Chord Progressions

A chord progression is a time-ordered sequence of step-combos. Each step-combo is identified by its root’s chromatic step-number (Position 0 through Position 11). In PhizMusic, the central question is geometric: how far does each voice move from one step-combo to the next? Small total movement tends to sound smooth and coherent; larger movement tends to increase contrast and perceived tension.

🎯 Simple version: A chord progression is a journey from one group of notes to another, labeled by root position (e.g., Position 0 → Position 7 → Position 0). Some journeys feel like “going home” (resolution), others feel like “still traveling” (tension). The brain predicts where the music is going; surprise creates emotion.

Progressions as Step-Combo Sequences

Write each simultaneous sonority as a set (or multiset) of chromatic steps relative to a chosen root frame. A progression is then:

S1 -> S2 -> S3 -> ... -> Sn

Example sequence:

{0,4,7} -> {0,5,9} -> {2,7,11} -> {0,4,7}

This is often labeled with Roman numerals in conventional theory (e.g., this sequence is I–IV–V–I), but PhizMusic identifies each step-combo by its root’s chromatic step-number: Position 0 → Position 5 → Position 7 → Position 0. The representation stays literal: actual step content over time.

Voice-Leading as Distance Minimization

Given two adjacent step-combos A and B, voice-leading chooses a mapping between notes in A and notes in B that minimizes total motion. Define circular step distance on the 12-step ring:

d(a,b) = min((b-a) mod 12, (a-b) mod 12)

Then total movement for a specific voice assignment is:

D(A,B) = sum d(ai, bi)

Lower D usually sounds smoother because fewer spectral components move far at once, preserving auditory continuity.

Stability, Tension, and Resolution

Step-combos that strongly match harmonic-series templates (for example {0,4,7} with 4:5:6 relation) are often perceived as stable endpoints. Moving to sets with weaker fusion or larger voice movement increases tension. Returning to stable sets with reduced movement is heard as resolution.

In this framing:

• Tension = departure from high-fusion patterns and/or larger aggregate movement
• Resolution = return toward high-fusion patterns and/or smaller aggregate movement

This avoids culturally specific rule language while still capturing the perceptual dynamics.

Concrete Hz example: Using Do4 = 261.63 Hz as reference, the Position 0 step-combo {0,4,7} produces frequencies 261.63, 329.63, 392.00 Hz (ratio ≈ 4:5:6). Position 7 step-combo {7,11,2} produces 392.00, 493.88, 293.66 Hz. When these two step-combos are played in sequence, the shared frequency 392.00 Hz provides continuity while the moving voices create directional pull.

Example 1: Closed Loop with Minimal Return Cost

Sequence (Pos 0 → Pos 5 → Pos 7 → Pos 0, i.e., I–IV–V–I in Western terms):

{0,4,7} -> {0,5,9} -> {2,7,11} -> {0,4,7}

One low-cost assignment:

Interpretation: the middle transition has the largest movement and is commonly heard as the point of greatest directional drive. The final return restores the opening spectral template.

Example 2: Alternating Stable and Ambiguous Sets

Sequence:

{0,4,7} -> {0,4,8} -> {0,4,7}

• {0,4,7} aligns with 4:5:6 (strong fusion)
• {0,4,8} is more symmetric and less harmonic-series aligned

Only one pitch shifts by one step each transition (7 <-> 8), so movement is minimal, but spectral interpretation changes sharply. This is a high-contrast, low-distance tension device.

Example 3: Stepwise Bass Trajectory

Sequence (root shift by +1 each event, same interval shape):

{0,4,7} -> {1,5,8} -> {2,6,9} -> {3,7,10}

Each voice can move by +1 each step, giving constant small motion (D = 3 per transition). Perceptually, this sounds smooth locally but directionally unstable globally because no high-fusion home set is re-established.

Psychoacoustics: Prediction Over Time

The auditory system does not evaluate each chord in isolation. It builds short-horizon expectations from recent transition statistics:

• Repeated transition patterns create strong predictions
• Predicted arrivals trigger reward when fulfilled
• Violations create surprise and orienting response

So musical emotion in progression space can be framed as prediction error over harmonic trajectories, not mystical harmony rules.

Hear the Progressions

Select a progression preset below, then click ▶ Play to hear the step-combos in sequence. Position numbers indicate the chromatic step of each triad’s root (e.g., Position 7 = root at step 7, the “dominant” in Western terms). Listen for the tension-resolution arc described above.

Translation Table

Connections

• Chords — defines step-combos used as progression states
• Intervals — step-interval metric underlying movement cost
• Consonance & Dissonance — explains fusion and roughness basis of stability
• Rhythm — progression is always embedded in onset timing
• Scales — progression choices are constrained by selected step-subset
• Notation Layer — progression trajectories are visualizable as geometric shifts