Lessons · Advanced

Selector harmony

A space of divisions, picked by number and by pattern

% The ground: four bars, I vi IV V in D, block chords over the roots.
% Every figure in this lesson is written over the tonic triad, so the
% other three chords are that same figure at '@~5', '@~3' and '@~4' —
% one shape, four harmonies, and only the shape still to choose.
 
bpm 120
meter 4
unit 1/4
key d maj
 
Chord ::= | {1, 3, 5} |
 
Bass ::= | .1 | .6 | .4 | .5 |
 
{Bass, Chord Chord@~5 Chord@~3 Chord@~4}
 
 
% A rule of alternatives is a SPACE of derivations, and 'Div#n' picks
% the nth out of it. 'enum' prints the space in enumeration order, and
% that order is the numbering: 1 quarters, 2 arpeggio, 3 Alberti, 4
% scale run, 5 upper pedal, 6 sixteenths. Three of them follow, and the
% number is the only thing that changes from line to line.
 
Div ::= | 1 3 5 3 |
      = | 1 3 5 '1 5 3 5 3 |
      = | 1 5 3 5 1 5 3 5 |
      = | 1 2 3 4 5 4 3 2 |
      = | 1 '1 3 '1 5 '1 3 '1 |
      = | 1 2 3 2 3 4 5 4 5 4 3 2 3 2 1 2 |
 
enum Div
 
{Bass, Div#1 Div#1@~5 Div#1@~3 Div#1@~4}
{Bass, Div#2 Div#2@~5 Div#2@~3 Div#2@~4}
{Bass, Div#3 Div#3@~5 Div#3@~3 Div#3@~4}
 
 
% A selector segment that is NOT a pure number is a PATTERN: it matches
% the derivation's leading items in order, 'any' matching any one item.
% All four basses leave the root, so the second item is what tells them
% apart, and '.5' asks for the ones that step to the fifth — walks 1
% and 3. The assert says which one the query lands on first.
 
Walk ::= | .1 .5 .1 .5 |
       = | .1 .3 .5 .3 |
       = | .1 .5 .3 .5 |
       = | .1 .7 .6 .5 |
 
enum Walk
assert Walk#any;.5 == Walk#1
 
{Walk#any;.5 Walk#any;.5@~5 Walk#any;.5@~3 Walk#any;.5@~4,
 Div#4 Div#4@~5 Div#4@~3 Div#4@~4}
{Walk#any;.5 Walk#any;.5@~5 Walk#any;.5@~3 Walk#any;.5@~4,
 Div#5 Div#5@~5 Div#5@~3 Div#5@~4}
 
 
% A bare number never reads as a pattern — 'Walk#2' is the second walk,
% not the walk that starts on 2 — so a number written beside a pattern
% picks among the MATCHES instead. The second bass that steps to the
% fifth is walk 3; it takes the pedal figure over from the line before,
% and then the sixteenths arrive.
 
assert Walk#any;.5;2 == Walk#3
 
{Walk#any;.5;2 Walk#any;.5;2@~5 Walk#any;.5;2@~3 Walk#any;.5;2@~4,
 Div#5 Div#5@~5 Div#5@~3 Div#5@~4}
{Walk#any;.5;2 Walk#any;.5;2@~5 Walk#any;.5;2@~3 Walk#any;.5;2@~4,
 Div#6 Div#6@~5 Div#6@~3 Div#6@~4}
 
 
% The close. Walk 4 is the stepwise descent, and no '.5' query reaches
% it — its second item is '.7' — so it is picked by number, carries the
% sixteenths and then the arpeggio, and the set ends on the block chords
% over the plain root bass it opened with.
 
