Polymeter & polyrhythm

Parallel fields, 3 against 2, nesting

% Braces superpose comma-separated voices IN PARALLEL over ONE span,
% and the FIRST field sets that span — everyone else bends to it. Six
% notes of galliard tune against four of bass is three against two, and
% neither voice carries a duration mark; the assert spells the bass out.
 
bpm 45
meter 6
key g min
 
Tune ::= 5 '1 7 6 5 4
Bass ::= .1 .5 .6 .5
 
assert {Tune, Bass} == {Tune, Bass _3 /2}
 
{Tune, Bass}
{Tune, Bass}@~-1
{Tune, Bass}@~-2
{Tune, Bass}
 
 
% The galliard cadences on a HEMIOLA. Pulse leads with six beats of
% the dominant, so Hemi's three notes stretch to two beats apiece and
% land on pulses 1, 3 and 5 — six heard as three — before the real
% dominant and the tonic close it.
 
Hemi  ::= 4 3 2
Pulse ::= .5 .5 .5 .5 .5 .5
Cad   ::= {Pulse, Hemi} {.5 _3, 2 7#} {.1 _3, 1 _3}
 
{Tune, Bass}@~-1
{Tune, Bass}@~-2
Cad
 
 
% Fields NEST, and the rule runs all the way down: {7 6, 2} lasts as
% long as ITS OWN first field — two beats — so the pair steps while the
% note above holds both, a sigh. Grace hangs two of them off the tune,
% and the accompaniment nests too, Bass over a two-note drone.
 
Grace ::= 5 '1 {7 6, 2} 5 {4 3, .6} 3
Under ::= {Bass, ..1 ..5}
 
assert {7 6, 2} == {7 6, 2 _2}
 
{Grace, Under}
{Grace, Under}@~-2
{Grace, Under}@~-4
{Grace, Under}
 
 
% The first-field rule is the whole trick. Lead with Tune and the
% twelve-note run halves to fit six beats; lead with Run and the span
% is twelve, so the tune's six notes double to two beats each. Same
% notes, two different pieces — the asserts name both spellings.
 
Run ::= '1 7 6 5 4 3 2 1 2 3 4 5
 
assert {Tune, Run} == {Tune, Run /2}
assert {Run, Tune} == {Run, Tune _2}
 
{Tune, Run, Bass}
{Run, Tune, Bass}
{Tune, Run, Bass}
{Run, Tune, Bass}
 
 
% The dance in order — galliard, the nested sighs, the run led from
% both ends, and the hemiola cadence closing each half — over a kit
% that divides every span into six however long that span happens to
% be, six against six, eight, and twelve in turn.
 
Kit ::= kick hat snare hat hat snare
 
{Tune, Bass, Kit}
{Grace, Under, Kit}
{Tune, Run, Bass, Kit}
{Run, Tune, Bass, Kit}
Cad
{Tune, Bass, Kit}@~-2
{Grace, Under, Kit}@~-2
{Run, Tune, Bass, Kit}
{Tune, Bass, Kit}
Cad

% Braces superpose comma-separated voices IN PARALLEL over ONE span,
% and the FIRST field sets that span — everyone else bends to it. Six
% notes of galliard tune against four of bass is three against two, and
% neither voice carries a duration mark; the assert spells the bass out.

bpm 45
meter 6
key g min

Tune ::= 5 '1 7 6 5 4
Bass ::= .1 .5 .6 .5

assert {Tune, Bass} == {Tune, Bass _3 /2}

{Tune, Bass}
{Tune, Bass}@~-1
{Tune, Bass}@~-2
{Tune, Bass}

% The galliard cadences on a HEMIOLA. Pulse leads with six beats of
% the dominant, so Hemi's three notes stretch to two beats apiece and
% land on pulses 1, 3 and 5 — six heard as three — before the real
% dominant and the tonic close it.

Hemi  ::= 4 3 2
Pulse ::= .5 .5 .5 .5 .5 .5
Cad   ::= {Pulse, Hemi} {.5 _3, 2 7#} {.1 _3, 1 _3}

{Tune, Bass}@~-1
{Tune, Bass}@~-2
Cad

% Fields NEST, and the rule runs all the way down: {7 6, 2} lasts as
% long as ITS OWN first field — two beats — so the pair steps while the
% note above holds both, a sigh. Grace hangs two of them off the tune,
% and the accompaniment nests too, Bass over a two-note drone.

Grace ::= 5 '1 {7 6, 2} 5 {4 3, .6} 3
Under ::= {Bass, ..1 ..5}

assert {7 6, 2} == {7 6, 2 _2}

{Grace, Under}
{Grace, Under}@~-2
{Grace, Under}@~-4
{Grace, Under}

% The first-field rule is the whole trick. Lead with Tune and the
% twelve-note run halves to fit six beats; lead with Run and the span
% is twelve, so the tune's six notes double to two beats each. Same
% notes, two different pieces — the asserts name both spellings.

Run ::= '1 7 6 5 4 3 2 1 2 3 4 5

assert {Tune, Run} == {Tune, Run /2}
assert {Run, Tune} == {Run, Tune _2}

{Tune, Run, Bass}
{Run, Tune, Bass}
{Tune, Run, Bass}
{Run, Tune, Bass}

% The dance in order — galliard, the nested sighs, the run led from
% both ends, and the hemiola cadence closing each half — over a kit
% that divides every span into six however long that span happens to
% be, six against six, eight, and twelve in turn.

Kit ::= kick hat snare hat hat snare

{Tune, Bass, Kit}
{Grace, Under, Kit}
{Tune, Run, Bass, Kit}
{Run, Tune, Bass, Kit}
Cad
{Tune, Bass, Kit}@~-2
{Grace, Under, Kit}@~-2
{Run, Tune, Bass, Kit}
{Tune, Bass, Kit}
Cad

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

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Polymeter & polyrhythm · Pattern Engine