The kind of music we’re talking about includes sorts of rhetoric and philosophy as well as what is usually called music. In any case, “music” is made up of rhythm and harmony, form and content. For Plato (and I expect many other ancients), music is an art for the soul. Well ordered music leads to a well ordered soul and vice versa. What can a well ordered soul do? Souls it would seem can influence other souls. The teacher influences the student. This is the primary relationship between teachers and students. But can the student also influence the teacher? Sure, why not? Before the teacher influences the student, the student’s soul is disordered in some way. The student thus influences the teacher to take the steps to be a good influencer of souls. Levels of transmission and receptivity are involved. How is one “moved” by a speech, a bit of philosophy, or what we call music? Our best orators, intellectuals, and musicians hold a special place in society, even if it is posthumously. . . . so do our best athletes and warriors.
I probably don’t need to get much more specific when it comes to gymnastic because it follows along the same lines as music does. But here’s the bottom line. Balance is key. Too much music and not enough gymnastic leads to a weak physical condition. Too much gymnastic and not enough music leads to bodily strength but intellectual dullness. For the top citizens a balance between the two encourages smooth sailing.