connecting links. Haydn’s greatest pianoforte sonata (which,
being probably his last, is of course No. 1 in most editions)
is in E♭, and its slow movement is in F♮ major (= F♭). That
key had already appeared, with surprising effect, in the wanderings
of the development of the first movement. No attempt is
made to indicate its connexion with E♭; and the finale begins
in E♭, but its first bar is unharmonized and starts on the one
note which most contradicts E♮ and least prepares the mind for
E♭. The immediate repetition of the opening phrase a step
higher on the normal supertonic strikes the note which the opening
had contradicted, and thus shows its function in the main
key without in the least degree explaining away the paradoxical
effect of the key of the slow movement. Brahms’s Violoncello
Sonata Op. 99, is in F; a prominent episode in the development
of the first movement is in E♯ minor (= G♭), thus preparing the
mind for the slow movement, which is in F♯ major (= G♭), with
a central episode in F minor. The scherzo is in F minor, and
begins on the dominant. Thus if we play its first chord immediately
after the last chord of the slow movement we have exactly
that extreme position of flat supertonic followed by dominant
which is a favourite form of cadence in Wagner, who can even
convey its meaning by its mere bass without any harmonies
(Walküre, Act 3, Scene 2: “Was jetzt du bist, das sage dir selbst”).
Converse harmonic relationships are, as we have seen, always weaker than their direct forms. And thus the relation of C major to B major or minor (as shown in the central episode of the slow movement just mentioned) is rare. Still more rare is the obtaining of indirect artificial relationships, of which the episode in the first movement just mentioned is an illustration in so far as it enhances the effect of the slow movement, but is inconclusive in so far as it is episodic. For with remote key-relationships everything depends upon whether they are used with what may be called cardinal function (like complementary keys) or not. Even a near key may occur in the course of wandering modulations without producing any effect of relationship at all, and this should always be borne in mind whenever we accumulate statistics from classical music.
d. Contrary and Unconnected Keys.—There remain only two pairs of keys that classical music has not brought into connexion, a circumstance which has co-operated with the utter vagueness of orthodox theories on the subject to confirm the conventionally progressive critic in his conviction that all modulations are alike. We have seen how the effect of modulation from major tonic to minor supertonic is, on a large scale, obscured by the identity of the primary dominant with the secondary subdominant, though the one chord is major and the other minor. Now when the supertonic becomes major this difference no longer obviates the confusion, and modulation from C major to D major, though extremely easy, is of so bewildering effect that it is used by classical composers only in moments of intensely dramatic surprise, as, for example, in the recapitulation of the first subject of Beethoven’s Eroica Symphony, and the last variation (or coda) of the slow movement of his Trio in B♭, Op. 97. And in both cases the balance is restored by the converse (and equally if not more contradictory) modulation between major tonic and major flat 7th, though in the slow movement of the B♭ Trio the latter is represented only by its dominant chord which is “enharmonically” resolved into quite another key. The frequent attempts made by easy-going innovators to treat these key-contrasts on another footing than that of paradox, dramatic surprise or hesitation, only show a deficient sense of tonality, which must also mean an inability to see the intensely powerful effect of the true use of such modulations in classical music, an effect which is entirely independent of any ability to formulate a theory to explain it.[1] There now remains only one pair of keys that have never been related, namely, those that (whether major or minor) are at the distance of a tritone 4th. In the first place they are unrelated because there is no means of putting any form of a tonic chord of F♯ into any form of the key of C, or vice versa; and in the second place because it is impossible to tell which of two precisely opposite keys the second key may be (e.g. we have no means of knowing that a direct modulation from C to F♯ is not from C to G♭, which is exactly the same distance in the opposite direction). And this brings us to the only remaining subjects of importance in the science and art of harmony, namely, those of the tempered scale, enharmonic ambiguity and just intonation. Before proceeding we subjoin a table of all the key-relationships from major and minor tonics, representing the degrees by capital Roman figures when the second key is major and small figures
- ↑ Many theorists mistake the usual extreme emphasis on the dominant chord of the dominant key, in preparation for second subjects, for a modulation to the major supertonic, but this can deceive no one with any sense of tonality. A good practical test is to see what becomes of such passages when translated into the minor mode. Illusory modulation to the flat 7th frequently occurs as a bold method of throwing strong emphasis on to the subdominant at the outset of a movement, as in Beethoven’s Sonata, Op. 31, No. 1.
