Lessons · Advanced

Canon over a ground

One rule entered twice, offset by a rest

% A ground bass repeats while everything above it changes. This one
% is eight chords in four measures (D A Bm F#m G D G A), and the tune
% and both canons below ride it without ever changing it.
 
bpm 45
instrument plain
key d maj
 
Ground<bass> ::= .1 _2 .5 _2 .6 _2 .3 _2 .4 _2 .1 _2 .4 _2 .5 _2
Ground*2
 
 
% Three variations, one turn of the ground each: halves, then
% quarters, then a line that climbs to a5. Every note sits in the chord
% under it, one passing f#5 aside, which is what lets any two stack.
 
V1   ::= '3 _2 '2 _2 '1 _2 7 _2 6 _2 5 _2 6 _2 7 _2
V2   ::= '1 '3 '2 7 6 '1 '3 7 '1 6 5 3 4 6 5 7
V3   ::= '5 '3 '2 7 '3 '1 '3 7 '4 '1 '3 '1 '4 '3 '2 7
Tune ::= V1 V2 V3
 
{Tune, Ground*3}
 
 
% A canon is ONE rule entered twice, offset by a rest. '-*16' is the
% offset (one full turn of the ground), so the follower stays a
% variation behind the leader, and the leader takes the same rest at the
% end, because the first field of a '{ , }' sets the length for the rest.
 
assert -*16 Tune == - _16 Tune
 
Canon ::= {Tune -*16, -*16 Tune}
{Canon, Ground*4}
 
 
% Enter the rule a third time, one turn later again, and two voices
% become three: one rule, three distances. Nothing new is written for
% the close: the texture thins as each voice runs off the end.
 
Canon3 ::= {Tune -*32, -*16 Tune -*16, -*32 Tune}
{Canon3, Ground*5}
 
 
% The offset can be a SPEED instead of a delay: '{Fanfare Fanfare} _2'
% is the same rule at half tempo under two statements at speed, and '*'
% augments the same way. Fanfare is 1, 3 and 5 only, so the two speeds
% agree wherever they land, over a d3 pedal that holds under both.
 
Fanfare ::= '1 5 '3 '5 _2 '3 '1 5 _2 3 5 '1 '3 _2 '1 _2
 
assert Fanfare*2 _2 == {Fanfare Fanfare} _2
{Fanfare*4, {Fanfare Fanfare} _2@-12, .1 _64}

% A ground bass repeats while everything above it changes. This one
% is eight chords in four measures (D A Bm F#m G D G A), and the tune
% and both canons below ride it without ever changing it.

bpm 45
instrument plain
key d maj

Ground<bass> ::= .1 _2 .5 _2 .6 _2 .3 _2 .4 _2 .1 _2 .4 _2 .5 _2
Ground*2

% Three variations, one turn of the ground each: halves, then
% quarters, then a line that climbs to a5. Every note sits in the chord
% under it, one passing f#5 aside, which is what lets any two stack.

V1   ::= '3 _2 '2 _2 '1 _2 7 _2 6 _2 5 _2 6 _2 7 _2
V2   ::= '1 '3 '2 7 6 '1 '3 7 '1 6 5 3 4 6 5 7
V3   ::= '5 '3 '2 7 '3 '1 '3 7 '4 '1 '3 '1 '4 '3 '2 7
Tune ::= V1 V2 V3

{Tune, Ground*3}

% A canon is ONE rule entered twice, offset by a rest. '-*16' is the
% offset (one full turn of the ground), so the follower stays a
% variation behind the leader, and the leader takes the same rest at the
% end, because the first field of a '{ , }' sets the length for the rest.

assert -*16 Tune == - _16 Tune

Canon ::= {Tune -*16, -*16 Tune}
{Canon, Ground*4}

% Enter the rule a third time, one turn later again, and two voices
% become three: one rule, three distances. Nothing new is written for
% the close: the texture thins as each voice runs off the end.

Canon3 ::= {Tune -*32, -*16 Tune -*16, -*32 Tune}
{Canon3, Ground*5}

% The offset can be a SPEED instead of a delay: '{Fanfare Fanfare} _2'
% is the same rule at half tempo under two statements at speed, and '*'
% augments the same way. Fanfare is 1, 3 and 5 only, so the two speeds
% agree wherever they land, over a d3 pedal that holds under both.

Fanfare ::= '1 5 '3 '5 _2 '3 '1 5 _2 3 5 '1 '3 _2 '1 _2

assert Fanfare*2 _2 == {Fanfare Fanfare} _2
{Fanfare*4, {Fanfare Fanfare} _2@-12, .1 _64}

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

Canon over a ground · Advanced