Seth, I've owned ONE Ric twelve and SIX Rix six-strings. Rickenbacker six-strings can be crystalline clean or richly overdriven. One quality I like is their attack; on both solid and semi-hollow Rics, the attack is immediate but followed with a sweet natural decay. You'll note a very present resonance on Rics, but nothing tubby like on a jazz box. Most Rics twang nicely if you want. They can be surfy -but never as thin as a Fender.
One thing which always happens when I play is that people compliment me on my tone. It is a testament to the Ric character of always cutting through the mix.
I can get a very Les Paul tone from my Rics -think of Les the player rather than the typical Les Paul/Marshall sound.
Rickenbackers have a harmonic purity which I don't hear on many other models. They can go as low or as high as you like. For me, they are the only Do-All instrument. All others are only temporary flavors.
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1.All The Stars - 1997SPC/VB on E-bow, solo, and rhythm (bandmate's 70s Strat on the Andy Summers part

).
2.Chachapoya - 1997SPC/VB on main electric, bends, lead - 360V64 on wah parts
3.Shoreline Gold - 1997SPC/VB on bent chords, harmonics, slow lead, one rhythm track
4.Nightfalling - 1997SPC/VB on rhythm and crunch tracks
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1.Seaside - 650A/VT on main electric (with bends), 1997SPC/VB on lead
2.Sand (intro) - 1997... on crunch (with Dano Longhorn

) and staccato single notes, 650A/VT on deep space liquid lead bend
3.Double Argent - 1997... on spy licks and double stops, 650A/VT on slide and lead
4.Desert Ship - 1997... on non-chirpy rhythm, Ebow, harmonics, tremolo washes, and crunch, 340 (desert gold) on leads (dig the bright, cutting tone)
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1.The 13th Step - 1997 main theme guitar, rhythm
2.Palace Gate Apts. - 360V64 sliding chords
3.Sleight Of Hand - 1997 main guitars (Tele lead, sorry)