B5) Polymetry and Temporal Structures
The Superpower of BP3
What if a musical grammar could make different temporal flows coexist—like a tabla player playing in 4 with the right hand and in 3 with the left?
Where does this article fit?
This article delves into the temporal dimension of BP3 (Bol Processor 3, the algorithmic composition software—see I2). M5 introduced the musical concept of polymetry; B2 defined the vocabulary; B3 formalized the derivation rules. Here, we see how BP3 represents musical time—compression, superposition, cycles—with a simple but powerful syntax. The details of the translation into SuperCollider code are covered in B7.
Why is it important?
Most musical languages treat time rigidly: a note has a duration, a rest has a duration, and everything adds up sequentially. It’s like a queue: everyone takes their turn, one by one. MIDI, MusicXML, staff notation—all work this way.
But real music doesn’t work like a queue. A tabla player can compress 7 bols into the space of 4 beats. A gamelan ensemble superimposes layers that move at different speeds. An Indian tāla is not a sequence of measures but a cycle that turns.
BP3 formalizes these three operations:
- Compressing or dilating a group of notes within a given time
- Superimposing independent voices that each move at their own pace
- Annotating cyclical time signatures from non-Western traditions
These are the operations that Bernard Bel developed to represent Indian musical time, and which he formalized in “Rationalizing Musical Time” [Bel2001].
The idea in one sentence
BP3 polymetry allows for compressing, dilating, and superimposing note flows with a {expr1, expr2, ...} syntax where the first field defines the duration, formalizing cyclical time that Western notation cannot express.
Step-by-step explanation
1. The first field defines the temporal frame
In any polymetric expression {field1, field2, ...}, the first field is a musical expression, executed at the current tempo. Its duration defines the temporal frame into which the following fields must fit.
When the first field is a number, it is a shortcut for that many rests. Thus:
BP3 Syntax:
{3, dha dhin dhin dha}
…is equivalent to {- - -, dha dhin dhin dha}: the 3 means “three rests at the current tempo,” i.e., 3 beats. The 4 bols dha dhin dhin dha must fit into these 3 beats—this is a temporal compression. Since the first field is inaudible (rests), only the bols are heard.
The first field can also be a sound expression: {dha ti, tira kita tira kita} means that dha ti (2 bols = 2 beats) sets the duration, and tira kita tira kita (4 bols) compresses into those 2 beats. Both voices are heard simultaneously.
Box: The accordion analogy
Imagine an accordion. The melody (the bols
dha dhin dhin dha) is fixed on the keys. But you can stretch or compress the bellows—that is the duration set by the first field. With{3, dha dhin dhin dha}, you compress 4 bols into 3 beats: each bol lasts 3/4 of a beat instead of a full beat. With{6, dha dhin dhin dha}, you stretch: each bol lasts 6/4 = 1.5 beats.
The formula
If you have N elements to play in M beats:
duration of each element = M / N
This is the only formula in this article, and it is enough to explain everything.
| BP3 Expression | N | M | Duration per element | Effect |
|---|---|---|---|---|
{3, dha dhin dhin dha} |
4 | 3 | 3/4 = 0.75 | Compressed |
{4, dha dhin dhin dha} |
4 | 4 | 4/4 = 1.0 | Normal |
{6, dha dhin dhin dha} |
4 | 6 | 6/4 = 1.5 | Dilated |
{1, dha dhin dhin dha} |
4 | 1 | 1/4 = 0.25 | Very fast |
When M < N, the notes are compressed (each lasts less than a beat). When M > N, they are dilated (each lasts more). When M = N, it is neutral.
2. Multi-voice polymetry: parallel flows
When the first field is an audible expression, it sets the duration while being played. The following fields fit into that same duration.
BP3 Syntax:
{dha dhin dhin dha, Sa Re Ga Ma Pa}
Two voices play at the same time:
- Tabla (1st field): 4 bols (
dha dhin dhin dha) at the current tempo → defines the duration (4 beats) - Sitar (2nd field): 5 notes (
Sa Re Ga Ma Pa) compressed into those 4 beats → each note lasts 4/5 of a beat
Both instruments start and end together, but the tabla plays 4 strokes while the sitar plays 5 notes.
This is a cross-instrumental polymetry typical of Indian classical music, where each instrument moves at its own pace within the same tāla cycle.
**Box: Tabla and sitar—two