William Parker is such a towering figure in modern avant-garde jazz that he’s in the enviable position of being able to release whatever he wants and still find an audience for it. And, in a way, one can’t help feel that’s pretty much what’s happening with this intriguing, maddening, fascinating and elusive amalgamation of ideas.

Okay, so here’s the theory. Long Hidden: The Olmec Series is an exploration of the buried connections that bind Africa and the Americas; more specifically, a meditation on the deep, inter-continental links between the Manding people of West Africa and the Olmecs, ancestors of the Mayans, who lived in Mexico from 1300 to 400 BC and who, inexplicably, spoke a dialect of the Manding language. For Parker, then, it’s a chance to reconfigure the meaning of being an African-American in the 21st Century, by reclaiming a dignified heritage from the mists of prehistory. So far, so ambitious.

In practice, what we have here is the fruits of four distinct and very different recording sessions, crowbarred onto the same album in the service of this grand historical-anthropological quest. It shouldn’t work ... and yet, somehow, Parker pulls it off.

At one end of this curious ethnographical trail, Parker presents three solo recordings of himself playing the Doson Ngoni, a traditional hunter’s guitar from West Africa, land of the Manding. Parker was first introduced to the instrument by that other world-jazz pioneer Don Cherry in 1975, and has been an enthusiastic student ever since, describing the sound as ‘‘daily music ... connected to the people sitting on the porch.’’ Here, its warm, rustic sound is beautifully suited to Parker’s unhurried, simple improvisations that provide a link all the way back to the very beginnings of civilisation.

Fast forward now to 21st century America and we find Parker stationed alone behind the double-bass, opening the CD with a deep, spacious reading of the traditional hymn “There is a Balm in Gilead” in the closest he comes to a straight-ahead jazz performance. However, any familiarity is soon blown away by three astounding and unsettling arco performances, which see Parker’s bow coaxing unearthly sounds out of the bass. “Cathedral of Light” conjures shards of raw noise while, according to Parker’s sleeve notes, embodying his entire theory of music: Sound is light and light is sound. “Compassion Seizes Bed-Stuy” is an almost melodramatic prayer for the young, black men of America. However, it’s the 14-minute “In Case of Accident”,  recorded live in Montreal in 1993 and included here as a bonus track, that really steals the show – with Parker descending into punishing regions to dredge up unnatural coruscations that sound like they’re stripping the varnish from his fiddle. It’s the angry, desperate sound of a man too sensitive for the circumstances of his own existence.

But there is redemption on hand. Providing the bridge between the two solo personae is the Olmec Group, a one-off conglomeration of Parker on percussion and Doson Ngoni with Todd Nicholson on bass, Dave Sewelson on sax and four remarkable young Merengue musicians, all in their early 20s: Omar Payano on congo, guiro and voice; Gabriel Nunez on timbales and bongos; Luis Ramierez on accordion; and Isaiah Parker on alto sax. The result is four tracks of joyous, infectious New-World Music that provide the real flavour of the album – a kind of avant-garde party music that takes the rhythms of Central America and employs them to stimulate the cerebellum as much as the feet. If there are moments when it doesn’t quite work – as when the accordion runs out of improvisational steam during ‘Codex’ and settles upon pedestrian scales to fill the gap – there are other moments of sublime synergy – as on “El Puente Seco” which finds Sewelson blowing up a gale of blistering baritone sax over an up-tempo repetitive dance riff, as though Sun Ra’s Arkestra had landed in the tropics.

You can see quite clearly what Parker is attempting to do here, even if it’s uncertain how much of the over-arching theme is post-rationalised to provide a good excuse to lump these various sessions together. In his extensive liner notes, Parker even tries tackling this question head on, explaining, “The music, although recorded at different times, is related in that it is in the family called sound and its intent is to heal and uplift the spirit, which in turn will keep us going another day.”

It may not be very convincing, but when the results are this intriguing and heartfelt we can probably give the big man a break.