The three duration marks

Double, extend, diminish

% Three marks set how long an item lasts: '_' MULTIPLIES it, '/'
% DIVIDES it, '+' ADDS whole units of the grid — dur = (1 + Σ+) × ∏_ ÷
% ∏/. A unit here is a sixteenth, and this falling line lasts one, two,
% three, four units a note, each answered by a rest as long as itself:
 
bpm 72
meter 4
unit 1/4
key eb4 maj
 
5 - 4 _2 -*2 3+2 -*3 1 _4 -*4
 
 
% '+' is the mark that COUNTS. A dotted eighth is three units — 5+2 —
% and the sixteenth answering it is bare, so each long-short pair fills
% one quarter and four pairs fill the measure, dotted throughout in the
% manner of a French overture. The ':' marks the four beats:
 
Overture ::= | 5+2 5 : 5+2 6 : 7+2 5 : '1+2 7 |
             | 6+2 7 : '1+2 6 : '2+2 '1 : 7+2 6 |
             | 5+2 6 : 7+2 '1 : '2+2 '3 : '4+2 '3 |
             | '2+2 '1 : 7+2 6 : 5+2 4 : 3+2 2 |
 
Overture
1 _8
 
 
% Where two spellings agree, say so and let the engine check it. Bare
% '_' doubles and bare '+' extends, so the marks meet only on powers of
% two; '+' fills in every length between, one unit at a time — a scale
% falling one unit slower at each step:
 
assert 1 + + == 1+2
assert 1 _ == 1+1
assert 1 _ _ == 1+3
 
'1 7+1 6+2 5+3 4+4 3+5 2+6 1+7
 
 
% Five threes and a one fill sixteen units; five, five, three, three
% fill them another way. The ground counts 3+3+3+3+3+1 underneath while
% the cantus climbs 5 6 7 '1 in 5+5+3+3 above it — two uneven counts,
% one bar, and only '+' can spell either:
 
Ground ::= .1+2 .5+2 1+2 .5+2 .1+2 .5
Cantus ::= 5+4 6+4 7+2 '1+2
 
{Cantus, Ground}*2
 
 
% '/' goes the other way, and a mark after a rule reference covers the
% whole expansion: Run/2 divides all eight degrees at once. The run
% states itself at four speeds, each half the last, the fastest twice,
% and lands on the dotted figure again:
 
Run ::= 1 2 3 4 5 6 7 '1
 
Run _2 Run Run/2 Run/4 Run/4 5+2 5 1 _4
 
 
% Extensions add BEFORE the factors scale, so a three-note group
% reaches two units two ways: ×2÷3, or +1÷2. Either way it is a triplet
% — three notes in the time of two — and four of them step the tonic
% arpeggio up the scale and back:
 
Arp ::= 1 3 5
 
assert Arp _2/3 == Arp+1/2
Arp _2/3 Arp@~2 _2/3 Arp@~4 _2/3 Arp@~2 _2/3 7+2 5 1 _4
 
 
% The pieces in order: the dotted subject, the two uneven counts over
% the ground, the triplets climbing, the run driving in, and the tonic
% held sixteen units — one note, one mark.
 
Overture
{Cantus, Ground}*2
Arp _2/3 Arp@~2 _2/3 Arp@~4 _2/3 Arp@~2 _2/3
Run _2 Run Run/2 Run/4 Run/4
1 _16

% Three marks set how long an item lasts: '_' MULTIPLIES it, '/'
% DIVIDES it, '+' ADDS whole units of the grid — dur = (1 + Σ+) × ∏_ ÷
% ∏/. A unit here is a sixteenth, and this falling line lasts one, two,
% three, four units a note, each answered by a rest as long as itself:

bpm 72
meter 4
unit 1/4
key eb4 maj

5 - 4 _2 -*2 3+2 -*3 1 _4 -*4

% '+' is the mark that COUNTS. A dotted eighth is three units — 5+2 —
% and the sixteenth answering it is bare, so each long-short pair fills
% one quarter and four pairs fill the measure, dotted throughout in the
% manner of a French overture. The ':' marks the four beats:

Overture ::= | 5+2 5 : 5+2 6 : 7+2 5 : '1+2 7 |
             | 6+2 7 : '1+2 6 : '2+2 '1 : 7+2 6 |
             | 5+2 6 : 7+2 '1 : '2+2 '3 : '4+2 '3 |
             | '2+2 '1 : 7+2 6 : 5+2 4 : 3+2 2 |

Overture
1 _8

% Where two spellings agree, say so and let the engine check it. Bare
% '_' doubles and bare '+' extends, so the marks meet only on powers of
% two; '+' fills in every length between, one unit at a time — a scale
% falling one unit slower at each step:

assert 1 + + == 1+2
assert 1 _ == 1+1
assert 1 _ _ == 1+3

'1 7+1 6+2 5+3 4+4 3+5 2+6 1+7

% Five threes and a one fill sixteen units; five, five, three, three
% fill them another way. The ground counts 3+3+3+3+3+1 underneath while
% the cantus climbs 5 6 7 '1 in 5+5+3+3 above it — two uneven counts,
% one bar, and only '+' can spell either:

Ground ::= .1+2 .5+2 1+2 .5+2 .1+2 .5
Cantus ::= 5+4 6+4 7+2 '1+2

{Cantus, Ground}*2

% '/' goes the other way, and a mark after a rule reference covers the
% whole expansion: Run/2 divides all eight degrees at once. The run
% states itself at four speeds, each half the last, the fastest twice,
% and lands on the dotted figure again:

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

Run _2 Run Run/2 Run/4 Run/4 5+2 5 1 _4

% Extensions add BEFORE the factors scale, so a three-note group
% reaches two units two ways: ×2÷3, or +1÷2. Either way it is a triplet
% — three notes in the time of two — and four of them step the tonic
% arpeggio up the scale and back:

Arp ::= 1 3 5

assert Arp _2/3 == Arp+1/2
Arp _2/3 Arp@~2 _2/3 Arp@~4 _2/3 Arp@~2 _2/3 7+2 5 1 _4

% The pieces in order: the dotted subject, the two uneven counts over
% the ground, the triplets climbing, the run driving in, and the tonic
% held sixteen units — one note, one mark.

Overture
{Cantus, Ground}*2
Arp _2/3 Arp@~2 _2/3 Arp@~4 _2/3 Arp@~2 _2/3
Run _2 Run Run/2 Run/4 Run/4
1 _16

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

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The three duration marks · Pattern Engine