Hence it appears to follow that in enharmonic modulation we attempt to get at least some of the effects of intervals smaller than semitones; but the indiscriminate and ill-considered use of the device will certainly tend to deaden the musical sense, which helps us to distinguish the true relations of harmonies through their external apparent uniformity.
A considerable portion of the actual processes of modulation is effected by means of notes which are used as pivots. A note or notes which are common to a chord in the original key and to a chord in the key to which the modulation is made, are taken advantage of to strengthen the connection of the harmonies while the modulation proceeds; as in the following modulation from G♯ major to B major in Schubert's Fantasie-Sonata Op. 78.
This device is found particularly in transitory modulation, and affords peculiar opportunities for subtle transitions. Examples also occur where the pivot notes are treated enharmonically, as in the following example from the chorus 'Sein Odem ist schwach' in Graun's 'Tod Jesu':
![{ \override Score.TimeSignature #'stencil = ##f << \new Staff { \time 4/4 \key ees \major << \new Voice { \autoBeamOff \stemUp \relative b' { b8[ c] c g aes! aes aes aes | gis4 gis8 gis a4 } }
\new Voice { \stemDown \relative g' { \autoBeamOff g4 g8 d ees ees f f | b,4 b8 b cis4_\markup { \halign #-1 etc. } } } >> }
\new Staff { \clef bass \key ees \major << \new Voice { \autoBeamOff \stemUp \relative d' { d8[ ees] ees b c c d d | d4 d8 d cis4 } }
\new Voice { \autoBeamOff \stemDown g4 g g8 g f f | e4 e a, } >> } >> }](http://upload.wikimedia.org/score/g/3/g3hq7lu5ff52moa90pli1okauq3377l/g3hq7lu5.png)
These pivot-notes are however by no means indispensable. Modulations are really governed by the same laws which apply to any succession of harmonies whatsoever, and the possibilities of modulatory device are in the end chiefly dependent upon intelligible order in the progression of the parts. It is obvious that a large proportion of chords which can succeed each other naturally—that is, without any of the parts having melodic intervals which it is next to impossible to follow—will have a note or notes in common; and such notes are as useful to connect two chords in the same key as they are to keep together a series which constitute a modulation. But it has never been held indispensable that successive chords should be so connected, though in earlier stages of harmonic music it may have been found helpful; and in the same way, while there were any doubts as to the means and order of modulation, pivot-notes may have been useful as leading strings, but when a broader and freer conception of the nature of the modern system has been arrived at, it will be found that though pivot-notes may be valuable for particular purposes, the range of modulatory device is not limited to such successions as can contain them, but only to such as do not contain inconceivable progression of parts. As an instance we may take the progression from the dominant seventh of any key, to the tonic chord of the key which is represented by the flat submediant of the original key: as from the chord of the seventh on G to the common chord of A♭; of which we have an excellent example near the beginning of the Leonore Overture No. 3. Another remarkable instance to the point occurs in the trio of the third movement of a quartet of Mozart's in B♭, as follows:—
etc.
Other examples of modulation without pivot-notes may be noticed at the beginning of Beethoven's Egmont Overture, and of his Sonata in E minor, op. 90 (bars 2 and 3), and of Wagner's Gotterdammerung (bars 9 and 10). An impression appears to have been prevalent with some theorists that modulation ought to proceed through a chord which was common to both the keys between which the modulation takes place. The principle is logical and easy of application, and it is true that a great number of modulations are explicable on that basis; but inasmuch as there are a great number of examples which are not, even with much latitude of explanation, it will be best not to enter into a discussion of so complicated a point in this place. It will be enough to point out that the two principles of pivot-notes and of ambiguous pivot-chords between them cover so much ground that it is not easy to find progressions in which either one or the other does not occur and even though in a very great majority of instances one or the other may really form the bond of connection in modulatory passages, the frequency of their occurrence is not a proof of their being indispensable. The following passage from the first act of Wagner's Meistersinger is an example of a modulation in which they are both absent:—
![{ \override Score.TimeSignature #'stencil = ##f << \new Staff { \time 2/4 << \new Voice { \stemUp \relative a'' { a16 g f a ~ a g e g | f e d bes' fis e dis b' g fis e g } }
\new Voice { \stemDown \relative f' { s8 \acciaccatura { f16[ g] } <a c,>8 s \acciaccatura { g16[ f] } <e c>8 | s \acciaccatura { d16[ e] } <f bes,>8 s \acciaccatura { fis16[ e] } <dis fis,>8 | s \acciaccatura { e16[ fis] } <g b>8 } } >> }
\new Staff { \clef bass f8 s c s d s b,! s e s } >> }](http://upload.wikimedia.org/score/n/h/nhvyo2yvqjlkomss6pc3ggheanacmp7/nhvyo2yv.png)
etc.
