E. Morricone: Chi Mai - Diatonic Analysis

Before we start analysing this piece, you can check it's real sound here where you can download notation too. Please note that this material probably is under copyrights so use it for study purposes only.
Generally it is good to be able to play the piece from memory before you start studying it's diatonic structure more thoroughly (unless you are a music professional). 

Chi Mai is here in A scale, but is happening in the minor mode, so it's root is diatonic 6 (F#). There are interesting and less interesing parts. The less interesting bars are 1, 2 (repeating melody tone 1), bar 19 and bars 29-31 (they are just roots 6 everywhere - melody, harmony, bass). Among these 'separating' sections there are three interesting parts. The first two we can see above. These two sections (bars 3-10 and 11-18) contain the same melody motive, the second version is a bit more developed, biggest difference is at the end. The first version ends at 3 with the intention to repeat whole section beginning 3, the second version ends around 'sensitive' tone 6/5 ready to end at home 6 (what happens in bar 19).

In the melody motive there is an interesting descending diatonic sequence with three P5 down intervals. In the second vesion with interesting non-diatonic ending that has something to do with 'sharpening' it's chord 3 to 3(+3) working as dominat to following root 6 (in bar 19).

As concerns the bass line, it is quite in line with chord structure with two equivalent exceptions - chords 26 based on root 7 (see the theory part).
We can see there movements 1 down and up, but more interestingly, we can detect following sequence there: 6 2 5 1 4. It is sequence of ascending P4 intervals, probably the most important bass sequence ever. Let's be aware and notice, that subsets of bass sequence 7 3 6 2 5 1 4 occur everywhere in the music. It is not a closed circle because interval 4-7 is TT, sequence of bare P4s is not pure diatonic and after tone 4 leaves diatonic system.
As well we can notice here a sequence 6 5 4 (not only bass tones, but chords). It is very favorite progression in minor (based on root 6) songs.

What can we say about the harmony (vertically middle) part here? Let's repeat again: 6 is a tonal root here and 3 is it's dominant. We can see the dominant here in bars 10 and 18, what is in line that dominant comes before the end (tonic). Moreover (as mentioned already) we can see 'sharpened' version of the 3 here, what is characteristics for this song.

Let's look at the third part, the most prominent one:

A nice melody here. The motive from bar 21 repeats in bar 23 (what brings natural transition 7/6) shifted P4 up. As well in bar 25 there is an interesting melody motive 7 TT 6/5, why it sounds so natural although it is non-diatonic? Maybe because it is equivalent to very natural sequence 523 (or 412).
After this whole section it continues either in bar 11, what means step 73 (P4), or in ending 76, what is -M2 - returning home.
As concerns bass line, in the first fragment (bars 21, 22) we can see one-step sequence 6 7 (3) 6 5 4 We can notice some 62 and 7362 P4 sequences too. What is worth mentioning, there are exclusively diatonic bass notes (all 7) in whole song with no exception.
Harmony part here looks quite hard. We didn't say much about harmony in the first two parts neither. Harmony is logic itself when we look at it from diatonic perspective. The best is to try to play the melody and the chords as they are named in the chart and appreciate how they work. Sometimes they don't work in the root position, but if you put them into the right inversion, they work well. It is important to appreciate that there are just the 6 chords. But in more variants, with some transitions, suspensions and there is one 'exceptional chord' - it is 77(+3+5) chord. It happens. Although we don't consider chord 7 as a regular diatonic chord, it's non-diminished variants can appear.
We would like to mention 'shapened' pair 2(+3) 3(+3) at the end of the third section that works as nice progression here.

Let's look at the summary of all chords:

We can see that only 6 diatonic chords are used (77(+3+5) can be considered as a kind of exception), although in more variants each. For ear recognition it is good enough to realize and try to recognize their basic triad forms and (+3) variants, eventually sus versions.