The landscape format of the paperback sounds like the collections taken from cartoon strips in newspapers or magazines, similar to some of the books in our own collection, e.g. Footrot Flats by NZ cartoonist Murray Ball, or Far Side by Gary Larsen or Garfield by Jim Davis. Usually the books have a colour cover but the pages are usually black print only and the paper quality is fairly low level. The books can look really old just because the paper quality is low and the pages start to brown with age.

However, you haven't given an indication/approximation of when you first saw the book. I know you said that your Grandfather owned it, but that doesn't tell us how long ago you first saw the book or when he may have acquired it. (I'm trying to put this diplomatically but Grandfathers can range in age from 30 to 100, depending on how quickly the generations are generated, so to speak. LOL)

My other suggestion is to try doing Google image searches to see if you recognise the book cover or the cartoonist's style.

Search terms could be, for example:

jazz cartoon book

music cartoon book

and then add or take away other words which might narrow down the search e.g.

Billy or Plunkett or 1920's etc

You are more likely to know the book or cartoons when you see them. It's difficult for me or others to look at the images and know whether it's the right book or cartoonist.