

The neutral quality of the sound of C-major in this kind of tuning is well suited to the quasi-ecclesiastical character of the subject. But notice also the welcome touch of subtle sprightliness in the F♯ in Bar 3 (making with G a slightly smaller semitone than does E with F in the subject):

Track 04: The first 3½ bars.

If the opening statement of the subject is transposed to B-major, it sounds a little peculiar because the third note seems a little too giddy:

Track 05: The first 3½ bars to B-major.

You may have noticed in the middle of Bar 4 the sour effect of the same note an octave higher. (The effect would be just as bad in D♭-major.)

When the music modulates in Bars 11-13 to the relative minor, the G♯’s sound appropriately spiced but do not sound sour as they do in Dr. Lehman’s rendition at YouTube (for which he happened to choose a 20th-century overall pitch-level, i.e. a semitone higher than that of Peter Sykes's performances).

Track 06: From the last beat of Bar 6 the first half of Bar 15.

The mood of this piece resembles that of a straightforward ecclesiastical fugue, and the subject could almost do duty in an old-fashioned organ verse; but the narrative differs from that of an academic fugue proceeding with Subject – Answer – Subject – Answer:

The length of a double-exposition is thus obtained in the first ten bars in a more interesting way than a Paris-conservatory-type double exposition would provide. (And meanwhile the use of C♯ in Bar 8 prevents the modulatory G♯’s in Bars 11–13 from sounding more dramatic than might be appropriate to the overall mood of the piece.) By making the initial fugue of the set so interesting in this rather sophisticated way, Bach may have intended to show off from the outset that his mastery of the genre was unique.

The C-minor prelude

The first phrase sounds heavier in C than when transposed to D, and then the high E♭ at the beginning of Bar 5 sounds more dramatic than does the even higher analogous F in the transposed version:

Track 07: The first 5½ bars in C-minor and then transposed to D-minor.

In the last part of the piece, the D♭ in Bar 36 sounds more expressive than the analogous E♭ in the transposed version; and, the Picardy 3rd at the end sounds even calmer in the original key than in the transposition:

Track 08: The last 4¼ bars in C minor, then transposed to D minor, then again in C.

The C-minor fugue

The A♭’s in the subject are more atmospheric and less plainly Dorian than are the B♭’s that would result from transposing it to D-minor:

Track 09: The subject in C, then transposed to D, then in C again.

The final chord sounds suitably conclusive in the proper key, but indecisively nervous in the transposition:

Track 10: The last 3 bars (plus an upbeat) in C, then transposed to D, and then again in C.

(And yet, nervous-sounding final chords are perfectly appropriate in some pieces, as we shall presently find.)

In Bars 17–19, the nuanced tuning adds grace to the cross-relations in the following sequence of chromatically ascending pitch-classes during the modulation from G-minor (at Bar 17) back to C-minor at Bar 20:

During the previous modulation to the relative major, the upper edge of the tune had descended obviously stepwise from G (at Bar 9) to F (Bar 10) to E♭ (Bar 11). Heinrich Schenker discerned in 1926 a descending line of salient notes in the upper edge of the tune:

But a current American professor doubts that Bach could possibly have been aware of this. (See Lawrence Dreyfus, Bach and the Patterns of Invention, Chapter 6, “Figments of the Organicist Imagination.”)

The C-major prelude

In this piece, the remarkably high tuning of the E♯’s in Bars 1, 3, 5 and 7, and of the A♯’s in Bar 4, brings out and garnishes the bright mood of the music:

Track 11: To Bar 9 in C♯, then in C, then again in C♯.

Bach had earlier composed a version in which the right hand’s first note was middle G♯, and thus with G♯-C♯-E♯ as the tune in the first half of Bar 1. Apparently he had felt that an initial E♯ would sound a little too spicy, but then realized that the amount of incisiveness would be just right with E♯ played on the first beat but not on the second one:

Track 12: To Bar 5 in the earlier version, and then in the final version.

It seems likely that in both versions the thumb was to play the G♯ in Bar 1.

The final pedal-point and final chord sound more engaging in C♯ than in C:

Track 13: The last 14 bars in C♯ and then transposed to C.

In the first 32 bars, the initial eight-bar theme is heard in four keys: C♯- and G♯-major, then D♯- and A♯-minor. The major-minor contrast is strengthened by the fact that whereas the third and sixth degrees of the C♯- and G♯-major scales are tuned relatively higher here than in Equal Temperament, those degrees of the D♯- and A♯-minor scales are tuned relatively lower. The tuning nuances strengthen also the harmonically kaleidoscopic effect of Bars 33–46, albeit so fleetingly that it would be too pedantic to describe the details here. Let me mention, however, that the contrast between the Subdominant key (F♯) in Bars 47–54 and the Tonic (C♯) at Bars 55. is beautiful not only because of the harmonic relationship between the two keys and the notable difference in register, but also because A♯ is tempered slightly less high in relation to F♯ than is E♯ in relation to C♯. This latter fact adds a dash of “freshness” to the return at Bar 55 to the home key:

Track 14: Bars 1––64.

Rameau used the phrase l’entrelacement des modes to distinguish (a) the basic harmonic relationship between two keys in the same piece from (b) the ancillary effect of tuning nuances. In 1737 he dismissed altogether the latter kind of effect – which he himself had praised, however, in 1726. Rousseau commented that the one kind of effect need not exclude the other. (See à propos pp. 248-251 in my Stimmung und Temperatur.)

The C-major fugue

The remarkably large major 6th (G♯-E♯) in Bar 1 helps the subject sing more in this key than when transposed to C (where the corresponding major 6th, G-E is smaller):

Track 15: The subject in C♯, then transposed to C, then again in C♯.

The same is true in the last five bars of the piece:

Track 16: The last 5 bars in C♯ and then transposed to C.

(The mood of the long episode in Bars 29–42 prevents the piece from becoming altogether too lyrical.)

The C-minor prelude

The opening bars sound less academic and more expressive when played in C♯ than when transposed to D. Notice the following differences: (a) between the pure (i.e. untempered) 12th, C♯-G♯, at the outset in C♯-minor, and the slightly beating and therefore less stark corresponding interval, D-A, in the transposed version; (b) between the suitably low and therefore melancholy-sounding melodic E’s in C♯-minor, and the more “poised” (and therefore less expressive) F’s in the transposition (they sound more poised because they are not tuned very low in relation to A, E and D); and (c) between the slitheringly high B♯ at Bar 3 in Bach’s music, and the relatively uninteresting C♯ in the transposed version:

Track 17: The first five bars in C♯ and then transposed to D.

In this key the semitone between the leading-tone and the tonic, B♯-C♯ (which is acoustically the same as C-D♭) is the smallest of all the twelve semitones in this style of tuning. Notice how thoroughly this leading-tone is exploited in the last 15 bars of the piece (and notice also how appropriate to the musical context is the nervous beating of the compound major 3rd at Bar 37):

Track 18: From the middle of Bar 23 to the end.

The C-minor fugue

As in the prelude, so also in the fugue subject, the slitheringly high leading-tone and reasonably dark third degree of the scale are virtues which are lost when the music is transposed to D (with its somewhat moderately tuned leading-tone and rather poised third degree of the minor scale):

Track 19: The subject in C♯, then transposed to D, then again in C♯.

It is true that this piece is an exercise in a genre, the ricercar, which was antiquated already in Bach’s day. But it is also true that nearly all the diatonic semitones involving accidentals in this piece (including A♯-B as well as E♯-F♯, B♯-C♯ and Fx-G♯) are smaller than their counterparts in Equal Temperament. Those four remarkably high leading-tones (A♯, E♯, B♯, Fx) help keep the music sounding vibrant rather than merely academic:

Track 20: Through Bar 76.

The D-major prelude

This piece exudes a moderate degree of sprightliness which is accommodated by the moderate tempering of F♯ and C♯. When the material is transposed to C, however, the downright tame temperings of E and B (corresponding to F♯ and C♯ in Bach’s version) tend to make the performer sound more like a beginning student and less like a talented player. Here is the comparison:

Track 21: The first 2½ bars in D, then transposed to C, then again in D.

Upon hearing the same kind of comparison in regard to the last few bars of the piece, we may well feel that the transposed version sounds a little too serious in Bar 32 and stodgy in the final chord:

Track 22: The last 4 bars in D and then transposed to C.

While the texture of this piece is uniform until Bar 29, the tonal plan involves, in the first 19 bars, a series of more-or-less fleeting modulations to various keys (some of which use sharps tuned relatively higher than in Equal Temperament), then at Bar 20 a restful perching on the Subdominant key (G-major, with smaller major 3rds and larger semitones than in Equal Temperament), and then a “final scene” in D with dramatic changes of texture and with a dip into the parallel minor. In the following performance, notice the pleasantly moderate quality of the tempering of F♯ and C♯ in the first couple of bars, the more spirited quality of D♯ and A♯ at Bars 7 and 8, and later, in G-major, the relatively tame third degree (B♮) of its scale and the moderate leading-tone (F♯); and notice also how well suited to the exact compositional context of the moment are the rates of beating of the C♯ at the end of Bar 34 and the F♯’s in the final chord:

Track 23: The whole piece.

The D-major fugue

The moderate beating of D-F♯, A-C♯ and G-B lends a welcome sense of poise to the sonorities in the middle of Bar 2, at the beginning of Bar 3, etc.:

Track 24: To the chord at the beginning of Bar 6.

The D-minor prelude

This piece is hardly sad (even when played at a moderate tempo):

Track 25: The first 5¼ bars.

When the material transposed to C, the first bar tends to sound a little too dark or heavy:

Track 26: The first 2¼ bars transposed to C (and played more softly).

The D-minor fugue

Here too there is no sadness. If one transposes the subject to C, the resulting E♭ and A♭ sound slightly darker than appropriate in such a context. The comparison is subtle:

Track 27: The subject in D, and then transposed to C; then the first ten notes in D, and then in C.

A♭ has no place in this piece, but colorful uses of E♭ are important to it. They begin to occur at Bar 9, by way of using the Neapolitan degree of the D-minor scale to harmonize B♭ in the tune. That B♭ is a cleverly surprising note. The context for it is that after a routine fugal exposition with entries of the subject on D in Bar 1, on A in Bar 3 and again on D in Bar 6, we have in Bar 9 the beginning of a curious entry on the second degree of the minor scale (namely E) – not a routine sort of thing to do in a fugue. This statement of the subject does not, however, proceed in a mechanical way with a G at bar 9; instead, there is a leap up to B♭, harmonized by the E♭ in the middle voice; the subsequent quarter-notes in the tune form a diminished 3rd (C♯-E♭) instead of a minor 3rd (as in the initial statements of the subject); and then a sequence makes nice uses of E♭ in Bar 11 and again Bar 12 (where we have the first hint of the fact that the subject is going to be inverted):

Track 28: To the beginning of Bar 13.

