(Following is a lengthy discussion on multiple voices - aimed at the newbie (such as 
myself) and based on my recent experience.  Apologies to the group's
experienced people for the length.)

Amelie has already answered the questions and her answer to #2 is right if the 
question is truly about chords, the following might help if it is about multiple
voices.  (Since you are new and talking about hymns, I think you want multiple voices)

The basic difference I like to use is:

- A chord is a 'multi pitched note' played on one instrument and shows up as multiple 
notes stacked vertically with a single ornament or articulation.  Thus
Amelie's statement about a single slur holds true.

- Multiple voices are usually different instruments (Soprano vs. Alto, 1st and 2nd 
Trumpet, and so on) that may be shown on the same staff for convenience.  Each
voice has it's own unique ornament or articulation, but if on the same staff the 
duplicated ornaments may hidden.  (Notice that an instrument capable of chords
usually is also capable of multiple voices.  A piano is a good example, so you can get 
both chords and multiple voices.)

So, there are a lot of possibilities for multiple voices.  Refer to the templates 
which are accessible on the web from the Lilypond home page (at
http://www.lilypond.org)

To look at your question on the slurs, consider the following (totally contrived) 
example:

Soprano:  a4 c ( ) b b ~ b a
Alto: a4 c ( ) a g e ~ e a

Using the 'chord' technique, which will cause the slur problem you notice, this could 
be written as

1.6: a4 c ( ) <b a > <b g > <b ~ e > a
1.7: a4 c ( ) <<b a >> <<b g >> ~ <<b e >> a

One alternate is to write the parts separately and combine them on a single staff as 
follows:

Soprano = \notes { a4 c ( ) b b ~ b a }
Alto = \notes {  a4 c ( ) a g e ~ e a }
\context Staff = SAvoice { < \Soprano \Alto > }

To force the Soprano stems up, Alto stems down (and appropriate slur, tie, etc. 
positioning) you could use

\context Staff = SAvoice { < \voiceOne \Soprano \voiceTwo \Alto > }

A second alternative is to use a 'main' and a 'harmony' voice allowing chords in the 
'main' except when it causes problems:

Main = \notes { a4 c () b <<b g >> <<b e >> ~ <<b e >> a }
Harmony = \notes { s4 c () a s s s s }
\context Staff = SAvoice { < \Main \voiceTwo \Harmony > }

Notice that the \Main does not force to voice one or voice two, but the \Harmony does. 
 I find this a generally pleasing effect but you may need to turn off
specific harmony notes using {\property Voice.NoteHead \set #'transparent = ##t  
...note(s) here... \property Voice.NoteHead \revert #'transparent}.

A third alternative is to use 'parallel threads' inline as follows (see the mailing 
list discussion this week titled "stems in multiple voices per staff"):

SA = \notes { a4 < { c () a } \\ { c () b } > <<b g >> <<b e >> ~ <<b e >> a }

Again, you might need to play with the trasnsparency property of NoteHead, Stem or 
Beam to make this work for you, and if you do, remember to turn it back on again
using the \revert capability.  (Also note that \voiceOne and \voiceTwo are 'reverted' 
to normal using \oneVoice ... use \voice? and \oneVocie as a bracket around
the notes in question.)

Hope this helps
/Hans




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