Harmony Study Guide

📖 Core Concepts Harmony – Combining different sounds (vertical frequency space) over time (horizontal time space) to create new musical ideas. Harmonic objects – Chords, textures, tonalities. Consonance vs. Dissonance – Consonance: simple pitch‑frequency ratios (e.g., 2:1 octave). Dissonance: rough, “unpleasant” intervals that tend to resolve. Interval – The pitch distance between two notes; classified as perfect, imperfect, or dissonant. Chord – Two or more pitch classes sounded together; triads (3 notes), seventh chords (4 notes), extensions (9th‑13th). Tertian, Quartal, Quintal harmony – Stacking thirds, fourths, or fifths to build chords. Close vs. Open position – Close: chord tones as near‑as‑possible; Open: spread over a wider register. Coordinate vs. Subordinate harmony – Coordinate links chords without hierarchy; subordinate creates a tonal hierarchy (functional harmony). --- 📌 Must Remember Perfect consonant ratios: 1:1 (unison), 2:1 (octave), 3:2 (perfect fifth), 4:3 (perfect fourth). Imperfect intervals – Seconds, thirds, sixths, sevenths (no exact overtone‑series ratios). Dissonant intervals – Minor 2nd, major 7th (roughest); tritone; minor 2nd/major 7th > major 2nd/minor 7th > tritone > minor 3rd/major 6th > major 3rd/minor 6th > perfect 4th/5th. Dominant seventh chord: \( \text{C7} = \{C, E, G, B\flat\} \). Major‑seven chord: \( \text{CΔ} = \{C, E, G, B\} \). Equal temperament: 12 equal steps; each interval is slightly off pure ratios. Enharmonic equivalence: Same pitch, different spelling → different harmonic function. --- 🔄 Key Processes Building a tertian chord – Stack a major/minor third above the root repeatedly: Root → +3rd → +3rd → (optional +3rd for seventh). Creating a quartal/quintal chord – Stack perfect fourths (quartal) or perfect fifths (quintal) from the root. Preparing & resolving tension – Prepare: Use a series of consonant chords to introduce a seventh (or other tension). Resolve: Move to a consonant chord (typically tonic or a related chord) where the tension note resolves stepwise. Voice‑leading for extensions – Add 9th, 11th, 13th by continuing the stack of thirds above a seventh chord. --- 🔍 Key Comparisons Tertian vs. Quartal/Quintal Tertian: built from thirds → traditional major/minor harmony. Quartal/Quintal: built from fourths/fifths → more open, modern sonorities. Close vs. Open Position Close: chord tones within one octave → denser texture. Open: spread > one octave → lighter, more spacious sound. Coordinate vs. Subordinate Harmony Coordinate: chords linked side‑by‑side, no sense of “goal.” Subordinate: chords function within a tonal hierarchy (tonic → dominant → resolution). Equal Temperament vs. Just Intonation ET: 12 equal steps, compromises pure ratios. JI: intervals tuned to exact simple ratios, sounding more consonant but less flexible for key changes. --- ⚠️ Common Misunderstandings “All thirds are consonant.” – Only major/minor thirds are considered consonant; stacked thirds can create dissonant seventh chords. “Tritone is always bad.” – In a dominant seventh context the tritone resolves smoothly (B♭–F♯ resolves to C–E). “Enharmonic notes are interchangeable.” – They sound the same but carry different functional meanings (e.g., G♯ vs. A♭). “Open position = less harmonic tension.” – Position affects texture, not inherent tension; a wide‑spaced dominant seventh is still tense. --- 🧠 Mental Models / Intuition Frequency‑ratio picture: Consonance = simple ratios → “clean overlap” of harmonic partials; dissonance = complex ratios → “beats” and roughness. Vertical vs. Horizontal: Think of harmony as a stack of bricks (vertical) placed along a timeline (horizontal). Tension‑Resolution as a Story Arc: Introduce a “question” (dissonance) → answer with a “statement” (consonance). --- 🚩 Exceptions & Edge Cases Tritone in a dominant seventh is less harsh because the chord’s other tones mask the beating. Minor 2nd in a melodic line can be acceptable if it occurs as a non‑harmonic passing tone rather than a vertical interval. Equal temperament beats: Some intervals (e.g., perfect fifth) are slightly mistuned compared to pure ratios, but the ear generally accepts them. --- 📍 When to Use Which Tertian harmony → Standard tonal music, functional progressions, pop, classical. Quartal/quintal harmony → Modal, jazz, film scores, “open” modern textures. Close position → Dense chordal accompaniment, piano voicings needing richness. Open position → Orchestral brass/strings, when you need space or want to avoid muddiness in lower registers. Coordinate harmony → Pedal‑point sections, static harmonies, ostinato patterns. Subordinate harmony → Cadences, functional progressions, tonal drama. --- 👀 Patterns to Recognize Dominant seventh → resolution to tonic (♭7 resolves down a half step). Stacked thirds → presence of seventh/extension (if you see a 4‑note stack, expect tension). Tritone appearing in a chord → likely a dominant function. Enharmonic spelling change → a pivot chord or modulation point. --- 🗂️ Exam Traps Choosing “perfect fifth” as a dissonant interval – It is actually consonant (ratio 3:2). Assuming all fourths are consonant – The tritone (augmented fourth/diminished fifth) is dissonant. Confusing “coordinate” with “parallel” motion – Coordinate refers to chord relationships, not voice‑leading motion. Selecting “just intonation” for modern key‑modulating questions – Most exam contexts assume equal temperament unless specified. Misidentifying a chord quality – Remember that “C7” is dominant (♭7), while “CΔ” is major‑seven (natural 7). ---