Different sizes of music groups can be imagined as a low rank approximation of a full sound.
Imagine a full symphony orchestra, with 100 members. They play a full symphonic arrangement, which we can assume to be the most high-fidelity, accurate representation of the composer’s intent. Now, let’s drop most of the members of the orchestra; maybe one person per instrumental section. There’s still one person to play every single part to get the musical information across accurately, but much of the symphonic “feel” is lost. How about if we arrange this piece for a quartet? With 4 musicians, the piece is almost entirely different; yet fundamentally it’s the same piece. What about with just one violin soloist with a piano accompaniment? We have reached the minimum number of people that can play this piece and have it still be the same song; the lowest rank approximation possible.
When reducing the number of members in a musical group, some information is inevitably lost, and each remaining member must perform more roles in order to express the piece. In the real world, bands often follow a natural convergence at each reduction in members to some ideal minima in low rank approximation. Of course, the direction and nature of reducing rank depends heavily on the genre of music; in essence, the type of data. Take a 6-piece rock band, with a vocalist, 2 guitarists, a bassist, a drummer, and someone on keys. Since it’s a rock band, if we had to kick one member we’d kick the pianist. Next, we’d probably teach our vocalist rhythm guitar to go from 5 to 4 members. Generally you don’t see bands reduce any below 4, but with some creativity we can replace the drummer and bassist with a DJ to get 3 members. Then, we’d get rid of the lead guitar and toss in some FL Slayer. In fact, we can throw Melodyne on the DJ’s vocals and get rid of the singer too! Now, we’ve arrived at a solo 1-man production, which can perform some rough approximation of our original 6-person band.