Shockingly, I will try to explain how music works. First I will explain the language of music that actually you already know quite well. Second I will explain how art such as music can appeal strongly to people. Third, I contrast with literary art.
Language of Music.
There is a 'language' in music. Actually you must know a lot of the language quite well. You learned the language if only because of the hours or so a day you have been exposed to music via TV, radio, movies, and more. By hearing the music in this language, you have picked up the language.
In simple terms, the language has some sounds that correspond to and somehow express emotions. That is, for each common emotion, there are some sounds that express it. For the common emotions, people know some corresponding sounds very well.
To get started with the language, play something just one note at a time on just the white keys on a piano. Start on C, play some other notes, and end on C. Then what you will hear is that some emotional experience starts, continues, evolves, and develops, and then ends.
Why do you hear this? Because starting on C and playing just on the white keys you will hear that the music is just in the key of C major. You know the key of C major very well, will know that the music is all in C major, and will recognize when the music gets back to C and seems to end. Indeed, in much early music, it gets back to C too often and sounds boring and then, from hitting C too often, irritating. That is, each time the music hits C it seems to stop; so, each few notes the music seems to stop, and that's about as much fun as a car that goes down a road but stops each few feet. Why did the music return to C so often? Because the composer was not very good and couldn't think of anything better to do.
So, start on C, go through this and that, and end on C. Due to the language you have learned, the return to C sounds like the music 'resolves'.
Then for the goes through this and that, if get away from the white keys, then things sound different. Why? Because your ear has been very well trained to hear leaving C major. Leaving C major can add variety to the this and that in the middle. So, when you get back to C, the resolution feels stronger.
For more in the language, playing more than one note at a time is 'polyphony' and offers a stronger beginning than just C itself, more variety during the this and that, and stronger resolution as we end. You have already learned these things as you learned the language.
The variety of polyphony is large and permits sounds that are fairly clearly like anger, frustration, happiness, tension, anticipation, and, of course, resolution.
E.g., if play two notes together that are close in frequency, then the sound is harsh and strident. So, the sound can represent anger, tension, or danger. You won't miss this part of the language for even an instant.
E.g., for anticipation, the note one lower than C is B, and it is in frequency close to C, that is, only a semi-tone lower. When the music plays B, you anticipate, correctly from the thousands of hours of music you have heard, that next the music will play C and 'resolve'. If the composer does not play C next, then he can delay the 'resolution' and keep you 'hanging' and strongly continue the this and that part. Actually, you know this very well. So here is some musical language you understand for 'anticipation'.
Then for Exercise 1 in Composition 101 to create some extended musical experience, start with something with a little tension, add this and that with a lot of tension, anticipation, etc., and then resolve and end.
There's some advertising music that does this effectively in just 21 notes: To be more explicit, as you play on the white keys, starting at C and going up (in frequency, to the right) you will play D, E, F, G, A, B, C -- easy enough to remember.
Well the first seven notes are C, D, E, C, D, B, C. I will put after each note the number of beats:
C 1, D 1, E 3, C 1, D 3, B 1, C 3.
Wonder of wonder, for some music trying to sell soap or some such to millions of TV viewers, it starts on C, uses just four notes, and ends on C. We're talking really simple musical language here: Anyone who doesn't know that much musical language won't have money enough to buy the soap anyway!
Then next seven notes are
D 1, E 1, F 3, G 1, E 3. F 1, D 3
So, these seven notes are much the same as the first seven except start just one note higher, on D instead of C. So, starting higher, there sense is that something has progressed. Since these seven notes do not end on C, the music seems not to be over and the viewer is left hanging, that is, listening for more, just as the advertiser wants.
The last seven notes are just the same as the first seven and end on C just as the ad ends thus resolving the music.
There is a little more: In the first and last seven notes,
C 1, D 1, E 3, C 1, D 3, B 1, C 3.
the first two notes are short and, thus, rise quickly; this is as if something was starting and helps get the attention of the viewer. The next three notes sound like a sigh and make the viewer comforted and more relaxed. The last two notes return to C with a nice resolution, especially since the B lets the viewer anticipate the C and, thus, follow along. All in just seven notes.
Hearing this you wouldn't miss the musical language.
A good musician with even just a violin, can add other elements of musical language, you readily recognize, with loudness, vibrato, brightness, harshness (press harder with the bow and play closer to the bridge), urgency (play faster and start notes suddenly instead of gradually), etc. Net, a good violinist can use musical language elements you already know well and, thus, be very 'expressive'.
For larger collections of instruments, can get much more in variety that can represent other emotions. Some of these representations are widely and clearly understood, and some, say, from some new music, are not. So, yes, there is a musical language, and some of it is widely understood and some is not.
In the end, in my view, classical, non-programmatic music is not so difficult to describe: The musician has an emotional experience that goes through various cases of this and that. So, he writes some music that roughly represents that.
If the music is 'good', then it is 'general' (sometimes people say 'universal'), that is, does well representing more emotional experiences than just the one the musician had and for many listeners seems to represent an emotional experience they have had, likely different experiences for different listeners.
One of the better approaches to reaching many listeners is to represent a person's yearning, typically for emotional security, and then struggle against obstacles with lots of variety during the struggle and finally resolution or victory. That is, everyone want emotional security, and nearly everyone has had struggles and pursued them with energy, frustration, anticipation, success, setbacks, etc.
My favorite example of such music is the solo violin piece the Bach 'Chaconne'.
The Appeal of Art and Music.
There is a fact about people and art: If people see some of their stronger emotions about some of their experiences displayed in front of them, then they like it, maybe because it confirms to them that they are not alone in such emotions. E.g., it can be that all 1000 people in the concert hall have had similar emotions.
People can also like music that displays emotions about experiences they have not had but would like to.
In movies, the effect is more particular: The music can combine with the film to suggest the intended emotion and, thus, make it easier for a viewer to 'get' what more specific emotional experience is intended to be communicated. E.g., in 'Star Wars', the 'Imperial March' clearly represents some power obsessed, brutal, militarism; a viewer can get that message from the music right away although just from the story it takes longer! That's part of why John Williams got paid the big bucks!
Tough to listen to the Brahms 'Lullaby' and not get the feeling of a mother's love for her child: There is a lot of gentle stroking and comforting sighing in that music! Similarly for 'Silent Night' which I caught on to well at about the age of three.
Tough to listen to the beginning of Beethoven's 5th symphony and not get that 'there's heavy stuff going down'. Lots of people have experienced heavy stuff.
Tough to listen to the Beethoven 6th symphony and not feel something like seeing a pastoral scene, say, a meadow with a stream flowing through it if only because this is programmatic music complete with bird calls.
So, programmatic music is a two edged sword: First, due to the program, it is easier to understand. Second, due again to the program, it is less general so that listeners who have not had, or don't want to have, the experience of the program won't like the music.
I know; I know; you had music lessons in the fourth grade, and the teacher told you none of this. Sorry 'bout that!
Literary Art.
For literary art, for me it is too specific: For the situations and corresponding emotions being presented, mostly I have not been in such a situation and even when I have very much both my thinking and emotions were very different.