Lessons · Grammars

Rules that generate

Zero-or-more and the timed optional

% A rule is a GENERATOR: it states a SPACE of patterns and every
% derivation is one of them. Postfix '&' is ZERO-OR-MORE — spelled
% '&' and not '*' because '*' is the fixed repeat mark — so 'Riff
% Riff&' is one or more bars of the vamp, and 'enum' walks that
% space, unrolling '&' three times unless '--reps' says otherwise:
 
bpm 90
meter 4
unit 1/4
key e min
 
Riff ::= | ..1 _4 ..1 _2 ..3 _2 ..4 _4 ..3 _2 ..1 _2 |
Vamp ::= Riff Riff&
 
enum Vamp
assert Vamp#1 == Riff
assert Vamp#2 == Riff Riff
Vamp#4
 
 
% 'x?' is a TIMED OPTIONAL SLOT: it derives x, or a REST of exactly
% x's length, so the beat grid never shifts. The empty branch comes
% first — Beat#1 leaves the syncopated kick out, Beat#2 plays it —
% and the parens keep that rest the default before the hat that
% follows. The assert spells the empty slot by hand:
 
Beat ::= | kick hat - hat snare hat - hat kick hat (kick?) hat snare hat - hat |
 
assert Beat#1 == | kick hat - hat snare hat - hat kick hat - hat snare hat - hat |
 
enum Beat
Beat#2 Beat#1 Beat#2 Beat#1
 
 
% With a SUBSTITUTE — 'x? y' — the slot derives x, or y scaled to
% x's EXACT duration. The order is the one above generalized: the
% substitute is #1, the literal x is #2. So enum prints the fill as
% '_2/3', six strokes in the beat that held one snare, and the assert
% spells that scaling by hand — a drummer who sometimes fills, and
% the bar measures the same either way:
 
Fill  ::= tom1 tom1 tom2 tom2 snare snare
Break ::= | kick hat - hat snare hat - hat kick hat kick hat (snare _4)?Fill |
 
assert Break#1 == | kick hat - hat snare hat - hat kick hat kick hat Fill _2/3 |
 
enum Break
Beat#2 Beat#1 Beat#2 Break
 
 
% The two marks compose. 'Beat#2&' repeats a PINNED derivation zero
% or more times — a bare name in a rule body ranges over all of them,
% '#2' holds the plain bar — and Break#1 ends every phrase with the
% fill. Each derivation is a different phrase LENGTH, fill last: one
% bar, then two, then four, over seven bars of fixed-count '*' bass.
 
Phrase ::= Beat#2& Break#1
 
assert Phrase#1 == Break
 
enum Phrase
{Phrase#1 Phrase#2 Phrase#4, Riff*7}
 
 
% The same slot ornaments a melody. Bar 1 climbs to 5 and steps
% back; bar 2 answers with a descent that holds a long 2 through the
% third beat — or spends that beat on a six-note turn. #2 is the
% literal reading, so one rule gives the plain statement and its
% ornamented repeat:
 
Turn ::= 3 2 1 2 3 2
Tune ::= | 1 _2 2 _2 3 _4 5 _4 4 _4 |
         | 5 _4 4 _2 3 _2 (2 _4)?Turn 1 _4 |
 
enum Tune
Tune#2 Tune
 
 
% Every part is a generator now, so the finale is one choice from
% each: two bars of vamp alone, then the tune plain and ornamented
% over the drummer's four-bar phrase and four bars of bass.
 
Vamp#2
{Tune#2 Tune, Phrase#4, Vamp#4}

% A rule is a GENERATOR: it states a SPACE of patterns and every
% derivation is one of them. Postfix '&' is ZERO-OR-MORE — spelled
% '&' and not '*' because '*' is the fixed repeat mark — so 'Riff
% Riff&' is one or more bars of the vamp, and 'enum' walks that
% space, unrolling '&' three times unless '--reps' says otherwise:

bpm 90
meter 4
unit 1/4
key e min

Riff ::= | ..1 _4 ..1 _2 ..3 _2 ..4 _4 ..3 _2 ..1 _2 |
Vamp ::= Riff Riff&

enum Vamp
assert Vamp#1 == Riff
assert Vamp#2 == Riff Riff
Vamp#4

% 'x?' is a TIMED OPTIONAL SLOT: it derives x, or a REST of exactly
% x's length, so the beat grid never shifts. The empty branch comes
% first — Beat#1 leaves the syncopated kick out, Beat#2 plays it —
% and the parens keep that rest the default before the hat that
% follows. The assert spells the empty slot by hand:

Beat ::= | kick hat - hat snare hat - hat kick hat (kick?) hat snare hat - hat |

assert Beat#1 == | kick hat - hat snare hat - hat kick hat - hat snare hat - hat |

enum Beat
Beat#2 Beat#1 Beat#2 Beat#1

% With a SUBSTITUTE — 'x? y' — the slot derives x, or y scaled to
% x's EXACT duration. The order is the one above generalized: the
% substitute is #1, the literal x is #2. So enum prints the fill as
% '_2/3', six strokes in the beat that held one snare, and the assert
% spells that scaling by hand — a drummer who sometimes fills, and
% the bar measures the same either way:

Fill  ::= tom1 tom1 tom2 tom2 snare snare
Break ::= | kick hat - hat snare hat - hat kick hat kick hat (snare _4)?Fill |

assert Break#1 == | kick hat - hat snare hat - hat kick hat kick hat Fill _2/3 |

enum Break
Beat#2 Beat#1 Beat#2 Break

% The two marks compose. 'Beat#2&' repeats a PINNED derivation zero
% or more times — a bare name in a rule body ranges over all of them,
% '#2' holds the plain bar — and Break#1 ends every phrase with the
% fill. Each derivation is a different phrase LENGTH, fill last: one
% bar, then two, then four, over seven bars of fixed-count '*' bass.

Phrase ::= Beat#2& Break#1

assert Phrase#1 == Break

enum Phrase
{Phrase#1 Phrase#2 Phrase#4, Riff*7}

% The same slot ornaments a melody. Bar 1 climbs to 5 and steps
% back; bar 2 answers with a descent that holds a long 2 through the
% third beat — or spends that beat on a six-note turn. #2 is the
% literal reading, so one rule gives the plain statement and its
% ornamented repeat:

Turn ::= 3 2 1 2 3 2
Tune ::= | 1 _2 2 _2 3 _4 5 _4 4 _4 |
         | 5 _4 4 _2 3 _2 (2 _4)?Turn 1 _4 |

enum Tune
Tune#2 Tune

% Every part is a generator now, so the finale is one choice from
% each: two bars of vamp alone, then the tune plain and ornamented
% over the drummer's four-bar phrase and four bars of bass.

Vamp#2
{Tune#2 Tune, Phrase#4, Vamp#4}

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Rules that generate · Pattern Engine