Lessons · Grammars

Sequences & selectors

Diatonic restatement, filters, the Alberti bass

% A SEQUENCE restates one figure on other scale steps. Write it ONCE
% and let '@~n' do the restating: the key, not the copy, decides where
% the whole and half steps fall, so Rise climbs four rungs of C major
% without a single accidental being spelled. Its last copy tops out on
% the octave, and that is the note Close walks back down from.
 
bpm 90
instrument plain
meter 4
unit 1/4
key c maj
 
Wave  ::= 1 _2 3 _2 2 _2 4 _2 3 _2 5 _2 4 _2 2 _2
Rise  ::= Wave Wave@~1 Wave@~2 Wave@~3
Close ::= '1 _2 7 _2 6 _2 5 _2 4 _2 3 _2 2 _2 1 _2
 
Rise Close
 
 
% ALTERNATIVES put several bodies under one name ('=' separates them)
% and 'Cell#n' pins the n-th. The ALBERTI BASS is that shape of thought
% exactly, one broken-chord cell per chord, so the rule holds the
% harmony and the progression is nothing but selector spelling. This is
% Mozart's own opening bass to K 545: I, V6/5, IV6/4, vii°6, each
% resolving home. Bare first, then under the sequence.
 
Cell ::= {1 5 3 5}_2 = {2 5 4 5}_2 = {1 6 4 6}_2 = {.7 5 2 5}_2
Bass<bass> ::= | Cell#1 Cell#1 | Cell#2 Cell#1 | Cell#3 Cell#1 | Cell#4 Cell#1 |
 
Bass
{Rise, Bass}
 
 
% A selector need not COUNT. A ';'-segment list MATCHES instead (each
% segment against the item at that position, 'any' the wildcard), and
% 'asc'/'desc' order the survivors by pitch. The asserts say what that
% buys: Fall's lowest body is also its only one opening on .5, and its
% highest is the only one whose second item is '1. Down asks for them
% top-first, Up bottom-first: one rule, two contrary lines.
 
Fall ::= .5 _2 .7 _2 2 _2 1 _2
       = 1 _2 2 _2 4 _2 3 _2
       = 3 _2 5 _2 '1 _2 7 _2
       = 5 _2 '1 _2 3 _2 2 _2
 
assert Fall#asc == Fall#.5;any
assert Fall#desc == Fall#any;'1
 
Down ::= Fall#desc Fall#3 Fall#2 Fall#asc
Up   ::= Fall#asc Fall#2 Fall#3 Fall#desc
 
Down Up
{Up Down, Bass}
 
 
% The two devices COMPOSE. A mark after a reference covers the WHOLE
% expansion, so Cell#1@~-1 is that pinned chord one scale step lower;
% Walk descends four of them and Walk@~-4 carries on below, making
% Ground a broken-chord bass on the roots 1 7 6 5 4 3 2 1, a full
% octave down, in eight tokens. Tune is its own sequence riding over
% it, and the pair is stated a third high before it answers at home.
 
Walk   ::= Cell#1 Cell#1@~-1 Cell#1@~-2 Cell#1@~-3
Ground<bass> ::= Walk Walk@~-4
Tune   ::= Wave@~4 Wave@~3 Wave@~2 Close
 
assert Walk@~-4 == Cell#1@~-4 Cell#1@~-5 Cell#1@~-6 Cell#1@~-7
 
{Tune@~2, Ground@~2}
{Tune, Ground}
 
 
% SLICES cut a selection python-style over its ITEMS, a sound with
% its marks, so '1 _2 is one position. [0:4] is the head, [4:] the
% tail, [::2] every other item, [::-1] the written-out retrograde.
% Taking a subject apart that way is what a development does, so that
% is what these three lines are: statement and retrograde, then head
% and tail sequenced against each other, then the pieces over Walk.
 
Theme ::= '1 _2 7 _2 '1 _2 5 _2 6 _2 5 _2 3 _2 1 _2
 
Theme Theme[::-1]
Theme[0:4] Theme[0:4]@~1 Theme[4:] Theme[4:]@~-1
{Theme[::2] Theme[::2]@~1 Theme[4:] Theme[0:4], Walk}
 
 
% Where '@~n' MOVES a written figure, RELATIVE pitch writes a figure
% with no fixed place at all: 's2' is two scale steps up from the last
% pitch written, so Arp spells a triad over whatever note it lands on
% and is in the key by construction. Sweep's four anchors are Walk's
% own roots, so bass and arpeggio break the same four chords, and the
% retrograde of Theme falls into the cadence.
 
