Well, that subject is VERY subjective, but there are some points commonly agreed upon: Chord progression plays an important role, but any given progression can have a different feeling depending on the context.
For example, take the vi - IV - I - V progression very common in pop music.
Sometimes, when played ballad-style and flowingly, it can give an image of desperation, and resolve.
But played with gusto, it could even suggest agitation or anger.
The piece that you mentioned, Adagio for Strings, uses a liberal amount of suspensions.
Often times the dissonances resolve to minor chords, rest for a bit, followed by a stronger but short intense passage before settling back down to a minor chord.
This, to me, suggests "fighting a losing battle with despair."
Texture and timbre are huge contributors.
I already mentioned it in my last bullet point.
Many, many, many pop songs have the same four chord progression (I - V - vi - IV or vi - IV - I - V), yet the good ones manage to remain unique.
It's little things, like the strings on the guitar, how mellow are they?
Does the piano have a slight ring to it, or is it percussive?
All these things can create a myriad of different emotions.
Both of the above tie in with tempo in obvious ways.
Mellow, sadder, songs tend to be played slower so that one can appreciate the unique textures.
Like I said, it's a VERY, VERY subjective area, but hope this helps.
music.stackexchange.com/users/234/cemulate
Very interesting question.
For a computer to understand whether song is happy or sad, you must define "happy" and "sad" first.
This alone seems almost impossible, since every human has his own understanding of happiness, sadness and all other emotions.
You can define "sad songs" as the "songs which induce a sad mood in the listener".
In this case, how can you know what effect the song will make on every individual human?
For example, you can write a very happy song with major tonality and lyrics about summer and children, and an old man will cry while listening to it, because he remembered that his son died last summer.
As for the theory: many people think that major = happy and minor = sad.
This is, generally, because of the relation to major and minor chords, which have a very different mood to them.
Major thirds, which are the basis for major chords, sound happy and bright; and minor thirds, which are the basis for minor chords, sound dark and sad.
This is the impression people usually get when they listen to the interval or chord alone.
When chords line up to make up a song, the mood of the song is produced not from individual chords, but by tension and release made by chord sequences.
You cannot tell that a song with minor tonality will be accepted as "sad" or in major as "happy", because tonality does not matter; A minor and C major have all the same notes.
It is tension/release and the listener's interpretation.
I don't think that computers will be able to understand music in any imaginable future.
music.stackexchange.com/users/431/Silver Light
As @user234 noted, this is very subjective, and depends hugely on your musical background and the culture that you're from.
Ever since these started mixing and merging, the matter became even more complicated.
Basically, there's nothing innately 'sad' or 'angry' in a given chord or a progression, it's just the way you've personally learned to associate them with some context.
I remember reading in some book about chord types, where it was mentioned that (and I quote very loosely) '
major resembles this
, minor resembles that and [something
more complex - aug? sus?]
resembles
Bambi deer emerging from the bush covered in mist droplets'.
While this may sound silly, I think that it provides huge insight into our musical perception, and emphasizes how the musical gustos of the generation that was raised on cartoons were shaped.
Of course everybody might have watched different cartoons (I for example, having never seen Bambi, was amazed
how much classical music I found familiar by reference to Tom and Jerry and Looney Tunes)
hence their associations might be slightly different.
Which, if you think of it, makes matters quite interesting.
:)
Ultimately some generalizations may be drawn, but immediately someone will beg to differ and that's normal
I guess.
music.stackexchange.com/users/519/neuviemeporte
"Happy" and "sad" songs are entirely defined by one's sociocultural environment.
That is to say, the definitions are entirely socially-constructed and largely subjective.
The current state of western music aligns major with happy and minor with sad, but back in the 17th century, a piece of music was sad regardless of the tonality as long as it had the "dying fall" in its melodic line.
The "nature" side of this "nature vs. nurture" argument is largely explained by this excellent video:
music.stackexchange.com/users/133/NReilingh
The feelings that you want to transmit es very relevant with scale or chords that you use.
For example: Minor scale and chords sound dark and sad (ballads).
Major scale and chords sound bright and happy (classic pop).
Power chords sound powerfull, with a lot of energy (rock, metal,punk).
At last, all this musical resources are very related, but they sound very different.
music.stackexchange.com/users/16864/Adrilojea
The "sound/tone/timbre" of the instruments and the atmosphere created by them give music a certain personality.
For soundtracks, the context of the movie gives personality to the music.
Other than this, I think it is an individual that gives personality to the music.
That is, it also depends on what mental and physical state you are in.
As already mentioned, it is a very subjective thing.
Same music can evoke different feelings in different persons.
The most important thing when listening to any music is how "you" "feel" it.
music.stackexchange.com/users/23908/LoveEnigma
What makes a piece of music sound angry, dark, sad, happy, or otherwise?  "La Chute" by Yann Tiersen sounds so angry to me and "A Dark Knight" from "The Dark Knight" movie sounds so dark and mysterious.  "Adagio for Strings" by Samuel Barber is a pure expression of sadness, and of course there's no need to even talk about "Adagio of Concierto De Aranjuez".    What gives a piece of music its personality?
What gives a piece of music its personality and feeling?
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music.stackexchange.com/questions/3066
music.stackexchange.com/users/245/Chiron
The feeling of a piece of music is very subjective and also culturally related. However, texture and timbre contribute to the perceived feeling as do, the "sound/tone/timbre" of the instruments and the chord progression. As for the theory: many people think that major = happy and minor = sad. The answer to this question will be very subjective and may well depend on your social and cultural upbringing. However, chords, chord progressions, timbre and tone will all contribute towards the feeling or character of a piece of music.
Chords and chord progressions can play a significant part in whether a song is perceived as happy or sad. The timbre and tone of instruments will be a signfiicant contributing factor. The answer to this question will be very subjective and may well depend on your cultural and social upbringing.