Solution to Canon 3. a 2 per Motum contrarium
How
many clefs are there?
There
is one G-clef on the upper line where the Royal theme is played.
There
are two C-clefs on the bottom counterpoint line.
This
indicates three voices.
Look
at the title.
“a2”
indicates that there are two voices in a canonical relationship with each
other.
Which
2 voices are in canonical relationship? Look again before you proceed.
When
you are ready to proceed:
Since
there are two clefs on the lower line, this means that there are two voices
which play the lower line in a canonical relationship.
Is
there a %
?
The
%
means that there is a second voice which starts there,
confirming that there are two voices playing the lower part.
So,
there are three voices in the puzzle. The upper voice plays the Royal theme,
and there are two voices playing a counterpoint line in canon, a leader and a
follower.
What
is/are the transformation principle(s)?
Hints:
Look
again at the placement the two clefs in the lower line.
When
you are ready to proceed:
What
are their relationships to each other?
The
second C-clef is placed a fifth higher than the first. What can this mean?
This
indicates that the follower starts in a different place than the leader.
What
is the orientation of the second clef in the lower part?
Upside-down.
What
can this mean?
Look
at the title.
What
does Motum contrarium mean?
Contrary
motion. What can this mean?
That
the canonical voices are going in contrary, or opposite directions.
What
can this mean?
The
leader plays the notes as shown, starting with a downward scale.
The
follower plays the notes in the opposite direction – starting with an upward
scale.
Therefore
we also have a transformation of direction – upwards and downwards. This is
called a mirror canon.
On
which notes, then, do the canonical voices start? Try to figure this out
before you proceed.
When
you are ready to proceed:
The
leader starts on “c’,” one octave above middle “c.”
The
follower starts on an “G” below middle “c.”
Is
there a (add
enter here symbol) ?
As
noted above, %
indicates that the follower should start when the leader arrives there
– therefore there is also a transformation in time, by a half measure.
How
many transformation principles are there in this canon?
Three:
Displacement
in musical space: The follower starts in a different place – an octave and a
fourth lower than the leader.
Opposite
directionality: The follower is played in the opposite direction than the
leader – upwards, and downwards.
Displacement
in time: The follower starts a half measure after the leader.
Look
at the realized version of this puzzle canon here:
Geometrical
projection:
Starting
from two superimposed like triangles, or other forms, perform the three
transformations.
The
result would look like this:
Performance:
Play
the upper Royal theme.
Listen here to the flute playing the Royal theme.
Play
or sing the first 1 ½ measure of the leader (lower) voice.
Listen
here: MP3
make
Play
or sing the leader and the follower together up to the middle of measure 2.
Here
is the complete leader. Add the follower to that.
Listen
here: MP3
make
Here is the Royal theme, played by the flute, and leader played by the piano.
Add the follower, playing all three voices together,
Invent
a musical example:
Invent
a four-note motive which goes in only one direction.
Add
a follower which is its mirror image, starting after two notes, and on
different note than the first.
Amend your motive if necessary, and perform the two.
