Harmony
Study how simultaneous pitches form sonorities, how those sonorities connect through time, and how voice leading, function, cadence, register, and tuning change what a progression does without reducing harmony to a single recipe.
A chord is vertical. Harmony also moves horizontally.
Keep the chord identities fixed and change only their voicing. The colored lines trace three voices from one sonority to the next, making common tones, stepwise motion, and larger leaps visible.
Tonic departs through predominant and dominant before returning.
The Roman-numeral progression did not change. Only register and inversion changed. Voice leading is one layer of harmonic organization, not a score for how “good” the progression is.
The same interval can be tuned more than one way.
Twelve-tone equal temperament divides the octave into twelve equal logarithmic steps. Just intonation instead describes selected intervals with whole-number frequency ratios.
One chord can participate in several different stories.
Harmonic analysis asks multiple questions at once. Roman numerals can describe scale-degree relationships in tonal music, but other repertoires may organize harmony through modes, drones, pitch-class sets, parallel sonorities, timbre, tuning systems, or practices that do not center functional tonality at all.
Which pitches are sounding together right now?
What role does this harmony play inside a tonal context?
How does one sonority lead to the next?
How do individual pitch lines move through those sonorities?
Does a phrase create arrival, continuation, interruption, or ambiguity?
Which frequency system determines the exact pitch relationships?