mere survival of ancient customs, at least where great masters
are concerned. (This final major chord is known as the Tierce
de Picardie.) The effect of the minor mode is thus normally
plaintive because it centres round the artificial concord instead
of the natural; and, though the keynote bears this minor
artificial triad, the ear nevertheless has an expectation (which
may be intensified into a powerful emotional effect) that the
final conclusion of the harmonic scheme may brighten out into
the more sonorous harmonic system of major chords. Let us
once more recall those ecclesiastical modes of which the 3rd
degree is normally minor. We have seen how they may be
regarded as the more oblique of the various cross-sections of the
16th-century harmonic scheme. Now, the modern minor mode
is too firmly rooted in its minor tonic chord for the 16th-century
feeling of an oblique harmonic scheme to be of more than
secondary importance, though that feeling survives, as the
discussion of key-relationships will show us. But it is constantly
thrust into the background by the new possibility that the minor
tonic chord with its attendant minor harmonies may give place
to the major system round the same tonic, and by the certainty
that if any change is made at the conclusion of the work it will
be upon the same tonic and not have reference to some other
harmonic centre. In other words, a major and minor key on
the same tonic are felt as identical in everything but expression
(a point in which the Tonic Sol Fa system, as hitherto practised,
with its identification of the minor key with its “relative”
instead of its tonic major, shows a most unfortunate confusion
of thought). The characteristics of the major and minor modes
may of course be modified by many artistic considerations, and
it would be as absurd to develop this account into a scheme of
pigeon-holed passions as to do the same for the equally obvious
and closely parallel fact that in drama a constant source of
pathos is the placing of our sympathies in an oblique relation
to the natural sequence of events or to the more universal issues
of the subject.
V. Key-Relationships.—On the modern sense of the identity of the tonic in major and minor rests the whole distinctive character of modern harmony, and the whole key-system of the classical composers. The masters of the 16th century naturally found it necessary to make full closes much more frequently than would be desirable if the only possible close was that on the final of the mode. They therefore formed closes on other notes, but they formed them on these exactly as on a final. Thus, a close on the second degree of the Ionian mode was identical with a Dorian final close. The notes, other than the final, on which closes could be made were called modulations. And what between the three “regular modulations” (known as the dominant, mediant, and participant) and the “conceded modulations,” of which two were generally admitted in each mode simply in the interests of variety, a composer was at liberty to form a full close on any note which did not involve too many extraneous sharps or flats for its correct accomplishment. But there was a great difference between modal and modern conceptions of modulation. We have said that the close on the second degree of the Ionian mode was Dorian, but such a modulation was not regarded as a visit paid to the Dorian mode, but merely as the formation of a momentary point of repose on the second degree of the Ionian mode. When therefore it is said that the modulations of 16th-century music are “purposeless and shifting,” the criticism implies a purpose in change of key which is wholly irrelevant. The modal composers’ purpose lay in purely local relationships of harmony, in various degrees of refinement which are often crowded out of the larger and more coarse-grained scheme of modern harmony, but which modern harmony is perfectly capable of employing in precisely the same sense whenever it has leisure.
Modulation, in the modern sense of the term, is a different thing. The modern sense of tonality is so firm, and modern designs so large, that it is desirable that different portions of a composition should be arranged round different harmonic centres or keys, and moreover that the relation between these keys and the primary key should be felt, and the whole design should at last return to the primary key, to remain there with such emphasis and proportion as shall leave upon the mind the impression that the whole is in the primary key and that the foreign keys have been as artistically grouped around it as its own local harmonies. The true principles on which keys are related proved so elastic in the hands of Beethoven that their results utterly outstripped the earlier theory which adhered desperately to the limitations of the 16th century; and so vast is the range of key which Beethoven is able to organize in a convincing scheme of relationship, that even modern theory, dazzled by the true harmonic possibilities, is apt to come to the conclusion, more lame and impotent than any ancient pedantry, that all keys are equally related. A vague conception, dubbed “the unity of the chromatic scale,” is thus made to explain away the whole beauty and power of Wagner’s no less than Beethoven’s harmonic system. We have not space to dispute the matter here, and it must suffice to state dogmatically and statistically the classical facts of key-relationship, including those which Beethoven established as normal possibilities on the suggestion of Haydn, in whose works they appear as special effects.
a. Direct Relationships.—The first principle on which two keys are considered to be related is a strengthening of that which determined the so-called modulations of the 16th-century modes. Two keys are directly related when the tonic chord of the one is among the common chords of the other. Thus, D minor is related to C major because the tonic chord of D minor is the common chord on the supertonic of C (see Ex. 6). In the same way the four other related keys to C major are E minor the mediant, F major the subdominant, G major the dominant and A minor the submediant.
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This last key-relationship is sometimes called the “relative” minor, partly because it is usually expressed by the same key-signature as the tonic, but probably more justifiably because it is the point of view from which to reckon the key-relationships of the minor tonic. If we take the minor scale in its “harmonic” form (i.e. the form deducible from its chords of minor tonic, minor subdominant and major dominant, without regard to the exigencies of melody in concession to which the “melodic” minor scale raises the 6th in ascent and flattens the 7th in descent), we shall find it impossible to build a common chord upon its mediant (Ex. 10). But we have seen that A minor is related to C major; therefore it is absurd to suppose that C major is not related to A minor. Clearly then we must deduce some of the relationships of a minor tonic as the converse of those of a major tonic. Thus we may read Ex. 6 backwards and reason as follows: A minor is the submediant of C major; therefore C major is the mediant or relative major of A minor. D minor is the supertonic of C major; therefore C major is related to D minor and may be called its flat 7th. Taking A minor as our standard key, G major is then the flat 7th to A minor. The remaining major keys (C major to E minor = F major to A minor) may be traced directly as well as conversely; and the subdominant, being minor, does not involve an appeal to the major scale at all. But with the dominant we find the curious fact that while the dominant chord of a minor key is major it is impossible to regard the major dominant key as directly related to the minor tonic, since it does not contain the minor tonic chord at all; e.g. the only chord of A in E major is A major. But the dominant minor key contains the tonic chord of the primary minor key clearly enough as subdominant, and therefore when we modulate from a minor tonic to a minor dominant we feel that we have a direct key-relationship and have not lost touch with our tonic. Thus in the minor mode modulation to the dominant key is, though frequent and necessary, a much more uphill process than in the major mode, because the naturally major dominant chord has first to be contradicted. On the other hand, a contrast between minor tonic and major dominant key is very difficult to work on a large scale (as, for example, in the complementary key for second subjects of sonata movements) because, while the major dominant key behaves as if not directly
