The first step is to solve each of the triangular logic puzzles. The blue diamond icons and brown words can be ignored while solving the puzzles.
Note: In the solutions below, diamonds whose binary assertions are true are colored blue, and false ones are colored red.
Note the first image in the key on the last page: It’s a shape with 13 triangles. We’re going to be assembling the 13 puzzles into one big grid with that shape, and orienting it such that the direction indicated by the arrow (only present on Filliamond, the center triangle) is pointing up.
The presence of binary statements, as well as the flavor text (“bit by bit by bit by bit by bit”), suggests we should try to read data as binary. There are a couple of 5-length segments of diamonds in the puzzle, and every other row of diamonds is shorter and hits the edge of its grid. We can assemble all of the grids together such that every diamond is part of a 5-length segment, which we can then read according to the order specified in the image on the second row of the key (with 1a, 1b, and 2):
With our heads turned for each direction, reading from top to bottom, the letters read:
Finally, the only part of the puzzle we haven’t yet used are the brown questions that are on 3 cells in each puzzle, and the similarly colored diagrams at the bottom of the key. The diagram indicates how we can order the binary answers on the cells to get 3-digit binary numbers. Those can only represent the letters A through G, which is all we need, because we are going to interpret them as musical notes (clued by “flat” in the extracted phrase and by “music” in the flavor text). In particular, As and Es are all flat (musically inclined solvers may notice that, as long as there are no Bs — which is the case in this puzzle — this can represent a valid musical key). When extracted from the fully assembled diagram, preserving the rotation of each grid from the previous step, we get the following notes:
G E♭ D C C D E♭ C E♭ G A♭ G F
You might play this and recognize the tune, or input the notes into a music search engine like Musipedia. The famous musical piece that has this phrase is “Waltz No. 2,” and its composer’s name is Dmitri SHOSTAKOVICH, which is the answer.