* The Claremont Quartet presents the second in a series of concerts tonight at Sanders Theatre, 8:30 p.m. On the program will be Beethoven's Quartet in C minor Opus 13, no. 4; Quartet in F major, Opus 59, no. 1; and Quartet in E flat major, Opus 127.

* The Second square dance of the season will be at the Union Tuesday, at 8:30 p.m. (No charge, privilege cards needed.)

* Recorded music schedule for Matthews Hall Common rooms is: Saturday afternoon, Bach's The Art of the Fugue; Corelli's Concerto Grosso in D major, Opus 6, no. 1; Vivaldi's Trio sonata in D minor, Opus 1, no. 12; and Stradella's Sinfonia in D minor. Sunday, Verdi's String Quartet in e minor; Tchaikovskii's Fatum, Symphonic Poem, Opus 77; Strauss's Symphonia domestica, Opus 53; and The Genesis Suite (Prelude by Schonberg, Creation by Shilkret, Adam and Eve by Tansman, Cain and Abel by Milhaud, Noah's Ark by Castelnuovo-Tedesco, Babel by Stravinsky, and The Covenant by Toch.

* At the Busch-Reisinger Museum garden, the schedule of recorded music at 1 p.m. daily, next Monday through Friday, is Handel's Royal fireworks Music, Beethoven's Quartet no. 8, Debussey's Nocturnes (work related to art); Granados' Goyescas (also related to art), Brahms' Two Quintets, and Mozart's Piano Concertos no. 9 and 15.

* Students who would like auto passengers to various destinations are asked to leave their names at Matthews Hall 3, where car pools are being formed.

* The first dormitory dance--for residents of Eliot, Greenough, Hollis, Straus, Mower, Wigglesworth E--K, and Holworthy only--will be held tomorrow night at the Union, 3:30 p.m. George Graham's Orchestra. (50 cents admission plus privilege cards).