The last use of E♭ in this piece, in Bar 36, is for the first appearance of a motif that is treated sequentially in the following two bars – with, in Bar 38, a melodic expansion (leaping up to B♭ instead of merely to G; this is nicely reminiscent of the previous use of B♭ instead of G at Bar 9). Notice the G♯ in Bar 37. The fact that it is tuned higher in relation of A than is C♯ in relation to D contributes to its effectiveness here, and helps lift the emotional plane of the discourse to a level justifying the unusually rich and scintillating quality of the final chord of the piece:

Track 29: From Bar 34 to the end.

The quality of that final chord depends in part on the moderate beating of the major 3rd, D-F♯.

The E-major prelude

Leaps of a 7th and major 6th are salient in the first three bars. The tuning renders them more expressive in E♭ than when the material is transposed to D (even though the transposition yields an expressive C♯ at Bar 3):

Track 30: To the beginning of Bar 5 in E♭, and then transposed to D; then to Bar 10 in E♭.

The E-major fugue

The tunes are more sprightly than in the prelude, but even so, the upward leaps are more telling in E♭ than when the music is transposed to D, and Bach’s D♭ in bar 5 is more telling than the corresponding C in the transposition:

Track 31: To the beginning of Bar 6 in E♭, then transposed to D, and then in E♭ again.

The E-minor prelude

The strongly tempered triads of this key convey better the dark and tense mood of the music than do the more dignified-sounding triads obtained by transposing it to D-minor:

Track 32: To the beginning of Bar 6 in E♭, then in D, then in E♭ again.

The D♯-minor fugue

The difference in notation between E♭ and D♯ is due to Bach and has no acoustical effect, though it certainly affects the way the music looks.

The semitone between A♯ and B is smaller than in Equal Temperament and rather smaller than the analogous semitone between A and B♭ when the subject is transposed to D-minor:

Track 33: The first eight notes of the subject, then the same notes transposed to D-minor, then the same comparison back and forth again.

Not only A♯ but also E♯, B♯ and Fx make slinky diatonic semitones with their upper neighbors and strongly tempered 3rds and 6ths with the major 3rds and 6ths below:

Track 34: To the beginning of Bar 12.

These acoustically and melodically tense qualities help sustain our interest in the contrapuntally complex (but texturally sparse) discourse:

Track 35: From the middle of Bar 61 to the end.

(This piece is a tour-de-force of learnèd counterpoint, but since the subject is not ideally suited to the making of perfect strettos, Bach had to tweak it here and there to get it to fit.)

The E-major prelude

Because of the somewhat nervous 3rd degree of the scale (G♯) and the high leading-tones (D♯ and A♯, the latter in relation of course to B) an expressively “walking-on-eggs” interpretation is well suited to this piece; but that possibility is lost (in this style of tuning) when the material is transposed to F-major:

Track 36: The first 4 bars in E and then in F; then the first 8 bars in E.

The E-major fugue

Here again, the material has just the right degree of sauciness in the original key, but when the same material is transposed in such a way as to obtain lazy leading-tones (E in relation to F, and B in relation to C) and a stodgy third degree of the diatonic scale (namely A, the dull quality of which is notable especially in the final chord of the piece), it seems like a salad with no dressing to give it savor:

Track 37: The first 4½ and last 3 bars in E, then in F, then (louder) in E again.

The statement of the subject in the relative minor at Bars 16-17 (in the inner voice) is preceded by a substantial minor-mode excursion, the somewhat perplexed mood of which is well served by the relatively high tuning of the leading-tones within it (B♯, Fx, E♯, then B♯ again); and then it is a pleasure, after these colorful tonal diversions, to revert to E-major for nearly a dozen more bars:

Track 38: From Bar 10 to the end.

The E-minor prelude

The poignant beginning (redolent of a cantata sinfonia as in BWV 202) sounds even darker when transposed to F than in the key chosen here by Bach:

Track 39: The first 3½ bars in E, then in F.

It is interesting apropos that for the Crucifixus in the so-called “B-minor Mass” (which I regard as a work in D major with its initial Kyrie in B minor) Bach transcribed into E minor a piece previously composed in F (in BWV 12). Here in this prelude, however, the “floating” effect of the modulations – to G major at Bar 9, back to E minor at Bar 11, on to C major at Bar 13 and A minor at Bar 15, then back to E at Bar 21 and on to A at the Presto (Bar 23) – is abetted by a chairoscuro of nuances in the notes that are pivotal to the modulations:

Track 40: Bars 7-26.

The leading-tone in Bar 39 and the final chord are more interesting in Bach’s key of E than when the material is transposed to F. Meanwhile, however, the sonority at the beginning of Bar 40 sounds more expressive – perhaps too much so – in the transposition:

Track 41: The last 3½ bars in E, then in F, then in E again.

The E-minor fugue

In the first 5 bars, the most salient notes are the D♯’s in Bar 1, the A♯’s in Bars 2, 3 and 5, and the E♯ in Bar 4. It is beneficial that they make smaller diatonic semitones in this tuning than in Equal Temperament. The benefit is lost when the material is transposed to F:

Track 42: To Bar 5 in E, then in F; then again (but louder) in E, in F, and again in E.

In each of the four modulations to a major key in this piece, there is (in this style of tuning) a series of successively less incisive sharps and analogous naturals: (1) A♯-G♯-F♯- B♮ at Bars 5, 7, 9, 11; (2) C♯, F♯, B♮, E in Bars 15-18; (3) D♯, C♯, B♮, F at Bars 24, 26, 28, 30; and then (4) G♯, C♯, F♯, B♮ in Bars 34-37. And, each of the modulations back into a minor key involves accordingly a salient use of a relatively incisive leading-tone. This systematic use of nuances contributes to the shapeliness of the piece – which wants such a contribution because the resources for interesting texture are limited from the outset since it is a fugue à 2:

Track 43: The whole piece.

