Cleonides is the author of a Greek treatise on music theory titled Eisagōgē harmonikē (Introduction to Harmonics). The date of the treatise, based on internal evidence, can be established only to the broad period between the 3rd century BCE and the 4th century CE; however, treatises titled eisagōgē generally began to appear only in the 1st century BCE, which seems the most likely period for Cleonides' work.

The attribution of the Eisagōgē in some manuscripts to Euclid

Euclid

Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...

 or Pappus

Pappus of Alexandria

Pappus of Alexandria was one of the last great Greek mathematicians of Antiquity, known for his Synagoge or Collection , and for Pappus's Theorem in projective geometry...

 is incompatible with the Aristoxenian approach adopted in the treatise. A few manuscripts name a "Zosimus" as the author.

Cleonides' treatise is the clearest account of the technical aspects of Aristoxenos's musical theory.