Rückert's poem has been changed a lot by Mahler. The first strophe of Rückert, became the second strophe of Mahler, where he skipped the second half of the first strophe, and added the last sentence of the poem. The second strophe became the first strophe.
The poem has to strophes. The first paints the moment where the mother enters the door, but her daughter is missing. The second strophe makes this more explicit; it is if you came you (the daughter) came in with her, and it ends with the lament that her life too quickly did extinguish.
The symbols of the poem are to a large extent related to those in the first two poems. "Kerze Schimmer" and "erlosch'ner" put into mind the "Lämplein verlosch" of the first poem. The words "Freudenschein" and "Freudenhelle" are like "Freudenlicht" in the first poem and "verblendenden Geschicke" in the second poem. "der Blick" refers to "Augen" in the second poem.
The structure of the music is consistent with the two strophes in the poem. The music on the second strophe is almost exactly the same as on the first strophe, and at the end is a short coda that brings back the introduction.
The harmony of song 3 is the same as that of song 2: c minor. Russell (p. 86) shows that the English horn motive is related with the last four bars of the second song; C-D-D-E, where the figure at the start of bar 2 is just a variation.
The orchestral introduction has resemblance with a Bach chorale in its polyphone setting, and the violoncello bass line (pizzicato). The entering of the voice could be a chorale melody (Russell, p. 87). Russell suggests that the pizzicato violoncello depicts the mother's footsteps, which I doubt. But I agree that the simplicity of the contrapuntal figures suggest a world of simple childhood. The top line, English horn, goes on as a continues stream, that gradually rises till bar 9, and then gradually becomes lower till the polyphonic character becomes homophonic. The long notes in this line are D-Es-G-G-D-D-D-G-G-D-D, where on most of those long notes the eighth movement continues in another instrument, except in bar 4, 11 and 13. The middle line (fagot) becomes very pronounced in bar 4-5 with its slow motive C-B-C-G. The harmony is very simple in c minor (I-V-I-IV-I-V-I-V-III-VI-V7-I) with a combination of English horn, cello and fagot, where in bar 6 the harmony III-VI with a Des instead of a D suggest V-I in As and the instrumentation is extended with oboe and bas-clarinet.
The voice enters with a simple motive in bar 8 that is an extraction from the English horn motive in bars 1 and the first half of bar 2. This motive is repeated in bar 9. The first three notes seem the steps of the mother entering the room, and the last two give the feeling that she enters the door. The oboe has a very expressive motive starting in bar 7 with Es-F-G followed by F-Es-Es-D-D in bar 8. In bar 10 the same motive is developed to wards a longer one that raises till a high C. Then, when the father moves his head, this is in a very simple downward motive that starts on the tonic and ends on the dominant, while on the word "drehe" the eight movement stops for half a bar, giving the feeling that something happens there. In bar 14, on "sehe" the Des and B suggest also something happening, as do the lowering of the tonic C to a Ces in bar 16 and the transformation becomes final in the extra half note in bar 16 where the dominant G becomes the tonic in bar 17: G aeolic (according to Odefey, p. 278). There the tension in the text is increased by telling that the father is not looking at the mother who enters. This is told on the motive of bar 8, a fifth higher.
And then, suddenly, the eighth contrapuntal movement ends and becomes an homophonic fourth movement. The horn motive is clearly derived from the voice motive in bar 12-13. The harmonic stability has ended and changed in fast fluctuations of harmony, with a lot of dissonants. In bar 19 a short suggestion of going back to c minor, but it ends in A major in bar 20, and continuing with IV-I, C in bar 24, F7 in bar 25, Es in bar 26- G7-C in bar 27 and with G in bar 28, Des a the end of bar 29, C-g in bar 30, f at the end of bar 31, and finally G-C in bar 32 towards 33. There the introduction to the second strophe starts almost the same as during the first strophe.
It is obvious that the passage in bars 19-32 is the essence of the first strophe of the poem: the daughter does not enter with the mother! The voice has a motive that is a combination of the first two motives of the voice (the beginning of the first, the end of the second). The motive that follows, with its chromatic line, feels more or less as an inversion of the motive on bar 20-21. The tension increases with a sharp dissonant on bar 24, where attention is given to the doorstep, and then the emptiness on this doorstep is expressed by the voice on a very high variation of the motive introduced in bar 4. The forte of the voice combined with the piano in the orchestra gives a very expressive coloring. The long note on a new motive (a little bit related to the oboe motive of bar 6) on "freudenhelle" gives extra emphasis to this word, that is so much related with a lot of comparable words elsewhere in the cycle. Also the accent in the bass line on Fis-G helps in expressiveness, and you may wonder if this half tone rise helps to remember this important motive of the first song.
The downward line colored with parallel thirds below the repetition of the freudenhelle motive on " trätest mit herein" is very beautiful, and ends more or less by being back on the tonic c minor. The accents on " wie sonst" in bar 31 are very expressive, and the G gives a dissonant with the As in the bass. Finally, the first strophe ends with a very clear cadence, where the voice has a very low G on " Töchterlein". During the whole phrase, the voice went downwards from a very high F to a very low G during bars 25-32.
The second strophe is much shorter qua text, but the music is a repetition of the first strophe with only minor variation. A lot of repetitions and lengthening of syllabus were used to reach this symmetry in the music without the symmetry in the poem. The addition of harp and contrabass pizzicato in bar 33 gives a little bit more depth and expression to the introduction. In bar 40 the repeated accentuated G in the middle voice gives a little bit more tension than was in bar 8, a rising 43 melody in the left hand of bar 42 gives a little bit more dynamics. The middle and lower voices are different in bar 28-29, where in bar 50 the voice takes the melody the piano had in the first strophe, while the piano has a variation of this line in a high pitch with eight notes. Then in bar 52-53 the piano takes the melody the voice had during the first strophe. The deep chords below "des Vaters Zelle" in bar 56-57 give more drama to those words, as does the dissonant on bar 58. The long and expressive repetition on "erloschner Freudenschein", including the sforzando on "schein" in bar 62, give these word an enormous emphasis.
At the end of the second strophe, the orchestra seems to take up the introduction of the two strophes, but horns and the legato instead of pizzicato celli, give a much more expressive and less childish atmosphere. The motive that was in bar 2 and is repeated at the end of bar 64 continues with a downward half tone, and is repeated in half speed in bar 66-67, and again in bar 67 till the end. The upward line of the celli in bar 67 gives a lost flickering of the remembrance of the child, and the song ends on the dominant chord, G, making the digestion of the grief unfinished, again.
If we look back now on the third song, then it seems to combine elements of the first two songs. The harmonically static polyphony of the first song is combined with the harmonically unstable homophony of the second song. But on the other hand, the text of the song is the most pessimistic of the three songs. While in the first two poems there was an attempt to put the grief in perspective of the heavenly light, the focus in this song is completely on the loss of the child.