How could a 12-tone row be changed through inversion, retrograde, and transposition?

In the 12-tone method of composition, a basic "row" is formed using the 12 independent tones of the chromatic scale. This row serves as the foundation for both melodic and harmonic material, and it can be systematically altered through three primary devices:1

• Inversion: The intervals of the original row are mirrored, meaning ascending intervals become descending intervals of the same size, and vice versa.
• Retrograde: The row is presented in reverse order, starting from the last note and ending with the first.
• Transposition: The entire row (or its inverted or retrograde forms) is shifted to start on a different pitch level while maintaining the original sequence of intervals.

By applying these techniques, composers can generate a total of 48 different permutations of the chosen row, providing a rigorous framework for serial composition.1