The F-major prelude

I think Bars 1-2 should be treated as a calm pedal-point because (a) F-major was always liable to be a “pastoral” key, (b) each of the first three chords is introduced with smoothly descending 16th-note arpeggiation, (c) the melody floats down (its top edge being F-E♭-D-C-B♭-A), and (d) the triads are only moderately tempered. However, when the same material is transposed to F♯, the rather sprightly tempering of A♯, D♯ (for both hands in the 3rd beat of Bar 1) and E♯ makes the music sound a little less calm:

Track 44: The first 2 bars in F, then in F♯, then in F again.

As it is (i.e. in Bach’s chosen key of F-major), the pastoral possibility is then dismissed, however, and the piece becomes a miniature toccata with, in the second half, a gaudy stepwise descent of the top edge of the right-hand’s line from high A in Bar 9 (gilded by a G♯ the shrillness of which is due in part to the temperament) down to middle G in Bar 14, and then a surge up to the top C from which the line floats down to high G (in the second half of Bar 17) before coming to perch on middle F. (Schenker would have inferred an implicit middle G in the second beat of Bar 18.) In the last 3½ bars, and especially in the second half of Bar 16, the moderate tempering of the 3rds and 6ths helps the performer produce radiant sonorities from the two-part texture:

Track 45: From Bar 8 to the end.

Let me give here, for players who may be distracted by handling the long trills and tricky clumps of 16th-notes in this little piece, some further remarks about its harmonic and linear structure. The upper edge of the tune, after descending stepwise from F to A in the first two bars, moves up chromatically to D in the next two, and the music is then in the key of D-minor until the end of Bar 8. There have thus been two surprises: (1) the onset of vigorous trills at Bar 3 and (2) gliding past C-major and having the second main key of the piece be the relative minor (D-minor) instead of the key of the Dominant. In the first part of the D-minor section, the upper edge of the tune glides down stepwise from the D in the middle of Bar 4 to the F in the middle of Bar 6. (The descent from F to A in Bars 1-2 had been over a pedal-point, but here in Bars 5-6 the left-hand part makes parallel 10ths with the right-hand part.) The right-hand part in Bar 7 includes not only alto’s high D but also an E hinting at the F in the second half of Bar 8 – but then the tune instead of returning to E goes up chromatically to the A in the middle of Bar 9, albeit with an F♯ tucked in at the beginning of the ornament on G♯.

I have mentioned that the context of nuances in the unequal temperament contributes to the shrill effect of that G♯. The nuances help in two other ways as well. (1) The fact that the C♯ in Bar 4 makes a higher leading tone to D than E has done to F in Bars 1-2, or indeed B to C in Bar 3, renders the surprise venture (so early in the piece) into the relative minor more colorful than it would be in Equal Temperament. (2) The tuning of E♭ slightly lower in relation to C, F and G than it would be in Equal Temperament augments the chiaroscuro effect in Bars 11 and 13:

Track 46: The whole piece.

The F-major fugue

The calm beginning is well served by the mild tempering of A in relation to F, whereas when the material is transposed to F♯-major, the A♯ at Bar 5 sounds slightly distorted:

Track 47: To the beginning of Bar 8 in F, then in F♯, then again in F.

A quasi-pastoral aspect of this piece is the remarkably unadventuresome harmony within (each of its four sections: (1) Bars 1-32 in F- and C-major (a double-exposition of the fugue subject), (2) Bars 34-46 in D-minor, (3) Bars 47-56 in G-minor, and (4) Bars 57-72 in F. Each section has thus a distinctive tonal palette. In the first one, the pitch-classes are the naturals and B♭; in the second one, B♮ is absent, and almost every bar displays C♯; the third one features a hovering between F♯ and E♭; and then the last one differs from the first one owing to the absence of B♮ and the repeated uses of E♭. The tuning-nuances strengthen the effects of these changes in tonal hue:

Track 48: The whole piece.

The F-minor prelude

The relatively low tuning of D♭ renders it more expressive than the analogous C when the music is transposed to E-minor:

Track 49: To Bar 4 F, then in E, then again in F.

The “drooping” affect extends to the mildly tempered leading-note (throughout the piece) and the Picardy 3rd at the end, whereas this virtue is lost when the material is transposed to a key where those notes are heavily tempered:

Track 50: The last 2 bars in F and then in F♯; then the same comparison again, then the last 2½ bars in F.

The mild tempering of F-A♮ is exploited also in Bars 4-5, where the applied dominant chord (F7) to B♭ sounds beautifully radiant in the second half of Bar 4 and then the A♮’s in Bar 5 sound appropriately tentative. Notice also in the following excerpt (showing the somewhat elaborate modulation from F-minor to its relative major) how the expressively low tuning of G♭ in Bars 4-5 echos that of D♭ in the last beat of Bar 3, and then how the low tuning of D♭ is exploited to different effect (no longer melancholy) in the context of A♭-major:

Track 51: From amidst Bar 2 to the beginning of Bar 9.

The F-minor fugue

The drooping D♭, A♭ and leading-tone E♮ are well suited to this material, and the dull intonation of B♮ at the beginning of Bar 2 is suited to the fact that the subject will not return to C but will go on down to chromatically to F. The opening material when transposed to E minor sounds in the first two bars slightly distorted and thereafter somewhat academic:

Track 52: To Bar 7 in F and then in E; then to Bar 10 in F.

