Duration

Stretching, dividing, repeating time

% Four marks set how long a thing lasts: '_' DOUBLES, '+' EXTENDS,
% '/' DIMINISHES, '*' REPEATS. This block is '_': bare '_' doubles the
% item before it, '_n' multiplies by n, and the mark is its own token,
% so it keeps its space. A unit is a sixteenth, so '_4' is a quarter and
% '_8' a half, and the Air is written in nothing else, closing on a
% whole note. Strain names its two halves and that close as one tune;
% every variation below answers it beat for beat, over the same ground.
 
bpm 72
instrument plain
meter 4
unit 1/4
key d4 min
 
Air    ::= 5 _4 '1 _4 7 _4 '1 _4 6 _8 5 _8
Airb   ::= 4 _4 6 _4 5 _4 4 _4 3 _8 2 _4 .7# _4
Close  ::= 1 _16
Strain ::= Air Airb Close
 
assert 5 _8 == 5 _4 _2
 
Strain
 
 
% THE GROUND. '*n' REPEATS: n separate attacks, not one long note
% held. The two lines below fill the same sixteen units: '.1 _16' is one
% sound and '.1 _2*8' is eight of them, and only the second can be a
% pulse. That is the bass this Air wants, eighths under every bar: d,
% then bb and a, then g, then f and a, home to d. Nothing after this
% changes it: every variation is five bars over the same Bass.
 
Pulse  ::= .1 _2*8 ..6 _2*4 ..5 _2*4
Pulseb ::= ..4 _2*8 ..3 _2*4 ..5 _2*4
Bass   ::= Pulse Pulseb .1 _16
 
assert ..5 _2*4 == ..5 _2 ..5 _2 ..5 _2 ..5 _2
 
.1 _16
.1 _2*8
 
{Strain, Bass}
 
 
% VARIATION 1: two to the beat. '+n' EXTENDS by whole units: '+2' adds
% two to the one an item already carries, which is the dotted eighth,
% and the marks compose as dur = (1 + Σ'+') × ∏'_' ÷ ∏'/'. Lilt is that
% dotted note and the step below it. Lilted states one a beat on the
% Air's own note, so the tune is still there, long note for long note;
% Snapped turns the pair around for the second half: the short note on
% the beat and the Air's note just after it.
 
Lilt ::= 5+2 4
Snap ::= 4 5+2
 
Lilted  ::= Lilt Lilt@~3 Lilt@~2 Lilt@~3 Lilt@~1 Lilt@~1 Lilt Lilt
Snapped ::= Snap@~-1 Snap@~1 Snap Snap@~-1 Snap@~-2 Snap@~-2 Snap@~-3 .7# _4
Dotted  ::= Lilted Snapped Close
 
assert 1+1 == 1 _
assert 1+3 == 1 _4
assert Lilt == 5 _3 4
 
{Dotted, Bass}
 
 
% VARIATION 2: three to the beat. '/n' DIVIDES, and it composes with
% '_': '_4/3' is times four over three, so three items fill the four
% units of one beat. That IS a triplet, spelled as arithmetic. Turn is a
% note, the step above it, the note again; the two halves put one on
% every beat of the tune, written plain. Braces with no comma inside
% only GROUP, so the one mark on the pair makes all sixteen turns
% triplets at once. The last turn is spelled out: the minor scale does
% not raise its seventh for you.
 
Turn ::= 5 6 5
 
Turns    ::= Turn Turn@~3 Turn@~2 Turn@~3 Turn@~1 Turn@~1 Turn Turn
Turnsb   ::= Turn@~-1 Turn@~1 Turn Turn@~-1 Turn@~-2 Turn@~-2 Turn@~-3 .7# 2 .7#
Triplets ::= {Turns Turnsb} _4/3 Close
 
assert Turn _4/3 == 5 _4/3 6 _4/3 5 _4/3
 
{Triplets, Bass}
 
 
% VARIATION 3: four to the beat, which is what a player of this music
% would call DIVISIONS. A bare item is one unit, so plain degrees are
% already sixteenths and need no mark: Run climbs a fifth and falls back
% inside half a bar. Put the mark on the tune instead and 'Air/4 Airb/4'
% is the strain itself at that speed, every quarter a sixteenth, four
% bars inside one. The variation sequences Run rather than divide the
% Air: a scale step lower each half bar down to d, then back up to f,
% and a last half bar by hand that falls to the C sharp.
 
Run ::= 5 6 7 '1 '2 '1 7 6
 
Runs      ::= Run Run@~-1 Run@~-2 Run@~-3
Runsb     ::= Run@~-4 Run@~-3 Run@~-2 2 3 4 5 4 3 2 .7#
Divisions ::= Runs Runsb Close
 
assert Run _2/2 == Run
assert Air/4 == 5 '1 7 '1 6 _2 5 _2
 
Air/4 Airb/4
 
{Divisions, Bass}
 
 
% Theme and variations end to end, each one putting another note in the
% beat: one, then two, then three, then four. Then a coda that uses all
% four marks at once ('/2' halves melody and ground together, one mark
% on each name, and '*2' says the halved pair twice) before the tonic
% is broadened over two whole bars.
 