Arp   ::= s2 _2 s2 _2 s3 _2
Sweep ::= 1 _2 Arp .7 _2 Arp .6 _2 Arp .5 _2 Arp
 
assert 1 _2 Arp == 1 _2 3 _2 5 _2 '1 _2
 
Sweep
{Sweep, Walk}
{Theme[::-1] Close, Cell#3 Cell#2 Cell#4 Cell#1}

% A SEQUENCE restates one figure on other scale steps. Write it ONCE
% and let '@~n' do the restating: the key, not the copy, decides where
% the whole and half steps fall, so Rise climbs four rungs of C major
% without a single accidental being spelled. Its last copy tops out on
% the octave, and that is the note Close walks back down from.

bpm 90
instrument plain
meter 4
unit 1/4
key c maj

Wave  ::= 1 _2 3 _2 2 _2 4 _2 3 _2 5 _2 4 _2 2 _2
Rise  ::= Wave Wave@~1 Wave@~2 Wave@~3
Close ::= '1 _2 7 _2 6 _2 5 _2 4 _2 3 _2 2 _2 1 _2

Rise Close

% ALTERNATIVES put several bodies under one name ('=' separates them)
% and 'Cell#n' pins the n-th. The ALBERTI BASS is that shape of thought
% exactly, one broken-chord cell per chord, so the rule holds the
% harmony and the progression is nothing but selector spelling. This is
% Mozart's own opening bass to K 545: I, V6/5, IV6/4, vii°6, each
% resolving home. Bare first, then under the sequence.

Cell ::= {1 5 3 5}_2 = {2 5 4 5}_2 = {1 6 4 6}_2 = {.7 5 2 5}_2
Bass<bass> ::= | Cell#1 Cell#1 | Cell#2 Cell#1 | Cell#3 Cell#1 | Cell#4 Cell#1 |

Bass
{Rise, Bass}

% A selector need not COUNT. A ';'-segment list MATCHES instead (each
% segment against the item at that position, 'any' the wildcard), and
% 'asc'/'desc' order the survivors by pitch. The asserts say what that
% buys: Fall's lowest body is also its only one opening on .5, and its
% highest is the only one whose second item is '1. Down asks for them
% top-first, Up bottom-first: one rule, two contrary lines.

Fall ::= .5 _2 .7 _2 2 _2 1 _2
       = 1 _2 2 _2 4 _2 3 _2
       = 3 _2 5 _2 '1 _2 7 _2
       = 5 _2 '1 _2 3 _2 2 _2

assert Fall#asc == Fall#.5;any
assert Fall#desc == Fall#any;'1

Down ::= Fall#desc Fall#3 Fall#2 Fall#asc
Up   ::= Fall#asc Fall#2 Fall#3 Fall#desc

Down Up
{Up Down, Bass}

% The two devices COMPOSE. A mark after a reference covers the WHOLE
% expansion, so Cell#1@~-1 is that pinned chord one scale step lower;
% Walk descends four of them and Walk@~-4 carries on below, making
% Ground a broken-chord bass on the roots 1 7 6 5 4 3 2 1, a full
% octave down, in eight tokens. Tune is its own sequence riding over
% it, and the pair is stated a third high before it answers at home.

Walk   ::= Cell#1 Cell#1@~-1 Cell#1@~-2 Cell#1@~-3
Ground<bass> ::= Walk Walk@~-4
Tune   ::= Wave@~4 Wave@~3 Wave@~2 Close

assert Walk@~-4 == Cell#1@~-4 Cell#1@~-5 Cell#1@~-6 Cell#1@~-7

{Tune@~2, Ground@~2}
{Tune, Ground}

% SLICES cut a selection python-style over its ITEMS, a sound with
% its marks, so '1 _2 is one position. [0:4] is the head, [4:] the
% tail, [::2] every other item, [::-1] the written-out retrograde.
% Taking a subject apart that way is what a development does, so that
% is what these three lines are: statement and retrograde, then head
% and tail sequenced against each other, then the pieces over Walk.

Theme ::= '1 _2 7 _2 '1 _2 5 _2 6 _2 5 _2 3 _2 1 _2

Theme Theme[::-1]
Theme[0:4] Theme[0:4]@~1 Theme[4:] Theme[4:]@~-1
{Theme[::2] Theme[::2]@~1 Theme[4:] Theme[0:4], Walk}

% Where '@~n' MOVES a written figure, RELATIVE pitch writes a figure
% with no fixed place at all: 's2' is two scale steps up from the last
% pitch written, so Arp spells a triad over whatever note it lands on
% and is in the key by construction. Sweep's four anchors are Walk's
% own roots, so bass and arpeggio break the same four chords, and the
% retrograde of Theme falls into the cadence.

Arp   ::= s2 _2 s2 _2 s3 _2
Sweep ::= 1 _2 Arp .7 _2 Arp .6 _2 Arp .5 _2 Arp

assert 1 _2 Arp == 1 _2 3 _2 5 _2 '1 _2

Sweep
{Sweep, Walk}
{Theme[::-1] Close, Cell#3 Cell#2 Cell#4 Cell#1}

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

Sequences & selectors · Grammars