Fugues with 2 themes, 4 voices, 4/4 beats, 120 bars
゛alla Decima゛, namely,゛by tenth degree゛is the title, and the piece is
composed by double counterpoint at tenth degree. We discuss the details
later on.
゛Contrap. a 4 ゛ at the fourteenth in the first edition of the art of fugue is
coming from the autograph version of Cp.10, though it is missing first
twenty two bars of Cp.10.
The theme unique to this piece is newly introduced at the beginning of the
piece and unusually starts with leading tone.
The theme in tenor responding to the theme in alto is subdominant key,
which is sometimes seen in Bach's fugues, however, is the only one in the art of fugue.
The inverted form is taken to the theme in bass from bar 7 and in the
following soprano. Comparing the opening theme in alto with the inverted
theme in bass, you might see the melodies over two bars are switched,
being the most interesting characteristics in this theme.
The themes in the basic form and the inverted make stretto from bar 14.
Here comes the variant theme in inverted form of the common theme from
bar 23, in which the same variant theme asCp.5,Cp.6,Cp.7is employed.
Previously mentioned ゛Contrap. a 4゛ begins at this bar 23.
The theme in alto from bar 24 is discontinued at bar 26. Soprano attached
with the slur between bar 28 and bar 29 is often used as a motive in the
piece, imitated and developed from bar 56 and bar 107.
Thematic combinations can be found both from bar 44 and bar 66.
゛f#゛of the theme and ゛a’゛of the common theme are stated from bar 44
whereas ゛a’゛of the theme and ゛a゛of the common theme are stated from
bar 66, meaning that the theme from bar 66 is placed tenth degree higher
than the theme from bar 44.
We call this relation that both themes are combinable, double counterpoint
even if shifted at tenth degree.
As the title shows, Canon alla Decima is also composed by double
counterpoint at tenth degree.
Unlike Cp.9, the double counterpoint in this piece makes it possible for two
gapped themes to be duplicated, so-called ゛harmonization゛.
(if it is done in twelfth degree, parallel fifth happens in succession.)
Either the theme or the common theme is duplicated after bar 75.
By the way, the theme in inverted form shown at the beginning of the piece
is never stated at the time of thematic combination.
Other than the motive between bar 28 and bar 29, previously mentioned,
several imitations or sequences by motive are discovered. The music is the
example of the imitation by two kinds of motif.
Old-fashioned ゛ricercare゛ includes the imitational style by several motif
like above, looking like ゛six parts ricercare゛ of ゛musical offering゛.