{Walk#4 Walk#4@~5 Walk#4@~3 Walk#4@~4, Div#6 Div#6@~5 Div#6@~3 Div#6@~4}
{Walk#4 Walk#4@~5 Walk#4@~3 Walk#4@~4, Div#2 Div#2@~5 Div#2@~3 Div#2@~4}
{Bass, Chord Chord@~5 Chord@~3 Chord@~4}

% The ground: four bars, I vi IV V in D, block chords over the roots.
% Every figure in this lesson is written over the tonic triad, so the
% other three chords are that same figure at '@~5', '@~3' and '@~4' —
% one shape, four harmonies, and only the shape still to choose.

bpm 120
meter 4
unit 1/4
key d maj

Chord ::= | {1, 3, 5} |

Bass ::= | .1 | .6 | .4 | .5 |

{Bass, Chord Chord@~5 Chord@~3 Chord@~4}

% A rule of alternatives is a SPACE of derivations, and 'Div#n' picks
% the nth out of it. 'enum' prints the space in enumeration order, and
% that order is the numbering: 1 quarters, 2 arpeggio, 3 Alberti, 4
% scale run, 5 upper pedal, 6 sixteenths. Three of them follow, and the
% number is the only thing that changes from line to line.

Div ::= | 1 3 5 3 |
      = | 1 3 5 '1 5 3 5 3 |
      = | 1 5 3 5 1 5 3 5 |
      = | 1 2 3 4 5 4 3 2 |
      = | 1 '1 3 '1 5 '1 3 '1 |
      = | 1 2 3 2 3 4 5 4 5 4 3 2 3 2 1 2 |

enum Div

{Bass, Div#1 Div#1@~5 Div#1@~3 Div#1@~4}
{Bass, Div#2 Div#2@~5 Div#2@~3 Div#2@~4}
{Bass, Div#3 Div#3@~5 Div#3@~3 Div#3@~4}

% A selector segment that is NOT a pure number is a PATTERN: it matches
% the derivation's leading items in order, 'any' matching any one item.
% All four basses leave the root, so the second item is what tells them
% apart, and '.5' asks for the ones that step to the fifth — walks 1
% and 3. The assert says which one the query lands on first.

Walk ::= | .1 .5 .1 .5 |
       = | .1 .3 .5 .3 |
       = | .1 .5 .3 .5 |
       = | .1 .7 .6 .5 |

enum Walk
assert Walk#any;.5 == Walk#1

{Walk#any;.5 Walk#any;.5@~5 Walk#any;.5@~3 Walk#any;.5@~4,
 Div#4 Div#4@~5 Div#4@~3 Div#4@~4}
{Walk#any;.5 Walk#any;.5@~5 Walk#any;.5@~3 Walk#any;.5@~4,
 Div#5 Div#5@~5 Div#5@~3 Div#5@~4}

% A bare number never reads as a pattern — 'Walk#2' is the second walk,
% not the walk that starts on 2 — so a number written beside a pattern
% picks among the MATCHES instead. The second bass that steps to the
% fifth is walk 3; it takes the pedal figure over from the line before,
% and then the sixteenths arrive.

assert Walk#any;.5;2 == Walk#3

{Walk#any;.5;2 Walk#any;.5;2@~5 Walk#any;.5;2@~3 Walk#any;.5;2@~4,
 Div#5 Div#5@~5 Div#5@~3 Div#5@~4}
{Walk#any;.5;2 Walk#any;.5;2@~5 Walk#any;.5;2@~3 Walk#any;.5;2@~4,
 Div#6 Div#6@~5 Div#6@~3 Div#6@~4}

% The close. Walk 4 is the stepwise descent, and no '.5' query reaches
% it — its second item is '.7' — so it is picked by number, carries the
% sixteenths and then the arpeggio, and the set ends on the block chords
% over the plain root bass it opened with.

{Walk#4 Walk#4@~5 Walk#4@~3 Walk#4@~4, Div#6 Div#6@~5 Div#6@~3 Div#6@~4}
{Walk#4 Walk#4@~5 Walk#4@~3 Walk#4@~4, Div#2 Div#2@~5 Div#2@~3 Div#2@~4}
{Bass, Chord Chord@~5 Chord@~3 Chord@~4}

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

Opening…

Selector harmony · Pattern Engine