Answer:
First, let's identify the notes in the given tone row.
Retrogradation is the reverse of the original tone row.
Inversion involves reversing the direction of the intervals in the original series.
Transposition shifts the entire series up or down by a consistent interval.
Let's start by identifying the notes in the original tone row in your image. Here they are:
C, D, E, F, G, A, Bb, B, Eb, Db, Ab, Gb.
Reverse the order of the original tone row:
Gb, Ab, Db, Eb, B, Bb, A, G, F, E, D, C.
To invert the tone row, you change the direction of each interval:
- C to D is up a major 2nd, so C to Bb is down a major 2nd
- D to E is up a major 2nd, so Bb to Ab is down a major 2nd
- E to F is up a minor 2nd, so Ab to Gb is down a minor 2nd
- F to G is up a major 2nd, so Gb to Eb is down a major 2nd
- G to A is up a major 2nd, so Eb to Db is down a major 2nd
- A to Bb is up a minor 2nd, so Db to C is down a minor 2nd
- Bb to B is up a minor 2nd, so C to B is down a minor 2nd
- B to Eb is up a major 3rd, so B to F is down a major 3rd
- Eb to Db is down a minor 2nd, so F to Gb is up a minor 2nd
- Db to Ab is down a major 3rd, so Gb to Bb is up a major 3rd
- Ab to Gb is down a major 2nd, so Bb to G is up a major 2nd
C, Bb, Ab, Gb, Eb, Db, C, B, F, Gb, Bb, G.
For transposition, let's say we transpose the row up by a major second (whole step). This would add a major second to each note in the series:
- C to D
- D to E
- E to F#
- F to G
- G to A
- A to B
- Bb to C
- B to Db
- Eb to F
- Db to Eb
- Ab to Bb
- Gb to Ab
D, E, F#, G, A, B, C, Db, F, Eb, Bb, Ab.