It is obvious that Schumann made a selection from the Heine's "Lyrisches Intermezzo". He choose the first four poems and the last poem, and a selection of the poems in between. Also Heine didn't conceive the "Lyrisches Intermezzo" as a whole. He first created the poems, and then organized them to a bundle that he considered to be of higher value than the sum of the separate poems. Schumann made a much smaller selection (16 or 20 instead of 65 poems), but also here the whole is much more than the sum of its parts. Below, I will present my interpretation of the cycle of poems. It is obvious that different interpretations are possible. In the discussion, I will refer to the poems in the published 1843 version, with 16 songs. The extra poems in the unpublished original version of 1840 will be referred to as poems 4a, 4b, 12a, and 12b.
The theme is presented in poem 11, "Ein Jüngling liebt' ein Mädchen, die hat einen andern erwählt". The digestion of the mourning about the lost love that has chosen for another. It seems that it hasn't been a long love affair, it is love mainly from the side of the poet, the I-figure in the poems. About the love his not told much, except in poem 5 that she once gave him a kiss. The cycle is not a story, but an emotional development.
This starts with the first five songs that focus on the longing and memory of the first and probably only kiss she gave him, as referred to in poem 5. In poem 1 the poet remembers that he confessed his love to her in the month of May. Already the second poem seems not to be very optimistic. From his tears and sighs (about his love?) beautiful flowers and nightingales may develop, and if she loves him, then he will sing the song of a nightingale for her. But it seems, that this didn't happen. The third poem about his admiration for her can be seen as the song he would sing. The fourth poem is again more pessimistic in character, where the poet first shows how happy he would be with her, but when she would say that she loves him, he must weep bitterly. It seems obvious to me, that he must weep because she will never say this. Then, in the version of 20 poems, there is first a poem (number 4a) that describes a dream where he saw the beautiful face of his love kissed by death. Is he really expecting her to die? Or is only the fact that he lost her seen by the poet as her death? The second extra poem (number 4b) is about his desire for his love, and how it would be if they would be together. Finally, the fifth song refers to the kiss he once got from his love.
The sixth poem is quite different in character. It tells about an image of the holy Mary in the cathedral of Köln (it really exists!) whose eyes, lips and cheeks are like those of his love. It is a normal stage in a mourning process to project characteristics of the lost one on someone else. And in this case, this is an image of someone, who gave stability in an environment that is called holy, i.e. the river Rhine, the city of Köln.
During the seventh till the ninth poem the poet projects his anger by imagining that his love is not happy with her husband. The seventh poem takes a theme back from poem 4a. In this case it is not a dream about death that kisses her, but a dream about the serpent eating her heart. He is not angry about here, he tells himself, because he knows that despite her seeming splendor (at her wedding day?), he knows how miserable she is. But it is obvious that he is angry and is transferring this anger! And this anger is projected also in poem 8 when he is walking in nature; nature doesn't understand him but would comfort him if it would know, but the woman that has broken his heart knows can understand him! The ninth poem tells about the pain during the wedding party, where again the motive emerges that the poet imagines (projected as the groaning angels) that she is not happy despite the overwhelming music at the wedding party.
The tenth poem is about the poet's drive to the top of the wood where his grief releases in tears. This poem shows he is not happy at all with the situation, and maybe he becomes aware that there is no reason to assume that his love is not happy without him.
Poem 11 may be seen as the turning point in the cycle. The poet sees the irony of his situation and generalizes it to something that happens everywhere. This is the one of the few poems of the cycle that is not written from the direct perspective of the poet. He looks at his situation from a distance, and feels that he shouldn't have so much self-pity. This is what the flowers tell him in poem 12.
In the long cycle, then song 12a tells a fairy tail about a knight who dies when his frightened girl flees for the giant of wilderness, where this fairy tail will be over when the poet will be buried. Poem 12b tells about the poet dreaming in a carriage, where he sees three shadow-forms that make fun of him, more or less like the flowers in poem 12 showed his self-pity.
Poem 13 describes the desolation of the poet does not depend on what his love is doing in his dreams; the worst grief is when he dreams that she loves him. See the parallel with the end of poem 4. The dreams continue in poem 14, where the poet dreams that his love looks at him with a look of pity, murmurs a word to him and gives him a spray of cypress (symbol of eternity of life?), but after the dream not much is left over. This resembles the theme of poem 12a where after the poet being buried the fairy tail vanished. It is the first moment in the cycle that he is able to perceive her in a more or less realistic manner.
Poem 15 is a very long poem about a dream land where the poet would like to be, but that vanishes when the morning rises. The "story" of poem 14 has more or less the same content as poem 14, except for that the dream is not about his love but about a large, general fantasy. In this way the poet puts his dream of poet 14 in a broader perspective and can digest his situation. The structure of the poem resembles poem 12a, where first the dream comes and then it vanished, in that case because of death. This paves the way to final step in the digestion process of his grief, poem 16. In this last poem the bad dreams and evil songs are buried. But a very large coffin is needed to do this, because with the dreams and songs also his love and suffering are buried.
What seems to remain open is to what extend this is completely positive. At the end of the mourning process not only his pain is buried, but also his love...
In summary, the first five poems have a focus on the longing for his love. In poem 6 the poet becomes starts to project his love on Mary, and in poems 7 till 9 he projects his anger on an image of his love not being happy with her husband, and searches some consolation in nature. In poem 10 the lack of rationality of his drive comes to the surface, so he can look at his situation from an ironic distance in poem 11. During poems 12 till 15 he becomes more and more aware that his grief is just an emotion that has become independent of his love, where he gets the ability to see how much self-pity he has, first projected through the flowers that tell him this (poem 12) and finally by his love looking at him (poem 14). In poem 15 the poet is able to see his situation as a dream, just like a fairy tail, so he can bury this dream with the positive and negative emotions together in a large grave, the sea. So, the cycle is a mourning process because of the loss of his love to another. First, the lack of acceptance, then the anger, then grief combined with taking distance to his own situation and finally the ability to bury the emotions.