### Period notation

In the same way it deals with superimposed sequences, the polymetric expansion algorithm works out equal symbolic durations between beat separators notated '•' -- the "period notation." A note sequence in period notation and the context-free grammar it originated from (composed by Harm Visser) are shown Fig.12. See "-gr.acceleration" in the VISSER & MONTAUDON folder.

In this example, beats contain increasing numbers of notes resulting in an accelerating movement. Velocity assignments have of course no effect on durations.

S --> _vel(60) A B _vel(65) C D _vel(70) E F _vel(75) G _vel(77) H _vel(80) I _vel(85) J _vel(87) K _vel(90) L
A --> E2 •
B --> D2 A
C --> B2 B
D --> G2 C
E --> F#2 D
F --> A#2 E
G --> C2 F
H --> G#2 G
I --> A2 H
J --> D#2 I
K --> C#2 J
L --> F2 K

BP2 score: Velocity controls have been left out
E2 • D2 E2 • B2 D2 E2 • G2 B2 D2 E2 • F#2 G2 B2 D2 E2 • A#2 F#2 G2 B2 D2 E2 • C2 A#2 F#2 G2 B2 D2 E2 • G#2 C2 A#2 F#2 G2 B2 D2 E2 • A2 G#2 C2 A#2 F#2 G2 B2 D2 E2 • D#2 A2 G#2 C2 A#2 F#2 G2 B2 D2 E2 • C#2 D#2 A2 G#2 C2 A#2 F#2 G2 B2 D2 E2 • F2 C#2 D#2 A2 G#2 C2 A#2 F#2 G2 B2 D2 E2 •

Fig. 12: A grammar producing an accelerating sequence of notes, and the resulting item in BP2 score notation

Once the grammar has been typed, the user may select "Produce items" to get a text or graphic display of its production, listen to it on the MIDI output, and optionally produce a Csound score. The output of the "acceleration grammar" of figure 2 is displayed on a piano-roll score:

Fig.13: A piano-roll of the item produced by the grammar of Fig.12