Workshop 82 mini-test

1. Why are augmented triads harmonically ambiguous?

2. Why are there only three unique diminished-seventh pitch collections?

3. Why are there only two whole-tone scales?

4. How can C→C+→F be understood as voice leading rather than a special chord formula?

5. What is a chromatic mediant relationship?

6. Why can a diminished seventh chord resolve toward several tonal destinations?

7. How is G7♭9 related to a diminished seventh chord?

8. What is the difference in flavor between whole-tone dominant tension and diminished/♭9 dominant tension?

9. Why can a globally symmetrical progression still contain strong local tonal function?

10. What is the deepest lesson of Workshop 82?

Answers

1. Because the augmented triad divides the octave into three equal major thirds. Every inversion has exactly the same interval structure, so the chord itself does not strongly identify a unique root without context.
2. A diminished seventh is built entirely from minor thirds. Transposing it by three semitones merely produces an inversion of the same pitch collection, so the twelve chromatic roots collapse into three distinct sets.
3. A whole-tone scale consists entirely of two-semitone steps. Transposing it by a whole step reproduces the same six pitch classes, leaving only two distinct complementary collections.
4. The essential line is G→G♯→A, while C/E may remain common or move smoothly. The augmented chord is the vertical consequence of that chromatic line between C and F.
5. A chromatic-mediant relationship generally involves chords whose roots are a third apart but whose relationship is not simply diatonic—often major chords such as C→E or C→A♭. They frequently combine harmonic surprise with common-tone or semitone voice leading.
6. Because all four members of a fully diminished seventh are structurally equivalent; any member can be reinterpreted as a leading tone to a note one semitone above, so the same pitch collection can acquire several functions through different resolutions.
7. G7♭9 = G plus B-D-F-A♭, and B-D-F-A♭ forms a fully diminished seventh chord. Thus the dominant contains a symmetrical diminished structure above its root.
8. Whole-tone dominant color emphasizes 9, ♯11 and ♯5 and tends to sound floating/brightly unstable; diminished/♭9 color contains stronger semitone friction and often sounds tighter, darker, or more urgent.
9. The large-scale roots can follow a symmetrical major-third system while each local destination is approached through an ordinary dominant or ii–V, giving strong local gravity inside geometrically organized global form.
10. Symmetrical harmony temporarily weakens ordinary tonal hierarchy, giving multiple destinations similar plausibility; its expressive power comes from controlling when gravity disappears and when it returns.

The central lesson of Workshop 82 is:

Functional harmony gives the listener an arrow. Symmetrical harmony gives the listener a crossroads. The musical decision is not how strange the crossroads can be, but which road you eventually make inevitable.