First make sure you have Timidity installed on your computer. It's a native application that plays the midi output from the game. On Ubuntu and other Debian based systems you can install Timidity by running the following command:

sudo apt-get install timidity

Start the game and choose TiMidity port 1 to be the output device.

Synthesia tries to fix a bug in windows sound systems by decreasing the master sound volume when closing the game. On Wine Synthesia will turn the sound volume to 0%. This feature can be disabled by making the following registry change to the settings of the game:

[HKEY_CURRENT_USER\Software\Synthesia]
"Disable Auto Volume"="1"

The game comes with two renderers: the OpenGL one and the Direct X one. Both are working perfectly under wine, but Direct X needs some tweaking.

If you want to use the OpenGL renderer add the following registry entries:

[HKEY_CURRENT_USER\Software\Synthesia]
"Renderer"="opengl"

If you want to use the Direct X you must first install the Direct X to your Wine installation. I don't tell here how to do it, because the OpenGL way is so much easier.

winetricks gdiplus