In 1662 he entered Christ Church, Oxford, and in 1689 was made dean in succession to the Roman Catholic, John Massey, who had fled to the continent. In 1692 he was vice-chancellor of the University. In 1702 he was appointed rector of Wem in Shropshire, but continued to reside at Oxford, where he died on December 14 1710. He was buried in the cathedral without any memorial at his own desire.
Aldrich was a man of unusually varied gifts. A classical scholar of fair merits, he is best known as the author of a little book on logic (Compendium Artis Logicae), a work of little value in itself, but used at Oxford (in Mansel's revised edition) till long past the middle of the 19th century.
Aldrich also composed a number of anthems and church services of high merit, and adapted much of the music of Palestrina and Carissimi to English words with great skill and judgment. To him we owe the well-known catch, "Hark, the bonny Christ Church bells."
Evidence of his skill as an architect may be seen in the church and campanile of All Saints, Oxford, and in three sides of the so-called Peckwater Quadrangle of Christ Church, which were erected after his designs. He bore a great reputation for conviviality', and wrote a humorous Latin version of the popular ballad A soldier and a sailor, A tinker and a tailor, etc.
Another specimen of his wit is furnished by the following epigrata of the five reasons for drinking: