The intersection between music and emotion is complex.
Musical preferences or predilections are often very personal and individual, and are often coloured by a person's past history (e.g. some songs may be associated with positive or negative past life events). Of course, the musical styles that you grow up with often become those you permanently prefer.
I've noticed quite often that patients of mine who struggle with sadness or anger may choose music that has a sad or angry emotional tone. In these situations I worry sometimes about whether the music itself is "feeding" the negative emotion. An extreme example of this would be music in which the performer is screaming, often about how bad life is, where the listener--often using headphones that are socially isolative--is absorbed for hours every day.
But I think that music is an external experience that can touch us, or resonate with emotions. In this way a musical experience can help us feel less alone, more understood, more "in synchrony" with something outside of ourselves, even if the music is laden with the same kind of sadness that we may experience internally.
Therapeutically, I have to acknowledge the value and power of this kind of "synchrony". So I generally would never try to dissuade the fan of "screaming angry music" from continuing their choice of genre (besides, I would be just one more person unsuccessfully attempting such subjectively intrusive and unwelcome advice). Yet I encourage people to gently explore types of music outside of their familiar territory, and to search for music which goes further than emotional synchrony alone, but also soothes, calms, inspires, provides hope, gives energy, or gives a thrill of joy. Some of the great works of music can touch us in our sadness, and therefore "resonate", while also guiding us towards hope or even making us smile with delight.
Here are some specific examples (off the top of my head) which work for me (everyone will have different tastes, of course, but if you're looking for something different, give these a try) :
-anything by W.A. Mozart. the piano sonatas (exquisite, sweet); the piano concertos (poignant and sometimes sad but always ending with hope and joy -- and the tunes stay in your mind); the wind concertos (clarinet & oboe).
And very specifically a vocal piece by Mozart called "Exsultate, Jubilate"; the piece in its entirety is a distillation of the joy of life. The last item in this piece is the perfectly beautiful and energetic "Alleluia". In fact, I would go so far as to make this whole piece--including the composition itself as well as the performers and their backgrounds--a metaphor for joy in life: to have joy, one must work at it for years (as the performers have done). One must hear others and learn from others. One must pursue poignancy as well as virtuosity. One must have moments of tension and dissonance, but they must always be relieved imaginatively and beautifully. Some of the joyous moments may be brief, but they stay with us forever even after they are literally over. My favourite performer of this piece is now Carolyn Sampson. Kiri Te Kanawa was my previous favourite. I'd recommend listening to it on the best possible stereo system available to you.
Another specific selection is the Goldberg Variations by J.S. Bach as played by Glenn Gould (who made two recordings of this piece, in 1955 and in 1980 -- I'd recommend hearing them both, starting with the 1955 version; the final aria at the end of the 1980 version is like a sweetly beautiful farewell from one of the great musical geniuses of the century). Also there's a version by Murray Perahia which is extremely good too, in case you find Glenn Gould's playing too eccentric. This piece is another metaphor for life: it starts with something simple and beautiful; it moves through many variations with different degrees of motion, emotion, and energy, yet always with the same underlying grounding theme; then it ends beautifully and serenely, almost just as it began. Implying a cycle that continues yet changes, beginning and ending at peace, but with lots of work and tension and playfulness and growth in-between.
Other specific suggestions:
1) Chopin, Piano Concerto #1 in E minor, Opus 11. The second movement is an example of sublime beauty.
2) Beethoven: Violin Concerto. Beethoven had a difficult life as a result of his own inner emotional problems (lots of depression, irritability, anger, relationship disappointment) in conjunction with various external sorrows, especially the total loss of his hearing. His music is full of emotion and power; underneath the sorrow there is sweetly touching beauty and joy, and I think the violin concerto is one of my favourite examples. Anne-Sophie Mutter is a great performer of this piece.
3) Beethoven: slow movements from many of the piano sonatas, such as "Pathetique" and "Moonlight".
With all of these suggestions, I realize that for some people, they would just rather listen to something else (musical taste is such a personal thing). Also, when feeling very unwell in any way (emotionally or physically), sometimes even your favourite music can feel irritating or can make you feel worse (it may remind you, for example, of how much you could be enjoying it if you were feeling well; your lack of enjoyment when ill could then remind you again of your illness and make you feel worse).