Chapter 7      


Click the links below to access additional content for Chapter 7.

Figure 7.28 Spectrogram of opening of If I Ain't Got You

Scores      Tonnetz Figure      Video of Tonnetz as a Torus   

Video on neo-Riemannian Theory (especially the use of P and L transformations)

Video of LR sequence in Beethoven's Ninth Symphony Video of the LR sequence of chords discussed in Example 7.2.2.  

Tonnetz Aspects of Stravinsky's Music (PDF)    

Tonnetz Aspects of Stravinsky's Music (Listening Examples)

Geometry of Harmony and Modes in Vaughan Williams' Romanza (PDF)

Vaughan Williams' Romanza (Tonnetz Animations)      Vaughan Williams' Romanza (Listening Example)