The theme (i.e. the subject or answer) is heard six times in the first 30 bars, each time in the top or bottom voice of the texture and each time in F- or C-minor. Between the statements that begin in Bars 7 and 13 with C-D♭-C, there is none beginning with F-A♭-G; this feature of the Exposition makes more salient the “fanning-out” effect of having entries at Bar 1 on middle C, at Bar 7 an octave lower and at Bar 13 an octave higher. The mood changes in Bars 34-43 with their two major-mode presentations of the subject (in inner voices of the texture). The fact that D♭-C and A♭-G are smaller than in Equal Temperament adds beauty to this change by strengthening not only (a) the morose quality of D♭ and A♭ when used as minor-scale sixth degrees of the scale, but also (b) their tender quality when used as major-mode fourth degrees. The listener’s subliminal memory of this transmutation adds beauty to the reversion of A♭ in Bar 47 to the minor-mode function that it had back in Bar 19, and also to the same kind of reversion of D♭ in Bar 53. And then the mild tempering of the Picardy 3rd (F-A♮) renders the sonority of final chord notably “radiant”:

Track 53: From Bar 33 to the end.

The F♯-major prelude

The meter (12/16) is as unusual as the key. There is clear impetus in the left hand’s straightforward lines of dotted eighth-notes, but in the right hand’s part, échappés and the like complicate the resolutions of most of the suspensions and thereby create an aura of evasive nimbleness. This peculiar music is well served by the relatively high tuning of the A♯’s, E♯’s and B♯’s:

Track 54: Bars 1-7.

When the same material is transposed to F, the mildly tempered analogous notes (A♮, E♮, B♮) sound less sprightly, and the (same) player thus seems unable to make the tune sing:

Track 55: To the first half of Bar 7, first as transposed to F, then in the proper key of F♯.

Some later notes which the tuning renders appropriately scintillating are the Fx’s in Bars 15-16, the E♯’s in Bars 18-21 and 28-30, and the A♯’s in Bars 29-30:

Track 56: From the second half of Bar 15 to the end.

The F♯-major fugue

The meter is more easy-going than in the prelude, but the lines are nonetheless full of “pins and needles”-type motivic material, albeit remarkably lyrical, thanks in part to the relatively high tuning of the extreme sharps (A♯, E♯, B♯) and the double-sharps. For instance, the small semitones E♯-F♯ and B♯-C♯ help the first four notes of the subject sing in Bars 1 and 3, and the high E♯’s (in relation to C♯) in Bars 3-4 help maintain a sense of lyrical tension in the dialogue between the subject and countersubject. When the material is transposed to F, these advantages are lost and the music sounds more academic and less interesting:

Track 57: To the middle of Bar 11 in F♯, then in F, then again in F♯.

You may recall that in the first four notes of the more athletic C-minor fugue subject and its tonal answer, the large semitones B-C and F♯-G helped the same scale-degrees “dance” rather than “sing.”

Here is the same kind of comparison in regard to the end of the piece:

Track 58: The last 2½ bars in F♯, then in F, then again in F♯.

All the notes in this piece seem radiantly beautiful to me in Equal Temperament, and yet I find even more radiant, in the right kind of nuanced tuning, certain notes at particularly “blossoming” moments of its structure: (1) the E♯’s in Bar 13 where the second of the two countersubjects – the one with the repeated-notes motif introduced in Bar 7 - draws to a conclusion the first time it is used (the other two times being in Bars 20-22 in D♯-minor and in Bars 28-30 in B-major); (2) the Cx at Bar 20 at the half-cadence introducing the statement of the subject in the relative minor; then, after its statement in the Subdominant key (B-major) in Bars 28-30; (3) the E♯ introducing its last statement in F♯; and then (4) the E♯ and the A♯ in the final two chords of the piece:

Track 59: The whole piece.

The F♯-minor prelude

This is a lively (though not frenetic) piece; there is nothing melancholy or even ecclesiastical about it. When the opening is transposed to F, the relatively low D♭ and A♭ give the material a “musty” aura:

Track 60: The beginning in F♯, then in F, then in F♯ again.

The high E♯'s in Bars 19 and 21 and concluding Picardy 3rd each want a bit of “edge” to them, which the unequal temperament supplies – whereas when the same material is transposed to F, the analogous E♮ and A♮ sound stodgy:

Track 61: The last six bars in F♯, then in F, then in F♯ again.

The B♯’s as well as the E♯’s and A♯’s have a welcome dash of energy in the unequal temperament:

Track 62: The whole piece.

The F♯-minor fugue

In the first two bars of the subject, there is a vital tension between (a) the obligation of the suspensions to resolve downwards and (b) the overall striving upwards to the fifth degree of the scale. This latter aspect is the main thing, and is well served by the relatively high tuning of A♯ and B♯ in the second bar. If the beginning of the piece is transposed to F, not only do the analogous A♮ and B♮ sound somewhat academic and dull, but also the low intonation of the A♭ in Bar 1 stresses the downward pull as if the piece was going to be full of sighs – which it is not: it is not morose like the beginning (and end) of Chaikovsky’s 6th symphony; it is, instead, a depiction of emerging and swelling strength:

Track 63: The subject in F♯ and then transposed to F; then the first 3 notes in F♯.

The first bar of the countersubject works its way downward twice to this or that sharp obliging a suspended note in the subject to resolve. (The episodes are then full of upward gestures derived from the quietly climactic moment of the subject.) The high tuning of some of the sharps in the countersubject and in the episodes augments their expressivity. Some nice paradoxes are that (a) the tuning of D♯, even though relatively higher than in Equal Temperament, sounds beautifully moderate (especially at Bar 9) in relation to the more incisive tuning of A♯ and E♯; (b) in Bar 13 the semitone between F♯ and G is relatively large, and then (c) the F♯ in the tune in Bar 14 is moderately tempered in relation to D and A:

Track 64: To Bar 15.

