AFTER a few hours with Charles Hamm's voluminous and all-inclusive survey, the reader may want to set it down, shaking his head in wonderment at a book that discusses Elliott Carter and Bob Dylan with equal interest and respect. Those who are disturbed by such a mingling of genres will find no relief if they pick up John Rockwell's more tightly focused study, which begins with essays on Ernst Krenek, Milton Babbitt and (of course) Carter, but also brings its reader into the diverse worlds of Stephen Sondheim, Neil Young and the Talking Heads. The publication, only a few weeks apart, of two books that cross traditional borders with such insouciance should tell us that here is an idea whose time has come. Simply stated, the idea is that music is music, whatever specialized labels we may pin on various specimens and whatever walls of snobism we may throw up to preserve one genre from contamination by another.

Such contamination is an integral part of the history of music in America--in fact, the most distinctive aspect of that history, the element that makes American music interesting to Europeans and others. The process was already far advanced in the 1840s when Louis Moreau Gottschalk began to enrich the classical piano (and, of course, himself) with styles and cadences that he had heard on the banjo as a boy in New Orleans. That music--essentially the music of black people--was a hybrid, mingling elements from several cultures and styles, a very fertile hybrid whose descendants include ragtime, jazz, spirituals, soul music and rock as well as a myriad of classical compositions. A cranky refusal to accept arbitrary divisions between "classical" and "popular" materials was one of the things that made the music of Charles Ives so hard to accept during most of his lifetime and has made it so fascinating in recent years.

Ultimately, whatever may be said about levels of complexity, the need for training in composers and performers, the diverse sociological roots and modes of presentation that distinguish classical from popular music, the main functional distinction is one of marketing. Both kinds of music--many kinds of music--coexist for any American who is musically aware to any significant degree, and their coexistence, their interaction, can be a source of mutual strength. "Sgt. Pepper's Lonely Hearts Club Band" was one of the most significant song cycles of the 1960s and was recognized as such by many classical composers.

John Rockwell makes the point obliquely but effectively in his essay on Milton Babbitt, the guru of total serialism and arch-exponent of music as a kind of advanced mathematics, whom he presents rightly as a symbol of "academic musical rationalism." Babbitt is one whose music has rigidly avoided contamination with anything that hints at popular styles or even serious romanticism, but he has an expert knowledge and an extensive record collection of pre-rock American popular song. "At a party a few years ago," Rockwell reveals, "Babbitt was asked convivially which composer he would like to be, were he given his choice. His answer was Jerome Kern." Rockwell then pauses briefly to wish that composers like Babbitt had "found a way to make a more successful synthesis of their instincts."

But where Babbitt and his school have drawn an uncrossable line, others have stepped over it in a dazzling variety of directions. David Del Tredici has gone into nostalgic romanticism, Philip Glass and Steve Reich into forms of amplified minimalism that cannot be clearly labeled either classical or popular, Laurie Anderson into something that Rockwell describes aptly as "solo opera," with an effect "like a highly attenuated art-rock concert, or perhaps a poetry reading writ very large indeed, with every aspect of the poetic concept amplified and counterpointed by aural and visual imagery." Rockwell has selected more than a score of representative figures who embody diverse contemporary tendencies in classical music, jazz, rock and various in-between genres that defy easy labeling. He writes about them expertly and with a high level of readability, even when the subject-matter becomes quite abstruse. His book is essential reading for those who want to know what is happening right now in serious American music of all kinds.

Hamm is useful for those who want to know what has happened in American music from the arrival of the first Indians up to the early 1970s. In a book of such enormous scope, he is able to make only the most perfunctory reference (or none at all) to artists who are given extended treatment by Rockwell, but that is not his primary purpose. His book is a cornucopia of information about the amazing variety of music that was brought here from elsewhere, imitated by Americans, and finally assimilated into the American tradition, undergoing changes in the process. The element of change is essential or the book would be twice its size.

Hamm is explicit on this point. "With the exception of music of the American Indian," he says, "I have dealt with music which has changed in style and form after being brought to the New World, music which has eventually taken on a different character in America, music which has been subjected to acculturation, or, if you will, 'contaminated' music." A simple list of the kinds of music excluded because they do not meet this dynamic formula fills nearly half a page. But what he does discuss is much more impressive--Puritan psalms and Appalachian folk songs, the unique music brought over by black slaves and its many descendants, the anthems of Billings and the shape-note hymns of the rural South, the origins of opera in colonial times, the sentimental ballads of the 19th century and the origins of Tin Pan Alley, ragtime and jazz and, out of this rich background, the emergence of American classical music as a serious international phenomenon in the present century. In a book of such daunting scope, it would be easy to challenge some of Hamm's emphases or opinions, but this would be quibbling. He is lavish with facts, sparing and solidly grounded in his opinions, and generally just in his emphases. A reader who assimilates Music in the New World will have a well-balanced and finely detailed idea of what has happened in American music--all American music, not merely the kinds we have labeled "classical."

Hamm is not quite the first to take all of our music as his field; it was done brilliantly by Wilfrid Mellers in Music in a New Found Land, which Hamm's title, perhaps unconsciously, echoes. But Mellers focuses his attention overwhelmingly on music of this century, and his book was published before the crucial developments of the '60s in both classical and popular music. All books about a living, developing phenomenon eventually lose some of their timeliness, and Hamm recognizes this inevitability in his final sentence. American music, he says, "happens to be calm as this book is written, reflecting the general political and social situation of the United States, but inevitably there will be turbulent and more fascinating times again."

The turbulent and fascinating times, as it happens, are already upon us--happening mostly in the lofts of SoHo, a rather dingy area of lower Manhattan, where new wave rock and post-avant-garde classical music are meeting and influencing each other. This new music is just beginning to make a strong impact elsewhere. Most of the music so knowledgeably discussed by Rockwell in All American Music has not yet settled into patterns amenable to Hamm's textbook-style treatment, but Rockwell's early reports from the world of tomorrow promise interesting times ahead.