A folksonomy is a classification system in which volunteers collaboratively create and manage tags to annotate and categorize content. The folksonomy has several problems in retrieving music using tags, including problems related to synonyms, different tagging levels, and neologisms. To solve the problem posed by synonyms, we introduced a mood vector with 12 possible moods, each represented by a numeric value, as an internal tag. This allows moods in music pieces and mood tags to be represented internally by numeric values, which can be used to retrieve music pieces. To determine the mood vector of a music piece, 12 regressors predicting the possibility of each mood based on acoustic features were built using Support Vector Regression. To map a tag to its mood vector, the relationship between moods in a piece of music and mood tags was investigated based on tagging data retrieved from Last.fm, a website that allows users to search for and stream music. To evaluate retrieval performance, music pieces on Last.fm annotated with at least one mood tag were used as a test set. When calculating precision and recall, music pieces annotated with synonyms of a given query tag were treated as relevant. These experiments on a real-world data set illustrate the utility of the internal tagging of music. Our approach offers a practical solution to the problem caused by synonyms.