Then again, in my opinion, the cerebral quality in Purple emerged much earlier, as far back as Rapture of the Deep, with the arrival of Airey.
I mean all three possible meanings you gave, Mike! 
Purple have become more cerebral in all departments over the decades - which I have no issues with.
Daniel, I love Mk III and IV dearly, but their music did not even pretend to be cerebral, it was good time stadium rock designed to overwhelm. That didn‘t turn them into AC/DC, KISS or Status Quo, there was still some refinement and elegance there, but from a mere technical and compositional viewpoint, yes, songs like Stormbringer or Lady Double Dealer are more simplistic than anything written by Mk VII-IX.
Ritchie was never afraid to be engagingly simple as long as he could add his own personal flourish to it - we all know he doesn‘t think too highly of rock audiences‘ mental capacity to digest more complex music. That‘s not a knock, it was one of Ritchie‘s strengths/talents and part of DP‘s success recipe. If music similar to Purpendicular, Now What?! and Splash! (albeit preformed by men in their 20s) had been released in 1970 by DP instead of In Rock, I rule out that DP‘s career trajectory would have been the same , they would have remained an obscure outfit somewhere between Prog and Hard Rock. Ritchie‘s sense for immediate accessibility as a writer was key to DP‘s mammoth success.
The other side of the coin was of course that Ritchie‘s favorite recipe of “a good riff + catchy vocals + flashy guitar and organ solos” did become confining and - heresy! - a bit one-trick-pony’ish over time. It was an accusation lobbed at DP by critics often enough in the 70s (and it had, forgive me, a grain of truth to it) and never something that, say, Led Zep was accused of. I’m far from a closet Led Zep fan as everyone knows, but to my mind Jimmy Page was open to a much wider array of music forms than Ritchie. Is it verboten to state here that Ritchie was to guitar playing and music a bit what Clint Eastwood was to acting? I would call neither of them eclectic in their choice of artistic expression (and yet I like them both for what they are/were)..
I think the keyword here is memorable and Ritchie had it as his middle name 
If it’s not memorable, there’s not much meaning to it.
Every house needs a foundation. In DP’s case it was the riffs, be it Stormbringer, Bad Attitude, Mad Dog or Hard Lovin Woman (Ian’s way of singing it a groove fest in itself).
The reason why they were memorable is because they were “simplistic” and hummable. But those riffs are likely also the hardest to come up with.
Agreed, Ritchie had an absolute ear and talent for memorable stuff. But that was also tied to a certain immediacy/simplicity which determined each other.
I mean comparing the riff of SOTW with the one of Black Dog (written by JPJ rather than Jimmy Page), just kind of says it all: One is four short segments (two of them identical) over a straight beat, the other a convoluted, ever-changing series of notes that leaves the standard 4/4 meter structure several times. Not that I don’t appreciate the Black Dog riff, but ask someone to whistle it to you in its complete form! In contrast, any small child can hum you the SOTW riff.
Which in itself is a clever permutation of the earlier “Mandrake Root” second riff, right?
To me, the SOTW riff is only a part of the charm of the song.
Roger’s also clever root-pedal-tone baseline and the brilliant re-entry of the riff (coming back earlier than your brain would expect it to) after the chorus all helped making it memorable.
Cheers, J.-
No argument at all, the arrangement of SOTW is grand, you can arrange something that is musically inherently simple in a very refined way and I think Purple’s arrangements were often of better or at least more accessible quality than, say, Led Zep’s.
Zep were better at creating an aura for their long players, that is where the engineers vs. architects schism between DP and LZ comes in.
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Engineers and architects, oh dear. I guess some people cannot help themselves. I can hear that we were talking about music which would have been created from feel alone, in more ways than one. Not notated or written down before hand…Oh well, some people cannot help themselves to ‘over "anal"yse’ the simplistic things in life eh? Be a good day Uwe. Try not to think too hard about it all. It’s all music as Keef often says! Cheers.
But Herr MacGregor, drummers have never been my target reading audience, I’m a bit selective … I applaud you valiantly making an effort just the same, keep tryin’!