Harmonic Spaces
for four-hands piano


Recordings of the four movments of this piece can be heard on YouTube:
I - II - III - IV

Each short movements in this set is based on one or two wide intervals that often mimic the spacing of overtones in the harmonic series. This approach was used to inspire different ways of producing harmonies, colors and atmospheres. The title “Harmonic Spaces” refers to both those widely-spaced intervals and to the concept that the pieces are musical spaces filled with colors and motion. While, for listeners, those musical spaces are what matter, they wouldn’t have been the same without the harmonic spacing.

I - Simply and gracefully moving forward. (9th and 3rd partials)
This movement is a slow progression of widely-spaced chords with gracefully rising and falling note patterns woven in and around them. The chords often appear in groups of two, with the second almost sounding like an echo of the first. That creates a sense of harmonic space within which the delicate lines move in and out of agreement with the chords.


II - With a steady, even flow (or groove). (7th and 5th partials)
The harmonic partials used in this movement are part of what give dominant 7
th chords their characteristic sound and function. Because 7th chords are an important part of jazz harmony, I let also let certain jazz influences enter into this piece. It isn’t jazz, but some listeners may notice the outlines of gliding 7th chords as well as swinging meters and syncopation that remind them of jazz.


III - Gentle, flexible, but rhythmically accurate. (11th Partial)
This movement unfolds slowly like a quiet summer afternoon under a shade tree watching lazy clouds. Because the 11
th partial is a note that falls “between the cracks” of the piano keyboard, I use both the perfect 4th and augmented 4th (in very wide spacing) to approximate it. Although this creates some non-traditional harmonies and “non-chord tone” effects, the piece is tranquil and peaceful.


IV - With precision, energy and excitement. (13th Partial)
This energetic finale uses much syncopation and rhythmic interplay as well as wide-ranging arpeggios that get shared between the two players. The primary interval often appears as widely spaced parallel motion, which adds a special color or flavor to the rhythms. The result sounds somewhat like a joyful romp in a playground of rhythm, color, motion and contrast.

(duration ca. 12 minutes)

This work was funded by the
National Culture and Arts Foundation of Taiwan (ROC)