The Internet of Sounds (IoS) combines sound sensing, processing, and transmission techniques, enabling collaboration among diverse sound devices. To achieve perceptual quality of sound synchronization in the IoS, it is necessary to precisely synchronize three critical factors: sound quality, timing, and behavior control. However, conventional bit-oriented communication, which focuses on bit reproduction, may not be able to fulfill these synchronization requirements under dynamic channel conditions. One promising approach to address the synchronization challenges of the IoS is through the use of semantic communication (SC) that can capture and leverage the logical relationships in its source data. Consequently, in this paper, we propose an IoS-centric SC framework with a transceiver design. The designed encoder extracts semantic information from diverse sources and transmits it to IoS listeners. It can also distill important semantic information to reduce transmission latency for timing synchronization. At the receiver's end, the decoder employs context- and knowledge-based reasoning techniques to reconstruct and integrate sounds, which achieves sound quality synchronization across diverse communication environments. Moreover, by periodically sharing knowledge, SC models of IoS devices can be updated to optimize their synchronization behavior. Finally, we explore several open issues on mathematical models, resource allocation, and cross-layer protocols.