Here is a spectrogram of the opening of this piece. Within the rectangles are palindromes played by a harp and clarinet. Each palindrome is a transposition of the first one. Following each of these harp-clarinet palindromes are three palindromes of violin tones. You can listen to this opening passage on Spotify:
The tone row that governs this concerto is
G B-flat D F-sharp A C E G-sharp B D-flat E-flat F.
Leonard Bernstein said the following about this tone row:
Berg chose for this concerto a tone row which is filled with tonal [diatonic] implications. Notice that the first nine notes of that row all proceed in intervals of the third--- mellifluous thirds, major and minor ones. Moreover, these thirds are symmetrically arranged in ``chiasmus'' fashion, if you recall, according to a pattern of AB:BA---that is, minor-major : major-minor, etc. And what's more, the triads that are formed by these thirds automatically alternate minor, major, minor, major, thus insuring all mellifluous possibilities. And what's even more tonality-making, every other note of these first nine combine into perfect fifths, of which the first four happen to correspond to the four open strings of the violin, a very handy tool to have around in a violin concerto. (L. Bernstein, The Unanswered Question, Lecture 5, pp. 301--302.)
You can buy this recording from Amazon, or iTunes, or Spotify.