shrillness vs timbre

shrillness and timbre both are nouns.

Word	Noun	Adjective	Verb	Adverb
shrillness	Yes	No	No	No
timbre	Yes	No	No	No

As nouns, timbre is a hypernym of shrillness; that is, timbre is a word with a broader meaning than shrillness:

shrillness: having the timbre of a loud high-pitched sound
timbre: (music) the distinctive property of a complex sound (a voice or noise or musical sound)

Other hypernyms of shrillness include quality, timber, tone.

shrillness (noun)	timbre (noun)
having the timbre of a loud high-pitched sound	(music) the distinctive property of a complex sound (a voice or noise or musical sound)
the quality of being sharp or harsh to the senses