Arnold Schoenberg · section 51 of 66

Closes

In example 218 a plagal close was used in place of a cadence. This is often necessary in chorale harmonization, as in 226a, where one must resort to a plagal close if G is not to be the third of E-flat. The plagal close is a formula capable of ending even larger pieces, yet its effect is less clear and confirmatory than that of the authentic close. The most perfect close is achieved through the cadence. But a close of such perfection is not always desired; other types must often be used simply for contrast. Exclusive use of a strong cadential close can also be disturbing in another respect: the articulation may become too definitive, and above all definitive too often. Whereas melodic requirements in the course of a piece scarcely produce a need for a full close more than once or twice, the necessity of keeping individual phrases distinct without separating them too sharply occasions the use of formulas that close halfway, apparently, deceptively, or imperfectly. Here, whereas the cadence favors ascending progressions or equivalent combinations, an occasion arises for using descending ones. There are many names for such closes. Besides the authentic and plagal close, we may mention the full and half close, the perfect and imperfect full and half close, the perfect or imperfect authentic or plagal full or half close—a mixture of all these elements. For example: imperfect authentic half close, combination of plagal and authentic close … “And those are only the names!”

Since full and perfect closes can occur in the middle of a composition, and half and imperfect closes at its end; since closes are not absolutely necessary to emphasize articulation, because all these formal effects depend on more than harmony alone; since, furthermore, the great number of possibilities precludes giving each a name, and such a name would scarcely say anything characterizing or delimiting its possible use—I consider it more practical to classify them so that the pupil can produce all or most cases through combination and variation.

I. For this purpose, we first divide closes into two groups. A. Those in which the final three chords occur in the order IV (II)–V–I: the authentic close. The succession VI–V–I, in which overcoming the subdominant region is outwardly imitated by the strong root progression VI–V, must be included in this category for lack of a better classification. B. Those in which this order is not maintained.

II. In both groups, variations can be made through: a) rearrangement of the chord tones, or inversions; b) use of the seventh, ninth, and similar chords corresponding to the degrees; c) replacement of diatonic tones by nondiatonic ones—secondary dominants, the minor-subdominant relationship, and so on.

III. Important subsidiary forms arise in both groups when the principal triads, I, V, and IV, are replaced by their substitutes. The alterations listed under II a, b, and c can be applied to these.

IV. A further series of closes is obtained by proportional displacement, or transposition, of the forms listed above to the diatonic degrees and, in the sense of expanded tonality, to all degrees of the chromatic series. These transpositions may be: 1. inexact, a) using exclusively diatonic tones, b) using some nondiatonic tones; 2. exact, treating the degrees as keys.

Note: the cadential form IV–I(6/4)–V–I is to be understood here merely as a variant of IV–V–I: IV–(I(6/4)–) V–I.

I. Of group A, the two relationships IV–V–I and II–V–I, with II substituting for IV, are full closes only: 1. when they lead to the tonic; 2. when V is the dominant and consists of diatonic tones; 3. when I and V occur in root position.

II. We call all diatonic displacements of the authentic close to other degrees, and all transpositions that treat those degrees as keys, forms resembling a full close, and count them among the half closes. For example: V(♭)–VI(♯)–II(♯), VI–VII(♯5, ♯3)–III, V(♭)–I–IV, I–II(♯)–V, and so on, with the penultimate chord in dominant form.

III. We call all forms of the authentic succession that differ from full closes through the use of inversions and so forth, and all closes that establish other relationships through a different order or different degrees, half closes. Of these, we first single out:

1. The plagal close, characterized by the complete absence of V, the dominant, in the actual closing region, while the subdominant region, IV and II, is generally developed very broadly, yielding the succession IV (II)–I. It is usually regarded as a full close, seemingly justified by its frequent use for a final ending. But, as can easily be demonstrated, many unquestionable half closes can end quite satisfactorily when all the rhythmic, melodic, dynamic, and other closing resources of compositional technique cooperate, thus equaling full closes in this respect. It is therefore more correct to regard the plagal close too as a half close.

2. The deceptive close: IV–V–VI, II–V–VI, VI–V–IV, and so on.

IV. We divide the remaining half closes leading to the tonic into: 1. those that replace characteristic degrees of the underlying order IV (or II or VI)–V–I with less characteristic ones; for example, IV–III–I, II–III–I, VI–III–I, IV–VII–I, II–VII–I, VI–VII–I, III–V–I, VII–III–I, and so on;

2. those that a) give a different order, such as V(♭)–IV–I, V(♭)–II–I, V–VI–I; b) in this different order replace characteristic degrees with less characteristic ones, such as III(7, ♭3)–IV–I, VII(7)–II(7, ♭5)–I, III–VI–I, and so on; and, insofar as this is not already covered by the earlier categories, c) use entirely different degrees.

V. We divide those leading to secondary degrees into: 1. diatonic closes, represented here only by their last two chords. These are nothing other than displacements of those shown previously to other degrees, producing many unusable and uncommon forms.

a) Particularly common are those leading to V, because, faintly recalling the imperfect closing methods of the church modes, they were used as imperfect closes for punctuation, to emphasize articulation in longer pieces: IV–V, VI–V, II–V, I–V, and perhaps also III–V. Why IV (II)–V is a half close is explained by IV (II)–V–I, in which one stops halfway, closing internally.

b) VI–V and I–V, displaced to I, yield II–I and IV–I: plagal, hence half, closes. Not all imitative displacements of these successions to other degrees are customary, however.

c) The half-close character of VII–I, I–II, II–III, III–IV, and V–VI, formed on the model IV–V, is immediately apparent. The last is known as a deceptive close.

d) A frequently occurring close is II–III, called the Phrygian close, in which II usually appears as a sixth chord and III usually with an artificially raised major third.

2. Closes treating the degrees as keys. These offer the widest scope for combination, since the means known from the study of modulation, used appropriately and with attention to stylistic conditions, ensure smooth attainment of the goal.

The relationships resembling full closes that belong here have already been discussed and classified. Naturally, the variations will primarily involve the alterations of II that we have learned: secondary dominant, diminished seventh chord, augmented six-five and four-three chords, Neapolitan sixth, and the like. But the augmented triad, artificial minor and diminished triads, and everything derived from the minor-subdominant relationship can likewise be used in the same way as in cadences.

Since all the important matters are familiar from the cadences shown earlier, example 229 gives only examples of closes and half closes on secondary degrees.

The half close can often be used in chorale harmonizations, above all where melodic or harmonic characteristics make it necessary, but also for variety, to obtain softer contours. Occasionally, though not excessively often, the pupil may also use a deceptive close, as is found here and there in Bach. The passage will then clearly approach I but, after its V, bring VI or IV.