(the following is a bit of an English abstract of my 1959 Yale dissertation and has served as raw material for various lectures on the subject).

Do you know what I think? asks Adrian Leverkuehn. "Musik ist die Zweideutigkeit als System." Music is Janus-faced by its very nature. It can move and paralyze.  "What passion cannot music raise and quell," exclaims John Dryden in his Song for St. Cecilia's Day, 1687. Music is an expert in  the use of opiates, asserts Settembrini in The Magic Mountain, and Nietzsche  speaks of her dual, intoxicating and befogging, nature.  Shakespeare's Desdemona "will sing the savageness out of a bear" (IV, i) and the merchants in Novalis' Heinrich von Ofterdingen tell the story of another Orpheus whose song so charms a sea "monster" that it saves the singer's life and returns his treasure to him. John Dryden's Thimotheus "to his breathing flute and sounding lyre, could swell the soul to rage, or kindle soft desire" (Alexander's Feast, 1697).  "Musica Consolatrix" and "Musica Tremenda". She is the "Mysterium tremendum et fascinosum" in Kleist's novella about the power of music.
While English late 17th and early 18th century literature offers a particularly rich harvest of poetry celebrating the contradictory qualities, or effects, of music, there is in fact testimony to this at all stages of our tradition.
In the beginning there is Orpheus, probably of Egyptian origin, whose song not only "moves" the deities of the underworld to release Euridice, he later on literally moves trees who uproot themselves to be closer to him and his music,  while wild animals become a tame audience in his presence. Tamino's magic flute has the same effect on the animals in Sarastro's game park, and Papageno's Glockenspiel disarms the lascivious Monostatos. Gregor Samsa, changed into a huge insect, asks himself at a critical moment: was he an animals since music so obviously moved him? The answer is as ambiguous as music itself: Jein / Yes and No. In myth it is all life forms, plants, animals and humans, who are touched by music. Why not an insect with a human soul?
David soothes the raging Saul with music. Oskar Mazerath's concentrated voice shatters church windows and cuts holes in display cases. Joshua's musical demolition squad brings down the walls of Jericho.  (Check the phenomenon of resonant frequency). The trumpet shall sound, and the dead shall be raised, sings the bass in Handel's Messiah. Singing proves deadly for the artist Antonia in ETA Hoffmann's Rat Krespel, and in the third part of Offenbach's Tales of Hoffmann. Playing the piano score of Wagner's Tristan and Isolde hastens the death of Gabriele Kloeterjahn. Homer's sirens and Heine's Loreley lure sailors to their death by means of exquisite song. And all ages and cultures know the magic of the lullaby on one hand, and of martial music on the other.

Rilke is quite aware of this tradition, less at first, fully during his later years. By his own admission he was tone deaf, a fate he shares with Goethe, Heine, and others. But he also realizes early on, that lyrical sound and musical melody have little in common, and that the laws governing both are different.
Rudolf Kassner, exaggerating to make a point, states that Rilke was so obsessed with spatial perception, seeing, that he seemed to have no ears at all. Like Rilke he was a trusted member of Marie von Thurn und Taxis' inner circle, and the two genuinely enjoyed each other's company. Princess Marie loved music, and there was plenty of it in Lautschin, her estate in Bohemia, and Duino, her castle by the Adriatic (destroyed in WWI).  In order to moderate his strident hostility towards Austria she takes Rilke to performances of Mozart masses.
While visiting the artists' colony in Worpswede he hears much music. On one occasion the whole group travels to Hamburg for a performance of Mozart's Magic Flute. Rilke enjoys it, typically with his eyes closed in order not to be distracted by what happens on stage, until Papageno's babble spoils the whole thing for him. He never develops a taste for opera or music drama, and will tolerate the combination of text and music only in song. Orpheus, therefore, becomes the artists par excellence (or, because Orpheus is the artists par excellence, Rilke feels obliged to tolerate the combination of text and music? You decide).
In 1914 he expects a miracle work from the gifted pianist Magda von Hattingberg, namely an access, once and for all, to the world of of music.  In 1919 he meets the young Wanda Landowska, a recent widow and a refugee from revolutionary Russia, already a musical legend, and attends her concerts. His Muzot landlord Werner Reinhart visits him and brings along Alma Moodie, a young violinist who creates a climate of music, he says, "in which I, dumb as a rock, cut a strange figure, dumb but grateful." His ears were sensitive, however, and unwanted sound could move him to rage. The installation of a saw mill in his vicinity prompts the confession  that for a thought to take hold he has to be able to hear it in his mind,  and for that he needs a noise free environment. He writes from Paris: "My apartment has finally settled and become mine; and just as I was to sit back and relax and say 'Now', my neighbor got himself a piano which will probably kill me. It is terrible, noisy children in Venice, the climate in Duino, and now this oaf who wants to amuse himself."  Princess Marie suggests that he slay the offender. But he takes the piano out of contention instead. It dare not move, he writes to Magda von Hattingberg, I have silenced it by force of fury.

But music for him is more than organized, or disorganized, sound. The word can stand for a variety of things, some of them having nothing to do with music at all.
There is an early poem called Musik from the year 1899 which serves as a good example. An anonymous "I" addresses a young man, a boy still, a flute player. It is one of the first examples of Rilke's use of the word to summon associations like danger, seduction, submission, squandering.  This "music" is an unproductive endeavor, it is fake artistry before experience, an expression of yearning and untested emotions rather than life.  "Music" here is a metaphor for premature and precocious creativity, unconscious, unstable, even destabilizing.
Similarly, in the cycle "David plays before Saul" David is incapable of recalling to the aging Saul the fullness of his former life, his erotic life in particular, because the singer David is too young to have experienced it himself. David's mission fails, but he pleads with the old king to allow him to lie with women "instead of my harp".

