1. Traditional ways: what’s vibrating? How does sound start?

Ways of classifying musical instruments

Hornbostel-Sachs classification system

2. Scientific classifications

Quantifiable ways of describing sound in terms of frequency, amplitude envelope, spectrum, etc.

More subjective, expressive ways of describing sound

A composition with a nice variety of isolated sounds to try describing: Varèse, Poème Électronique (1958)

3. Pictograms

Also called graphic scores or graphic notation. See examples here.