Lessons · Techniques

Canon & counterpoint

Rounds, invertible voices, crab canon

% The tune is three eight-unit phrases, and every one of them spends
% four units over i and four over V. That shared frame is the whole
% trick: any phrase sounds against any other.
 
bpm 45
instrument hollow
key d harm
 
Head   ::= '1 _2 5 '1 7 _2 5 _2
Run    ::= 5 /2 4 /2 3 /2 2 /2 1 _2 5 4 /2 3 /2 2 _2
Close  ::= 3 5 '1 5 2 _2 '1 7
Tune   ::= Head Run Close
 
Ground<bass> ::= .1 _4 .5 _4
 
Tune
{Tune, Ground*3}
 
 
% A ROUND is that line entered against itself a phrase apart. The
% delay is rests, and every field is written out to the same 48 units
% so no voice stretches. From unit 1/64 on, all three sound at once.
 
Round ::= {Tune Tune,
           -*8 Tune Head Run,
           -*16 Tune Head}
 
Round
 
 
% Counter meets Head only in thirds and sixths (never a fifth, never
% an octave), so it can move above the tune without changing a note.
% Both layouts, and both again at the answer's fifth.
 
Counter ::= 3 6 3 _2 2 _2 .7 _2
 
{Head, Counter}
{Head, Counter}@7
{Head, Counter@12}@7
{Head, Counter@12}
 
 
% A CRAB canon needs a frame that reads the same backwards, so Crab
% runs i V V i, and its ground is Ground against its own retrograde.
% Against the reversal not one column is a second or a seventh.
 
Crab ::= 1 3 5 '1 '2 7 5 2 .7 _2 2 5 '1 _2 5 3
 
assert Crab[::-1] == {Crab}~
 
Crab
{Crab, {Crab}~@-12, {Ground {Ground}~}@-12}
 
 
% A MIRROR canon runs the line against its own inversion. 'axis 3'
% mirrors through the third: 1 and 5 trade, 3 holds, 2 and 4 trade, so
% Mirror, built from degrees 1 to 5, inverts into the same five notes.
 
axis 3
 
Mirror ::= 1 3 /2 2 /2 3 5 '1 5 /2 4 /2 3 5 3 1 /2 2 /2 3 5 '1 _2 5 _2
 
Mirror
{Mirror, {Mirror}^@-12, ..1 _16}
 
 
% All of it at once: the round in three voices over Counter in the
% bass. The countersubject was written to the same i-V frame, so it
% fits every entry, not just the first.
 
{Round, {Counter*6}@-12}
{'1 _8, 1Min _8, ..1 _8}

% The tune is three eight-unit phrases, and every one of them spends
% four units over i and four over V. That shared frame is the whole
% trick: any phrase sounds against any other.

bpm 45
instrument hollow
key d harm

Head   ::= '1 _2 5 '1 7 _2 5 _2
Run    ::= 5 /2 4 /2 3 /2 2 /2 1 _2 5 4 /2 3 /2 2 _2
Close  ::= 3 5 '1 5 2 _2 '1 7
Tune   ::= Head Run Close

Ground<bass> ::= .1 _4 .5 _4

Tune
{Tune, Ground*3}

% A ROUND is that line entered against itself a phrase apart. The
% delay is rests, and every field is written out to the same 48 units
% so no voice stretches. From unit 1/64 on, all three sound at once.

Round ::= {Tune Tune,
           -*8 Tune Head Run,
           -*16 Tune Head}

Round

% Counter meets Head only in thirds and sixths (never a fifth, never
% an octave), so it can move above the tune without changing a note.
% Both layouts, and both again at the answer's fifth.

Counter ::= 3 6 3 _2 2 _2 .7 _2

{Head, Counter}
{Head, Counter}@7
{Head, Counter@12}@7
{Head, Counter@12}

% A CRAB canon needs a frame that reads the same backwards, so Crab
% runs i V V i, and its ground is Ground against its own retrograde.
% Against the reversal not one column is a second or a seventh.

Crab ::= 1 3 5 '1 '2 7 5 2 .7 _2 2 5 '1 _2 5 3

assert Crab[::-1] == {Crab}~

Crab
{Crab, {Crab}~@-12, {Ground {Ground}~}@-12}

% A MIRROR canon runs the line against its own inversion. 'axis 3'
% mirrors through the third: 1 and 5 trade, 3 holds, 2 and 4 trade, so
% Mirror, built from degrees 1 to 5, inverts into the same five notes.

axis 3

Mirror ::= 1 3 /2 2 /2 3 5 '1 5 /2 4 /2 3 5 3 1 /2 2 /2 3 5 '1 _2 5 _2

Mirror
{Mirror, {Mirror}^@-12, ..1 _16}

% All of it at once: the round in three voices over Counter in the
% bass. The countersubject was written to the same i-V frame, so it
% fits every entry, not just the first.

{Round, {Counter*6}@-12}
{'1 _8, 1Min _8, ..1 _8}

running…edit it and it re-runs as you type

Canon & counterpoint · Techniques