Is there a theory behind grouping notation?
Yes! It’s quite interesting in fact. Here are the number of relationships (including solos and silence) possible in an ensemble of size n (1-12 people).
| 2n = | Total Groupings Available |
| 21 = | 2 |
| 22 = | 4 |
| 23 = | 8 |
| 24 = | 16 |
| 25 = | 32 |
| 26 = | 64 |
| 27 = | 128 |
| 28 = | 256 |
| 29 = | 512 |
| 210 = | 1024 |
| 211 = | 2048 |
| 212 = | 4096 |
These relationships can be further broken down into a list of solos, duets, trios, quartets and so on, by using the binomial triangle:
Credit: Wikipedia
For example, take the bottom row. An ensemble of seven people has 128 potential relationships, including 7 soloists, 21 duets, 35 trios, 35 quartets, 21 quintets, 7 sextets, and 1 septet. (As with ensembles of any size, there is one combination which includes no one.)
Using a process called refraction we can articulate the first, second, third, fourth, and so on, people in any grouping. The symbols I use to indicate firstness, secondness, and so on, are called placeholders:
{α, β, γ, δ, ε … }
In 2015 when I started on this work, I decided to use lower-case Greek letters because they were convenient and looked cool. But as with the groupings themselves, any consistent symbols can be used.
Placeholders do not signify particular people. They signify firstness, secondness, and so on. So where grouping notation measures cardinality, placeholders measure ordinality. Using these symbols, it is possible to fully articulate groupings and transitions. This theoretical notation can also be used in reverse, to compose groupings and transitions via curation (described below.)
