Harmony & Chord Progressions

This document explains the harmonic system in MIDI Sketch.

Chord Progressions

MIDI Sketch includes 22 built-in chord progressions, covering common pop music patterns.

4-Chord Progressions

ID	Name	Degrees	Character
0	Pop4	I-V-vi-IV	Ubiquitous pop
1	Axis	vi-IV-I-V	Melancholic
2	Komuro	vi-IV-V-I	Bright J-pop
3	Canon	I-V-vi-iii-IV	Classic
4	Emotional4	vi-V-IV-V	Emotional build
5	Minimal	I-IV	Simple two-chord
6	AltMinimal	I-V	Power pop
7	Progression3	I-vi-IV	Three-chord
8	Rock4	I-bVII-IV-I	Rock feel

5-Chord Progressions

ID	Name	Degrees	Character
9	Extended5	I-V-vi-iii-IV	Extended canon
10	Emotional5	vi-IV-I-V-ii	Complex emotional

Full Progression List

Total of 22 progressions including:

• Pop variants (bright, dark)
• Emotional variants
• Minimal (2-3 chord) patterns
• Rock-influenced
• Jazz-influenced with ii-V

Degree System

Chord degrees are represented as integers:

enum Degree {
    I   = 0,   // Tonic
    ii  = 1,   // Supertonic
    iii = 2,   // Mediant
    IV  = 3,   // Subdominant
    V   = 4,   // Dominant
    vi  = 5,   // Submediant
    vii = 6,   // Leading tone
    bVII = 10  // Flat seven (borrowed)
};

Chord Quality

Quality is determined by degree in major key:

ChordQuality getQuality(Degree degree) {
    switch (degree) {
        case I: case IV: case V: case bVII:
            return Major;
        case ii: case iii: case vi:
            return Minor;
        case vii:
            return Diminished;
    }
}

Chord Extensions

Extensions add color to basic triads:

Extension Types

Type	Notes Added	Example (C)
Triad	Root, 3rd, 5th	C-E-G
Sus2	Root, 2nd, 5th	C-D-G
Sus4	Root, 4th, 5th	C-F-G
7th	+ 7th	C-E-G-B/Bb
9th	+ 7th + 9th	C-E-G-B-D

Extension Application Rules

Configuration

struct ChordExtensionParams {
    bool enabled = true;
    float sus_probability = 0.3f;     // 30% chance
    float seventh_probability = 0.4f;  // 40% chance
    float ninth_probability = 0.2f;    // 20% chance
};

Voice Leading

Principles

1. Minimize movement: Each voice moves by smallest interval
2. Common tones: Retain shared notes between chords
3. Avoid parallel fifths/octaves: Classical constraint
4. Smooth bass: Stepwise or small leaps preferred

Algorithm

Voicing optimizeVoicing(Voicing prev, Chord next) {
    vector<Voicing> candidates = generateAllVoicings(next);

    return min_element(candidates, [&](auto& a, auto& b) {
        int distA = totalVoiceDistance(prev, a);
        int distB = totalVoiceDistance(prev, b);

        // Also penalize large leaps
        int leapA = maxSingleVoiceDistance(prev, a);
        int leapB = maxSingleVoiceDistance(prev, b);

        return (distA + leapA * 2) < (distB + leapB * 2);
    });
}

Voicing Types

Bass-Chord Coordination

The chord track uses bass analysis to avoid doubling:

struct BassAnalysis {
    bool hasRootOnBeat1;   // Root on downbeat
    bool hasRootOnBeat3;   // Root on beat 3
    bool hasFifth;         // Fifth present
    Tick accentTicks[];    // Strong beat positions
};

// When bass has root, chord uses rootless voicing
if (bassAnalysis.hasRootOnBeat1) {
    voicing = generateRootlessVoicing(chord);
}

Key Modulation

Modulation Points

Structure	Modulation Point	Amount
StandardPop	B → Chorus	+1 semitone
RepeatChorus	Chorus 1 → 2	+1 semitone
Ballad	B → Chorus	+2 semitones
Full patterns	Varies	+1 to +2

Implementation

struct Modulation {
    Tick tick;           // When to modulate
    int8_t semitones;    // How much (+1, +2)
};

// Applied during MIDI output
void MidiWriter::writeTrack(MidiTrack& track, Modulation mod) {
    for (auto& note : track.notes) {
        if (note.tick >= mod.tick) {
            note.pitch += mod.semitones;
        }
    }
}

Chord Tone Analysis

Used for melody generation to determine note consonance:

bool isChordTone(uint8_t pitch, Chord chord) {
    uint8_t pitchClass = pitch % 12;

    // Check against chord pitch classes
    for (auto& chordPitch : chord.pitchClasses()) {
        if (pitchClass == chordPitch) return true;
    }
    return false;
}

uint8_t nearestChordTone(uint8_t pitch, Chord chord) {
    // Find closest chord tone by semitone distance
    int minDist = 12;
    uint8_t nearest = pitch;

    for (auto& target : chord.pitches()) {
        int dist = abs(pitch - target);
        if (dist < minDist) {
            minDist = dist;
            nearest = target;
        }
    }
    return nearest;
}

Tension Notes

Non-chord tones used for melodic interest:

Tension	Interval	Resolution
9th	Major 2nd	Down to root
11th	Perfect 4th	Down to 3rd
13th	Major 6th	Down to 5th
b9	Minor 2nd	Down to root
#11	Aug 4th	To 5th

Usage by Vocal Attitude

Attitude	Tensions Allowed
Clean	None (chord tones only)
Expressive	9th, 13th on weak beats
Raw	All tensions, any beat