The melody of "A Train" doesn't, by itself, necessarily imply whole tone.
Well, but the melody for that two bar section (which is only two notes) doesn't not imply whole tone either. It's two notes that happen to be part of a whole tone collection, played over a root note which is also part of that same whole tone collection, and when you add the third and seventh of that chord, yep, they're all still part of that same whole tone collection. So while it's not necessarily "implying" whole tone, it's presenting the improvising musician with a rather well fleshed-out set of hints suggesting that A) whole tone could work for those two bars; and/or B) making something besides whole tone work there would require the musician do some extra lifting: You'd be bringing more to the performance than the composer (may have) intended*, which then puts the onus on that performer to be able to justify their "wiggle room" via appropriately strong and relevant ideas. (Not that there's anything wrong with that, nor am I suggesting that jazz musicians shouldn't be striving for that type of stretch all the time.)
*I guess the real question is, what was Strayhorn thinking when he first wrote the tune?
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