Bach’s Cycle, Mozart’s Arrow: An Essay on the Origins of Musical Modernity

2 A Crystal Flying Like a Bullet

2 A Crystal Flying Like a Bullet A reader of Bach’s two sets of preludes and fugues The Well-Tempered Keyboard (WTC) will be struck by the emphatic gestures with which the composer often announces the approaching end of a fugue. In most of these fugues something happens a few measures before the end that alerts the listener to expect closure.Take the very first, the C-Major, fugue of the first set (Example 3). For the greater part of its duration it is impossible to predict when or how soon the fugue will come to an end.Then quite suddenly, in m. 23, it becomes apparent that Bach is wrapping things up. Indeed, the final cadence comes at the beginning of the next measure; the remaining four measures merely prolong the final tonic chord over the tonic pedal point.The ending, impossible to predict for most of the duration of the discourse , yet comes not abruptly but is, rather, emphatically announced five measures ahead. To understand how this effect is achieved, and, more important, why it is sought,it is necessary to understand how a fugue works.1 Like every fugue in the two sets, the C-Major Fugue begins by presenting its melodic subject successively once in each voice, either on the first or on the fifth scale step of the tonic key (mm. 1–71). In this case, though by no means always, the subject is constructed in such a way that the statement on the fifth scale step will reproduce the exact intervals of the original, first-scale-step, statement without any hint of a key change; this enables a so-called real answer. (In the case of a tonal answer the intervals of the fifth-scale-step presentation have to be adjusted to ensure that the key remains unchanged. Regardless of which method is used, what matters is that the subject be presented on both the first and fifth scale steps in the same key. Fugues more complex than this one may, of course, also introduce countersubjects and, 89 D4b D4a 15 D5b D5a vi/I/ 12 D 1 10 SET I D2 7 4 EXPOSITION I SET II example 3. Bach, WTC I, Fugue No. 1 in C Major; D = Demonstration later on,additional subjects.)What follows,in this and every fugue,is Bach’s demonstrations of what can be done with the subject contrapuntally. In the C-Major Fugue there are seven such demonstrations,each designed to show how the subject can be combined with itself in imitation (this is known as a stretto fugue). Most of these demonstrations involve the subject ’s statement on the first scale step and an answer on the fifth scale step. In this fugue the subject can be so imitated at the distance of one beat, with the answer either above the statement (Demonstration 1,mm.103–122,bass and alto, marked D1 in Example 3) or below (Demonstration 2 [D2], mm. 71–84, soprano and tenor), that is, in invertible counterpoint.2 Imitation is A Crystal Flying Like a Bullet / 91 example 3 (continued) 25 CODA D 6 I 22 D 7 V 20 D 3 (V) 18 also possible in minor (Demonstration 3 [D3],mm.191–204,tenor and alto), but then the real answer introduces a sharp sixth scale step that conflicts intolerably with the flat sixth scale step toward the end of the statement and hence necessitates at least one chromatic adjustment.Bach chose to sharpen the offending note in the statement. This imitation, too, might be inverted, but Bach makes no use of this possibility. What works better in minor, requiring no chromatic adjustments, is imitation at a fifth below and at the distance of two beats (Demonstration 4a [D4a],mm.171–191,tenor and bass). Again, this imitation might be inverted, and, again, Bach makes no use of the possibility.Instead,he does something much fancier (Demonstration 4b [D4b], mm. 162–191, soprano and alto, tenor and bass). Rather than use Demonstration 4a alone he combines it with Demonstration 2 to produce four-part imitation. He achieves this by following Demonstration 2 in C major at the distance of three beats by Demonstration 4a below in D minor . This causes fairly obvious parallel octaves between the first two notes of the bass and the alto, but Bach mitigated the problem somewhat (though only somewhat!) by eliminating the...