Violins aren't supposed to go out unaccompanied.

They're basically single-line instruments, except when J.S. Bach devised ways for the instrument to sketch great musical edifices by means of ingenuity and suggestion. But in two concerts over three days, solo violin music by Eugene Ysaÿe and Fritz Kreisler (presented by Astral Artists) and Mark O'Connor (presented at the Curtis Institute of Music) arrived without provoking unflattering comparisons to Bach. Nor did you long for the dueña-like presence of the piano.

O'Connor's name in this lineup shouldn't be a surprise - though for some people, it was. The violinist/composer of Yo-Yo Ma's best-selling

Appalachia Waltz

album is nearly as well known in classical circles as in the country/bluegrass world he comes from. His long-standing pedagogical streak is being accessed by the Curtis Institute in a series of master classes preceded by Tuesday's recital, from which dozens were turned away.

O'Connor is in a period of renewed commitment to virtuosic violin playing, returning to his

Caprices Nos. 1-6

, written in the early 1990s when he was a session musician in Nashville. Like George Gershwin's and Astor Piazzolla's, O'Connor performances are more about reporting musical ideas than interpreting content. The piece comes before the performer - not what you'd expect when the music itself exists to show off performers. Others might play it better but not with such clear intentions.

In effect, his concert was a convincing manifesto of his Euro-Americana fusion of violin playing. The solo violin forces any given musical idea into a starkly distilled form. Bach used plenty of dances in his solo violin sonatas; so did O'Connor, but American ones. As in Paganini's caprices, O'Connor employed miniature musical ideas repeated at great velocity and on all regions of the fingerboard - but with gestures and cadences that could come only from American folk tradition.

A graphically descriptive composer, O'Connor said his fantasy on the hymn "Amazing Grace" was partly inspired by a racially motivated police-brutality incident. That translated into a tiny "Amazing Grace" fragment repeated like a Philip Glass ostinato but at an anguished, frenetic speed.

The arrival of his greatest classical hit,

Appalachia Waltz

, in solo violin version showed what I've felt was missing in some other O'Connor works. Instead of imagining a lost American past, he expresses nostalgia for what it could have meant, which comes from a deeper place. Or maybe it seems that way because, unlike some O'Connor, the piece is uncluttered and doesn't sound as if it's fleeing.

The Astral concert on Sunday at the Trinity Center had four of the violinists on its roster alternating among Bach, Kreisler and Ysaÿe, those last pieces being a considerable revelation. Though known for flashy encore pieces, the Belgian violin virtuoso Ysaÿe (1858-1931) wrote his

Sonatas Nos. 1-4

in minor keys with a Mahlerian sense of soliloquy. The pieces are dense, wild and mercurial, more inclined to quote the "Dies Irae" than, in lighter moments, Bach. With such emotional traffic, the clean, vibrant performances of Ayano Ninomiya (who played No. 3) were most communicative.

The heaviest lifting came from Jennifer Curtis, who played Bach's

Partita No. 3, Sonata No. 3

and Ysaÿe's

Sonata No. 1

. She's an interesting musical thinker who wasn't having her best day, technically speaking. Larger purposes were obscured. Maybe Ysaÿe wouldn't have minded: He dedicated the piece to Joseph Szigeti, not the sturdiest player, but one of the smartest.

Contact music critic David Patrick Stearns at dstearns@phillynews.