In his monograph "Worpswede" (1902/publ.03) the associations become even more negative. Music is non-art, it stands for formlessness, is without contour, and is therefore the opposite of painting.
The most striking rejection of music is found in a letter to Lou Andreas-Salomé dated 8/8/1903. Overwhelmed by Rodin's art, the making of "real things" (Verwirklichung) he discards music as formless and sloppy, of dissolving reality, a liquefaction of solids as it were. There is more here than meets the eye. It is also a description of two vastly different work habits. Rodin's (and, later, Cézanne's) disciplined methodical manner ("on faut travailler, toujours travailler, rien que travailler" he tells the young poet who is now his secretary) and the literal making of things, as opposed to Rilke's impulsive, irregular, "musical" habit of creating whole cycles in a few days or weeks or, the Cornet, in a single night. He is desperate to learn to make poems 9 - 5 as it were. Music has become a metaphor for dilettantism, his own easy wordiness included.  He will change, he will work in solitude. Even casual conversations will be shunned because they are wasteful, "sin", "music" and "surrender' (this from a letter to his wife Clara dated July 24, 1904).
Lou's answer, however, to Rilke's violent denunciation of music contains words like non-verbal art, rhythm, form, Gesetz, vocabulary not entirely unknown to Rilke, and he becomes increasingly willing to consider the other side of music: organization, creation, re-creation. Still, music as mortal danger - because it weakens the will and destroys those under its spell - prevail in such poems as The Island of the Sirens (Die Insel der Sirenen) and Snake Charmer (Schlangenbeschwoerung). But there are wonderfully appreciative descriptions of music like Abelone's Song in Malte, Gregorian chant he hears on Rodin's newly acquired phonograph, the birth of music from the silent grief over the death of Linos (First Duino Elegy). And no music is ever formless when played in a cathedral, for its outer contours are those of the church' interior.
Beethoven, as Rilke portrays him in  his Malte, becomes the supreme laborer in the medium of music, as Rodin is in his. Deaf, he no longer rearranges and brings order to a world of sound, but he creates such a world from within himself, out of nothing as it were, like the divine creator creating ex nihilo, and his creation, small wonder, is truly a musica tremenda et fascinosa.

Theory usually comes along in time to fortify impressions. While in Spain in late 1912 and early 1913 he encounters a book by Fabre d'Olivet. La Musique tells of the mathematical foundation of music and its revered role among ancient peoples. That in China a certain basic tone (frequency) had the status of supreme law, that the reed (flute) producing it was used as a measuring device both for length and content (space and volume) remaining in force generation after generation. Fabre speaks of secret Pythagorean schools that taught the secrets of music, the magic of numbers, to a select few. Rilke finds himself in enthusiastic agreement. Schopenhauer had held similar notions about the relationship of music and the universe (i.e. matter and energy, sound and knowledge): if one could adequately render in conceptual language what music (sound) expresses directly, one would have an instant and complete explanation of the universe, i.e. true philosophy.
Mathematics as the foundation of music (die andere Seite der Musik); the most formal of human instruments and expressions intimately related to what he had once believed to be the most formless. Music, then, as a revelation of cosmic laws, of what governs the universe at the core (Faust's "was die Welt im Innersten zusammenhaelt"). Hearing, properly schooled, a much finer instrument of perception than the eye.  "Werk des Gesichts ist getan, tue nun Herzwerk" he would exhort himself a few months later, replacing sight with insight.
And the gifted pianist Magda von Hattingberg was to make it all possible. But Rilke remained basically insensitive to formal musical training, and the whole experience turned out to be an unproductive detour, much as he appreciated her musicianship.

It wasn't formal music anyway that fascinated him now, but the phenomenon of sound in general, and what it might reveal about objects both small and cosmic in scale. How to make visible things audible  and to comprehend them, better, with two senses simultaneously. He remembers a physics lesson. You speak into a kind of funnel the narrower end of which is covered by a membrane with a needle stuck in it. The vibrations of the membrane are transferred to the needle which engraves them in a wax covered drum that is slowly rotated by means of a crank. Reverse the process, the needle will  retrace its own path and the "written image" of the human voice becomes sound again and is heard from the funnel which now acts as a loudspeaker. The rudimentary imitation of a phonograph.
In a fertile mind this creates fabulous possibilities. What if we lead the needle along any irregular line in nature, say, the sagital suture of the skull, or along the ragged edge of a rock, or the path of an insect under the bark of a tree? What music would we hear, and what would the ear teach us that the eye cannot? Crazy? Maybe. Until we remember that mystics and philosophers saw creation as God's signature (Boehme speaks of signatura rerum) to be deciphered by man. We then realize that this seemingly hare-brained scheme has a long and venerable tradition. Looking over God's shoulder. It is here that physics and mysticism confess to the same agenda. And if you don't believe me please read Stephen Hawking's Brief History of Time and take it up with him. What Rilke has in mind is an intensity of experiencing and absorbing that engages all senses at once: that must lead to perfect poetry at last.

In a late poem, again called Musik,  musical vibrations recreate and transform our visible world in sound. Music becomes a mystical/mythical force, the ultimate art, spanning the here and the beyond, and is at home in  the same unity of space and time in which Rilke's angels reside.