How to map a song time signature that goes off beat?

Hi guys.

I'm familiar with tempo mapping a song. The best (read easiest) are the pop songs with only 4/4 time and a steady rhythm. But it gets harder when the time signature must also be mapped.

Sometimes I find a song puts me off. For example, "Heaven is a place on earth" jumps to 2/4 for a bar then switches back to 4/4. I found this out when I noticed my bars were off by two beats. I found a score and then could insert the changes to match.

But other songs do my head in after a while. For example, I've been mapping out "In a big country" by Big Country. And it has some unusual changes. In the beginning there is an obvious change to 2/4. But finding a score was proving difficult. One was a guitar tab with a 2/4 change in an odd spot. There is a four beat drum fill before the main drum rhythm starts, and putting in a 2/4 before or at the drum fill lines it up.

But then there is another change later in the song that is doing my head in. A drum fill that goes one beat off from 4/4 timing, which really is odd! Just as the chorus repeats and the drums drop. I can only compensate by going 2/4, 3/4, then 4/4 to get an odd 5 beats in a row, but it just seems wrong. I can also change it to 1/1 in the odd section but that looks even more wrong, even if it perfects the timing. But I can see there is an extra beat length right on the end of the bar. It sounds all right musically but it looks wrong in a grid.

I know you can buy a score but most are transcribed and not always the original song. I don't want to pay for a cover version! I need the one for the exact song I'm working with. I'm not trained in musical theory and just have basic knowledge. So I can't make an educated guess at what is going on, I just see it when it goes wrong. What I do see is patterns of beats and where they line up and where it doesn't.

What do you guys do when you need to map out a time signature?