This has been reported several times:
http://lists.gnu.org/archive/html/lilypond-user/2015-11/msg00594.html
https://lists.gnu.org/archive/html/lilypond-devel/2016-07/msg00196.html
Here's the summary made by Abraham. I highlighted point 4, since it would require a change in the source code:
There is no "Feta" font. It's called "Emmentaler", but it consists of
two sub-sets of glyphs: "Feta" (the classical notation glyphs) and
"Parmesan" (the ancient notation glyphs).Since Emmentaler comes in 8 different optical sizes, the commands to
load them only require the root name "emmentaler" to load them all.The fonts are located, not in the system's font directory(s), but in the
program's own font folder, typically
"[LilyPondDir]/usr/share/lilypond/current/fonts/".4. To use Emmentaler (or whichever is the main font, if using an
alternative) for a grob that supports the font-interface, it can be set via
the 'font-family property, but the value isn't 'emmentaler, it's 'feta
(sigh). It's a shorter name, which is nice, but it isn't technically
accurate.
In a \markup, the fonts can be accessed directly with the real font
name, like "emmentaler-23".In the NR, section A.8 is entitled "The Feta font", but the opening line
starts out with "The following symbols are available in the Emmentaler
font..."In other words, there's some inconsistency floating around.