Czerny, Praktische Studien des Generalbasses, Op. 838: ninth chords

Czerny introduces the dominant with a minor ninth relatively early in his harmony exercise book. Much later he has a section titled "Der Nonen-Accord." It consists of one two-page composition, a 43-bar agitato that begins in C minor but ends triumphantly in C major.

With only three exceptions, the ninth chords are again dominants with a minor ninth--as at the first arrow below--and those ninths are resolved within the chord--as at the second arrow. Only over pedal point basses are the ninths allowed to resolve directly. In other words, Czerny's treatment of ninth chords is very conservative for the 1850s.

Two of the three dominants with major ninth are close together--see arrows below--and both resolve their ninths within the chord. (Chords with minor ninth are boxed.)

All this being the case, the primary closing cadence is a surprise: not only does it have a chord with major ninth (boxed) but that chord is treated in the manner I call the "waltz ninth," where 9 moves upward, the result being an emphatic ascending cadence gesture (beamed at (a)).  (At (b) is an example of the minor ninths over a pedal point.) Here it is Beethovenian heroic transcendence we are hearing, definitely not a lilting upward turn to end a waltz or polka.

A Curiosity: Czerny, Praktische Studien des Generalbasses, Op. 838

Carl Czerny's Studien zur praktischen Kenntniss aller Accorde des Generalbasses auf dem Pianoforte sowohl in festen als bewegten Finger-Übungen, Op. 838—or simply "Praktische Studien des Generalbasses," as the interior title page has it—was published in Vienna by Spina in the early 1850s.

Czerny's foreword is a short paragraph that immediately suggests his attitude toward the subject:

The study of figured bass can only be of real value to the student if he learns to play all the chords in their many forms on the piano and is able to play them securely. The present work offers a contribution to that goal, in that the first nine numbers present the chords in block-chord form, and the remaining numbers the same chord repertoire in elaborated form, so that the student can be made more familiar with the various harmonic combinations. (my translation)

His footnote to the title of the first section is decidedly more revealing: "The figures in all of these examples must be worked out by the student, who can avail himself if necessary of help from a textbook or a teacher." Thus, Czerny is really offering a practical diatonic and chromatic chord primer, not a figured-bass textbook.

The first example is of interest here. It covers all 24 major and minor triads in a total of 13 bars. The upper most voice covers the distance of an ascending octave, C5-C6.

The pattern of thirds within fifths—C-a-F in bars 1-2—is strictly maintained throughout, and it charts a simple path through the Riemannian Tonnetz. Here is a fragment of a common representation of the Tonnetz, with arrows showing the starting path of Czerny's progression:

And here is the entire sequence, separated out from the diagram:

I should note, incidentally, that is impossible to maintain the close voicing in the right hand with anything other than a rising line. Analogously to suspensions, which tend to force voice leading down, relative (R) and leading-tone (L) relations force voice leading upward.