Three against two

Cross-rhythm in one field

% A polymetric field divides ONE span among its ITEMS. '{1 5 3, .1 .5}'
% puts three notes and two notes in the same measure, so three against
% two is notation, not counting: Arp takes thirds of the bar, Walk takes
% halves of it, and neither voice carries a duration mark.
 
bpm 33
meter 3
unit 1/16
key d maj
 
Arp  ::= 1 5 3
Walk ::= .1 .5
Duo  ::= {Arp, Walk}
 
Fall ::= Duo Duo@~-1 Duo@~-2 Duo@~-3
Fall
 
 
% ITEMS, not beats — broaden the field and each voice keeps its own
% share. Spelled out voice by voice, Arp's notes run two units and
% Walk's three; Broad names neither length, it scales the span and
% lets the commas divide it. The asserts hold the two spellings level.
 
Broad ::= Duo _2
 
assert Arp _2 == 1 _2 5 _2 3 _2
assert Walk _3 == .1 _3 .5 _3
 
Broad Broad@~-2 Broad@~-4 Broad
 
 
% A third voice divides the same span again. Arp leads, so the measure
% stays three units; Run puts four items in it and Walk two — four
% against three against two, one comma apiece, with the sequence still
% stepping down a degree each measure.
 
Run  ::= '1 7 6 5
Trio ::= {Arp, Run, Walk}
 
Fall3 ::= Trio Trio@~-1 Trio@~-2 Trio@~-3
Fall3
 
 
% The HEMIOLA contradicts the bar. Hemi's three items share six units,
% so they land on pulses 1, 3 and 5 while Pulse sounds all six: two
% measures of three heard as three of two. That is how a Baroque phrase
% asks for its cadence — the last measure of the sequence, the hemiola,
% then the tonic.
 
Hemi  ::= 4 3 2
Pulse ::= .1 .1 .1 .5 .5 .5
Cad   ::= {Hemi, Pulse} _2 {1 _3, .1Dia _3}
 
Trio@~-3 Cad
 
 
% The whole phrase in order: two voices, then four against three
% against two, then the hemiola cadence. Nothing here counted a
% subdivision — every cross-rhythm came out of a comma.
 
Fall
Fall3
Cad
 
 
% The same comma carries a West African bell. Twelve pulses hold the
% seven-stroke gankogui; Feet strikes four times, once every three
% pulses, and Hand three times, once every four — four against three
% inside the bell's twelve, from one field.
 
bpm 99
meter 12
 
Bell  ::= cowbell - cowbell - cowbell cowbell - cowbell - cowbell - cowbell
Feet  ::= kick kick kick kick
Hand  ::= clap clap clap
Cycle ::= {Bell, Feet, Hand}
 
Cycle*8

% A polymetric field divides ONE span among its ITEMS. '{1 5 3, .1 .5}'
% puts three notes and two notes in the same measure, so three against
% two is notation, not counting: Arp takes thirds of the bar, Walk takes
% halves of it, and neither voice carries a duration mark.

bpm 33
meter 3
unit 1/16
key d maj

Arp  ::= 1 5 3
Walk ::= .1 .5
Duo  ::= {Arp, Walk}

Fall ::= Duo Duo@~-1 Duo@~-2 Duo@~-3
Fall

% ITEMS, not beats — broaden the field and each voice keeps its own
% share. Spelled out voice by voice, Arp's notes run two units and
% Walk's three; Broad names neither length, it scales the span and
% lets the commas divide it. The asserts hold the two spellings level.

Broad ::= Duo _2

assert Arp _2 == 1 _2 5 _2 3 _2
assert Walk _3 == .1 _3 .5 _3

Broad Broad@~-2 Broad@~-4 Broad

% A third voice divides the same span again. Arp leads, so the measure
% stays three units; Run puts four items in it and Walk two — four
% against three against two, one comma apiece, with the sequence still
% stepping down a degree each measure.

Run  ::= '1 7 6 5
Trio ::= {Arp, Run, Walk}

Fall3 ::= Trio Trio@~-1 Trio@~-2 Trio@~-3
Fall3

% The HEMIOLA contradicts the bar. Hemi's three items share six units,
% so they land on pulses 1, 3 and 5 while Pulse sounds all six: two
% measures of three heard as three of two. That is how a Baroque phrase
% asks for its cadence — the last measure of the sequence, the hemiola,
% then the tonic.

Hemi  ::= 4 3 2
Pulse ::= .1 .1 .1 .5 .5 .5
Cad   ::= {Hemi, Pulse} _2 {1 _3, .1Dia _3}

Trio@~-3 Cad

% The whole phrase in order: two voices, then four against three
% against two, then the hemiola cadence. Nothing here counted a
% subdivision — every cross-rhythm came out of a comma.

Fall
Fall3
Cad

% The same comma carries a West African bell. Twelve pulses hold the
% seven-stroke gankogui; Feet strikes four times, once every three
% pulses, and Hand three times, once every four — four against three
% inside the bell's twelve, from one field.

bpm 99
meter 12

Bell  ::= cowbell - cowbell - cowbell cowbell - cowbell - cowbell - cowbell
Feet  ::= kick kick kick kick
Hand  ::= clap clap clap
Cycle ::= {Bell, Feet, Hand}

Cycle*8

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

Opening…

Three against two · Pattern Engine