The secondary sense of monotonous (same or tedious) has so nearly swallowed up its primary (of one pitch or tone) that it is well worth while to remember the existence of monotonic, which has the primary sense only. [Fowler, 1926]
"unvarying tone in music or speaking, utterance at one unvaried pitch," 1640s; see monotony. OED says use of the word as a noun is peculiar to English.
Monotone is a natural device for increasing the sonority of the voice, so that it may readily fill a large space, and is also thought by some to have a peculiar solemnity of effect. It is much used as an element in chanting. [Century Dictionary]
European bird noted for its love-note cry and notorious for parasitism, c. 1300, cokkou (late 12c. as a surname), from Old French cocu "cuckoo," also "cuckold," echoic of the male bird's mating cry (compare Greek kokkyx, Latin cuculus, Middle Irish cuach, Sanskrit kokilas).
Slang adjectival sense of "crazy" is American English, 1918, but noun meaning "stupid person" is recorded by 1580s, perhaps from the bird's unvarying, oft-repeated call. The Old English name was ʒeac, cognate with Old Norse gaukr, source of Scottish and northern English gowk, which also has insulting senses. The Germanic words presumably originally were echoic, too, but had drifted in form. Cuckoo-clock is from 1789.