Motifs & sequences

Reusable ideas, sequence, call and answer

% A MOTIF is the smallest idea a listener can catch and keep: five
% notes and their rhythm, two seconds of music. Motif holds the tonic,
% turns on the third, and arrives on the fifth. Stated three times over
% its own chord it is already a section — and a section here is one
% rule, tune and chords braced together, so the piece is five names:
%
%   Statement · Sequence · Call · Fragment · Answer
 
bpm 60
key d min
 
Motif ::= 1 _2 3 2 3 _2 5 _2
Ton   ::= {.1, .3, .5} _8
 
Statement ::= {Motif*3 1 _8, Ton*4}
 
Statement
 
 
% A SEQUENCE restates the motif on another step of the scale. '@~1'
% moves the whole reference ONE DEGREE, so the shape bends to the key
% as it climbs: the motif's minor third d-f comes back two rungs up as
% the major third f-a. Three rungs is the usual dose — the fourth
% statement never comes, and Fall walks from the octave down to 3 and
% lifts to 5 for a half cadence, over a bass that climbs a degree under
% each statement and reaches 4 as Fall begins.
 
Climb ::= Motif Motif@~1 Motif@~2
Fall  ::= '1 _2 7 _2 6 _2 5 _2 4 _2 3 _2 5 _4
 
Walk ::= .1 _8 .2 _8 .3 _8 .4 _8
Dom  ::= {..5, ..7#, .4} _8
 
Sequence ::= {Climb Fall, Walk Dom}
 
assert Motif@~2 == 3 _2 5 4 5 _2 7 _2
 
Sequence
 
 
% Why the tilde. '@2' moves the motif two SEMITONES: every interval is
% copied exactly, so the shape survives and the key does not — the copy
% wants an f# and a b that D minor has never owned, and the chord under
% it has to travel too. The two asserts differ by exactly those two
% sharps. Neither line below is part of the piece; they are here to be
% compared.
 
assert Motif@~1 == 2 _2 4 3 4 _2 6 _2
assert Motif@2 == 2 _2 4 3# 4 _2 6# _2
 
{Climb, Ton*3}
{Motif Motif@2 Motif@4, Ton Ton@2 Ton@4}
 
 
% CALL AND ANSWER is one motif with two destinations. Call sequences it
% up a step and joins Fall late — 'Fall[2:]' drops the descent's first
% two items, so it starts on 6 — then stops on the dominant and holds a
% rest for a question mark. Its second chord is a bare .2: the motif's
% own g and bb finish it. Answer drops the motif a third instead, onto
% the sixth degree under a B flat chord, and walks home through the
% raised seventh — same first eight units, opposite endings.
 
Sub ::= {.1, .4, .6} _8
Six ::= {..6, .1, .3} _8
 
Call ::= {Motif Motif@~1 Fall[2:] - _4,
          Ton .2 _8 Sub Dom}
 
Answer ::= {Motif Motif@~-2 4 _2 3 _2 2 _4 .7# _4 1 _8,
            Ton Six Sub/2 Dom Ton}
 
assert Fall[2:] == 6 _2 5 _2 4 _2 3 _2 5 _4
 
Call
Answer
 
 
% A motif can be cut and stay recognizable. 'Motif[:3]' keeps the first
% three items — the tonic and its turn — and throws the arrival away.
% The head alone then carries a sequence of its own, four rungs down the
% scale over a bass falling with it, and the cadence it reaches is
% DECEPTIVE: the tune gets home to 1, but the bass steps up to 6 instead
% of landing on the tonic — which is why the answer still has work to do.
 
Head ::= Motif[:3]
Drop ::= .1 _4 ..7 _4 ..6 _4 ..5 _4
 
Fragment ::= {Head Head@~-1 Head@~-2 Head@~-3 .5 _4 .7# _4 1 _8,
              Drop Dom Six}
 
assert Head == 1 _2 3 2
 
Fragment
 
 
% The whole piece, and nothing in it is new — five names, one motif:
% the statement, the sequence stopping on the dominant, the call and
% its rest, the head alone over the falling bass into its deceptive
% cadence, and the answer that finally closes on the tonic. Eight
% seconds each, ten for the sequence and nine for the answer.
 
