Herbie Hancock -- pianist, composer and maker of musical revolutions -- is coming to San Francisco this week (May 16-18) for a series of sold-out shows at SFJazz. With his visit in mind, wheels began to turn: Why not create a list of the dozen greatest living jazz musicians? Hancock would be on it; that was a no-brainer. But who else would make the cut?

Why bother with such a list? It's a good way to generate conversation and debate, to shine a light on this ever-changing river of music that has largely fallen out of the mainstream. When I was a kid, you could turn on the television and see Miles Davis, Ella Fitzgerald or Duke Ellington. Things have changed -- and, so, here we have this list, my attempt to stir the pot.

I've decided to focus on musicians who remain active and whose contributions have shaped the work of significant numbers of other musicians, if not the entire jazz landscape. Octogenarian legends who no longer are touring -- Ornette Coleman, Horace Silver, Cecil Taylor -- are not on the list. Neither is my favorite living musician, pianist McCoy Tyner, whose sound permeates much of jazz, but whose playing lately has been compromised by age and health issues.

Inevitably, my choices have been subjective, even random. There are so many possibilities, as the music is deep and wide and now international. But in the end, this is my list. No smooth jazz. And for one reason or another, it doesn't include Keith Jarrett, Eddie Palmieri, Anthony Braxton, Esperanza Spalding, Vijay Iyer, Roscoe Mitchell, Dave Holland, Jack DeJohnette, Eric Harland and 50 other worthy candidates. Next time. Here goes:

1. Herbie Hancock

He is the classiest of musicians, as well as the funkiest, the most impressionist, the most inquisitive and free. From Miles Davis to "Rockit," from "Maiden Voyage" to his Joni Mitchell remakes, pianist Hancock has brought to bear his harmonic and compositional genius. You can accuse him of periods of pandering, but when you step back to look at the 50-year landscape, you see his vision and the way he's gone after new experiences, new technologies and (always) new sounds. Hancock, 74, knows how to grow old. Try "Maiden Voyage," "Mwandishi" and "Head Hunters."

2. Wayne Shorter

Over 50-plus years, the saxophonist-composer has combined deep currents of innovation, oftentimes enigmatic, with popular success. He helped launch musical revolts with Miles Davis' 1960s bands and with the electric fusion group Weather Report. His extended solo on Steely Dan's "Aja," from 1977, is one of the great pop instrumental statements. His canon of tunes -- going back to his days with drummer Art Blakey -- is unsurpassed. Now in his ninth decade, he composes for symphony orchestras and leads the most celebrated working group in jazz. Here's to Wayne! Try "JuJu," "Native Dancer" and "Beyond the Sound Barrier."

3. Sonny Rollins

If there were a Mount Rushmore of jazz, Rollins' face would be on it. From his first recordings (at age 18 with Bud Powell on Blue Note) to his most recent (from 2012, the year he turned 82, on his brand new "Road Shows, Vol. 3"), the tenor saxophonist's solos erupt with all the joy in the world. An unstoppable rush of creative force, of musical ideas, Rollins is now 83 and hatching plans for a new studio album. Here's to Sonny! Try the above-named recordings or (chosen almost randomly) "Sonny Rollins Plus 4," "Freedom Suite," "East Broadway Run Down."

4. Cassandra Wilson

Not unlike Billie Holiday or Miles Davis, the singer savors and stretches the sound of a single word or note. She imbues her music with mood, often poignant, her voice like amber or dark honey or smoke, spreading like a shadow, creating an environment for the listener. Twenty years ago, she discarded the standard singer-plus-jazz-trio approach and began to sing acoustic blues tunes, Joni Mitchell and Van Morrison tunes, Philly Soul and country tunes. She has never sounded like anyone but Cassandra Wilson, however, while opening a door for other, often younger jazz singers and instrumentalists to follow their own muses. Try "Blue Skies" and "Blue Light 'Til Dawn." Wilson performs Thursday at Yoshi's Oakland and Friday and Saturday at Yoshi's San Francisco.

5. Brad Mehldau

Like Hancock, Tyner, Chick Corea and others before him, Mehldau is a template for new generations of pianists. There is something both studious and absolutely free about his playing; his contrapuntal improvisations are mind-blowing. How can anyone spontaneously spin that much information? And what other jazz musician includes the Beach Boys' "Friends" in his song book? Try his albums "Day Is Done" and "Highway Rider." Mehldau performs Dec. 5 at Bing Concert Hall at Stanford University.

6. Steve Coleman

There's a common complaint that jazz needs a shake-up, that it's gone stale since the innovations of Ornette Coleman and John Coltrane more than 50 years ago. In fact, jazz has undergone a radical makeover over the last 30 years, and much of the change is traceable to alto saxophonist Steve Coleman. His performances move through long cycles of polyrhythm and grooves in unpredictable meters: hypnotic, ritualized music, uncompromising and unrelenting, reflecting his research into African music, Cuban music and ancient mystery systems. A math wiz with a diamond-hard saxophone sound and rhythmic attack, he is equal parts Charlie Parker and Maceo Parker. It's jazz as matrix music, bebop complexity with new grooves; his influence is everywhere. Search out his album "Curves of Life" and read his theories at www.m-base.com.

