The construction of cyclic polyrhythms
To start building cyclic polyrhythms, we distinguish two main groups: 2-voice polyrhythms (simpler) and 3-voice polyrhythms (more complex). Although we can also make polyrhythms in 4 or more voices, in this introduction we focus on these two options:
The following is a proposal to start building cyclic polyrhythms, some examples, the possible combinations of the proposal, and finally some important observations about the process and the results.
- Proposal for the construction of polyrhythms
- Examples of polyrhythmic construction
- Remarks
- Map and classification of possibilities
PROPOSAL FOR THE CONSTRUCTION OF CYCLIC POLYRHYTHMS
How do we specify the velocity of each voice?
The first step is to define the velocities to be overlaid. The voice 0 is already defined since it always corresponds to the pulsations: it is our reference velocity, with fraction 1/1 and fixed iT (1).
For the rest of the voices, we must specify the speed by choosing the type of fraction and the value of the fixed iT. We can combine the velocities in the following ways:
- a fraction 1/1 with fixed iT other than 1:
- a simple fraction with fixed iT 1, or fixed iT other than 1:
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| simple fraction with fixed iT = 1 (simplest) |
simple fraction with fixed iT other than 1 |
- a complex fraction with fixed iT 1, or fixed iT other than 1:
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| complex fraction with fixed iT = 1 (simpler) |
complex fraction with fixed iT other than 1 |
EXAMPLES OF POLYRHYTHMIC CONSTRUCTION
To construct a 2-voice cyclic polyrhythm, remember that voice 0 is already predetermined with the fraction 1/1 and the fixed iT 1. And for voice 1, we choose one of the three options above, organized according to the type of fraction chosen and the value of the fixed iT. For example, we define the voice 1 with the fraction 1/3 with fixed iT other than 1, in this case iT (2):
To construct a 3-voice cyclic polyrhythm, we choose one of the three options above for both voice 1 and voice 2. For example, we define voice 1 with a simple fraction with fixed iT other than 1 (in this case 1/3 with fixed iT 2), and we define voice 2 with a complex fraction with fixed iT 1 (in this case 3/2):
Equivalences in the combinations between fractions and fixed iT:
Realize that through different combinations we can arrive at the same cyclic polyrhythm. For example a 2-voice polyrhythm, where voice 1 is built with:
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In both cases the velocity of voice 1 is the same, although they are constructed differently. You can learn more about it in the section on the resulting fraction of the voice.
Which cyclic polyrhythmias are likely to be of most interest?
Of all the possible combinations, some are more interesting than others. For example, in a 2-voice polyrhythm, when the velocity of voice 1 is defined by a simple fraction and a fixed iT 1, no counterpoint is generated between the voices, so it is not interesting as a polyrhythm:
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polirr. sin contrapunto |
On the contrary, in a 2-voice example, when the velocity of voice 1 is defined by a complex fraction, a counterpoint is generated between both voices, which is the essence of the sonorous and compositional interest of cyclic polyrhythms:
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polirr. con contrapunto |
Construction in the Nuzic app:
When we use the Nuzic app to build cyclic polyrhythms in a temporal segment, the fractions of all voices have to conclude their cycle. If not, the app will indicate an error:
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ERROR IN APP |
For this to occur, we need to adjust the length of our temporal segment, establishing a proportional relationship between the total length of the temporal segment and the cycle length of the polyrhythm we want to construct: all the numerators of the voices must be divisors of the length of the segment. Or, seen in another way, the length of the segment must be a multiple of the numerators:
In this case of segment length 12, the fractions of the voices can also carry the numerators 1, 2, 4, 6 and 12, in addition to 3 in the example. |
CORRECT IN APP |
MAP AND CLASSIFICATION OF POSSIBILITIES
In the following map we present all the possible combinations that we can build following the proposal we have just presented. They are ordered by degree of difficulty from left (simpler) to right (more complex). Below the map you can listen and visualize in the PMC all the examples presented, and also read the ranking order.
Listen and visualize in the PMC the examples of the previous map (in blue color). Voice 0 corresponds to a Chinese box, voice 1 to a high-pitched agogo and voice 2 to a cymbal:
Two-voice polyrhythm
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polirritmias a 2 voces
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Three-voice polyrhythm
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polirritmias a 3 voces
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