With the goal of "filling in the canvas" of all twelve tones, using only diatonic material:
- all of the possible ways to combine only major and minor triads to make 12 tones -
explanation of this picture
- all of the possible harmonizations of four different notes using two major and two minor triads to make 12 tones -
- harmonization of the C major scale and chromatic scale into 12-tone triadic structures, using the table on the previous page -
LEFT:
- harmonization of the C pentatonic scale into 12 tones, in preparation for pentatonic study -
- some ideas about how to visually represent triads, resolving the conflict in a "nested" diagram -
RIGHT:
- a "zoomed out" version of the previous diagram, using it to make another version of the 12-tone harmonization table above -
(written in base-12 notation)
- a normal and "zoomed out" version of the first page, showing rotational structures -
- a three dimensional view of the chromatic circle with two triads and their shadows -
(the shadow is the major/minor pair visible in the other diagrams)
- a three dimensional view of the previous structure progressing through six rotations -
(compare to the drawing on the first page)
- all of the possible chord progressions produced by this structure, moving from one triangular "tile" to another -
- an idea for voice leading through one of the previous progressions, moving one note at a time -
- a comparison of the "smoothness" of the voice-leading for all of the previous chord progressions -
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