An object, in its simplest form, is singular and forms its own category.
An object is composed of properties, which, in your musical analogy, can be likened to musical notes played on a stringed instrument.
A collection of these properties (or notes) played together forms a chord.
When another entity in the room resonates at the same frequency as this chord, it can be said to belong to the same category as the original object. Thus, the singular object’s category gains a second member due to this resonance or association.
Objects, properties, and chords are parallel in the sense that they exist independently yet can influence each other.
A category, while parallel to other categories, contains a serial structure within itself. This internal structure allows it to contain and account for multiple members.
This introduces a complex interplay between the concepts of singularity and multiplicity, and between the concepts of parallelism and serialism. It also adds a dimension of resonance or association as a form of categorical membership, which is a fascinating concept.