Solution
to Canon
5. a 2 per Tonus
Ascendenteque Modulatione ascendat Gloria Regis (As the modulation
ascends, so may the glory of the king also ascend).
Play
the upper part, a variation of the Royal theme, twice through, observing the
repeat. See if you notice anything strange.
What
happened?
The
repetition had to start one whole note higher than the original!
What
happens if you continue to repeat.
You
will see that the same thing happens with the lower voices.
This
puzzle is a modulating spiral, in which each repetition of the canon rises in
pitch by a whole step!
How
many voices are there, and what are the other transformation principles?
The
F-clef and C-clef (on the same line) and the
%,
indicate
that the counterpoint is played by two canonical voices, separated by the
interval of a 5th, with the follower starting one measure after the
leader.
There
are three transformation principles:
1.
the
modulating spiral
2.
the
displacement in musical space by a fifth.
3.
the
displacement in time by one measure
Geometrical
projection:
Starting
from two superimposed like triangles, or other forms, perform the three
transformations.
How
could you show the modulating spiral?
The
result would look like this:
Listen
to the recording of this canon here: make
MP3
