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From a midi, I extracted this set of notes. Each row is a set of notes played together. The order is not temporal order, as I write each set only once.

I want to simplify the music (I will play it with a PSG) to max three notes at a time. How should I simplify the 4 notes sets?

The complete MIDI can be downloaded here.

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I feel like writing a quick little program to parse these, but the feeling will probably pass... –  Bob Broadley May 30 at 16:35
    
Wall of note names wasn't really practical -- I've put it into a linked gist. –  NReilingh May 30 at 23:27

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Right, this is the first time I've done this - I'm going to post another answer! My other answer deals with the process of working from frequency lists and more general comments (and I didn't realise that your chord list wasn't temporal - by the way, musicians would never, ever, ever think like this - it's like trying to work out what a painting looks like by being given a list of the colours in it!). This answer deals with the specific chords in your MIDI file...

Now that I've looked through the MIDI file, it's pretty clear that most of the track is two guitars playing the same thing (in unison). You only get four note chords where they play different notes. The first time this happens you want to retain the bass notes and very top notes, so you want to lose the note just above the bass notes. Therefore, F2 C3 D#5 G5 becomes F2 D#5 G5 and D#2 C3 D#5 G5 becomes D#2 D#5 G5 (this happens a few times):

enter image description here

I would lose the second note up in the next different four-note chords too. So, D#2 C3 G#4 C#5 becomes D#2 G#4 C#5 and F#2 C#3 G#4 C#5 becomes F#2 G#4 C#5:

enter image description here

I think that's all of them! Great song, BTW…

Well, this certainly hasn't been the most conventional way to analyse music, but it has been a great "puzzle" to solve, and a really different way of doing things. I'll put some excerpts of the actual music in this answer later, so everyone else knows what we're talking about!

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I had a feeling it was one of the inner voices that would go, but I wasn't about to make that call without more context. I'm resisting the urge to be pedantic about the proper spelling of accidentals, since MIDI doesn't care. –  Caleb Hines May 30 at 20:39
    
Thanks, Caleb - I didn't do any proper editing of the MIDI after importing it, just enough to see what was actually going on!! –  Bob Broadley May 30 at 20:40
    
thank you very much Bob! This really helps! And yes, slayer rocks ;) –  Fabio Dalla Libera Jun 2 at 0:11

HAVING GOT A LOT MORE INFO FROM THE OP, MY OTHER ANSWER (BELOW) DEALS WITH THE SPECIFICS OF THIS SONG. I'VE LEFT THIS ANSWER HERE TOO, AS IT DEALS WITH THE PROCESS (FOR ANYONE WHO DIDN'T SEE THIS QUESTION BEFORE, IT WAS ORIGINALLY JUST A LIST OF FREQUENCIES AS FLOATING POINT NUMBERS…!)

Your question is a little unclear, but let me see if I can suggest some ways forward for you.

Firstly, reading what I presume is a series of chords (notes played together), as lines of multiple frequencies is pretty tricky. I would suggest that you need to turn these into pitch names first, whatever you want to do with them before playing them with a PSG.

Converting your list of frequencies into pitch names or MIDI numbers.

It's relatively easy to find out which pitches (and so which MIDI notes) these frequencies correspond to. There are many tables online with this information. Here is one, which also has a frequency to note converter. Even using this it would still take quite a bit of time to convert all your pitches one at a time. Ideally, you would use some kind of software solution, which could take your list of frequencies as input and give you pitch names or MIDI notes out.

I haven't done this for you - my life is too short! But, converting your first set of four pitches gives: Eb C Ab Db. This is an Ab major chord with an added 4th. This is quite an individual sounding chord. If you wanted to simplify this, by missing out one of the notes, to make a three note chord, you will certainly lose some of the character of this chord. However, I suppose you could lose the bottom note and retain the "major-chord-add-4th" character. I'm not going to go through all your frequencies and convert them to then analyse what would be the best way to simplify them. If you do want to take advantage of the expert advice on music.SE, in order to get suggestions for how you can simplify each of your four note chords down to three note chords, you will get far more responses if you give the pitch names of these frequencies.

Once you have decided which pitches to miss, I'm not sure whether you would want to play them using frequencies or MIDI numbers; presumably either would work, depending upon the format required by your PSG (sorry, I'm no expert on this…)

EDIT: Okay, having had another look at this, you have only actually got 5 four-note chords, and I think one of these is probably wrong (77.7817 138.591 77.7817 155.563), as it has the same pitch twice - maybe this is supposed to be on two lines(?) As it happens, your other 4 four note chords all have an interesting property, they fall into a pair and two single chords, where in each case the bottom note has been present in a large number of chords leading up to them:

77.7817 130.813 415.305 554.365

77.7817 130.813 622.254 783.991 (preceded by 10 chords with 77.7817 as bass note)

87.3071 130.813 622.254 783.991 (preceded by 6 chords with 87.3071 as bass note)

92.4986 138.591 415.305 554.365 (preceded by 1 chord with 92.4986 as bass note, but also followed by 6 more with the same bass note)

This being the case, you can omit the lowest pitch of these four note chords - the fact that it is present in the preceding chords means that the ear "fills in" this note for you. They are known as pedal notes, and in this case they have been strongly established and so probably don't need to be repeated in the four note chords.

This has required quite a bit of deduction - it would be far easier with conventional notation to look at!

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thank you very much for you comments! I added the notes. actually, the order in the list is not the temporal order, but simply a lexicographical ordering of the sets. the repeated note probably comes from the fact that the mid has two tracks, and there can be the same note at the same time in the two tracks –  Fabio Dalla Libera May 30 at 19:05
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It didn't even occur to me that these weren't ordered by time. To understand which notes in a piece are more important, it's crucial to know their function in terms of horizontal melodic lines, not just vertical harmonic combinations. It's impossible to get a feel for the former from the way you've listed them. Providing the midi file was a really good idea though (I'm just not in a situation where I can look at it right now). –  Caleb Hines May 30 at 19:19
    
Back to the drawing board then... –  Bob Broadley May 30 at 19:25

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