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Harmonic Spaces
for four-hands piano
(2016)

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

(The score of Harmonic Spaces can be purchased from Sheet Music Plus)

The title Harmonic Spaces refers to both the idea that these pieces are musical spaces filled with colors, motion and character and to the widely-spaced harmonic intervals upon which the colors are built. Each movements is based on one or two wide intervals that mimic the spacing of overtones (or partials) in the harmonic series. This approach helped inspire different ways of producing harmonies, colors and atmospheres. For listeners, of course, the musical spaces are what really matter, but they wouldn’t have been what they are without the harmonic spacing that shaped them.

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 being quieter, 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 of this movement are help give dominant 7
th chords their characteristic sound and function. Because 7th chords are an important part of jazz harmony, I let certain jazz influences enter into this piece. Therefore, some listeners may notice the outlines of gliding 7th chords, swinging meters and syncopations reminiscent 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 that 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)