Explain the arrangement of beads on the wires.

The Glass Bead Game centers on the idea that one can achieve greatness through a new intellectual discipline. This intellectual discipline obliterates what the narrator calls the "excessive aestheticism" of the Age of Feuilleton. According to the Merriam–Webster dictionary, a feuilleton is the section of a newspaper that focuses on entertainment or stories of common interest.
In the book, the narrator refers to these "uncommonly popular sections of the daily newspapers" as "mental pabulum." So, what is the Glass Bead Game exactly? It is played by intellectuals from every human sphere. However, the book doesn't fully explain the rules of the game. It does, however, tell us how the game is set up.
First, glass beads of various "sizes, shapes, and colors" are strung across wires on an abacus-like frame. The wires represent the musical staff, while the beads represent the various time-values of musical notes. A player can use different combinations of beads to represent a musical quotation or a musical theme. The narrator likens the playing of the game to the execution of a musical fugue.
A fugue begins with a musical theme (or thesis) and is continued by different voices that expound upon the main theme in varied pitches. The musical theme variations are interweaved with each other, resulting in a pleasing harmonic composition. The narrator tells us that this game was initially played as a challenging musical exercise. Eventually, intellectuals from other disciplines adapted the game to fit their needs.
For example, instead of using the beads to represent musical themes, mathematicians used the beads to represent mathematical symbols and formulas. Soon, scientists and other intellectual scholars made their own adaptations, complete with special rules for the game. All enjoyed intricate intellectual exercises that, according to the narrator, brought an end to the Age of Feuilleton.
The narrator thus argues that the Glass Bead Game is the game of true intellectuals. So, to answer your question, the arrangement of beads on the wires is dependent upon the intellectual pursuits of the players.