Last semester in my Theory III class, we spent time looking at the final movement of Mozart’s Symphony No.40, and we focused for a day on that wonderful, nearly-dodecaphonic passage that begins the movement’s Development Section. In the span of just a few measures, Mozart manages to include every pitch except G, the tonal center of the movement and entire symphony.

I began to wonder if there are any “12-tone” passages in any of Bach’s 371 chorales, and since the chorales have been the focus of an ongoing project of mine, I set out to investigate. While many of the chorales use all twelve pitches, I wanted to know if there are any single phrases among the 371 chorales that use them all.

Before answering the question, it should be pointed out that composing a non-modulating passage that utilizes traditional functional harmony and that contains all twelve pitches is fairly simple to do. In a minor mode, it only takes this simple progression: i6–viio7/iv–iv–V6/V–V7–i.

If we exclude the notes of the harmonic minor scale (which are introduced by the most basic of diatonic progressions: i–iv–V), the remaining tones to be included are the following scale degrees: flat-2 (ra), #3 (mi), #4 (fi), #6 (la), and natural-7 (te). Fi and la are included via the tonicization of V, while mi, te, and ra are included via the tonicization of iv with a leading-tone seventh chord. (A secondary dominant of iv fails to include ra.)

While two tonicizations are featured in the basic progression above, the overall tonal center (C, in the basic example above) is by no means obscured as it is in Mozart’s Development.

Now to Bach. There are no fewer than six chorale phrases that make use of all twelve chromatic pitches:

1) Chorale 132, phrase 16

2) Chorale 138, final phrase

3) Chorale 242, phrase 6

4) Chorale 279, final phrase

5) Chorale 300, phrase 1

6) Chorale 360, final phrase

All six of these phrases make use of tonicizations of both the subdominant and dominant, and therefore are to varying degrees elaborations of the simple progression above. Of these six phrases, five are in a minor mode (all but #279). Two of these five in minor (#242 & #360) tonicize the subdominant with a secondary dominant rather than a secondary leading-tone seventh chord, requiring that ra be introduced in some other way. Turning now to the one remaining phrase in the major mode (#279), other scale degrees are left untouched by the tonicizations of the subdominant and dominant. The V65/iv and V65/V included in the final phrase of Chorale #279 leave ra, me, and le to be included by other means.

The simplest, most straightforward phrase comes from Chorale #300 “Warum betrübst du dich, mein Herz.” Here is the initial phrase of that chorale:

The ascending chromatic bass line that characterizes the basic progression above is present here. Simple unembellished secondary leading-tone seventh chords introduce the necessary chromatic pitches while the prominent contrapuntal interplay occurs between soprano and bass: the soprano initially imitates its counterpart before working in contrary motion towards the half cadence. Even with the tonicizations, the tonal center of A is never obscured.

The sixteenth phrase of the lengthy Chorale #132 (“Kyrie, Gott Vater in Ewigkeit”) also features a rising chromatic bass line to the dominant, though here the upper voices provide more embellishments on the basic progression than did Chorale #300.

Aside from the added suspensions and the resolution of V to I creating an authentic cadence, the progression is very similar to #300.

The final phrase of Chorale #138 (“Jesu, meine Freude”) is further removed from the basic progression. While the same chromatic chords are used to produce the missing chromatic pitches, the progression is shuffled.

With the tonicization of iv resolving to a major IV chord instead of minor iv, le (C-natural in this case) is left untouched by the basic progression. Here the C is included by both a viio7 chord and a passing tone in the bass between inversions of the secondary leading-tone chord tonicizing iv. (The viio7 chord ensures that all twelve tones occur in the structural progression, rather than chromatic tones being introduced as embellishing non-chord tones.)

The remaining three “12-tone” phrases are more intriguingly complex. The sixth phrase of Chorale #242 (“Wie bist du, Seele”) and the final phrase of Chorale #360 (“Wir Christenleut’”) are related. Both feature the rising chromatic bass line; both feature a tonicization of III in addition to the other tonicizations of iv and V; and both use a secondary dominant chord rather than a secondary leading-tone seventh chord to tonicize iv, leaving ra to be introduced in some other way.

