If High Sierra is 64-bit, it should.

Have you considered downloading the demo to check?

specs available at

https://makemusic.zendesk.com/hc/en-us/articles/216545087-System-Requirements-for-MakeMusic-Notation-Products 

>I currently have  Finale PrintMusic 2010 and want to update. <

You are not being clear. The last version of PrintMusic was 14.5. The Mac version is no longer available and it won't install in High Sierra.

The current version of Finale, 26, is available and works great in High Sierra. There is an upgrade path from PrintMusic. Log into your MakeMusic account and upgrade from there or contact your favorite reseller to see if they offer it.

Thank you! I did download the upgrade (version 26) and it works wonderfully.  I didn't want to purchase it and it not work on my Mac