The fact that there is no answer on C♯ between the two entries of the subject on F♯ in Bars 8 and 15 should not be surprising after the displays of such freedom in the C-major and F-minor fugues.

In the final statement of the subject in F♯-minor at the end of the piece (after four previous such statements, and two statements in C♯-minor in Bars 4-7 and 25-28, and then the inversion on F♯ in Bars 32-35), E♯ is pitted not only against the suspended B♮ in the middle of Bar 38 but also against (a) the long A♮ in Bars 37-38, the (b) C♯ at the beginning of Bar 39 and (c) the G♯ at the end of that bar. Meanwhile, A♯ and B♯ also sound melodically interesting in Bar 38, and then A♯ radiant in the final chord. When the music is transposed to F, the analogous A♮, E♮ and B♮ sound dull and church-like:

Track 65: The last 4 bars in F♯, and in F; then the last 7½ bars in F♯.

The G-major prelude

F♯ in Bar 3 sounds “just right” as it is tuned slightly higher in relation to A than is E (in Bar 1) in relation to G; and, in Bar 3 C♯ is tuned nicely higher in relation to A than is B in relation to G in the second half of the preceding bar. When the music is transposed to F-major, the resulting E’s in Bar 2 and the B’s in Bar 3 sound less fresh than their counterparts (F♯ and C♯) in G-major:

Track 66: To Bar 5 in G, then in F, then again in G.

The G-major fugue

Here as in the prelude, F♯ and C♯ have – for a piece of the given character – just the right amount of incisiveness in their tuning. The music when transposed to F sounds tepid, and when transposed to A sounds slightly crazy:

Track 67: Through Bar 10 G, and then in F; then to the beginning of Bar 6 in A and in G.

The G-minor prelude

This piece is neither sad nor light, and therefore the sixth degree of the scale should sound less dark than D♭ does in F-minor, but slightly weightier than F does in A-minor:

Track 68: To the beginning of Bar 4 in G, in F, and in A; then to the middle of Bar 4 in G.

The leading-tone at the beginning of the last bar of the piece should sound neither dull nor as incisive as it would sound in Equal Temperament. In this style of tuning, F♯ is tempered suitably whereas G♯ is tuned a little more incisively than in Equal Temperament. (I admit that the final Picardy 3rd sounds lovely per se when the music is transposed to A. You may judge how well suited this particular kind of loveliness is to the ending of this prelude.)

Track 69: The last two bars in G and then in A; then the last 2¼ bars in G.

The trills in this piece point up nicely the overall key plan, starting in G-minor, modulating in Bars 5-6 to B♭-major at Bar 7, and then modulating again in Bar 10 to C-minor at Bar 11 (before signaling in Bar 12 the return home to G).

The G-minor fugue

How grave and/or how athletic should this piece be? The moderate temperings of F♯, C♯ and B♭ accommodate a fairly bright interpretation. The music when transposed to F-minor is charming in a heavy way, but with a gratuitously excessive rate of beating in some of the resulting compound major 3rds (A♭-C in the middle of Bar 6 and at the beginning of Bar 12; D♭-F on the last beat of Bar 10):

Track 70: To Bar 12 in G and then in F; then to the middle of Bar 18 in G.

In the context of such a lively interpretation of this fugue, it is (nevertheless) appropriate for the major 10th in the final chord to tempered quite moderately:

Track 71: The end of the piece.

This is paradoxical in relation to what I will say about the next piece –

The A-major prelude

The strongly tempered 3rds and 6ths of A♭-major suit this lively prelude better than do their moderately tempered counterparts in G-major:

Track 72: To Bar 5 in A♭, in G, and again in A♭; followed by the last 6 bars in A♭ and then in G.

The A-major fugue

The subject is more expressive melodically with the heavily tempered major 6th (A♭-F) and major 3rds (A♭-C and D♭-F) of A♭-major than with their ecclesiastical-sounding counterparts (G-E, G-B, C-E) when the music is transposed to G:

Track 73: The beginning in A♭, then in G, then again (at greater length) in A♭.

The G♯-minor prelude

The meter-signature is 6/8, but to a modern listener this piece flows along in a bewitchingly waltz-like way, owing to (a) the construction of its theme with 16th-notes in the first half of the bar gyrating to an arc of 8th-notes in the second half; (b) the persistent restatements of the theme – in Bars 1 and 2 on G♯, Bars 5 and 6 on B, Bar 7 on D♯, Bar 8 on C♯, Bar 9 on G♯ again, Bar 10 on A♯ but this time inverted, etc.; (c) the slightly dizzying harmonies entailed by some of these statements; and (d) the fact that the episodic material (introduced in Bars 3-4) is of the same, gently swirling quality:

Track 74: The whole piece.

The harmonic diminished 7th (or augmented 2nd) at the pivotal point of the theme should be between an incisive leading-tone and a fairly carefree-sounding sixth degree of the minor scale (i.e. not very low), rather than between a stodgy leading tone and a rather dark sixth degree of the scale as becomes the case when the music is transposed to G-minor:

Track 75: Bars 1-2 in G♯, and then in G; then Bars 1-4 in G♯.

And, it is suitable for the concluding major 10th to beat in a radiantly “surging” way (as G♯-B♯ = A♭-C does) rather than very slowly (as is the case for G♮-B♮ in this disposition):

Track 76: The last 3 bars in G♯, then in G, then again in G♯.

