IPA: /ɛkˌstɛmpəˈreɪniːɪti/
KK: /ɛkˌstɛmpəˈreɪniːɪti/
The quality or state of being done without preparation or planning, often in a spontaneous manner.
The speaker's extemporaneity impressed the audience, as he delivered his speech without any notes.
Extemporaneity → It is formed from "ex-" (meaning out of) and "temporaneus" (from Latin, meaning temporary or of time). The word refers to the quality of being done without preparation, as if coming out of the moment or time.
Think of something happening 'out of' ('ex-') the 'moment' ('temporaneus') — that's why extemporaneity means doing something spontaneously or without prior planning.