Red Sox almost accomplish unusual feat

Over their last four games, the Boston Red Sox have posted scores of 15, 22, 8, and 2.  Had it not been for a late rally last night, they would have finished the last of these games with just one run instead of two, and this would have made for what must be an uncommon if not unprecedented oddity.  They’d have had four consecutive different scores, each one exactly 7 runs apart from the closest of the other scores.

What they did accomplish is probably also quite rare: four consecutive games in which no two scores are within 6 runs of each other. To see if any other team has ever accomplished this feat, I might look through’s play index for games with 18 runs scored or more and then look through game logs to see the scores of the adjacent games, but with over 300 results to look through, that’s more work than I can finish on my lunch break.  So I leave it to you, baseball community:  can you find any team that has done this before?