Left-side
己 supplies the sound, with jǐ shifting to gǎi in
改 — a known j/g initial alternation in this phonetic series.
己 also adds a faint semantic flavor: 'change one's self' is exactly the most common use of
改 (
改变 change,
改正 correct,
改善 improve). Phonetic family:
纪 (record),
起 (rise),
记 (note),
妃 (consort).