Thus far we have the set of key-relationships universally recognized since the major and minor modes were established, a relationship based entirely on the place of the primary tonic chord in the second key. It only remains for us to protest against the orthodox description of the five related keys as being the “relative” minor or major and the dominant and subdominant with their “relative” minors or majors; a conception which expresses the fallacious assumption that keys which are related to the same key are related to one another, and which thereby implies that all keys are equally related and that classical composers were fools. It cannot be too strongly insisted that there is no foundation for key-relationship except through a tonic, and that it is through the tonic that the most distant keys have always been connected by every composer with a wide range of modulation, from Haydn to Brahms and (with due allowance for the conditions of his musical drama) Wagner.
b. Indirect Relationships.—So strong is the identity of the tonic in major and minor mode that Haydn and Mozart had no scruple in annexing, with certain reservations, the key-relationships of either as an addition to those of the other. The smoothness of Mozart’s style makes him prefer to annex the key-relationships of the tonic minor (e.g. C major to A♭, the submediant of C minor), because the primary tonic note is in the second key, although its chord is transformed. His range of thought does not allow him to use these keys otherwise than episodically; but he certainly does not treat them as chaotically remote by confining them to rapid modulations in the development-portions of his movements. They occur characteristically as beautiful purple patches before or during his second subjects. Haydn, with his mastery of rational paradox, takes every opportunity, in his later works, of using all possible indirect key-relationships in the choice of key for slow movements and for the trios of minuets. By using them thus sectionally (i.e. so as not to involve the organic connecting links necessary for the complementary keys of second subjects) he gives himself a free hand; and he rather prefers those keys which are obtained by transforming the minor relationships of a major primary key (e.g. C to A major instead of A minor). These relationships are of great brilliance and also of some remoteness of effect, since the primary tonic note, as well as its chord, disappears entirely. Haydn also obtains extreme contrasts by changing both modes (e.g. C minor to A major, as in the G minor Quartet, Op. 72, No 6, where the slow movement is in E major), and indeed there is not one key-contrast known to Beethoven and Brahms which Haydn does not use with complete sense of its meaning, though his art admits it only as a surprise.
Beethoven rationalized every step in the whole possible range of key-relationship by such harmonic means as are described in the article [Beethoven]. Haydn’s favourite key-relationships he used for the complementary key in first movements; and he at once discovered that the use of the major mediant as complementary key to a major tonic implied at all events just as much suggestion of the submediant major in the recapitulation as would not keep the latter half of the movement for too long out of the tonic. The converse is not the case, and where Beethoven uses the submediant major as complementary key in a major first movement he does not subsequently introduce the still more remote and brilliant mediant in the recapitulation. The function of the complementary key is that of contrast and vividness, so that if the key is to be remote it is as well that it should be brilliant rather than sombre; and accordingly the easier key-relationships obtainable through transforming the tonic into minor do not appear as complementary keys until Beethoven’s latest and most subtle works, as the Quartet in B♭, Op. 130 (where we again note that the flat submediant of the exposition is temporarily answered by the flat mediant of the recapitulation).
c. Artificial Key-relationships.—Early in the history of the minor mode it was discovered that the lower tetrachord could be very effectively and naturally altered so as to resemble the upper (thus producing the scale C D♭ E♮ F, G A♭ B♮ C). This produces a flat supertonic (the chord of which is generally presented in its first inversion, and is known as the Neapolitan 6th, from its characteristic use in the works of the Neapolitan school which did so much to establish modern tonality) and its origin, as just described, often impels it to resolve on a major tonic chord. Consequently it exists in the minor mode as a phenomenon not much more artificial than the mode itself; and although the keys it thus connects are extremely remote, and the effect of their connexion very surprising, the connexion is none the less real, whether from a major or a minor tonic, and is a crucial test of a composer’s sense of key-perspective. Thus Philipp Emanuel Bach in a spirit of mere caprice puts the charming little slow movement of his D major Symphony into E♭ and obliterates all real relationship by chaotic operatic 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.[6] 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 when minor. Thus I represents tonic major, iv represents subdominant minor, and so on. A flat or a sharp after the figure indicates that the normal degree of the standard scale has been lowered or raised a semitone, even when in any particular pair of keys it would not be expressed by a flat or a sharp. Thus vi♭ would, from the tonic of B♭ major, express the position of the slow movement of Beethoven’s Sonata, Op. 106, which is written in F♯ minor since G♭ minor is beyond the practical limits of notation.
TABLES OF KEY-RELATIONSHIPS
2 Very rare, but the slow movement of Schubert’s C major String Quintet demonstrates it magnificently.