While the contrary motion between outer voices provides an engaging counterpoint, the more interesting interplay occurs between the inner voices. Through imitation of each other, the two voices create a kind of overlapping heterophony, coming together at several places along the way. While the predominant surface level gestures are downward, the structural line is upward, matching the bass’s ascent: B–D–E(–F#). Ra (F—natural here) is introduced as an appoggiatura figure that signals the oncoming tonicization of the subdominant.

(If one wishes to include this ra as a structural chord tone, there are several options. One might argue that the appoggiatura figure creates an unresolved V7/VI; or one might say that a VII7/iv (or even a “V7/III of iv”?) is created by the F-natural; or, finally, one might suggest that the III(7)–V6/iv–V65/iv–iv progression is really a deceptive progression in C minor in which the arrival of the vi chord is embellished with a tonicization.)

The final phrase of Chorale #360 (“Wir Christenleut”) is similar to the phrase from Chorale #242. The interplay and heterophonic treatment of inner voices is prevalent, though the bass participates to a greater extent, embellishing its ascent to sol. The melody is the same as in #242 apart from reiterations of me and fa on the way up to the sol at its midway point.

Interestingly, these reiterations in the melody allow Bach to tonicize ra (flat-2) that would otherwise be missing: the VI chord on the added me in the melody functions as a V/N resolving to N53 on the added fa in the melody. What this also does is extend the chromatic rising bass line to nine pitches (from ti to sol) rather than just six (from re to sol).

The final phrase of Chorale #279 (“Ach Gott und Herr”) is the most tonally ambiguous of the six.

It begins with a V6 that implies the Bb major tonal center of the entire chorale but moves immediately to what initially sounds like a tonicization of the supertonic: V65/ii. However, the chord that immediately follows, what appears to be a V65/iii, alters one’s assessment of the V65/ii chord as being a IV65/iii instead. One anticipates the common progression IV65–V65–i in the key area of iii (d minor here). However, the tonicized chord, d minor, is never reached. The soprano does no cooperate with the lower voices’ tonicizing project. The soprano’s A, which should be functioning as the dominant of the tonicized d minor, functions as if remaining in the home key of Bb–that is, as ti resolving to do. The resulting aural effect is one of a displaced resolution of the V6 that began the phrase, with two intervening tonicizing chords that in retrospect are heard almost as mistakes, as an aborted effort to modulate.

As mentioned at the beginning of the discussion about Bach’s “12-tone” phrases, in the major mode, ra, me and le are left untouched by the tonicizations of IV and V using secondary dominant seventh chords. The reader may also have noticed that in my initial description of this phrase, I referred to the “V65/iv,” tonicizing the minor iv rather than the major IV that is diatonic in the major mode. This is because Bach uses mode mixture in the second half of the phrase, creating the aural effect of a picardy third ending. The minor iv chord introduces the missing le (Gb), (which is also introduced as a si in the viio7/vi chord). Ra (Cb) is introduced as a di (B-natural) in the V65/ii chord., and me (Db) is introduced as ri (C#) in the V65/iii chord.

The minor v chord in the phrase’s second full measure, the first mode mixture chord, creates perhaps even more tonal ambiguity than the toniciztions of ii, iii and vi that precede it. The reason is that the Ab (te) of the minor v chord is a chromatic tone that is not imbued with tonicizing implications, as were all previous chromatic tones. After the minor v, the agogic accent of the Bb in the soprano emphasizes the return to a Bb tonal center. The ensuing tonicization of iv leading into the plagal ending creates an engaging descending sequence of tonicizations of minor key areas–vi, then v, then iv. When all is said and done, not only are all 12 chromatic pitches present in this phrase, but every nearly-related key area in Bb is tonicized, despite the fact that not all tonicized chords appear where expected (as well as the fact that the minor iv and v chords are substituted as mode mixture).