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Six Organs of Admittance, "Hexadic"
I have always been a rather casual Six Organs fan, generally enjoying whatever it is that Ben Chasny is up to at a given time, but not exactly salivating over the prospect of a new album.  Something about Drag City's cryptic description of Hexadic piqued my interest though and rightly so: this is strange and fascinating album.  The most notable aspect, certainly, is that Chasny used a self-created system of playing cards based upon the wisdom of a 14th century monk to compose a "rock" album.  That certainly does not happen every day.  Aside from that, Hexadic boasts an absolutely incendiary psych-guitar tour de force called "Wax Chance" that easily stands with anything by Les Rallizes Denudes or Mainliner.  I definitely did not expect that either.
Hexadic takes its name from Chasny's card-based open system, which is largely rooted in the number six.  The system itself is going to be explained in detail later in a book, but the gist is that Ben synthesized the ideas of Gaston Bachelard, Frances Yeats, Morton Feldman, Heinrich Cornelius Agrippa, and (most significantly) Ramon Llull into an algorithm that provides a loose compositional blueprint that points toward a specific key, scale, and time signature.  How a given song actually takes shape afterwards is largely dependent on the artist, of course, but the hexadic system works by pushing the composer out of what is comfortable and routine.  That is at least the general idea, anyway.  Hexadic certainly still sounds a hell of a lot like a Six Organs album to me, but it definitely feels like one that Chasny was very enthusiastic about and is different enough to stand out from the rest of his discography in several ways.  It is more of skewed, unpredictable version of the familiar than a complete reinvention.
I have always had a hard time defining "the Ben Chasny sound," as he has covered a lot of stylistic ground over the years between Six Organs, Rangda, Comets on Fire, and other projects.  In general, however, I associate him with Eastern/raga-tinged acoustic guitars and guitar-solo heavy psych-rock.  Pieces from both of those admittedly vague directions turn up with regularity on Hexadic with varying degrees of success, but the pieces that I find most interesting are the ones that do not quite fit either category.  That said, Hexadic’s 9 pieces do lean quite heavily towards loud, wild psych-rock, which makes sense, given that Ben's backing band contains members (or former members) of bands like Comets on Fire, Deerhoof, and Sic Alps.  The rock in question is much more unhinged than I would have expected though, particularly on the face-melting, bulldozing "Maximum Hexadic," which is essentially 2 minutes of gnarled, free-form, and brain-melting guitar-spew over a driving bass-and-drum groove.  Elsewhere, "Sphere Path Code C" sounds like a guitar solo plucked from the midst of longer piece by a wildly indulgent guitar visionary like Keiji Haino or Kawabata Makoto: there is not really any "song" to speak of, just a cacophony of howling guitars, amp sizzle, and collapsing grooves.  "Hollow River" is quite similar, but alters the formula by slowing down to a doom crawl and offering some hints of correspondingly doomy riffage amidst all the noise and sizzle.
Most of the other "songs" are in a cleaner, more subdued vein, which is both somewhat disorienting and somewhat refreshing.  "The Ram," for example, sounds like a languorous surf instrumental that has been slowed down to such a degree that the drummer cannot even find the stumbling beat anymore.  "Future Verbs" sounds like a quiet interlude from the same imaginary doom album as "Hollow River," unraveling overlapping, woozy, descending melodies over a menacing sludge-slow bass progression.  Stranger still is "Hesitant Grand Light," which combines shimmering washes of hazy electric guitar over tremolo-picked acoustic noodling and yet another broken non-beat.  The weirdest part for me is that the scale used for the acoustic parts sounds like a weird cross between the pentatonic scale and some Eastern mode, tonally approximating some non-existent Indian rockabilly sub-genre.
Of the remaining, harder-to-define pieces, all three are quite wonderful.  The first, "Vestige," is an abstract drone piece featuring a surprisingly dissonant bed of squirming, oscillating, and nightmarish guitars that sound wonderfully sick and wrong.  "Wax Chance," on the other hand, sounds wonderfully sick and right.  In a lot of respects, it is every bit as harsh and indulgent as the rest of the noisy rock songs on the album, but in this case the drums and bass lock into a kind of sultry blues shuffle.  Also, Chasny's white-hot, overdriven guitar occasionally finds its way into an unexpectedly coherent and bad-ass riff.  That little bit of structure makes all the difference, as Ben's brilliantly outre free-form soloing desperately needs some kind of solid foundation to be truly effective (which "Wax Chance" definitely is).  The album's final piece, "Guild," initially seems like yet another sizzling flurry of overdriven guitar squall over a too-slow beat, but it gets gradually better.  Though it probably goes on for way too long, it has a weirdly appropriate valedictory feel to it and Ben's solo seems to at least hint at fragments of melody.  It also benefits from some unexpected transitions and a beautifully restrained and bittersweet coda.
Ultimately, I would describe Hexadic as an uneven experiment with a few flashes of brilliance rather than as a clear success or failure.  While its flaws are probably primarily due to its fundamental mathematic constraints, they also tend to be both glaring and recurring: the idea of slow-motion, electric guitar free-jazz is not at all appealing to me.  As much as I enjoyed Ben’s go-for-broke guitar squall, a little of that truly goes a long way and Hexadic is an album direly in need of more hooks and better grooves to balance its more indulgent aspects.  When Ben has both a riff and groove to work from, as with "Wax Chance," I am happy to let him go as far out as possible.  When he has neither, he just sounds like a guy pointlessly shredding in some weird scale until he gets tired of it.  More devoted fans might appreciate that freedom and intensity much more than I do and it might even work live, but it can be very tedious on an album when it is not couched within anything more rewarding.  On a more positive note, however, Hexadic at least strives for something surprising and different, which I heartily appreciate.  Also, it does not sound conspicuously chance-based, which is an impressive feat as well.  More significantly, three of its nine songs are quite good.  While I doubt I will ever listen to the rest of the album again, I am now considerably more interested in Ben's future work than I was before, which I suppose makes Hexadic a moral and intellectual triumph at least (just not quite a musical one).
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