Statement
Sequence
Call
Fragment
Answer

% A MOTIF is the smallest idea a listener can catch and keep: five
% notes and their rhythm, two seconds of music. Motif holds the tonic,
% turns on the third, and arrives on the fifth. Stated three times over
% its own chord it is already a section — and a section here is one
% rule, tune and chords braced together, so the piece is five names:
%
%   Statement · Sequence · Call · Fragment · Answer

bpm 60
key d min

Motif ::= 1 _2 3 2 3 _2 5 _2
Ton   ::= {.1, .3, .5} _8

Statement ::= {Motif*3 1 _8, Ton*4}

Statement

% A SEQUENCE restates the motif on another step of the scale. '@~1'
% moves the whole reference ONE DEGREE, so the shape bends to the key
% as it climbs: the motif's minor third d-f comes back two rungs up as
% the major third f-a. Three rungs is the usual dose — the fourth
% statement never comes, and Fall walks from the octave down to 3 and
% lifts to 5 for a half cadence, over a bass that climbs a degree under
% each statement and reaches 4 as Fall begins.

Climb ::= Motif Motif@~1 Motif@~2
Fall  ::= '1 _2 7 _2 6 _2 5 _2 4 _2 3 _2 5 _4

Walk ::= .1 _8 .2 _8 .3 _8 .4 _8
Dom  ::= {..5, ..7#, .4} _8

Sequence ::= {Climb Fall, Walk Dom}

assert Motif@~2 == 3 _2 5 4 5 _2 7 _2

Sequence

% Why the tilde. '@2' moves the motif two SEMITONES: every interval is
% copied exactly, so the shape survives and the key does not — the copy
% wants an f# and a b that D minor has never owned, and the chord under
% it has to travel too. The two asserts differ by exactly those two
% sharps. Neither line below is part of the piece; they are here to be
% compared.

assert Motif@~1 == 2 _2 4 3 4 _2 6 _2
assert Motif@2 == 2 _2 4 3# 4 _2 6# _2

{Climb, Ton*3}
{Motif Motif@2 Motif@4, Ton Ton@2 Ton@4}

% CALL AND ANSWER is one motif with two destinations. Call sequences it
% up a step and joins Fall late — 'Fall[2:]' drops the descent's first
% two items, so it starts on 6 — then stops on the dominant and holds a
% rest for a question mark. Its second chord is a bare .2: the motif's
% own g and bb finish it. Answer drops the motif a third instead, onto
% the sixth degree under a B flat chord, and walks home through the
% raised seventh — same first eight units, opposite endings.

Sub ::= {.1, .4, .6} _8
Six ::= {..6, .1, .3} _8

Call ::= {Motif Motif@~1 Fall[2:] - _4,
          Ton .2 _8 Sub Dom}

Answer ::= {Motif Motif@~-2 4 _2 3 _2 2 _4 .7# _4 1 _8,
            Ton Six Sub/2 Dom Ton}

assert Fall[2:] == 6 _2 5 _2 4 _2 3 _2 5 _4

Call
Answer

% A motif can be cut and stay recognizable. 'Motif[:3]' keeps the first
% three items — the tonic and its turn — and throws the arrival away.
% The head alone then carries a sequence of its own, four rungs down the
% scale over a bass falling with it, and the cadence it reaches is
% DECEPTIVE: the tune gets home to 1, but the bass steps up to 6 instead
% of landing on the tonic — which is why the answer still has work to do.

Head ::= Motif[:3]
Drop ::= .1 _4 ..7 _4 ..6 _4 ..5 _4

Fragment ::= {Head Head@~-1 Head@~-2 Head@~-3 .5 _4 .7# _4 1 _8,
              Drop Dom Six}

assert Head == 1 _2 3 2

Fragment

% The whole piece, and nothing in it is new — five names, one motif:
% the statement, the sequence stopping on the dominant, the call and
% its rest, the head alone over the falling bass into its deceptive
% cadence, and the answer that finally closes on the tonic. Eight
% seconds each, ten for the sequence and nine for the answer.

Statement
Sequence
Call
Fragment
Answer

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Motifs & sequences · Pattern Engine