ISA Marketing. Call zapped by Phone Tray Free but their web site seems to indicate that they do a lot of subscription renewal reminders (see http://isamarketingcorporation.com/Feature%20Services.html) This would explain why they can legally call numbers that are on the Do Not Call Registry: If you have an "existing business relationship" (you've subscribed to a magazine) they can call you to bug you when it's running out.
I've now added their number to my permanent block list.
Good luck. Most telemarketers keep changing their number to prevent people from being able to do this. They want to pick up and tell them to stop. They figure once they get your ear they can rope you in.
If your phone lets you block area codes and exchanges as well, it will be more effective, because telemarketers often have a whole bank of numbers from one or two exchanges.
I have my phone set to announce the number (but if they leave a message, I set it to shut off having to hear it while they are recording it). That way I can tell whether it's a human or a telemarketer.
The only magazine I subscribe to is Consumer Reports, and I am less than pleased with their marketing department. It's bad enough that I had to switch to their paper edition, because their web site was so full of spyware, popunders, and other sleaze and annoyances that it didn't work with my security settings.
Now I get tons of junk mail asking me to renew my subscription 10 months before it expires.