The G♯-minor fugue

The theme is not very expressive (although its last five notes provide a serviceable motif for the episodes); incisive leading-tones and strongly tempered harmonic major 6ths (e.g. in Bars 3-6) prevent the piece from becoming too stodgy – as it would do if transposed to G-minor:

Track 77: The beginning in G♯, then in G, then at greater length in G♯.

As in the prelude, so here too in the fugue it is good for the concluding major triad to beat at a surging rate:

Track 78: From Bar 36 to the end.

The A-major prelude

If this piece had a tempo marking, I think it would be “Allegretto.” It calls for a certain degree of incisiveness in the tuning. In the top line in the first few bars, the temperings of the various sharps are just right, but when the music is transposed to G-major, the resulting B♮ in Bar 1 sounds slightly tepid, whereas a transposition to B-major yields a slightly too edgy A♯ in the middle of Bar 2 and at the beginning of Bar 4:

Track 79: The beginning in A, then in G, then in A, then that comparison again (more briefly), then in B, then in A again.

The first E♯ in Bar 11 also sounds rather edgy, but the others in Bars 11-14 are (in my opinion) OK, and then the returns to E-major and (at Bar 17) A-major sound warmer owing to the fact that D♯ and G♯ make successively less incisive leading-tones than E♯:

Track 80: The whole piece.

The A-major fugue

Consider the D♯ at the end of Bar 2 in comparison with (a) the corresponding C♯ in the transposition to G-major and (b) the corresponding E♯ in the transposition to B-major:

Track 81: The beginning in A, then in G, then again in A, then in B, then once more in A.

When A♯ and E♯ come into play, they too – in addition to F♯, C♯, G♯ and D♯ – have suitably nuanced tunings:

Track 82: From the beginning to the beginning of Bar 20.

This “stretto fugue” is composed with lavish freedom as if to ensure that no musician familiar with it could possibly say that all the fugues in the set are “strict.”

The A-minor prelude

It is unusual to have an augmented 2nd in a melodically ascending minor scale, but this is how the upper edge of the tune climbs up from E to A in the first four bars. So, the leading-tone in the tune in Bar 3 should, in order to indicate that it will in fact lead up to the tonic, be equipped with a modicum of incisiveness in the tuning – which G♯ has in A-minor, but A itself lacks in the transposition to B♭-minor:

Track 83: Through most of Bar 4 in A, then through most of Bar 8 in B♭, then (louder) in A.

The A-minor fugue

The affect is less dark than in the other remarkably long fugues in the set. So, the tuning of the leading tone should provide a modicum of incisiveness (not too much, not too little). G♯ serves perfectly (whereas the resulting F♯ when the music is transposed to G-minor sounds a bit musty for such a long piece) – and D♯ is nuanced properly to serve as a slightly more incisive leading-tone than G♯:

Track 84: The head of the subject in A, and then in G; then through most of Bar 5 in A.

The B-major prelude

The first beat of Bar 2 ought to sound strong, and the fact that E♭-G is tempered more than B♭-D is helpful in this regard. When the music is transposed to A-major, the resulting D-major chord at Bar 2 sounds relatively retiring (because D-F♯ it is tempered less than A-C♯ or E-G♯) and this is, in my opinion, out of sorts with the virile quality of the piece:

Track 85: To the middle of Bar 3 in B♭, then in A, then again in B♭.

The B-major fugue

After the extravagant rhetoric of the prelude, this piece expresses a more moderate kind of jubilance. The sense of moderation is well served by the nuances of the tuning. In the head of the subject, the leading-tone and the 3rd degree of the scale are somewhat “laid back,” but not as much as they would have been if transposed to C-major:

Track 86: The first half of the subject in B♭, then in C, then again in B♭.

Four subsequent ways in which the nuances intensify discreetly the beauty of this piece (hovering as it does between jubilation and serenity) are as follows: (1) In Bars 6-16, the fact that E♮ makes an even less incisive leading-tone to F than A does to B♭ infuses a subtly moderate quality into the use of the key of the Dominant, F-major. (2) A rather mildly tuned leading-tone, F♯, is featured in Bars 17-25, culminating (logically) in the presentation of the subject in the relative minor (G-minor) in Bars 22-25. (3) For its presentation in C-minor in Bars 26-29, the head of the subject is altered, evading what would have been an expressively sinuous semitone between G and A♭ in Bar 26 by using B♭ there instead of A♭. (The idea that the subject may begin with a leap of a 3rd rather than with a neighbor-note motion has been established already in the tonal answers at Bars 5 and 13; but there is no such reason for the alteration here in Bar 26. It makes the alto’s quick A♭ sound more like a sweet 4th degree of A♭-major than a dark 6th degree of C-minor.) (4) Next come the smallest semitones in the piece – C♯-D in Bars 33-34 and A♭-G in Bars 34-40. The fact that A♭-G is smaller in this kind of tuning than it would be in Equal Temperament garnishes nicely the Subdominant feeling of E♭-major – after which the return to the Tonic key at Bar 42 is joyful in a delightfully moderate way, as what seems initially, in Bar 41, to be a tonal answer (to the statement that had begun in Bar 37) becomes instead a modulating statement of the subject. (And then the fact that the music has indeed returned to the Tonic key is celebrated by repeating the second half of the subject in Bars 45-47.)

Track 87: The whole piece.

