Ok, class, ready for a little Purploid trivia excursion again?!
While DC was with the Purps he never sounded like Gillan (Mk III DP only ever played three Mk II songs: Smoke, Highway Star and Space Trucking, Mk IV dusted off Lazy live with Bolin giving the song a totally different feel). Or was asked to. He never did attempt Child in Time or the screechy call and response of vocs and guitar in the MiJ version of Strange Kind of Woman, Purple wanted him to have his own identity (in fact Jon Lord has repeatedly lamented how Coverdale pushed up his register over the years for no good reason other than perhaps athletic relish).
By 1972, Blackmore had grown tired of Gillan's increasingly off-the-wall vocal melodies on new material. The two fell out not only over "Painted Horse", which Blackmore refused to have even released from the "Who do we think we are" sessions, but Blackmore also disliked Gillan's psychedelic singing on "Our Lady"
http://www.youtube.com/watch?v=znumd9aXa_s&feature=relatedand on "Place in Line" which sounded like Gillan was taking the piss on Blackmore's new-found love for more gravelly sounding singers:
Blackmore wanted someone with more of a blues feel. That is why he jammed with Lynott and that is why Paul Rodgers was approached as his first choice (Blackers had been singing the praises on Free in the press for a while and his comments that he rated Rodgers "the best British rock singer" had riled Gillan no doubt). But Rodgers bowed out of joining Deep Purple when the Purple management divulged the nascent talks with him to the press - enter Bad Company ... Listen here at 3.24 for how DP might have sounded with Herr Rodgers:
http://www.youtube.com/watch?v=5chZyRnK8dU&eurl=http%3A%2F%2Fwww%2Ethehighwaystar%2Ecom%2Fnews%2F2009%2F07%2F30%2Frock%2Daid%2Darmenia%2D20%2Dyears%2Dafter%2F&feature=player_embedded#t=207Subsequently there were contacts to Jess Rhoden and Snips, the singer from Sharks which came to nothing. Another singer approached was Lucifer's Friend singer John Lawton (a man with a decidedly black and bluesy voice, later with Uriah Heep) who does not realize that Purple are looking to replace Gillan and turns down the offer "to jam" with them in favor of a paid gig with German MoR outfit Les Humphries Singers (watch for 0.57 in the following clip, I guess he could have actually matched Gillan's range).
He doesn't get a second invite from the Purps, silly boy! But Uriah Heep will remember him in the future (after Coverdale declines to join them after the Purple split in 76) ... and don't mind his balding pate and overt use of eye shadow:
In the meantime, the remaining members moan about having to wade through tapes of people trying to sound like Gillan. Glenn Hughes is then pulled on board who Blackmore liked for his bass playing and singing with Trapeze (plus his looks which were remotely like Gillan's, which was important to the management), but the Purple management makes it clear that Purple would also need a non-instrument playing lead singer as a frontman. Moreover, Blackmore rates Hughes' range, but wants someone "with a more manly voice" plus is interested in having harmony vocals within Purple (Gillan always sang alone live and harmonized comparatively little in the studio, preferring to simply doubletrack his voice without harmony most of the time), something he admired with Uriah Heep (nicknamed "You're all sheep" by Deep Purple Mk II members, who are to this day adamant that Heep stole ideas and sound from them back in the day when the two bands had adjacent rehearsal rooms).
And then Ian Paice listens to a bad audition tape from the "unknown boutique salesman from Redcar", gets goose bumps, calls Lord who likes what he hears too, Coverdale is invited, put on slimming pills (amphetamine), gets his cross-sight operated and the rest is history. He's never ever pushed by Blackmore to sing any higher than his natural range (and Blackmore later on moves to Dio who is not a hi-note-hitter either).
It's only when Coverdale decided for his own ego that with Whitesnake he would have to eclipse DP's US success that he embarked on that silly quest to sing higher and higher. That and the ill-fated vocal chord and septum operation he had. In the liner notes to the new remaster of Slip of the Tongue he even admits himself that he got carried away and pushed the keys on that particular recording higher and higher (and had subsequently a hard time singing them live), I guess Steve Vai's widdlings were an unholy influence.