7. Wynton Marsalis

Millions of words have been spilled over the trumpeter -- so much ink that it's hard to persuade anyone to see beyond the stereotypes. Namely, that 1. He's a retro ideologue, relegating jazz to a box; or 2. He's an articulate spokesman for the music and a supreme player, both guarding and expanding the tradition.

Like him or resent him, he has been the face of jazz for decades -- through tough times for jazz -- while building the Jazz at Lincoln Center organization and winning a Pulitzer Prize in music. Ever mindful of jazz's African-American heritage, he is the composer of ambitious works for symphony orchestra, gospel choir and jazz big band, while leading his own well-honed ensembles. And -- I'll give away where I stand on all this -- he is an important trumpeter, an effervescent swinger and exquisite balladeer. Try "Live at Blues Alley" and "Live from the House of Tribes."

8. Joe Lovano

The saxophonist breathes this music as much as anyone. With massive sound and lungs like a bellows, he stalks the stage, grabbing one horn and then the next: his tenor, his soprano, his double-belled aulochrome. With his nonet, he plays exhilarating bebop. With his Us Five quintet, which includes two drummers, he digs into tribal music from an imaginary land where Ornette Coleman and Babatunde Olatunji are patron saints, along with John Coltrane and Rahsaan Roland Kirk. Try "On This Day at the Vanguard" and "Joyous Encounters."

9. Robert Glasper

The pianist's music is warm and riffy. I hear his music synesthetically: Neon reds, yellows and greens glow through his chords, which billow like Herbie Hancock's in a world inlaid with hip-hop rhythmic detail. In fact, Glasper has led parallel careers in jazz and hip-hop; one day, he's playing with Terence Blanchard, the next with Mos Def. Lately, he's been merging influences, trying to bring jazz back to the dancing mainstream -- and not caring whether people regard what he does as "jazz." A weather vane for many young musicians, Glasper has albums that include "In My Element" (very jazz) and the Grammy-winning "Black Radio" (very hip-hop and R&B). He performs Wednesday at the Warfield in San Francisco.

10. Brian Blade

The first time I saw drummer Blade -- it must have been 20 years ago with Joshua Redman's band -- he looked like the proverbial kid in a candy shop. His face beamed; clearly, he loved playing music, while propelling it with power and ease. The "ease" is key: Jazz is living through an age of groove -- tricky ones in asymmetrical meters, mastered by macho drummers. Blade can handle that, but what distinguishes him is his taste: the clarity and spaciousness of his playing, as well as its soulful and explosive drama. Hear him on Wayne Shorter's "Beyond the Sound Barrier" (he's been a member of Shorter's quartet since 2000) and on his own "Landmarks" (by the Brian Blade & the Fellowship, merging Coltrane spirituality with a sense of backcountry Americana).

11. Jason Moran

The pianist may be jazz's most out-of-the-box thinker, and he isn't afraid to enjoy himself. He throws Fats Waller dance parties and his bristly trio, known as the Bandwagon, has performed alongside all-star skateboarders. (It will do that again at SFJazz on June 7-8. Moran also performs there June 5-6.) Respect for jazz tradition and his African-American ancestry moves through his music like a spirit, even while he unmoors and yanks the tradition forward. Try his album "Modernistic" or his duet with saxophonist Charles Lloyd on Bob Dylan's "I Shall Be Released," from Lloyd's "Hagar's Song."

12. William Parker

A musical community builder, the bassist has catalyzed "outside" jazz innovations for decades. He has the earthiest of bass tones, deep into the instrument's wood, like Jimmy Garrison, Wilbur Ware and Charles Mingus. His music is about vibration. Burly pulses and grooves move from blues to Africa and the universal. His hookups with drummer Hamid Drake can be overwhelming; they are half of the William Parker Quartet, a criminally overlooked band. Parker is a torchbearer for jazz's ecstatic tradition. Try his "O'Neal's Porch" or "Raining on the Moon."

Contact Richard Scheinin at 408-920-5069, read his stories and reviews at www.mercurynews.com/richard-scheinin and follow him on Twitter at www.twitter.com/richardscheinin.

HERBIE HANCOCK
Honored by SFJazz gala (Friday), performing with Vinnie Colaiuta, Zakir Hussain, Lionel Loueke and Marcus Miller (Saturday-Sunday)
When: 7:30 p.m. Saturday, 3 and 7 p.m. Sunday
Where: SFJazz Center, 201 Franklin St., San Francisco
Tickets: All shows sold out, check for turn-back tickets on day of each show, 866-920-5299, www.sfjazzorg.