The text consists of two strophes, again with four lines per strophe and rhyming second and fourth lines of the strophes. It is about tears. This may suggest that the longing for love in the first song is not reciprocal. It may also be that the tears are tears of happiness. But if she will love him, he will give her the flowers and sing like a nightingale. Recognize that the first strophe ends with a chorus of nightingales, while he will sing the song of a nightingale in the second strophe.
The song starts with the singer accompanied by the piano. It is only A-Cis. Because of the first song, a Fis added would be the complete solution of the longing towards the tonic. The piano has it in the bass line of the second measure, but then continues towards the D chord followed by A. In the third measure, it is stated again through E7 followed by A that A is the tonic. So, measure 2 and 3 are harmonically IV-I-V7-I. The feeling of sadness is expressed by the dominant seventh around the last tone of the first sentence. Also the B of the singer is suggesting a lack of harmonic solution. The fermata on this tone gives this lack of solution an extra tension. The harmonic solution is given immediately afterwards by the piano, but pianissimo, i.e. softer than the passage before. So, the solution is more or less an afterthought.
Although the second half of the first strophe is an almost exact repetition of the first half (only the singer makes a small variation), the meaning is different, because the listener knows already from the start that it is in A major, and not in fis, as could be expected at the start after the first song. The change in melody around "Nachtigal" seems to mimic the singing of the nightingale.
Let us have a look at some melodic aspects. First, the melody of the singer is very horizontal, centered around Cis-B, with a lot of tone repetitions. Second, the bass line creates gradually more fundament during the first two measures, and suggests an atmosphere of melancholy with its downward line. This downward line can also be found in song 3. Third, the staccato chords in the piano may suggest the tears going downwards. The metric accents on the first beats in m. 2-4 create a very clear metrical structure; only the binding over of the first chord in the piano towards m. 1 create a connection with the start of the first song.
The second strophe is harmonically completely different. It starts with a clear E major, in the same atmosphere as the start of the first strophe. This would suggest a repetition of the first strophe in the dominant, but it doesn't happen. The parallel minor chord becomes the II in b. This explains also the Ais in m. 10, that becomes part of a Fis7 chord in the second half of m. 10 with the Fis of the right hand piano line. So, the chord progression is II-V7-I in b. By the way, the interpretation of the start of the song after the first song had a possible option of being fis minor instead of A major, but appeared to be major. Now, while the suggestion is major, it appears to be minor!
Adding Gis in the base half way m. 11 suggest more stability of the Cis major chord, and the seventh is left out in measure 12. This is made more clear in the third and second chord of m. 12. The Cis chord suggests a solution towards fis as a tonic.
The start of the last phrase gives a harmonic surprise. Suddenly an A7 chord is presented, as a V7 of D, i.e. the IV of A. The difference with the start of the song is not as much as it seems at first sight. It is the same chord with additions of E and G, implying that the harmonic interpretation has been made explicit, and different from both most obvious hypotheses in m. 1. The horizontal structure of the bass line and the increase in rhythmic tension bring only a small suggestion towards D, and at the end it is clearly stated that we are in A. The small crescendo, the rhythm and the harmonic surprise together make from "klingen" the main focus of the song.
During m. 15 this is going back to A through the addition of the V of A. The singer ends on a dominant seventh chord again, with a fermata. But at the end of the song this is solved harmonically towards A. But this A seems to be again a dominant of D, when we look at the start of song 3.
If we have a look at the large structure of the form, we can describe it as A-A'-B-A'', each part with 4 measures, and A" a much larger deviation from the original A than A'. In contrast with song 1, the general atmosphere of the song is melancholic and horizontal.