Where does “conservatory” come from?

Conservatory comes from English -ory and -y, from Latin con- and -ia, ultimately from Latin com meaning "with" and Latin -ia forming abstract nouns.

conservatory (English): Having the quality of preserving from loss,...

Definitions

conservatory traces back through two separate lines of ancestry.

Step	Language	Word	Meaning
1	French	conservatoire	conservative; conservatory; music academy
2	French	conserver	to keep; to retain, conserve, preserve
3	German	konservieren	to conserve, to preserve
4	Italian	conservare	to keep, preserve, retain, conserve, hold, save;...
5	Spanish	conservar	to conserve
6	Latin	cōnservō	to conserve, to preserve, to save, to guard, to protect
7	Latin	cōn-	Used in compounds to indicate a being or bringing together of several objects
8	Latin	cum	with, along with; at; -fold
9	Old Latin	com	Alternative form of cum
10	Proto-Italic	kom	with, along, at
11	Proto-Indo-European	ḱóm	beside, near, by, with
12	Proto-Indo-European	ḱe	Deictic particle, here; Post-positional...
13	Middle English	kyt	—
14	German	kitt	putty certain kinds of cement used for fixing e.g. window panes
15	Old High German	kuti	—
16	Proto-West Germanic	kwidu	gum, resin
17	Proto-Germanic	kweduz	resin
18	Proto-Indo-European	gʷet-	resin, gum; to say, speak
19	Proto-Indo-European	gū-	to bend; curve; arch; vault; to bow, bend, arch,...

Step	Language	Word	Meaning
1	Italian	conservatorio	conservatory, conservatoire