Just woke up from about 8 hours of sleep!

Once's Falling Slowly Music Notes.
The song is very much similar to the classic singer songwriter songs by David Crosby, Steven Stills, Cat Stevens, James Taylor and Neil Young. Which can be framed to the 1970s genre.
Among other things those guys (CSNY) are known for their intricate vocal harmonies.
The song’s genre could be labeled under soundtrack, indie or pop.
The combination of the acoustic guitar and piano brings out complementary tones which are also emotionally effective.

Most classic guitar based songs start with C.
The chords of the song are C, F, G and Aminor-- similar to the famous and classic Led Zeppelin’s Stairway to Heaven.
The beginning of the song is scale-like. On the piano it goes:
C, D, E, D.
C, D, F, E.
C, D, E, C-D.
E, F, G, F.
E, F, A, G.
E, F, G, F-E.
The chorus is just as simple:
C, D, B, C.
C, D, B, C.
C, D, B, C-F.
The harmony is one and a half steps down from the melody.
It gets closer by moving one steps away, then two and a half after each chorus.
The surprise high note of the chorus is of the F chord.

The style of the song is a stripped down, singer songwriter acoustic. Which is almost stereotypical singer songwriter.
Takamine— standard acoustic electric model guitar. I assume was the model used in the film and song.

INTRO
[C] [F] [C] [F]
E --------0------- --------1---0--- --------0------- ----------------|
B 1---3-------3--- 1---3----------- 1---3-------3--- 1---1---1---1---|
G --0---0---0---0- --0---0---0---0- --0---0---0---0- --0---0---0---0-|
D ---------------- ---------------- ---------------- ----------------|
A 3--------------- ---------------- 3--------------- ----------------|
F ---------------- 0--------------- ---------------- 0---------------|

VERSE (play 2x)
[C] [F] [C] [F]
E --------0------- --------1---0--- --------0------- ----------------|
B 1---3-------3--- 1---3----------- 1---3-------3--- 1---1---1---1---|
G --0---0---0---0- --0---0---0---0- --0---0---0---0- --0---0---0---0-|
D ---------------- ---------------- ---------------- ----------------|
A 3--------------- ---------------- 3--------------- ----------------|
F ---------------- 0--------------- ---------------- 0---------------|

BRIDGE
[Am] [G] [F] [G] [Am] [G] [F] [G]
E ---------------- ---------------- ---------------- ----------------|
B ----1---0-----0- ----1---0-----0- ----1---0-----0- ----1---0-----0-|
G 2---------0----- 2---------0----- 2---------0----- 2---------0-----|
D --2---2-----0--- --3---3-----0--- --2---2-----0--- --3---3-----0---|
A 0--------------- ---------------- 0--------------- ----------------|
F --------2------- 0-------2------- --------2------- 0-------2-------|

CHORUS (strummed, 4x)
[C] [Fadd9] [Am] [Fadd9] [F]
E 3--------------- 3--------------- 0--------------- 3-------1-------|
B 1--------------- 1--------------- 1--------------- 1-------1-------|
G 0--------------- 2--------------- 2--------------- 2-------2-------|
D 2--------------- 3--------------- 2--------------- 3-------3-------|
A 3--------------- 0--------------- 0--------------- 0-------0-------|
F X--------------- 0--------------- X--------------- 0-------0-------|