In which mode do half steps occur between notes 1-2 and 4-5?

The correct choice is the Locrian Mode, which is characterized by a specific arrangement of whole and half steps. In the Locrian scale, the half steps are found between the first and second notes (1-2) as well as between the fourth and fifth notes (4-5).

To illustrate, consider the Locrian scale built on the note B: B, C, D, E, F, G, A. The half step occurs between B and C (1-2), and again between E and F (4-5). This arrangement creates a diminished fifth from the first note to the fifth, which contributes to the unique sound of the Locrian mode.

Other modes have different configurations of whole and half steps. For instance, in both Phrygian and Aeolian, the half steps are located in different intervals which do not align with the specific half step placements of the Locrian. The Lydian mode also does not exhibit this half step pattern. Understanding the distinctive half step placement in the Locrian mode highlights its unique tonal structure compared to the other modes listed.