Chord from a variable

[Volker Paul]

Hello,

there is something I don't understand. In the following example:

\version "2.12.3"
v = { c }
\chordmode { c }
\chordmode { \v }

I expected to see two times the same result, but
only the first expression yields a chord.
The second yields only one C note, and it is
surprisingly one octave deeper.

Questions:
How can I get a chord from a variable?
Why doesn't it work this way?
Why is this result one octave deeper?

Greetings,

Volker