Lessons · Advanced

Cross-rhythm

Voices of different lengths sharing one span

% Cross-rhythm is voices of DIFFERENT lengths sharing ONE span. A
% structure lasts exactly as long as its FIRST field; every other field
% stretches to fill it. Twelve notes of tune against eight of bass is
% three against two (the hemiola), and each bass note lasts 3/2 units.
 
bpm 75
instrument plain
key f maj
 
Tune ::= 1 3 5 '1 '1 7 5 3 4 3 2 1
Bass<bass> ::= .1 .5 .3 .5 .4 .6 .5 .1
 
assert {Tune, Bass} == {Tune, Bass _3 /2}
 
{Tune, Bass}
{Tune, Bass}@~4
{Tune~, Bass}
 
 
% The ratio is a composer's choice, not a syntax. Nine against twelve
% is four of the figure to every three of the walk; and because the
% FIRST field sets the span, leading with the walk shrinks the span to
% nine and compresses the figure instead. The asserts name both.
 
Roll ::= 1 5 3 5 2 6 4 6 1 5 3 5
Walk<bass> ::= .1 .3 .5 .6 .5 .4 .3 .2 .1
 
assert {Roll, Walk} == {Roll, Walk _4 /3}
assert {Walk, Roll} == {Walk, Roll _3 /4}
 
{Roll, Walk}
{Roll, Walk}@~4
{Roll, Walk}
{Walk, Roll}
 
 
% Inside a single beat the same idea is a duration mark: '/3' cuts a
% unit in three, so each sweep is three notes in the time of one while
% the bass still divides those twelve units into eight and the kit
% keeps the grid at twelve.
 
Sweep ::= 1/3 3/3 5/3
Rise  ::= Sweep 3 Sweep@~2 5 Sweep@~4 7 5 4 3 2 1 -
Kit   ::= kick hat snare hat
 
{Rise, Bass, Kit*3}
{Rise@~4, Bass@~4, Kit*3}
{Rise, Bass, Kit*3}
 
 
% A third length, and nothing has to agree. The tune divides these
% twelve units into twelve, the bass into eight, and a five-note ground
% into five: its notes fall 12/5 units apart, so the ground meets the
% others nowhere but the downbeat.
 
Ground<bass> ::= ..1 ..3 ..5 ..4 ..1
 
{Tune, Bass, Ground}
{Tune, Bass, Ground, Kit*3}
{Tune~, Bass, Ground, Kit*3}
{Tune, Bass, Ground, Kit*3}
 
 
% The dance in form: the hemiola, the four-against-three, the sweeps,
% then a tutti where twelve, nine, five and twelve divide one span
% between them. A document plays every production it states, in order,
% so this block is the recapitulation.
 
{Tune, Bass, Kit*3}
{Roll, Walk, Kit*3}
{Rise, Bass, Ground, Kit*3}
{Tune, Walk, Ground, Kit*3}
{Roll@~4, Walk@~4, Ground}
{Tune, Bass, Ground, Kit*3}

% Cross-rhythm is voices of DIFFERENT lengths sharing ONE span. A
% structure lasts exactly as long as its FIRST field; every other field
% stretches to fill it. Twelve notes of tune against eight of bass is
% three against two (the hemiola), and each bass note lasts 3/2 units.

bpm 75
instrument plain
key f maj

Tune ::= 1 3 5 '1 '1 7 5 3 4 3 2 1
Bass<bass> ::= .1 .5 .3 .5 .4 .6 .5 .1

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

{Tune, Bass}
{Tune, Bass}@~4
{Tune~, Bass}

% The ratio is a composer's choice, not a syntax. Nine against twelve
% is four of the figure to every three of the walk; and because the
% FIRST field sets the span, leading with the walk shrinks the span to
% nine and compresses the figure instead. The asserts name both.

Roll ::= 1 5 3 5 2 6 4 6 1 5 3 5
Walk<bass> ::= .1 .3 .5 .6 .5 .4 .3 .2 .1

assert {Roll, Walk} == {Roll, Walk _4 /3}
assert {Walk, Roll} == {Walk, Roll _3 /4}

{Roll, Walk}
{Roll, Walk}@~4
{Roll, Walk}
{Walk, Roll}

% Inside a single beat the same idea is a duration mark: '/3' cuts a
% unit in three, so each sweep is three notes in the time of one while
% the bass still divides those twelve units into eight and the kit
% keeps the grid at twelve.

Sweep ::= 1/3 3/3 5/3
Rise  ::= Sweep 3 Sweep@~2 5 Sweep@~4 7 5 4 3 2 1 -
Kit   ::= kick hat snare hat

{Rise, Bass, Kit*3}
{Rise@~4, Bass@~4, Kit*3}
{Rise, Bass, Kit*3}

% A third length, and nothing has to agree. The tune divides these
% twelve units into twelve, the bass into eight, and a five-note ground
% into five: its notes fall 12/5 units apart, so the ground meets the
% others nowhere but the downbeat.

Ground<bass> ::= ..1 ..3 ..5 ..4 ..1

{Tune, Bass, Ground}
{Tune, Bass, Ground, Kit*3}
{Tune~, Bass, Ground, Kit*3}
{Tune, Bass, Ground, Kit*3}

% The dance in form: the hemiola, the four-against-three, the sweeps,
% then a tutti where twelve, nine, five and twelve divide one span
% between them. A document plays every production it states, in order,
% so this block is the recapitulation.

{Tune, Bass, Kit*3}
{Roll, Walk, Kit*3}
{Rise, Bass, Ground, Kit*3}
{Tune, Walk, Ground, Kit*3}
{Roll@~4, Walk@~4, Ground}
{Tune, Bass, Ground, Kit*3}

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

Cross-rhythm · Advanced