The B-minor prelude

The nuances enable this dark piece to sound darker in B♭ than at the lower pitch-level of A-minor. In the middle of Bar 4 the dissonant harmonic semitone, F-G♭, is smaller and therefore more acutely incisive than its counterpart, E-F, in A-minor:

Track 88: To the beginning of Bar 5 in B♭, then in A, then again in B♭.

The expression of pathos in the last few bars is abetted by the throbbing effect, owing to the use of A♮ or D♮ in various chords, of beating at slower rates than would be the case in Equal Temperament:

Track 89: From Bar 19 to the end.

The B-minor fugue

The minor 9th between F and G♭ is more expressive than its counterpart (E-F) in A-minor:

Track 90: The first six notes of the subject in B♭ and in A, back and forth thrice.

The B-major prelude

The sense of delicacy in this piece is expressed better by the relatively high tuning of A♯ and E♯ than by their somewhat dull-sounding counterparts (B♮ and F♯) when the music is transposed up to C-major:

Track 91: To Bar 6 in B, then in C, then again in B.

The B-major fugue

The relatively high tuning of the leading-tone, and the brisk quality of D♯ in the tonic triad, prevent the piece from sounding routinely ecclesiastical as it would tend to do if transposed to C-major:

Track 92: The subject in B, then in C, then (louder) to the beginning of Bar 9 in B.

It was appropriate for the exposition of the first fugue in the set (the one in C-major) to sound ecclesiastical in a more laid-back way, but it would be insipid to revert to same kind of nuances in this fugal exposition, after all that has transpired in the preceding five pieces, i.e. the four in B♭-major and minor and the remarkably tender prelude in B-major.

The B-minor prelude

There is vital tension between (1) the extraordinarily strong sense of steady pacing in this piece on account of the left hand’s walking 8th-notes, and (2) an apparent call for rubato in the expressive chromaticisms toward the end of the piece: I have in mind (a) the sequence in Bars 36-38 as the top line ascends from F♯ to B garnished by a Neapolitan C (the highest note on the presumed instrument); (b) the left hand’s flagrant chromaticisms in Bars 43-45 (accompanying the right hand’s sequential pattern of syncopations to regain high B momentarily in the middle of Bar 45); and (c) the right hand’s tapering-off material in the last 1½ bars. (In Bar 46 there is an elision whereby an extra mini-coda – extra because a coda was embarked upon already in the middle of Bar 42 – postpones the arrival of the final B in the tune. It seems to me as if Bach were, with these two codas, boasting about his ability to write a Corelli-type slow movement more expressive than Corelli himself could do.)

When playing this piece in Equal Temperament I never yearn for nuances in the tuning (as I am likely to do when playing in Equal Temperament some of the other pieces in the set); and yet I do find certain notes even more beautiful in a properly nuanced tuning than in Equal Temperament – for instance most of the A♯’s and E♯’s in the last part of the piece, and the D♯ in Bar 48 (tempered less in relation to B than A♯ is relation go F♯):

Track 93: From the middle of Bar 31 to the end.

The B-minor fugue

The nuances are helpful throughout:

Track 94: The whole piece.

Now I have to admit that since the transpositions in this set of examples have been limited to the beginnings and ends of pieces, and since we have not confronted (a) all the instructive transpositions of this kind that could be extracted from the music with (b) recordings of the same transpositions performed in Equal Temperament, many possibilities for deriving beautifully interpretive performances from the nuances of an historically and aesthetically suitable style of unequal temperament have not been demonstrated here.

The full value of the nuances can gradually become apparent as the harpsichordist delves at length into exploiting them (by means of subtle nuances of articulation and timing) throughout the tonal fabric of the music. This calls for being alert to them and for shedding certain second-nature habits of interpretation resulting from the venerable tradition of playing these pieces in Equal Temperament and in concert halls (for which Bach did not intend them).

Prof. Sykes has expressed a similar opinion in his remarks about our collaboration:

"It has been a great pleasure for me to probe these pieces in this superbly suitable kind of tuning. I am looking forward with pleasure to further exploration in combination with the kinds of analytical thinking that are illustrated by Prof. Lindley's comments on the music. As a keyboard player, I have for many years been aware of the effect of this kind of unequal temperament harmonically: different chords having different degrees of purity. It requires a deeper level of awareness and musical focus to hear the effect of the temperament melodically: equivalent intervals nuanced differently in different keys. This has been the great discovery for me in participating in this project – listening for those inflections and letting them affect the shaping of the music.

Prof. Lindley's approach does involve the issue of genre. These pieces have never featured prominently in concertizing. They are better suited to 'Schubertiad'-type social occasions than to the kind of public solo recital (devoted entirely to compositions by people other than the soloist) that Franz Liszt pioneered in Berlin in 1842. They are even more suitable for private study and reflection, the ideal audience being the player himself. They embody the notion of pedagogy to an extent very rarely found in such great music. The player becomes both teacher and student in the act of playing, and the communication of musical values is deep as well as rich.

Bach is known to have played an entire set of WTC pieces on two occasions in a presumably intimate setting, i.e. for one of his students. He may well have played them on a harpsichord – and thus the qualities of the harmonic intervals due to the various rates of beating in the unequal temperament would have been more evident than in a public performance in a coffee house or a concert hall.

Now that high-quality recordings can convey to a large public the acoustical features of an intimate performance, Prof. Lindley's findings can help give to these exquisite pieces a special kind of beauty which Bach very may well have intended for them but which was lost in the meantime."

The kind of tuning discussed and demonstrated in this website is a thus resource for mitigating the mechanical nature of the harpsichord and the organ – and for augmenting the expressive possibilities of the piano in music that is historically suited to this style of unequal temperament.