CLASSICAL A fundamental proposition in the aesthetics of tonality is that key-relationship subsists between two tonics only and has nothing to do with the intervention of a third tonic. Observe the word tonic ; the proposition commits us to no specified mode on either side of the relation.
Direct relationship exists between two keys when the tonic chord of one is among the common chords of the other. If our first key is major, we simply identify its related keys with its common-chords other than its tonic; thus Ex. 14 shows that C major is directly related to five keys, D minor the supertonic, E minor the mediant, F major the subdominant, G major the dominant, and A minor the submediant.
The relatives of a minor tonic have to be discovered by a con verse process, for the minor scale is so unstable that the evidence of its common chords is conflicting and misleading. For instance, the dominant chord of a minor key is major. But you will receive a shock if you try answering the subject of Bach's G minor Fugue, Bk. I., No. 16, of Das W ohltemperirte Klavier in D major in stead of D minor ! Evidently the only directly related dominant key to a minor tonic is also minor. This being so, the sub dominant must be minor also, for it is the converse of the dominant, the key to which the tonic is dominant. In order to reach it the tonic chord must become major, a pathetic effect constantly to be found near the end of classical slow movements in minor keys.
The other relations of a minor tonic are converse to the rela tions of a major tonic. Thus, if D minor be the supertonic of C major, we must find a name for the relation of C major to D minor. We run up the scale of D minor and find that C is its flat 7th. Similarly, if E minor is the mediant of C major, then C major is the flat 6th or submediant of E minor; and, lastly, if A minor is the submediant or relative minor of C major, then C major is the mediant or relative major of A minor. And so the relations of a minor tonic may be obtained by reading Ex. 14 backwards, with A minor as the key of reference. Transpos ing Ex. 14 so that vi. becomes C minor, we obtain the following five relations: B flat major the flat 7th, A flat major the sub mediant, G minor the dominant, F minor the subdominant, E flat the mediant (or relative major).
It is now easy to describe the drift of the Handelian chords of Ex. 13. The key-signature is that of E major, a key that differs only in pitch and in minute instrumental technicalities from all other major keys. (Ideas as to the characters of keys in themselves are entirely subjective, and no agreement is to be expected about them.) The first chord is a common-chord of B major, the dominant of E. In its present context it represents not only the dominant chord, but the dominant key, for it happens to be the close of a passage in B major. The next chord is still a dominant chord, but effects a return to E, being the last inversion of the dominant 7th thereof. The 7th is in the bass, and duly resolves on G sharp in the next chord, a first inversion of E (bar 3). Handel would have had less scruple than many later writers in letting the bass skip down to E, so long as the G sharp was somewhere in the chord, but here he is making his bass regularly descend the scale. The next step, F sharp, supports another dominant chord, that of C sharp minor (vi. from our tonic) in its last inversion, like that in bar 2. It also resolves in bar 5. Bar 6 passes to the subdominant (A major) and bar 7 establishes that key in a manner to remove all doubt by striking its subdominant chord, which is wholly outside the range of E major. The natural result is the full close in A major in bar 8. Such is the normal way of using key-relations in the essentially Neapolitan art of Handel; and all the intensity of Bach's thought adds nothing to its essential elements. When Bach modulates more widely his purpose is, like that of Handel in "Thy rebuke hath broken his heart," not to explain, but to astound.
Another great change had to enlarge the art of music before key-relationships could attain their full meaning; but this time the change was accomplished without a period of chaos. It was like Kant's "Copernican revolution" in philosophy; and its more general aspects are discussed in the articles INSTRUMENTATION, MUSIC, OPERA and SONATA FORMS.
Its first effect on harmony was shown in a drastic simplifica tion of style ; for music had now become dramatic, and there was no musical resource of more cardinal dramatic importance than changes of key. Consequently the baldest facts of key-relation became dramatically significant, out of all proportion to their direct intellectual import. A musical historian can make no graver blunder than to mistake Mozart's and Haydn's harmonic simplicity for an intellectual simplicity. To prolong a prepara tory harping on the dominant of a new key is equivalent to working up the entry of an important person in a drama.
