Charlie Rouse on "Green Chimneys"

Fats Navarro and Charlie Rouse, c. 1946-8 (?)
In the fall of 1958, the saxophone spot in Thelonious Monk's working quartet had become a highly coveted position; after Johnny Griffin and then Sonny Rollins left Monk's band, a number of saxophonists vied for the spot, as Robin D.G. Kelley writes:

“Monk’s choice of Rouse surprised some, and disappointed many young saxophonists gunning for the slot. Nellie recalls fielding dozens of phone calls from players interested in working for her husband, including one call from a talented newcomer named Wayne Shorter.” 
Rouse got the gig—fortunately, as many would argue, considering that Rouse's swing-bebop style was complementary to Monk's distinct, rhythmically and harmonically angular style. In 1959, Wayne ended up getting with Art Blakey and working with Freddie and Cedar Walton, among others; Wayne also had the chance to flex his writing chops, which would prepare him for his tenure with Miles. If Wayne had been in Monk's band for a while, he would have likely had less of an opportunity to develop his compositional style, although his playing and approach might have been quite different as a result of learning from Monk.

On "Green Chimneys," Rouse, to my ears, plays as a foil to Monk—rather than experimenting with phrase lengths and stretching out harmonically over the static harmony fo the A section, Rouse plays pretty conservative phrases that wouldn't lose a listener checking out the form of the tune. He develops riffs and isn't afraid to repeat himself, which lets Monk and the rhythm section work out some comping interplay as a group. Monk's solo, by contrast, is very hard to follow—phrases start and end with complete freedom, and Monk varies texture and harmony as he feels appropriate. Still, Rouse's solo is a great example of how to play something swinging (and, importantly, engaging) over static harmony, which I hear as a swing approach to making modal music interesting (and oh, how different from the post-Brecker era of subs, subs, subs, subs, subs). Monk was also probably responsible for a significant portion of Rouse's approach, which was to keep the melody in mind at all times—every chorus, Rouse unfailing gestures towards Monk's writing, which is an anchor for a tune that has little harmonic stimuli to work off of. Also, for saxophone players: check out those low Bbs! I think Rouse and Stanley Turrentine are two tenor players who took advantage of the power of the low register to surprise and catch a listener's attention. Here's the solo:

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Kelley also reports that Monk and Rouse had a relatively amicable parting; although Rouse split after getting into a fight with Monk the bandstand (Monk called a tune that Rouse didn't know and "lashed out at him" for not being able to play it), Monk stood up for Rouse even after Rouse left and others spoke negatively of him. Paul Jeffreys, a tenor player who later played in Monk's band, recalled:
"'Nellie and them, they didn't like Charlie Rouse towards the end after he left. So one day I was over Monk's house and they were talking about Rouse like a dog. Monk's not saying a word the whole time. Then suddenly Rouse knocks on the door and they let him in...And Monk waited until everybody greeted him. And do you know what Monk did? He tells Rouse, 'This one said you couldn't play shit. This one said that,' and so forth...he made all of them look bad.'"
I'm not too familiar with Rouse's music post-Monk, but as I've heard from one friend who heard Rouse play on an L.A. studio session in the '70s, Rouse adjusted his playing with the times, adding Breckerish funk playing to his bag (not verified, but hopefully I'll follow up on this in the future).