In its final concert of the season (repeating tonight at the Paliku Theatre), Chamber Music Hawaii engages in a thoroughly enjoyable evening of musical instruction centered on Bach's "Musical Offering," a series of musical riddles and pieces on a theme provided by Frederick the Great of Prussia.

It began as a pastime — the king challenged Bach to improvise a fugue on the spot — and later became an extended examination of contrapuntal possibilities. By the time Bach finished, the king's eight-measure theme had become two fugues, a four-movement trio sonata, and 10 riddle canons.

"Musical Offering" is not often performed in its entirety, in part because of its length (not quite a full concert, but a very long half-concert), but also because half the fun lies in the original notation. It is the ultimate "insiders" piece: listeners need to be musically literate to appreciate its intricacies and genius.

Chamber Music Hawaii's Tresemble, the mixed forces of its three ensembles, Spring Wind Quintet, Honolulu Brass, and Galliard String Quartet, presents an elegant solution that not only lets the audience in on the riddles but makes the time fly, so that the piece seemed, if anything, too short.

Oboist Scott Janusch serves as "narrator," seated to one side of the stage, introducing each movement. While the musicians play from "solved" arrangements, Janusch explains the original notation and how performers must figure out how movements work and what to play from clues such as "notulis crescentibus crescat fortuna regis" (as the notes increase, so may the king's fortune increase).

It would have been nice to have an overhead projector so that the audience could see the notation, but Janusch describes it clearly without resorting to "retrograde inversion" terminology. His explanations allow the audience to hear how Bach manipulated the theme in each canon, playing with its possibilities, and then to appreciate how Bach pulled it all together to create the astounding beauty of the final, climactic six-voice fugue.

Tresemble extracts the sonata from "Musical Offering" and present it in the first half of the concert in a trio of trios: Jacques Ibert's "Deux interludes" (Two Interludes) in a delightful opening performance by flutist Susan McGinn, violinist Claire Sakai Hazzard and pianist Thomas Yee on harpsichord; the second of Jan Dismas Zelenka's famed wind Trio Sonatas, exceptionally performed by obosists J. Scott Janusch and Pavel Morunov, bassoonist Marsha Schweitz-er, cellist Karen Bechtel and Thomas Yee on harpsichord; and finally, Bach's Trio Sonata featuring the same ensemble as in the Ibert, with the addition of cellist Bechtel.

The harpsichord on loan to Chamber Music Hawaii — a dual-manual, double-strung instrument, with "lute" option (a muting lever analogous to the una corda pedal on pianos) and a decorated soundboard — was built by Mark Russell in 1999; it became the center attraction at intermission during this week's performance at the Doris Duke Theatre.

Each of the trios had a different number of musicians: three for Ibert, five for Zelenka, and four for Bach. As odd as that may seem, given that "trio" means "three" in the Baroque era, trio sonatas were more about texture than a number of players — two treble parts and a bass, with or without continuo.

The trick to counting lies in the continuo part, a single part usually performed by two musicians, one playing a single bass line (as by a cello, viol or bassoon) and one playing a chordal "realization" of the bass line (as by an organ, harpsichord, lute or harp). Both played the bass line, but the musician on the chordal instrument also improvised or "realized" the part, according to symbols in the bass line indicating which chords to use when.

Although most realizations today are written out beforehand by arrangers, in the Baroque era, realizations were invented in performance, were highly individualistic, and reflected the skill of the musicians, much like jazz improvisations today.

In short, the Ibert was a modern trio (three parts, three musicians); the Zelenka had a trio plus continuo (four parts, five musicians); and the Bach had two treble parts and continuo (three parts, four musicians).

The reason all this matters is because the number of parts and their relationships suggest how the musicians are to be arranged on stage, thereby impacting how they relate and how they sound.

The focus of the Baroque sonata is on the interplay of the solo parts. Consequently, the soloists are usually placed prominently and facing one another, so they can engage in dialogue, tossing themes back and forth, musically commenting on the other's part. The two musicians sharing the continuo part belong together and are situated less prominently for their supporting role.

In the Zelenka, Tresemble follows that general format, and the resulting dialogue is a lively mix of playing both in concert (together) and in contrast (against one another).

In the Bach, the two soloists sit together on one side, across from the cellist, throwing the bass line into uncharacteristic prominence and presenting the soloists nicely in concert but with little contrast.

All in all, the performance closes out the year on a high note, undoubtedly ensuring an enthusiastic and committed audience next season.