Chambers 1908 defines this as "to talk big". Whether it refers to acting like an army major, or something in musical notation, I do not know. Hard to attest because of the music stuff. Equinox ◑ 04:12, 30 August 2019 (UTC)
4. large: great in number or proportion A major part of the meeting was devoted to agreeing on our report. Microsoft® Encarta® 2009
--Backinstadiums (talk) 16:53, 9 November 2019 (UTC)
(intransitive) usually followed by in: us canadian austral nz to do one's principal study (in a particular subject): to major in English literature (intransitive) usually followed by on: to take or deal with as the main area of interest: the book majors on the peasant dishes Collins Concise English Dictionary © HarperCollins Publishers
--Backinstadiums (talk) 11:07, 6 December 2019 (UTC)
BBC News: "The Open Championship - one of golf's four majors - has been cancelled." Equinox ◑ 16:08, 6 April 2020 (UTC)