flatness (n.)

c. 1300, "stretched out (on a surface), prostrate, lying the whole length on the ground;" mid-14c., "level, all in one plane; even, smooth;" of a roof, "low-pitched," from Old Norse flatr "flat," from Proto-Germanic *flata- (source also of Old Saxon flat "flat, shallow," Old High German flaz "flat, level," Old High German flezzi "floor"), from PIE root *plat- "to spread."

From c. 1400 as "without curvature or projection." Sense of "prosaic, dull" is from 1570s, on the notion of "featureless, lacking contrast." Used of drink from c. 1600; of women's bosoms by 1864. Of musical notes from 1590s, because the tone is "lower" than a given or intended pitch. As the B of the modern diatonic scale was the first tone to be so modified, the "flat" sign as well as the "natural" sign in music notation are modified forms of the letter b (rounded or square).

Flat tire or flat tyre is from 1908. Flat-screen (adj.) in reference to television is from 1969 as a potential technology. Flat-earth (adj.) in reference to refusal to accept evidence of a global earth, is from 1876.

word-forming element denoting action, quality, or state, attached to an adjective or past participle to form an abstract noun, from Old English -nes(s), from Proto-Germanic *in-assu- (cognates: Old Saxon -nissi, Middle Dutch -nisse, Dutch -nis, Old High German -nissa, German -nis, Gothic -inassus), from *-in-, originally belonging to the noun stem, + *-assu-, abstract noun suffix, probably from the same root as Latin -tudo (see -tude).