Check out Lilypond: http://lilypond.org/
It's free and powerful, and although it won't do audio playback, I believe it can do the rest of what you ask.
It's text-based, and if you are at all familiar with TeX or LaTeX, Lilypond will feel similar.
It has a somewhat steep learning curve, but there are some GUIs in active development that make things easier, and there's also some software that allows for input via MIDI keyboard.
Edit:
Seems Lilypond can output MIDI files, so presumably you could get audio playback that way.
music.stackexchange.com/users/36/Alex Basson
MuseScore is getting some attention.
It's free, cross-platform, and imports and exports MusicXML.
I have not tried it.
music.stackexchange.com/users/None/
rosegarden is another option.
It's mostly meant to be used as a MIDI sequencer/DAW, but has a score facility which I believe will let you edit scores directly.
It's only available for linux.
music.stackexchange.com/users/1563/intuited
I agree with everyone else that is suggesting Lilypond.
Here is a Linux Journal article on creating Schenker Graphs with Lilypond .
music.stackexchange.com/users/1374/ObscureRobot
As little addon to the Lillypond suggestion: Check out this snippet from the Lilypond Snippet Repository I also found the channel #lilypond on Freenode being quite a good resource when getting stuck with something.
music.stackexchange.com/users/42816/nath
With Lilypond, the example of the OP could be drawn like follows: \score { \relative c { \time 2/4
\clef bass
\key
f \major << { \override NoteColumn.ignore-collision =
##t \stemDown \phrasingSlurDown \phrasingSlurDashed \once
\override
NoteHead.duration-log =
#1 \once
\override Beam.positions
= #'(-6.47 . -6.47)
\once
\override
PhrasingSlur.control-points = #'((1 . -.5)
(3 . -5) (22 . -5) (24 . -3)) f8*4[\( ~ \hide Stem f8*4] ~
f4
*2( \newSpacingSection g4 a)
( \phrasingSlurSolid \undo \hide Stem f,\)\()( \once \hide Stem c')
d\)\
(( \once \hide Stem a')
\once
\override Stem.length =
#9.27 \newSpacingSection
\time 4/4
bes8
*8/3\)\( \once \hide Stem e,4
*4/3( f) \newSpacingSection \time 8/2 \once \hide Stem d4
*2 \once
\override Beam.positions
= #'(-5.97 . -5.97)
\once
\override Beam.transparent =
##f \once \hide Stem e8*4[\) \once
\override
NoteHead.duration-log = #1 f8*16] }
\\ { \hide NoteHead
\hide Stem \slurUp s2*6 \once
\override
Slur.control-points = #'((1 . 3.5) (3 . 5) (11 . 4)
(13.5 . 1))
bes2
( bes,4*4) \undo \hide Stem e4*2 } \\ { \hide NoteHead
\hide Stem s2*6 \once
\override
Slur.control-points = #'((1 . -7) (10 .
-10)
(17 . 7.5) (20 . -.5))
bes'2( s4 e,4) } >
> \bar "|." } \layout { \omit Score.
TimeSignature }}
music.stackexchange.com/users/54798/Jasper Habicht
What is the best free or cheap music editing software available? I am looking for something to write and edit scores with. I know that Finale and Sibelius are the best on the market, but I wouldn't use them enough to justify the price.  I don't need many features, though here are a few that I could really use:   Audio play back  Ability to write without a time signature  Able to draw non-conventional notation (i.e. Schenker graphs)   Here's an example of what I'd like to draw:
Is there any notation software that supports unconvential notation like Schenker graphs?
music.stackexchange.com
<software>
music.stackexchange.com/questions/4718
music.stackexchange.com/users/1546/Reina Abolofia
For notation software that supports unconvential notation like Schenker graphs try MuseScore, rosegarden, or Lilypond. There are a number of different programmes that might be suitable, such as Lilypond, MuseScore or rosegarden.
There are a number of different programmes that might be suitable, such as Lilypond, MuseScore or rosegarden.