A conductor's full score is a chart, a graph which indicates frequencies, intensities, volume changes, melody and harmonies all at once and with the most exact control of time. Music is mathematical. It is rhythmically based on the subdivisions of time into fractions which must be done instantaneously, not worked out on paper. Music is another language. The semantics of music is the most complete and universal language.
Music is history.
Music is physical education. Music is all these things, but most of all, music is art. That is why music is taught.