Lessons · Advanced

Anchor application

One gesture stamped at every anchor

% A ground bass walks down a sixth from the tonic and turns back
% through the subdominant to the dominant. 'Roll' owns no pitch of its
% own — three scale steps up from whatever came before — and ANCHOR
% APPLICATION stamps it onto each argument in turn, as the assert spells:
 
bpm 72
meter 4
unit 1/4
key g min
 
Roll ::= s2 s2 s3
 
assert Roll(.1 ..7) == { .1 Roll ..7 Roll }
 
.1 _4 ..7 _4 ..6 _4 ..5 _4
..4 _4 ..3 _4 ..4 _4 ..5 _4
Roll(.1 ..7 ..6 ..5) Roll(..4 ..3 ..4 ..5)
 
 
% The anchors ARE the harmony and the figure is the hand: eight stamps
% roll eight triads — i VII VI v iv III iv v — and 'Air' is eight quarter
% notes, one chord tone per stamp, filling the same thirty-two units:
 
Air ::= 1 _4 2 _4 3 _4 5 _4 4 _4 3 _4 6 _4 5 _4
 
assert Roll(.1) == .1 .3 .5 1
 
Air
{Roll(.1 ..7 ..6 ..5) Roll(..4 ..3 ..4 ..5), Air}
 
 
% A stamped run is an expression like any other, so a mark after the
% ')' covers the whole of it: '@~2' answers all eight stamps a third
% higher, and '_2' gives the same chords at half speed:
 
assert Roll(.1)@~2 == .3 .5 .7 3
 
Roll(.1 ..7 ..6 ..5)@~2 Roll(..4 ..3 ..4 ..5)@~2
Roll(.1 ..7 ..6 ..5) _2
{Roll(..4 ..3 ..4 ..5) _2, 6 _8 5 _8 4 _8 5 _8}
 
 
% Change the hand and the harmony does not move. 'Turn' circles each
% anchor — a step up, back, and one below — where 'Lean' reaches the
% fourth above and steps down through the third. Same eight anchors,
% same ground, two different pieces:
 
Turn ::= s1 s-1 s-1
Lean ::= s3 s-1 s-1
 
Turn(.1 ..7 ..6 ..5) Turn(..4 ..3 ..4 ..5)
Lean(.1 ..7 ..6 ..5) Lean(..4 ..3 ..4 ..5)
{Lean(.1 ..7 ..6 ..5) Lean(..4 ..3 ..4 ..5), Air}
 
 
% Anchors need not be a bass. Stamp onto the eight notes of the tune
% and the figure becomes written-out ornament: every pitch of 'Air'
% keeps its place and leads its own four units, now in sixteenths:
 
assert Turn(5) == 5 6 5 4
 
Turn(1 2 3 5) Turn(4 3 6 5)
Lean(1 2 3 5) Lean(4 3 6 5)
{Turn(1 2 3 5) Turn(4 3 6 5), Roll(.1 ..7 ..6 ..5) Roll(..4 ..3 ..4 ..5)}
 
 
% The chaconne whole, one ground under every hand: the bass plain, the
% roll under Air, the turn stamped on both lines at once, the lean, then
% the roll at half speed under Air stretched to match, and the tonic.
 
.1 _4 ..7 _4 ..6 _4 ..5 _4 ..4 _4 ..3 _4 ..4 _4 ..5 _4
{Roll(.1 ..7 ..6 ..5) Roll(..4 ..3 ..4 ..5), Air}
{Turn(.1 ..7 ..6 ..5) Turn(..4 ..3 ..4 ..5), Turn(1 2 3 5) Turn(4 3 6 5)}
{Lean(.1 ..7 ..6 ..5) Lean(..4 ..3 ..4 ..5), Air}
{Roll(.1 ..7 ..6 ..5) _2 Roll(..4 ..3 ..4 ..5) _2, Air _2}
{.1, .3, .5, 1} _8

% A ground bass walks down a sixth from the tonic and turns back
% through the subdominant to the dominant. 'Roll' owns no pitch of its
% own — three scale steps up from whatever came before — and ANCHOR
% APPLICATION stamps it onto each argument in turn, as the assert spells:

bpm 72
meter 4
unit 1/4
key g min

Roll ::= s2 s2 s3

assert Roll(.1 ..7) == { .1 Roll ..7 Roll }

.1 _4 ..7 _4 ..6 _4 ..5 _4
..4 _4 ..3 _4 ..4 _4 ..5 _4
Roll(.1 ..7 ..6 ..5) Roll(..4 ..3 ..4 ..5)

% The anchors ARE the harmony and the figure is the hand: eight stamps
% roll eight triads — i VII VI v iv III iv v — and 'Air' is eight quarter
% notes, one chord tone per stamp, filling the same thirty-two units:

Air ::= 1 _4 2 _4 3 _4 5 _4 4 _4 3 _4 6 _4 5 _4

assert Roll(.1) == .1 .3 .5 1

Air
{Roll(.1 ..7 ..6 ..5) Roll(..4 ..3 ..4 ..5), Air}

% A stamped run is an expression like any other, so a mark after the
% ')' covers the whole of it: '@~2' answers all eight stamps a third
% higher, and '_2' gives the same chords at half speed:

assert Roll(.1)@~2 == .3 .5 .7 3

Roll(.1 ..7 ..6 ..5)@~2 Roll(..4 ..3 ..4 ..5)@~2
Roll(.1 ..7 ..6 ..5) _2
{Roll(..4 ..3 ..4 ..5) _2, 6 _8 5 _8 4 _8 5 _8}

% Change the hand and the harmony does not move. 'Turn' circles each
% anchor — a step up, back, and one below — where 'Lean' reaches the
% fourth above and steps down through the third. Same eight anchors,
% same ground, two different pieces:

Turn ::= s1 s-1 s-1
Lean ::= s3 s-1 s-1

Turn(.1 ..7 ..6 ..5) Turn(..4 ..3 ..4 ..5)
Lean(.1 ..7 ..6 ..5) Lean(..4 ..3 ..4 ..5)
{Lean(.1 ..7 ..6 ..5) Lean(..4 ..3 ..4 ..5), Air}

% Anchors need not be a bass. Stamp onto the eight notes of the tune
% and the figure becomes written-out ornament: every pitch of 'Air'
% keeps its place and leads its own four units, now in sixteenths:

assert Turn(5) == 5 6 5 4

Turn(1 2 3 5) Turn(4 3 6 5)
Lean(1 2 3 5) Lean(4 3 6 5)
{Turn(1 2 3 5) Turn(4 3 6 5), Roll(.1 ..7 ..6 ..5) Roll(..4 ..3 ..4 ..5)}

% The chaconne whole, one ground under every hand: the bass plain, the
% roll under Air, the turn stamped on both lines at once, the lean, then
% the roll at half speed under Air stretched to match, and the tonic.

.1 _4 ..7 _4 ..6 _4 ..5 _4 ..4 _4 ..3 _4 ..4 _4 ..5 _4
{Roll(.1 ..7 ..6 ..5) Roll(..4 ..3 ..4 ..5), Air}
{Turn(.1 ..7 ..6 ..5) Turn(..4 ..3 ..4 ..5), Turn(1 2 3 5) Turn(4 3 6 5)}
{Lean(.1 ..7 ..6 ..5) Lean(..4 ..3 ..4 ..5), Air}
{Roll(.1 ..7 ..6 ..5) _2 Roll(..4 ..3 ..4 ..5) _2, Air _2}
{.1, .3, .5, 1} _8

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Anchor application · Pattern Engine