While it is widely accepted that music evokes moods, there is disagreement over whether music-induced moods are relevant to the aesthetic appreciation of music as such. The arguments against the aesthetic relevance of music-induced moods are: (1) moods cannot be intentionally directed at the music and (2) music-induced moods are highly subjective experiences and are therefore a kind of mind-wandering. This paper presents a novel account of musical moods that avoids these objections. It is correct to say that a listener's entire mood is not relevant to the aesthetic appreciation of music. However, the experience of mood consists of having different feelings. Music induces feelings that are intentionally directed at the music and clusters of these feelings can be recognized as typical of a specific mood. Therefore, mood-feelings are relevant to the aesthetic appreciation of music.