It looks like stocks and crude are starting to pay closer attention to each other.

In the past few months, as stocks surged while crude stagnated and then slumped, the commodity and the measure of large-cap stocks actually began to experience an inverse relationship. That is, on a day when oil settled lower, stocks were more likely to rise than to fall.

Since then, the pair has begun to enjoy a closer relationship. Over the past 60 sessions, WTI crude oil and the have seen a correlation of about 0.28. While this hardly suggests that they are identical twins, it does imply that oil's daily move is now more relevant to equities.

"The dollar has come under some pressure of late and this pushes up oil as well as the U.S. dollar value of offshore earnings," Max Wolff, market strategist at 55 Capital, wrote to CNBC. "This generally increases correlation."

In other words, currency moves are driving both stocks and oil.

But for a truly brotherly relationship between the S&P and crude, one must go back to early 2016, when oil's fall into the mid-$20s, and subsequent rebound, led it to be a primary focus for stock investors.

Looking forward, traders say oil is likely to remain in its recent wide range.

Most traders "can't see any reason for it to go any higher. And technically, between $48 and $54 seems to be a very comfortable spot for crude oil right here," Harvest Volatility Management portfolio Manager Dennis Davitt said Tuesday on CNBC's "Trading Nation."

From a fundamental perspective U.S. producers have become so efficient, "they can operate at $50 a barrel, and they will just keep flooding the market as long as the price keeps staying at these levels."

Crude oil ticked higher on Thursday morning, after settling on Wednesday at $51.15.