I've done two things. First, I've rewritten your code in a way that's easier for me to read. Second, and more to the point, I've changed the "outside" set of slurs to phrasing slurs. AFAIK, you can't nest regular slurs. Please take a look at <http://lilypond.org/doc/v2.19/Documentation/learning/ties-and-slurs> .

That's not true anymore: In recent versions (starting at some point in the 2.19.xx series), slurs can be assigned a "name" allowing them to be referenced, and in particular, nested (cf. http://lilypond.org/doc/v2.19/Documentation/changes/index.html):


\version "2.19.83"
\language "english"

\fixed c'
{ <<
  {
    f4 e8 c8~( c4 e8\=inner( f8\inner) ) |     % the \( and \) are phrasing slurs.
  }
  \\
  {
    f4 e8 c~ 4~ 4 ||
  }
  >>
  }

Though I admit that the layout engine handles the phrasing slur better in this specific situation.

By the way, it's even possible to do

\version "2.19.82"

\fixed c' {
  c\=1( d e^\=2( f\=1) g a\=2)
}

IMHO this feature alone is worth the (negligible) trouble of switching to recent development versions.

Best
Lukas

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