Two things stand up and change places with each other. Or one whole thing is lifted out of where it sits and set down somewhere else - the same thing, a new position. Nothing is added and nothing is taken away; only where things sit has changed.
From the word’s history
Wiktionary records transpose from Middle English transposen, from Old French transposer, from Latin transpositus, from transpono meaning to put across - trans (across) plus pono (to put). The modern uses all keep that plain picture: put it over there.
Wiktionary 記載 transpose 來自中古英語 transposen、古法語 transposer，再往前是拉丁文 trānspositus，出自動詞 trānspōnō「放到另一邊」，由 trāns（越過）加上 pōnō（放）組成。今天所有的用法都還守著這個很單純的畫面：把它放到那邊去。數字互換、戲搬到別的城市、曲子換到別的調，都是同一個動作換了對象。
Wiktionary (kaikki extract, source_ref kaikki:3f6f69a190036ae4:786419915:22857), transpose verb etymology 1
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