What's in a polymetric expression?

May be you liked the way this item sounded (on a "Koto" patch of the D-50, or vibraphone in QuickTime music) and want to understand its time structure. Click the "Data" window (or type cmd-d) and select the item with the mouse. Then click button "Expand display ". You get this:

Fig.17 Expanding a polymetric expression

Expressions with curled brackets {} and commas are called polymetric expressions and represent polyphonic sound-object structures. These expressions are incomplete descriptions of the actual precedence relationships between sound-objects and/or notes in the structure. BP2 is able to construct a complete polymetric expression by adapting tempos in superimposed sequences. (This process is explained in great detail in Bel 1990a-b,1991,1992.) The expanded display shown Fig.17 is an outcome of the expansion algorithm.

BP2 expands any polymetric expression (including a simple sequence) before making sounds. Once the expression has been expanded, the following score-like phase diagram is constructed:

in which it is clear, for instance, that the first occurrence of 'f' begins with the first occurrence of 'a'.

Symbols '_' prolongate sound-objects or notes. For instance, the symbolic duration of the first occurrence of 'b' is three time units whereas the last occurrence of 'f' is five time units. (In this particular example, a time unit is one third of a beat.)

Symbols <<f>>, <<chik>> and <<sync>> represent out-time sound-objects, i.e. objects with no duration. Here for instance (from the information found in the "-mi.abc1" file), <<f>> will be a NoteOn on key F4 followed immediately with a NoteOff. <<chik>> is a chord plucked in the same way. It is only audible if the NoteOff instruction does not suppress sound immediately. Therefore we used a "plucked string" patch.

Out-time sound-object <<sync>> produces a C5 on MIDI channel 15 that does not make any sound but may be used to synchronise another BP2 running on the same MIDI network (see §6.4).

Performance controls _vel(127) and _volume(40) are attached to the next object or silence appearing in the same sequence, and are not displayed on graphics. Remember that you can attach very subtle variations of all MIDI parameters, notably pitchbend, modulation, aftertouch, to any structure of sound-object or/and simple notes. (See §1.4-10 regarding performance controls.)

Many polymetric expressions are found in project "-gr.polyphony1".

You may select only part of the item (even a single terminal symbol) and listen to the way it sounds (type cmd-p). Try to figure out the difference between "striated" and "smooth" time by carefully looking at the graphics these different settings generate. (See §9 regarding smooth time.)