A PRESIDENT WHO'S serious about serious music is a serious business - just imagine, for instance. What might happen to office procedure at Coca Cola or General Motors if every other corporation head in the country suddenly decides to emulate the Chief Executive.

Jimmy Carter, by his own report, spends 8 to 10 hours a day listening to concert music and opera.

The President has been observed with eyes dampened by a performance of a Haydn string quartet. He has personally handpicked a cache of classical recordings from the White House collection to keep at his fingertips outside the Oval Office and in his living quarters. And in the midst of his Inaugural week, he listened intently to chamber pieces by Mendelssohn, Ravel and Samuel Barber, and then went out of his way to compliment the musicians afterward.

Just what kind of a Georgia peanut farmer have we got here?

Cater's personal secretary, Susan Clough, who shares his liking for classical music, confirms the President's estimate of his record listening habits during the working day. "He generally gets in at 7 in the morning, and when I arrive about five minutes after I put on some music then - usually something quieter for the morning, some Bach perhaps - and it goes on right through the day. When he has appointments I turn the volume down - but not off."

The records, turntable and amplifier are kept in the secretary's portion of the executive office adjoining the Oval Room, and the music is piped into speakers in the President's study. The Carters brought the hi-fi equipment with them from Georgia.

"The recordings all come from the White House library," Clough says, "but the President selected out the ones he wanted for his personal use. The ushers showed him the catalog when he first came, and he chose from there and maybe changes them from time to time.

"He also keeps some in his living quarters, but the ones there, about 25 albums I'd say, are all classical." She reads some names off stone of the record labels - Beethoven, TchaikovskyM Brahms, Ravel Rachmaninoff, Copland, Schumann. There are some Segovia guitar records and some opera, too - Wagner and Mascagni's "Cavalleria Rusticana," for example.

Robert Shaw, the noted conductor of the Atlanta Symphony who organ- ized the musical side of the inaugural receptions, says Carter's musical enthusiasms are "perfectly genuine. He's a bona fide consumer - his interest isn't political. In Atlanta, during his days as governor, I'd bring the orchestra up every so often at his request to play for state dinners and such. But he'd also come to our regular concerts all the time - and he'd stand in line and buy tickets."

Several weeks before the Inauguration, Mrs. Carter called Shaw about the coming receptions, and he arranged for seven different small instrumental groups, including the Juilliard and Cleveland Quartets, to perform.

"There were people walking back and forth and talking all the while. Shaw recalls. "Never in their lives had these superbprofessionals played for conversation.But they were very good about it, and it was touching to see how concerned the President was about this. Afterward he spoke to each player individually, assuring them that he would have them back to the White House, and that next time, everyone would be perfectly quiet."

The Juilliard Quartet played for the diplomatic corps reception on Jan. 22. When it was over, and Shaw had introduced President and Mrs. Carter to the ensemble, Carter said he was sorry he'd been unable to give his undivided attention to the Beethoven quartets they'd played. Robert Mann, the first violinist, replied that he hoped the group might someday have the chance to play for them again. Whereupon Carter asked if they could play something right then and there for a brief while. So they did, for an audience consisting solely of Jimmy and Rosalynn Carter, and Shaw.

"The Carters sat down," Mann remembers, "and we played the hymn like slow movement from Haydn's Op. 20, No.1. We fully expected them selves gracefully. But they sat and listened, - after 30 years of performing, one can sense the kind of quietness that implies deep concentration.

"There was a silent pause after we finished, a quite wonderful moment, and the President said, 'you know, this is the kind of music that brings tears to the eyes.'"

When the Cleveland Quartet played for the governors' reception the next day, another observer reports, Carter stood behind first violinist Donald Weilerstein, looling at the music over his shoulder and telling him, "I just want to be sure you don't make any mistakes." Later on in a conversation with cellist Paul Katz, he remarked that through recordings he'd come to know all 17 of Beethoven's string quartests quite well.

"His love for music goes back to his Annapolis days," says Susan Clough, "when he used to listen a lot to distract himself from the routine of the Academy."

Carter himself, in his book "Why Not the Best?," recalled how "my roommate and I spent most of our meager money on classical phonograph records. Other midshipmen would visit our room and we would argue for hours about the relative quality of performance of orchestras and concert soloists. For some reason, each time we reached the final part of "Tristan and Isolde," a large group would quietly gather in the corridor to listen to Liebestod."

In the same book, Carter traces his affection for music back still further, to his years as a schoolboy in Plains and to a school superintendent, Miss Julia Coleman. "Miss Julia was spinster, who died recently, and she encouraged all of her students to seek cultural knowledge beyond the requirements of a normal rural classroom," especially in the arts. "Each of us had to learn the rudiments of music and play some musical instrument - if it were only a ukelele, harmonica, or even a small piccolo...As a school boy who lived in an isolated farm community, my exposure to classical literature, art, and music was insured by this superlative teacher," Carter wrote.

Apparently, it was a lesson that stuck.