and in the twelfth. It is also necessary that there should be contrast, both melodic and rhythmic, between the two subjects, so that each may be easily recognized whenever it appears.
369. It is best that a double fugue should be written for at least four voices, and in vocal music this is almost invariably the case. It is nevertheless possible, though less advisable, to write a double fugue with only three parts. In any case, the student will do well to attend to Albrechtsberger's recommendation that a fugue should always have at least one more voice than it has subjects. Thus, a double fugue ought to be in at least three parts, and a triple fugue (with three subjects) in at least four. But in fugues with more than three subjects (which are very rare), this rule is not always observed, probably because in a fugue with four subjects it is seldom that all four are present at once. The object of the extra voice is, to be able to add a free part when all the subjects are going on at the same time.
370. The exposition of a double fugue can be managed in more than one way. In a four-part fugue, the best arrangement is to let two of the voices announce the two subjects, which the other two follow with the two answers by inversion—that is to say, the upper of the two subjects will appear as the lower of the two answers, and vice versa. A few examples will make this quite clear.
![\new ChoirStaff << \override Score.BarNumber #'break-visibility = #'#(#f #f #f) \override Score.Rest #'style = #'classical
\new Staff \relative g' { \key g \minor \time 4/4 \partial 4.
g8^"S1." g f | e4 a d, r8 d' |
g,8 a16 bes c d c bes a8 bes16 c d ees d c |
bes8 c16 d ees f ees d c d c bes a d c d | bes8 g r4 r8 g d g |
g e e a a f f bes | bes g g e a[ fis] }
\new Staff \relative g { \clef alto \key g \minor
r8 r4 | R1*3 | r4 g^"A2." bes b | c cis d2 ~ | d4 cis d_"&c." }
\new Staff \relative d' { \clef tenor \key g \minor
r8 r4 | R1*2 | r8 d^"A1." c bes a4 d |
g, r8 g d ees16 f g a g f |
e8 f16 g a bes a g f8 g16 a bes c bes a |
g a g f e a g a fis8[ d] }
\new Staff \relative g { \clef bass \key g \minor
\tiny g8 bes a | g bes a g f e \normalsize d4^"S2." | ees e f fis
g2. fis4 | g8. \tiny f16 ees d ees c g'4 g, |
c a d bes' | g e8 a d,4 } >>](http://upload.wikimedia.org/score/q/b/qb302idnx0v0al37mde3aft1x54sztx/qb302idn.png)
The small notes on the bass staff here show the instrumental bass; the bass voices have only the second subject, which is
