I was reading a short response by Joshua Kosman, SF Chronicle, A 'modernist' view of classical music. The reader's husband doesn't like 20th century composers, so the reader was looking for suggestions as to "Modernist CD's" he might like, "rather than the more obvious 'Rite of Spring.'" In Kosman's reply he starts by saying, "Let me start by quibbling a little with your terminology. "Modernist" refers to a particular view that sees music history as a forward march, with each composer extending and building on the innovations of his or her predecessors. It's been an important and influential way of approaching artistic creation, but it's not the only strand in 20th century music..."
Hmmm... I beg to differ with your opinion Mr Kosman. According to Wikipedia (for quick reference)
Musicologist Carl Dahlhaus restricted his definition of musical modernism to progressive music in the period 1890-1910:
The year 1890...lends itself as an obvious point of historical discontinuity....The "breakthrough" Mahler, Strauss and Debussy implying a profound historical transformation....If we were to search for a name to convey the breakaway mood of the 1890s (a mood symbolized musically by the opening bars of Strauss's Don Juan) but without imposing a fictitious unity of style on the age, we could do worse than revert to [the] term "modernism" extending (with some latitude) from the 1890 to the beginnings of our own twentieth-century modern music in 1910....The label "late romanticism"...is a terminological blunder of the first order and ought to be abandoned forthwith. It is absurd to yoke Strauss, Mahler, and the young Schoenberg, composers who represent modernism in the minds of their turn-of-the-century contemporaries, with the self-proclaimed anti-modernist Pfitzner, calling them all "late romantics" in order to supply a veneer of internal unity to an age fraught with stylistic contradictions and conflicts. (Dahlhaus 1989, 334)
In the Oxford Music Online: Modernism
A term used in music to denote a multi-faceted but distinct and continuous tradition within 20th-century composition. It may also refer to 20th-century trends in aesthetic theory, scholarship and performing practice. Modernism is a consequence of the fundamental conviction among successive generations of composers since 1900 that the means of musical expression in the 20th century must be adequate to the unique and radical character of the age.
So, if we're going to quibble with the definition of modernism, let's at least make sure we're talking about the same thing. If we're going to speak specifically about Modernist composers we should be limiting ourselves to Debussy, Skryabin, Strauss, Schoenberg & Webern - with Busoni and Schreker as lesser known but still modernist composers. All of these composers provide a healthy selection of music the reader's husband might enjoy.
However your comment, "sees music history as a forward march, with each composer extending and building on the innovations of his or her predecessors." suggests to me you think some composers are not following in a direct line from his/her predecessors. You then go on to suggest Shostakovich, Britten, Barber, Berio, Reich and Adams. This suggests you're thinking 'Modernist' includes anything in the avant-gard of the 20th century (or maybe you're thinking your reader thinks this.
While I agree (heartily) to your selections of possible pieces, I think you do your reader a dis-service by suggesting they are 'modernist' composers. Reich considers himself very minimalist and Adams post-minimalist (at least now). It is true, your list of composers don't follow in the line of the pan-tonal music of Schoenberg, Webern, Berg, Babbitt and on to post-serialists of Ferneyhough and Fox. But I think all the composers in your list would say they are building on what previous composers have done, creating a contiguous line of musical development.
If I were to add to your list, Copland and Bernstein would be on that list. I think your reader would be surprised at how familiar their works sound, even if he's never specifically listened to them, for later 20th-early 21st century add Ligeti's etudes.
Again, I don't quibble with your selections Mr Kosman, but let's be clear to our readership the definitions already accepted in music. It is our role to educate them in all manners of music.