Another Match in Reich's The Desert Music

This is the beginning of the third year of this blog. To celebrate, I am combining the idea from the first post of two years ago – relating pitch and time – with music by a composer featured in the post from one year ago – Steve Reich. A repeating five-chord progression occurs in the first and last movements of the five-movement The Desert Music. These chords are indicated below. In the first movement, the progression starts with the chord in the upper right and loops clockwise several times. The chord with the D in the bass sounds like a jazzy tonic harmony, whereas the next chord with the A in the bass sounds like a jazzy dominant harmony. In the first movement, adjacent chords after a while begin to overlap with and blur into one another. (This overlap is more conspicuous in the Michael Tilson Thomas recording than in, for example, the Kristjan Järvi recording.)

The ten circles outside the five chords use a circular piano keyboard to indicate notes irrespective of octave and diatonic spelling: C is at the top of each circular piano keyboard. The five circles next to the five chords simply translate the chords into this circular keyboard notation. The other five circles – the ones with arrows pointing toward them – show the union of two adjacent chords. The color coding – with reference to my blog post from a year ago – shows that the union of the dominant and tonic harmonies perfectly matches Reich’s characteristic rhythm, with the note C corresponding with the downbeat.

Furthermore, my Pythagorean slant of a year ago works on the pitch side: the union of Reich’s dominant and tonic chords is the smallest kind of note group that contains an augmented triad, a fully-diminished seventh chord, and a Guidonean hexachord (a major scale without ^4 or ^7). Moreover, the tonic chord is the constituent Guidonean hexachord (the blue star: in fifths, F-C-G-D-A-E), while the dominant chord contains both the constituent augmented triad (the red triangle: A-C#-F) and fully-diminished seventh chord (the purple square: C#-E-G-Bb), and both chords are the usual dominant-functioning harmonies of their respective chord qualities (V+ and vii°7) of the D tonic. In other words, if you trace the purple, red, or blue line in the figure above, you will put the colored dots in the same order that they are on the side of the right triangle from the October 2014 figure of length 3, 4, or 5, respectively: that is, green-purple-orange-purple-..., green-red-red-...,  and purple-red-blue-orange-blue-red, respectively.