A hundred years before the problem which Alessandro Scar latti solved in his youth might be described as that of finding the dominant. The simple-seeming Mozart is, as often as not, mock ing us with the riddle "When is a dominant not a dominant?" Musical perspective has gained another new depth in its command of planes. A modulation may establish a new key firmly enough for an incident in the course of a melody, but not nearly firmly enough for a new stage in the whole scheme. Conversely, a passage which at first sounded like vehement emphasis on the local dominant may, long afterwards, when the dominant key has been firmly established, be given note for note at the same pitch with a triumphantly tonic effect. And the dimensions over which Mozart's tonality maintains its coherence are enormous; sometimes almost on Beethoven's largest scale.
Music, which in Palestrina's age was "a linked sweetness long drawn out," with the links extending only from one accent to the next, had by the beginning of the 18th century trained the mind to measure harmonic relations over melodic periods of eight or more bars ; and the mighty polyphony of Bach and Handel broke down the melodic regularity, but did not greatly enlarge the range over which the listener must depend on his memory. These masters can visit the same key several times in a composition without inciting the listener to notice the fact either as a purpose or as a tautology. But Mozart, Haydn and Beethoven build confidently on a knowledge of the exact effect that a modulation in one passage will have on a passage five or even ten minutes later. Beethoven's enormous architectural and dramatic power enabled him to discover and command the whole range of key relationship theoretically possible within any definite meaning of the term. There is no limit to the possible range of modulation, as Bach took pains to show ; but "the unity of the chromatic scale" is a feeble dogma on which to base the notion that Beet hoven ought to have treated all keys as equally related, instead of drawing the line where he did. Great artists discover facts and resources, not licences and vagaries.
Haydn, Mozart, Beethoven, Schubert, Brahms and Wagner all agree in one simple and cogent method of extending the direct or natural series of key-relations. They merely changed the modes of either or both numbers of a directly related pair. Certain reservations were necessary; the supertonic of a major key which is quite happy as a minor neighbour completely fails to sound like a major key in its own right and behaves merely like "dominant preparation" for the ordinary dominant. An analyst who imputes the key of A major to bars 19-24 of the first movement of Beethoven's G major sonata op. 14, No. 2, when he hears them in their context, should not attempt to discuss key relationship until he can discriminate between a passage on the dominant and a passage in the dominant.
What is true of one key-relationship will be true of its con verse : the key of the flat 7th refuses to assert itself as a real key in relation to a major tonic. A dozen accessory chords in D major would not make the 7th bar of Ex. 13 amount to more than the subdominant chord in A major until they included a chord of G. The testimony of such openings as those of Beetho ven's sonatas opp. 31 (No. 1) and 53 is emphatic.
In the rare cases where such keys do not thus explain them selves away, their effect is startling. (Ineptitudes may be neglected.) The passage that follows the return of the main theme in the first movement of Beethoven's Eroica symphony is one of the supreme dramatic strokes in music. The hard-won tonic of E flat gives way first to F major and then to the opposite extreme, a 3rd lower, D flat. Another third down brings us safely to our own dominant chord.
One other type of key-relation is derived from a special form of the minor scale, in which the lower tetrachord is made to correspond with the upper— conclusive evidence as the return of the opening theme.
Here are two tables, indicating by Roman figures the whole scheme of key-relationships, first from a major tonic, secondly from a minor tonic. Flats indicate degrees flattened in compari son with those of the major scale of reference; and in Table B sharps are used to distinguish cases where the key is a semitone above the corresponding degree of a minor scale. Thus, if C be the tonic, E major will be represented by III in Table A, and by III# in Table B. In either table the figure iiib would, reckoned from C, be E flat minor.
The first inversion of its flat supertonic chord is known as the Neapolitan 6th ; and the Neapolitan key-relations are the flat supertonic major, equally related (as the E natural in Ex. 16 shows) to a major and a minor tonic, and the converse relation of the sharp 7th. A minor tonic has no direct converse relation, for the Neapolitan chord is major. But, as Schubert shows at the end of the first movement of his D minor quartet and in the slow movement of his string quintet in C, an indirect relation may be established by making the Neapolitan chord minor.
