Lessons · Advanced

Slice development

Heads, tails, strides: variation by index

% A slice takes ITEMS out of a derivation python-style, so a theme is
% not one object but a shelf of them. These sixteen notes and this
% ground (d minor, roots falling d c bb a, each answered by its own
% fifth) are the material: every block below cuts them, or asserts
% itself equal to a cut.
 
bpm 60
instrument plain
meter 4
unit 1/4
key d min
 
Ground<bass> ::= .1 _2 .5 _2 ..7 _2 .4 _2 ..6 _2 .3 _2 ..5 _2 .2 _2
Theme  ::= 1 5 4 3 2 3 4 2 '1 7 6 5 4 3 2 1
 
{Theme*2, Ground*2}
 
 
% 'Theme[:8]' is the first eight items and 'Theme[8:]' the rest, so the
% tune turns out to be a period: Head stops open on e, Tail falls a
% whole octave d5 to d4. Head then answers itself a third and a fifth
% lower before Tail closes, and the assert says the halves still add up.
 
Head ::= Theme[:8]
Tail ::= Theme[8:]
 
assert Head Tail == Theme
{Head Head@~-2 Head@~-4 Tail, Ground*2}
 
 
% A cut from the MIDDLE is a motif nobody wrote down: 'Theme[2:6]' is
% the four notes g f e f at the tune's waist. Restated a degree lower
% each time it is a falling sequence; walk the same steps the other way
% and it climbs. Both land on a tonic d, an octave apart.
 
Turn ::= Theme[2:6]
 
{Turn Turn@~-1 Turn@~-2 Turn@~-3 Turn@~-4 Turn@~-5 Turn@~-6 1 _4, Ground*2}
{Turn@~-3 Turn@~-2 Turn@~-1 Turn Turn@~1 Turn@~2 Turn@~3 '1 _4, Ground*2}
 
 
% '[::-1]' plays a derivation backwards, each duration riding its own
% note. So Crab opens with the rising scale d e f g a bb c d' that Theme
% spends its second half falling. Reverse twice and the theme is back
% (a failed assert is an ERROR, so that claim is checked on every run),
% and setting the pair against its own mirror is a crab canon.
 
Crab ::= Theme[::-1]
 
assert Crab[::-1] == Theme
{Theme Crab, Ground*2}
{Theme Crab, Crab Theme, Ground*2}
 
 
% A rule of alternatives is a SPACE of derivations: '#n' picks the nth
% one and the slice cuts THAT derivation. Fall's three links overlap on
% a shared note (a, then e), so dropping each follower's first item
% with '[1:]' closes the chain into Tail exactly. Four of those falls,
% each entering a third lower, cascade from d5 down to e3.
 
Fall ::= '1 7 6 5 = 5 4 3 2 = 2 1
 
assert Fall#1 Fall#2[1:] Fall#3[1:] == Tail
Fall#1 Fall#2 Fall#3
Fall#1 Fall#2[1:] Fall#3[1:]
{Tail Tail@~-2 Tail@~-4 Tail@~-6, Ground*2}
 
 
% One line can BE two voices, alternating. '[::2]' takes the odd items
% and '[1::2]' the even, so Comp parts into a walking bass d a bb f g d
% a d and a tune that is Tail over again; the assert says so, and the
% last statement plays the two voices unfolded at half speed.
 
Comp ::= .1 '1 .5 7 .6 6 .3 5 .4 4 .1 3 .5 2 .1 1
 
assert Comp[1::2] == Tail
Comp*2
{Comp[::2] _2, Comp[1::2] _2}

% A slice takes ITEMS out of a derivation python-style, so a theme is
% not one object but a shelf of them. These sixteen notes and this
% ground (d minor, roots falling d c bb a, each answered by its own
% fifth) are the material: every block below cuts them, or asserts
% itself equal to a cut.

bpm 60
instrument plain
meter 4
unit 1/4
key d min

Ground<bass> ::= .1 _2 .5 _2 ..7 _2 .4 _2 ..6 _2 .3 _2 ..5 _2 .2 _2
Theme  ::= 1 5 4 3 2 3 4 2 '1 7 6 5 4 3 2 1

{Theme*2, Ground*2}

% 'Theme[:8]' is the first eight items and 'Theme[8:]' the rest, so the
% tune turns out to be a period: Head stops open on e, Tail falls a
% whole octave d5 to d4. Head then answers itself a third and a fifth
% lower before Tail closes, and the assert says the halves still add up.

Head ::= Theme[:8]
Tail ::= Theme[8:]

assert Head Tail == Theme
{Head Head@~-2 Head@~-4 Tail, Ground*2}

% A cut from the MIDDLE is a motif nobody wrote down: 'Theme[2:6]' is
% the four notes g f e f at the tune's waist. Restated a degree lower
% each time it is a falling sequence; walk the same steps the other way
% and it climbs. Both land on a tonic d, an octave apart.

Turn ::= Theme[2:6]

{Turn Turn@~-1 Turn@~-2 Turn@~-3 Turn@~-4 Turn@~-5 Turn@~-6 1 _4, Ground*2}
{Turn@~-3 Turn@~-2 Turn@~-1 Turn Turn@~1 Turn@~2 Turn@~3 '1 _4, Ground*2}

% '[::-1]' plays a derivation backwards, each duration riding its own
% note. So Crab opens with the rising scale d e f g a bb c d' that Theme
% spends its second half falling. Reverse twice and the theme is back
% (a failed assert is an ERROR, so that claim is checked on every run),
% and setting the pair against its own mirror is a crab canon.

Crab ::= Theme[::-1]

assert Crab[::-1] == Theme
{Theme Crab, Ground*2}
{Theme Crab, Crab Theme, Ground*2}

% A rule of alternatives is a SPACE of derivations: '#n' picks the nth
% one and the slice cuts THAT derivation. Fall's three links overlap on
% a shared note (a, then e), so dropping each follower's first item
% with '[1:]' closes the chain into Tail exactly. Four of those falls,
% each entering a third lower, cascade from d5 down to e3.

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

assert Fall#1 Fall#2[1:] Fall#3[1:] == Tail
Fall#1 Fall#2 Fall#3
Fall#1 Fall#2[1:] Fall#3[1:]
{Tail Tail@~-2 Tail@~-4 Tail@~-6, Ground*2}

% One line can BE two voices, alternating. '[::2]' takes the odd items
% and '[1::2]' the even, so Comp parts into a walking bass d a bb f g d
% a d and a tune that is Tail over again; the assert says so, and the
% last statement plays the two voices unfolded at half speed.

Comp ::= .1 '1 .5 7 .6 6 .3 5 .4 4 .1 3 .5 2 .1 1

assert Comp[1::2] == Tail
Comp*2
{Comp[::2] _2, Comp[1::2] _2}

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

Slice development · Advanced