How does timbre differ from pitch and loudness?

In acoustics, sound is characterized by several distinct attributes, including pitch, loudness, and timbre. While these properties often work together to define a musical tone, they are physically and perceptually distinct.12

Pitch

Pitch refers to the highness or lowness of a sound and is directly determined by the frequency of the vibration producing the sound wave. A higher frequency results in a higher pitch, while a lower frequency results in a lower pitch.13

Loudness

Loudness is the attribute that determines the intensity of the auditory sensation. It is a product of the intensity of the vibration—essentially the amplitude or force of the motion. While physical intensity can be measured objectively (e.g., in decibels), loudness is often perceived subjectively, with scales like the phon and sone used to describe how the human ear experiences these variations in intensity.41

Timbre

Timbre, or tone colour, is the quality of a sound that distinguishes one instrument or voice from another, even when they are playing the same pitch at the same loudness. It is determined by the wave form, which is shaped by the specific combination of overtones (harmonics) present, their frequencies, and their relative intensities. Unlike pitch and loudness, timbre lacks a formal, standardized taxonomy, often being described with subjective terms like "mellow" or "nasal".512