Some authentic instruments from ancient Greece that you could use in your song include:

- Aulos - a double-reed instrument similar to a oboe, often used to accompany singing or poetry recitals
- Lyre - a stringed instrument similar to a small harp, considered a noble instrument and used in education
- Kithara - a larger stringed instrument, similar to a lyre butwith thicker strings and a deeper sound

These instruments can be purchased from specialty music stores or luthiers that create replicas of ancient instruments. Some other characteristics of ancient Greek music to incorporate:

- Use of modes like Dorian, Phrygian, and Mixolydian which have distinctive sounds
- Focuses on melody rather than harmony, with instrumental accompaniment and solo sections featuring virtuosic playing
- Lyrics were an important part, with poetry played an integral role in performance
- Rhythms tended to be relatively simple, based on poetic meter

Incorporating some of these elements into your song can help give it a more authentic Greek feel and reflect the music of Plato's time. The melody, modes, and instrumental accompaniment in particular can help capture the melancholy and philosophical character you described.
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