In C major, the scale A to A is considered to be in which mode?

The scale from A to A in the context of C major is indeed in the Aeolian mode, which is also known as the natural minor scale. This mode is constructed by taking the sixth degree of the major scale as the root. In the case of C major, the sixth degree is A.

The notes in A Aeolian (or A natural minor) are A, B, C, D, E, F, and G, which correspond to the same pitches as the C major scale starting from A. This gives A Aeolian a minor sound and a specific pattern of whole and half steps that characterizes the natural minor scale.

When considering other modes, such as Ionian (which is the major scale), Dorian (which has a raised sixth), and Locrian (which has a lowered second and a lowered fifth), they each have different tonal centers and interval structures that do not align with the A to A scale under consideration. Thus, recognizing that the A to A scale leverages the characteristics of the Aeolian mode clarifies why this choice is correct within the framework of C major.