As a tribute to the centuries-old musical tradition of the city of Arezzo, CaMu is headquartered in Piazza Grande, within one of the oldest and most important buildings in Arezzo, the Palazzo della Fraternita dei Laici. The Laymen's Fraternity is a historic charitable institution founded in 1262, and still very active with social and cultural projects.

The building of the palace was started in 1375, and finished only as late as the 1650s. The façade was completed between 1550 and 1560 with the addition of the balcony and of the tower, whose Aristotelian-Ptolemaic lunar clock was installed in 1552 by Felice di Salvatore da Fossato as commissioned by the Fraternity's board of rectors.

The building extension towards the apse of the Church of S. Maria dates from the second half of the 17^th Century and was based on a design by Giorgio Vasari. The renovation of the Palazzo di Fraternita, promoted by Grand Duke Pietro Leopoldo of Lorraine in 1781, resulted in the opening to the public of the Fraternity Library and the foundation of an art academy called Scuola Libera di disegno e modellazione (Free School of Drawing and Modeling),

Subsequently, the Fraternity's rectors undertook an extensive decoration campaign which included a mural painting of Pallas Athena by Angelo Ricci.