Grishka, I think my HARMONY does all that except LINUX. It is written in VB6, which is only available on Windows (Unlss anyone tells me otherwise). It also prevents me from deploying an internet version. I know a 'catter did try to get it working with WINE, but not fully successfully.

1. include support of multivoice tunes, particularly SATB choral music in modern clefs,

I think so, but let me know if it needs tweaking. Certainly up to 10 voices, and aligned lyrics as well

2. be supported by some free software for producing sheet music,

It prints sheet music itself

3. be supported by some free software for producing sound and MIDI files,

It produces sound and MIDI files itself - playback is via temporary MIDI files, which can be saved.

4. be supported by some free software for conversion to MusicXML,

It can export basic MusicXML, though I haven't fully implemented all decorators yet.

5. It supports much of abc2.1 as I understood it at the time.

It has many other facilities and functions that may or may not be unique, e.g. generating random tunes in the style of a jig or reel - some are almost usable. I am not sure that many people want to play tunes backwards, either - it is supposed to give inspiration for your composing.

Adding harmony/accompaniment to a melody line was the original aim.
It allows tune structures to be specified and played (eg AC(2ABc)) Also Melodeon tablature, string tablature, on-score drag and drop editing, note styles, tonic solfa, coloured notes - the list goes on.

Due to lack of interest, I haven't done any work on it for ages (And been too busy writing my book, which has now been published). Due to lack of LINUX, I haven't even looked to see what the other packages offer.