In my effort to identify a typeface (the one mentioned in this post), I contacted one of the music publishers who used it in the 1920s.

The company responded;  unfortunately, the representative does not know the identity of the typeface.  However, he offered to work with me to search their catalogue to identify as many of the glyphs as possible.  

As we were discussing particulars, the representative brought up the matter of copyright.  He stated that the company possesses copyright to 600 pieces of music, and he suggested that copyright might extend to the title typeface.  

My understanding of is that either 1) one has rights to the intellectual property of a typeface, 2) one licenses said rights, or 3) one does not have them.  Can it be said the company possesses copyright by virtue of it being used on the titles of sheet music?  More specifically, is copyright something that has to be established, or is it assumed unless successfully challenged?  Put another way, who has the burden of proof?

There aren’t easy answers for that unfortunately. For works like music and photography, the rights are well-established, for typefaces it is rather tricky and handled differently in different jurisdictions. 

But if these letters were already published in the USA in 1902 or even earlier, you can be sure that the original design is public domain now, no matter who might have had a copyright at some point. Any possible copyright is already expired.