Musical theory has built on the premise that musical structures can refer to something different from themselves (Nattiez and Abbate, 1990). The aim of this work is to statistically corroborate the intuitions of musical thinkers and practitioners starting at least with Plato, that music can express complex human concepts beyond merely "happy" and "sad" (Mattheson and Lenneberg, 1958). To do so, we ask whether musical improvisations can be used to classify the semantic category of the word that triggers them. We investigated two specific domains of semantics: morality and logic. While morality has been historically associated with music, logic concepts, which involve more abstract forms of thought, are more rarely associated with music. We examined musical improvisations inspired by positive and negative morality (e.g., good and evil) and logic concepts (true and false), analyzing the associations between these words and their musical representations in terms of acoustic and perceptual features. We found that music conveys information about valence (good and true vs. evil and false) with remarkable consistency across individuals. This information is carried by several musical dimensions which act in synergy to achieve very high classification accuracy. Positive concepts are represented by music with more ordered pitch structure and lower harmonic and sensorial dissonance than negative concepts. Music also conveys information indicating whether the word which triggered it belongs to the domains of logic or morality (true vs. good), principally through musical articulation. In summary, improvisations consistently map logic and morality information to specific musical dimensions, testifying the capacity of music to accurately convey semantic information in domains related to abstract forms of thought.