There is a musical scale embedded in each of Plato's dialogues. Symbolic passages at regular intervals are used to mark successive notes.

The surface conversations in the dialogues can seem meandering. Some of the dialogues are even thought to be composites of material written at different times and in different styles. The musical scales give each dialogue an elegant formal unity.

The dialogues often end aporetically. They reach important conclusions at intermediate points and then end negatively with unresolved puzzles. The musical scales explain this. The dialogues each reach their climax at more consonant, intermediate notes and then peter out with the last dissonant notes of the scale.

Platonic forms are generally found by making comparisons and measurements. Applying the same methods to the dialogues themselves reveals the forms beneath their surface narratives.

The early Pythagoreans reportedly held that the entire cosmos was filled with an inaudible “harmony of the spheres”, an unheard melody accessible only to philosophers. Plato has filled his dialogues with a similar music.

The early Pythagoreans reportedly held that each object had an inner, mathematical constitution. Vitruvius believed they even gave their writings a mathematical organization. Perhaps for the first time since antiquity, the dialogues are presented below in the style characteristic of classical, literary papyri and so of Plato's own autographs: as a parade of mathematically uniform columns.