We must beware of imputing relationship to keys separated by discursive modulation unless we have strong collateral evi dence from the key-functions of a musical design. Tonality and form are inseparable ; and great composers do not even expect the tonic to be recognized after long wanderings without some such The characters of key-relationships are solid facts, and they probably have some bearing on the various subjective ideas which many music-lovers entertain as to the character of keys in them selves; for nobody can name a key without being aware of its distance from C major. Be this as it may, it is an undisputed fact that modulations in a dominant direction have an effect of action, while modulations towards the subdominant have an effect of retirement. With a major tonic the three remaining directly-related keys are minor, a contrast which outweighs their other distinctive characters. To move from a major tonic to the relations of its tonic minor, such as IIIb and VIb, is to pass into deep and warm shadow. Such modulations form characteris tic purple patches in the course of Mozart's "second subjects." Changes from a major tonic to the major mode of its mediant or submediant are extremely bright. Haydn, who explored all the range of tonality in contrasts between whole movements, or between a minuet and its trio, is very fond of using them in this way in his later works. Beethoven incorporates them in the most highly-organized functions of his sonata-movements. The Neapolitan relations appearing once as a paradox in Haydn's last pianoforte sonata, are completely rationalized by Beethoven, Schubert and Brahms. The flat supertonic casts a deep warm shadow over the tonal scheme, and becomes sheer blackness in the rare cases where it is changed to minor. Conversely, the move a semitone downwards from the tonic (to VII# or vii#) is a move into mysterious brightness. Other extreme depths are sounded in the double changes from a major tonic to iiib or vib; which (with convenient change of notation) may be found in Beethoven's sonata op. 106 and Schubert's last pianoforte sonata. The converse relations III# and VI# from a minor tonic are very bright ; the only really bright contrasts that the minor key-rela tions possess. Beethoven's C minor concerto shows III#, and his F minor quartet shows VI#.
The great classical tradition cares little for the study of chords as things in themselves ; and the art of harmony perishes under a discipline that separates its details from counterpoint and its larger issues from form. An excellent means of mastering a good harmonic vocabulary is to practise the filling-out of classi cal figured basses at the keyboard ; in other words, to exercise the function of the continuo-player who, from the time of Monte verdi to that of Beethoven's organ-teachers, used to supply ac companiments from a bass with figures indicating the gist of the chords required. Fluency in such a practice does not of itself confer the ability to produce original harmony, but it means that music can be read with understanding. It is an empiric craft. But it had the misfortune to become a science, when, early in the i 8th century, Rameau discovered the theory of the funda mental bass. This is an imaginary bass (best when most imagi nary) that gives "roots" to all the essential chords of the music above it. The conception is true only of the most obvious har monic facts ; beyond them it is as vain as the attempt to ascer tain your neighbour's dinner from a spectrograph of the smoke from his chimney. The augmented 6th which arose so innocently in Ex. 12 requires a double root. The first chord of Beethoven's sonata in E flat, Op. 31 No. 3, is an "eleventh" with its root on the dominant in flat defiance of the fact that the dominant is the most inconceivable bass-note in the whole passage until it arrives as a climax in the sixth bar. But musical fundamentalists refuse to look six bars ahead.
Philipp Emanuel Bach, in conversation with Dr. Burney (The Present State of Music in Germany, etc.), said that Rameau's theory was "childish, for it reduces all music to full closes." This is perfectly true, and the theory did no harm to i 8th century French music, which eschewed long sentences and seldom strayed far from the regions of the full close. But in England Rameau's doctrine raged unchecked by taste or common sense, and culmi nated in Dr. Day's famous application of homoeopathy to the art of music. This would have mattered less if Dr. Day had not gained the ear of the greatest English academic musicians of Mid-Victorian times. As Sir Charles Stanford aptly says (Musi cal Composition), Day's theory "irrigated a wide area of low lying ground, and we are still suffering from the effects of its miasma." The remedy lies in cultivating vivid impressions of the actual relations between counterpoint and harmony in detail, be tween tonality and form in general, and between key-relations and chromatic chords. To this end, thorough-bass should be culti vated not on paper but at the keyboard, with passages (graded according to difficulty) from the continuos of Bach's cantatas and Mozart's church music.