Changed Apple ID PW, can't log in to Messages, FaceTime, and other native apps.

Title says it all, or at least most of it. I recently changed my Apple ID password, and now, when I try to sign in to the programs cited above (and probably others that I haven't tried to use yet, for all I know) I get a message that "An error occurred during authentication." (I think it one case it says "during authorization". The new PW works for log-ins for just about everything else I've used it for, on 6 different devices.

iMac (Retina 5K, 27-inch, Late 2014)

OS 10.12.5 5

3.5 GHz Intel Core i%

8gb 1600 MHz DDR3

AMD Radeon R9

Thanks.

Tony