Midi import issue

I don't have Synthesia, but I have experience in attempting to load in MIDI files. It's often hit or miss depending on its being a human performance, or a digital programming, and even then the digital programming can use offsets and variations rather than a clean mechanical application of notes. I usually use Sekaiju to look at a piano roll quickly to tell. For instance, here is some of Sekaiju's piano roll view of your Midi:

As you can see, it has offsets everywhere. If you want a nice clean sheet music from this, you're going to have to quantize it first and then see how it looks. Importing into Musescore standardly, here's a small portion of the results:

 
This isn't very pretty, but if you really know what you're doing you can take it from here and manually start making it look right. Another option is to import into another Midi program (Musescore isn't really a MIDI program) like the mentioned Sekaiju or Rosegarden or something. If I do a quick quantization application in Sekaiju, save to midi, then re-import into Musescore, here are some results:

This may give a better starting position to manual work depending on your methods.
 

Another option to show you is Rosegarden. I imported the MIDI file, used its quantization function, and then exported not to MIDI but to MusicXML and then reimported this into Musescore. The result in Rosegarden itself looks pretty decent after a quantization.The result looks like this:

 
After exporting this into MusicXML and importing into Musescore, I get

Looks like it's using hidden rests to help aid the design: With the invisibility option not showing in Musescore finally there is:

 
Anyways, you can see that's it's not just a one button job. I've seen forum posts asking others to do things for them like transcribe a midi or pdf and it's like asking someone to spend hours of work out of gratuity. I always try to first import into Musescore to see what it looks like, and if it's a bloody mess then use either the old fashioned by hand method depending on what it looks like or an import/quantize like mentioned above to be imported afterwards. or attempt some conversions in another program. If you go manual, it's nice to have two tabs open of the messy version and a clean manual form to switch back and forth. It's good to be aware that sometimes with multiple instrument MIDIs, one or two instruments will work just perfectly by default, and then one instrument will be all messed up looking. You can always copy and paste the good parts and then do some manual input of the problem-causing instrument. Piano tends to give the biggest problem because of the grand-staff, multiple voicings, and being able to have a wide polyphony. I hope this information helps you a bit. Good luck.
 
P.S. I think I read that they're working on better midi import for later.
 
P.P.S. You might check to see if Synthesia has MusicXML export so you can import that into Musescore, or maybe it has some sort of quantization function before saving to a midi file. If not, you might want to send them a feature request; it wouldn't hurt.
 
P.P.P.S I'd be interested to see what the default form of notation looks like for this midi file if you'd be willing to take a screenshot and post it here.

That looks much cleaner :)
It's strange though that right after the first two notes of the pick-up measure, Synthesia uses a rest, yet if you look at the raw MIDI as in the first screenshot of the post from Sekaiju, there's clearly a note being played along with the extended low note; this isn't done with the Synthesia results, so like you said it's doing some sort of quantization with rests on its own for notation display. It definitely did a better job in separating bass and treble clefs.
 
If Synthesia doesn't offer a score export like MusicXML or a PDF of the notation version of MIDI, then they are implying that their notation results aren't intended to be usable outside their program. If it's a paid-for program, it'd definitely be nice if it allowed MusicXML for further manipulation in another editor, and I'd talk to them about that.
 
By the way, if this piece of music is an actual tune and you know the title (it sounds familiar), you might want to look around on the Internet to see if there is an alternative MusicXML or PDF document of the score. Maybe someone has already done this. Either way, you're quite right that Musescore has some hiccups with MIDI importing depending on the data, and since MIDI isn't designed as a music notation file type (each importing program has its own algorithms it seems), your best bet is to sharpen your skills to do it manually and/or use importation as a guide; but not necessarily: I've had MIDI files that imported perfectly without requiring any editing for the most part, but they were all very "on the spot" with monophonic instrument lanes that I later combined manually into multiple voicings.
Good luck with what you're trying to accomplish.
 
Chordially

This piece is freely played (not in strictly metronome). In musical term: ad libitum or a piacere (play in free time).

Not a way to correctly notation this. (also Synthesia's notation isn't correct. Just looking clear)

i found original: http://www.ireland-information.com/irishmusic/dannyboy.shtml

download midi and open with musescore.

note: for flute part, select maximum voices : 1