This study investigates developing a single-layer composite material to provide acoustical comfort conditions due to sound transmission in a building. The aim of the study is to increase the sound transmission loss (STL) of mortars produced with LC3 (limestone calcined clay cements)1 ecological binder, barite, and rubber aggregates compared to Portland cement and river sand aggregate mortars. The flow and aggregate/binder ratios by volume in each mortar mixture were kept constant and compared. Instead of river sand aggregate, barite aggregate was used to provide weight, which is one of the most important parameters effective in sound insulation and waste rubber aggregate was used to control stiffness. Mortars were produced in 40 × 40 × 160 mm for experimental analyses that include unit weight, capillary of water absorption, open porosity, and compressive and flexural strengths, while in 90 mm thick cylindrical mortars were produced for sound transmission loss measurements. As a result of the experimental study, it is revealed that mortar with LC3 binder, two-part barite, and 1-part waste rubber aggregate by volume (LC3-2B1R-8) can be used as an acoustical material for sound insulation. Using combined aggregates (barite and rubber) for increasing the sound insulation properties of the mortar is very effective not only in high frequencies but also in low frequencies. The study also shows that increasing the weight of the mortars does not always increase the sound insulation properties of the material.