When American pop music shattered on the rocky shore of the 1990s, a thousand shards flew in every direction. Some have lamented the fragmentation, not to mention the difficulty with selling recordings in this climate. Other musicians have seen the newly flattened music market as a do-it-yourself opportunity, and they’ve created idiosyncratic art not designed for mass consumption. Thus, the proliferation of ways for the industry to put the prefixes “indie” and “alt” in front of genre names. Except for Coldplay and Kayne West, almost everything’s a little “indie” these days, right?

And certainly the accordionist Miss Murgatroid (actually, photographer Alicia Rose) and the singer/string player Petra Haden (daughter of jazz bassist Charlie Haden) qualify. The duo recorded together once before (1999’s Bella Neurox), creating a series of overdubbed mini-symphonies weaving together Miss M’s accordion, Haden’s violin and viola, and their singing. Almost a decade later, they’re back at it, and the results are sophisticated, anachronistic, naïve, lush, and minimalist—a jumble of impulses that aren’t easily defined. Not rock, not folk, not jazz, not classical. This, for sure: fascinating.

Some background: Rose seems to be a true polymath—an art photographer, a music booker for clubs, a composer, and a singular accordionist who manages to take the instrument out of its typical awkward style and impose it on a different kind of music. Haden is very nearly as eclectic, playing and singing with indie-rockers, the Decemberists, with jazz guitarist Bill Frisell, with her own rock band “that dog”, with Sean Lennon, Green Day, and Victoria Williams, and also with herself, most notably on her complete a cappella remake of the rock album The Who Sell Out. Together, the duo crafts otherworldly music that seems to derive from a free-floating logic all its own. More than anything, these pieces of music strike me as classical in arrangement and approach—they’re abstract, and unlikely to break down into obvious verses and choruses. Yet they move with the simplicity and tools of rock music—based on riffs, grooves, textures, and elements of distortion.

“Baroque Lullaby” certainly seems to invoke the classical tradition. Miss M’s accordion sets a bouncy-happy groove over which Haden dubs a series of string parts that enhance the cheeriness with a dash of hill music. These episodes of cheer are, however, contrasted with brief suspensions of the rhythm, during which Haden’s vocals underpin the tune with a sad dreaminess. There is nothing “baroque” about it. Indeed, it is a tone poem with two contrasting themes, but it could function as a kind of lullaby. Most of the compositions (credited, largely, to both performers together) contain no words, using the voices as additional instruments rather than as a featured “lead.” In most cases, the arrangements blend the three elements—accordion, strings, and vocals—so deftly that you lose the sense of distinction between them. “Hummingbird” is a good example of how this orchestral effect is achieved. The initial two-chord vamp is set up on squeezebox, but there is a subtle underpinning of plucked strings. Several seconds in, the bowed strings enter, overdubbed violins and violas simulating a fairly large section, which are given a short spot without the accordion rhythm. Then, the voices enter in quiet, but beautiful counterpoint—six, seven?—but as accompaniment rather than melody at first. Eventually the voices rise to the top of the arrangement, only to have the suspended string passage return. This sequence repeats with variations, the last of which pushes the singing into a garbled shout before the strings snap it off quickly. It truly seems like a three-minute symphony.

A couple of songs use brief passages containing words. “Fade Away” contains a complexly rhythmic vocal arrangement based around breath-like staccato notes (“Huh-huh-huh-huh ... Huh-huh-huh-huh”) that could have come from a Steve Reich work. But when the pulse drops, the two voices intertwine in two overdubbed choruses: “Every time you walk near, you’re not here. So you fade away.”  Then: “In the time I was here, it was clear, I would fade away.”  “Something’s Wrong” seems to contain muted words in a few spots, but then a true lead emerges toward the end in a short melody that sounds Beatles-y—a heart given and broken. “See Me See Me”, and a few others, contain shadowy pronunciations of the song titles amidst the vocalizing.

There are also tracks that include percussive or recorded sounds. “Ballad for Anne Bonney” begins with the crash of a thunderstorm without obvious explanation—an ominous start to a song that ventures in many directions. “We Formulate” features a subtle percussive underpinning of shaker, and a digital effect that sounds like a tuned talking-drum creating a bass line. It’s well done, as are the moments when the singing mimics the percussion in polyrhythm. “Another Day” sounds more overtly modern, with a chittering techno groove blending with some lovely arpeggiated violin. There is even what could pass as a kind of rock or jazz-styled solo, with Haden (or is it Miss M’s processed squeezebox?) laying out something that would have been not entirely alien to Jimi Hendrix.

Hearts and Daggers is an enchanting set—a dreamy movie in music, a set of tone poems made out of pop music but made by unlikely instruments, a collection of pocket symphonies with surprising beauty. This is music that surprises without grating, that spins around your head without being easy to categorize.  Made by musicians happy to be on the experimental edge, Hearts and Daggers manages to be less avant-garde than ingenious. Less played than conjured, the music of Petra Haden and Miss Murgatroid is a pleasant dream.