Oceans of harmony resonate from the strings of Leo Kottke’s guitar as he just sits there and finger-picks his little symphonies into existence.

It’s always deliciously disorienting at first to try and associate the depth of Kottke’s music — the dynamism of volume and momentum, the precision and sudden shift in direction of the phrasing, the tonal and rhythmic undertow swirling back to meld with the next phrase — with such an economical tableau. Kottke is almost universally described as self-deprecating, and it’s true that his dry, deadpan humor often makes him either the butt or the bystander of his quirky between-song stories. But the effect is magnified because after watching him sojourn through a particularly inspired or serendipitous song, it’s natural to expect him to pump his fist in the air, or kick out his leg, or hold his instrument in front of him and bow — something to acknowledge the preceding triumph. Instead, he might just nod his head and start re-tuning for the next go-round.

For how much longer? A resident of the western suburbs, Kottke’s increasingly rare live performances have almost never omitted his annual Thanksgiving weekend gig in the Twin Cities over the past 20-plus years. The Ordway was the best venue because its august and elegant confines so befitted the music Kottke plays.

The past few years it has been at the State Theatre, and that works too — at least much better than nothing at all. Kottke will be eligible for Medicare next September, and while Segovia and many other masters of the guitar have played into their 80s and beyond, the little infirmities of the digits and shoulders deepen through the decades. Already Kottke isn’t as fast or showy as he was in the 70s and 80s, a matter of both stylistic taste and physical limitation. And lately he’s recruited sidemen for these November shows; on Saturday it will be Nick Urata and Tom Hagerman of the group DeVotchKa, which will expand Kottke’s customary olio of classical, jazz and folk stylings with elements of Greek, Mexican and Slavic music.

But watch and listen: The Kottke solo spots will remain the highlights.

Here is a solo Kottke medley from January 2009, complete with humorous introduction.

Here he is in a duet with Phish’s Mike Gordon.

Here is one of his infrequent vocals, on his best-known cover song, The Byrds’ “Eight Miles High.”

Leo Kottke at the State Theatre, Saturday, Nov. 28, 8 p.m., tickets $30-$42.