Explain how a secondary dominant chord functions to heighten tension and create a stronger resolution in a chord progression.

A secondary dominant chord is a dominant chord (V) that resolves to a chord other than the tonic (I). Its function is to temporarily tonicize a chord within a key, creating a stronger pull towards that chord and thereby heightening harmonic tension before the resolution. In the key of C major, the dominant chord is G7, which resolves to C. A secondary dominant, for example V/V, would be the dominant of the dominant. The dominant chord of G is D. Therefore, D7 is V/V in the key of C. This D7 chord functions as a secondary dominant because it resolves to G (the V chord in the key of C) rather than directly to C (the tonic). The presence of the tritone in the secondary dominant (in D7, it's C and Gb) creates a strong expectation for resolution. This expectation is directed towards the chord being tonicized (G in this example), making its arrival feel more significant and impactful. The use of a secondary dominant adds chromaticism (notes outside the key) to the chord progression, which further intensifies the harmonic tension. By creating a temporary shift in tonal center and then resolving back to the main key, secondary dominants add complexity and sophistication to the harmony. The heightened tension and stronger resolution are what make secondary dominants a valuable tool for creating musical interest and emotional depth.