Apps similar to Perch include Grav, which is free and open source. Other options are Backdrop CMS. Between them they cover self-hosting and the web.
Grav is an easy to use, yet powerful, opensource CMS that requires no database. In a nutshell, installing Grav is a matter of unzipping the file. It is fast, has sophisticated caching, and a light footprint for optimal performance.
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Backdrop CMS is a simple, lightweight, and easy to use Content Management System used to build attractive, professional websites. Use it for everything from a single-administrator's personal blog site, to a complex, multi-role, business e-commerce platform.