{Strain, Bass}
{Dotted, Bass}
{Triplets, Bass}
{Divisions, Bass}
 
{Strain/2, Bass/2}*2
{Close, .1 _16} _2

% Four marks set how long a thing lasts: '_' DOUBLES, '+' EXTENDS,
% '/' DIMINISHES, '*' REPEATS. This block is '_': bare '_' doubles the
% item before it, '_n' multiplies by n, and the mark is its own token,
% so it keeps its space. A unit is a sixteenth, so '_4' is a quarter and
% '_8' a half, and the Air is written in nothing else, closing on a
% whole note. Strain names its two halves and that close as one tune;
% every variation below answers it beat for beat, over the same ground.

bpm 72
instrument plain
meter 4
unit 1/4
key d4 min

Air    ::= 5 _4 '1 _4 7 _4 '1 _4 6 _8 5 _8
Airb   ::= 4 _4 6 _4 5 _4 4 _4 3 _8 2 _4 .7# _4
Close  ::= 1 _16
Strain ::= Air Airb Close

assert 5 _8 == 5 _4 _2

Strain

% THE GROUND. '*n' REPEATS: n separate attacks, not one long note
% held. The two lines below fill the same sixteen units: '.1 _16' is one
% sound and '.1 _2*8' is eight of them, and only the second can be a
% pulse. That is the bass this Air wants, eighths under every bar: d,
% then bb and a, then g, then f and a, home to d. Nothing after this
% changes it: every variation is five bars over the same Bass.

Pulse  ::= .1 _2*8 ..6 _2*4 ..5 _2*4
Pulseb ::= ..4 _2*8 ..3 _2*4 ..5 _2*4
Bass   ::= Pulse Pulseb .1 _16

assert ..5 _2*4 == ..5 _2 ..5 _2 ..5 _2 ..5 _2

.1 _16
.1 _2*8

{Strain, Bass}

% VARIATION 1: two to the beat. '+n' EXTENDS by whole units: '+2' adds
% two to the one an item already carries, which is the dotted eighth,
% and the marks compose as dur = (1 + Σ'+') × ∏'_' ÷ ∏'/'. Lilt is that
% dotted note and the step below it. Lilted states one a beat on the
% Air's own note, so the tune is still there, long note for long note;
% Snapped turns the pair around for the second half: the short note on
% the beat and the Air's note just after it.

Lilt ::= 5+2 4
Snap ::= 4 5+2

Lilted  ::= Lilt Lilt@~3 Lilt@~2 Lilt@~3 Lilt@~1 Lilt@~1 Lilt Lilt
Snapped ::= Snap@~-1 Snap@~1 Snap Snap@~-1 Snap@~-2 Snap@~-2 Snap@~-3 .7# _4
Dotted  ::= Lilted Snapped Close

assert 1+1 == 1 _
assert 1+3 == 1 _4
assert Lilt == 5 _3 4

{Dotted, Bass}

% VARIATION 2: three to the beat. '/n' DIVIDES, and it composes with
% '_': '_4/3' is times four over three, so three items fill the four
% units of one beat. That IS a triplet, spelled as arithmetic. Turn is a
% note, the step above it, the note again; the two halves put one on
% every beat of the tune, written plain. Braces with no comma inside
% only GROUP, so the one mark on the pair makes all sixteen turns
% triplets at once. The last turn is spelled out: the minor scale does
% not raise its seventh for you.

Turn ::= 5 6 5

Turns    ::= Turn Turn@~3 Turn@~2 Turn@~3 Turn@~1 Turn@~1 Turn Turn
Turnsb   ::= Turn@~-1 Turn@~1 Turn Turn@~-1 Turn@~-2 Turn@~-2 Turn@~-3 .7# 2 .7#
Triplets ::= {Turns Turnsb} _4/3 Close

assert Turn _4/3 == 5 _4/3 6 _4/3 5 _4/3

{Triplets, Bass}

% VARIATION 3: four to the beat, which is what a player of this music
% would call DIVISIONS. A bare item is one unit, so plain degrees are
% already sixteenths and need no mark: Run climbs a fifth and falls back
% inside half a bar. Put the mark on the tune instead and 'Air/4 Airb/4'
% is the strain itself at that speed, every quarter a sixteenth, four
% bars inside one. The variation sequences Run rather than divide the
% Air: a scale step lower each half bar down to d, then back up to f,
% and a last half bar by hand that falls to the C sharp.

Run ::= 5 6 7 '1 '2 '1 7 6

Runs      ::= Run Run@~-1 Run@~-2 Run@~-3
Runsb     ::= Run@~-4 Run@~-3 Run@~-2 2 3 4 5 4 3 2 .7#
Divisions ::= Runs Runsb Close

assert Run _2/2 == Run
assert Air/4 == 5 '1 7 '1 6 _2 5 _2

Air/4 Airb/4

{Divisions, Bass}

% Theme and variations end to end, each one putting another note in the
% beat: one, then two, then three, then four. Then a coda that uses all
% four marks at once ('/2' halves melody and ground together, one mark
% on each name, and '*2' says the halved pair twice) before the tonic
% is broadened over two whole bars.

{Strain, Bass}
{Dotted, Bass}
{Triplets, Bass}
{Divisions, Bass}

{Strain/2, Bass/2}*2
{Close, .1 _16} _2

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

Duration · Basics