The 16-tone harmonic piano
Something I wanted to do when I was creating Sanctuary (Overtones and Deviations) was to be able to play natural overtones (see my post on Fantasia) as scales on conventional instruments, particularly the piano, my instrument. Generally speaking, I wanted to make music in an entirely different tonal system but with all the advantages of performing on a familiar musical instrument. The scale I decided to use is based on harmonics 16-31 of the harmonic series, which I settled on because it is a full musical octave, divided into 16 clearly distinguished parts. I wanted to base the scale on A, the pitch that has a rounded frequency in the most widespread Western tuning convention (440 Hz), and is familiar to our ears.
The idea of playing this scale across a standard piano keyboard seems confusing in one respect—as you hear in the video, the octave A-A on the standard piano is actually much further apart, A-C sharp. However, since the 16-note scale and the 12 piano notes both divide into groups of 4, I could actually use patterns of notes used in traditional Western music to produce new musical results. You can see these in the video (feel free to skip over the musical jargon, or leave a comment if you want me to explain something):
- Augmented triads based on A form natural harmonics 4-7 (which sounds like a dominant seventh chord).
- Whole-tone patterns based on A form a kind of “natural octatonic” scale (harmonics 8-15).
- Messiaen's modes of limited transposition with four transpositions create unique 8-note scales.
One of the things I was struck by was the clarity of the sound. Even when playing thick chords in the low register of the piano which would sound powerful but pretty muddy on a standard piano tuned to equal temperament, practically every note can be heard clearly. You can hear the 16-tone piano on Reflexion, Microcosm, Below The Edge and Hexes (tracks 3, 5, 6 and 8 of the album).