Since we ten to oppose the mechanical with the organic, this is a surprise
organ (n.) from Online Etymologoical Dictionary.
Applied vaguely in late Old English to musical instruments; by late 14c. the sense of the word (used in both singular and plural form) narrowed to the musical instrument now known by that name (involving pipes supplied with wind by a bellows and worked by means of keys), though Augustine (c. 400) knew this as a specific sense of Latin organa. The meaning “body part adapted to a certain function” is attested from late 14c., from a Medieval Latin sense of Latin organum. Organist is first recorded 1590s; organ-grinder is attested from 1806.
1510s, “serving as an organ or instrument,” from Latin organicus, from Greek organikos “of or pertaining to an organ, serving as instruments or engines,” from organon “instrument” (see organ). Sense of “from organized living beings” is first recorded 1778 (earlier this sense was in organical, mid-15c.). Meaning “free from pesticides and fertilizers” first attested 1942. Organic chemistry is attested from 1831.
I like the musical aspect but don’t like the tool side. So do we need another word for “organic?” I have often quote Manuel DeLanda, “in the mechanical parts maintain their integrity when part of a larger system. In the organic the parts do not maintain their integrity when part of a larger system.” I like this distinction but is not sonsistent with its origin in “tool”