��The real point of difficulty in modulation is not the manner in which the harmonies belong- ing to different keys can be made to succeed one another, but the establishment of the new key, especially in cases where it is to be per- manent. This is effected in various ways. Fre- quently some undoubted form of the dominant harmony of the new key is made use of to confirm the impression of the tonality, and modulation is often made through some phase of that chord to make its direction clear, since no progression has such definite tonal force as that from dominant to tonic. Mozart again, when he felt it necessary to define the new key very clearly, as representing a definite essential feature in the form of a movement, often goes at first beyond his point, and appears to take it from the rear. For instance, if his first section is in C, and he wishes to cast the second section and produce what is called his second subject in the dominant key G, instead of going straight to G and staying there, he passes rapidly by it to its dominant key D, and having settled well down on the tonic harmony of that key, uses it at last as a dominant point of vantage from which to take G in form. The first movement of the Quartet in C, from bar 22 to 34 of the Allegro, will serve as an illustration. Another mode is that of using a series of transitory modulations between one permanent key and another. This serves chiefly to obliterate the sense of the old key, and to make the mind open to the impression of the new one directly its permanency becomes apparent. The plan of resting on dominant harmony for a long while before passing definitely to the subjects or figures which are meant to characterise the new key is an obvious means of enforcing it; of which the return to the first subject in the first movement of Beethoven's Waldstein Sonata is a strong example. In fact insistance on any characteristic harmony or on any definite group of harmonies which clearly represent a key is a sure means of indicating the object of a modulation, even between keys which are remote from one another.
In transitory modulations it is less imperative to mark the new key strongly, since subordinate keys are rightly kept in the background, and though they may be used so as to produce a powerful effect, yet if they are too much insisted upon, the balance between the more essential and the unes- eential keys may be upset. But even in transitory modulations, in instrumental music especially, it is decidedly important that each group which represents a key, however short, should be dis- tinct in itself. In recitative, obscurity of tonality is not so objectionable, as appears both in Bach and Handel ; and the modem form of melodious recitative, which often takes the form of sustained melody of an emotional cast, is similarly often associated with subtle and closely woven modu- lations, especially when allied with words. Of recitative forma which show analogous freedom of modulation in purely instrumental works, there are examples both by Bach and Beethoven, as in an Adagio in a Toccata in D minor and the
Fantasia Cromatica by the former, and in the Introduction to the last movement of the Ab Sonata (opus, no) of the latter.
When transitory modulations succeed one an- other somewhat rapidly they may well be difficult to follow if they are not systematised into some sort of appreciable order. This is frequently effected by making them progress by regular steps. In Mozart and Haydn especially we meet with the simplest forms of succession, which generally amount to some such order as the roots of the chord falling fifths or rising fourths, or rising fourths and falling thirds successively. The following example from Mozart's C major Quartet is clearly to the point.
���Bach affords some remarkably forcible examples, as in the chorus ' Mit Blitzen und Donner ' in the Matthaus Passion, and in the latter part of the Fantasia for Organ in G (Db'rfFel 855), in which the bass progresses slowly by semitones downwards from Cjf to D. A passage quoted by Marx at the end of the second volume of his Kompositions- lehre from the 'Christe Eleison' in Bach's A major * Mass is very fine and characteristic ; the succession of transitions is founded on a bass which progresses as follows :
� � � � � � �
� � � � �
� � � ��In modern music a common form is that in which the succession of key-notes is by rising or falling semitones, as in the following passage from the first movement of the Fj-oica Symphony :
���i see Bachgesellschaft, 1858, p. 53, 60.