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The complete working grammar of Western tonal music: how scales and key signatures are built, how intervals and chords are constructed, how Roman numeral analysis labels any progression, how cadences
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# Music Theory Foundations
Credit: SteTy — published free in the Skills Hub
The complete working grammar of Western tonal music: how scales and key signatures are built, how intervals and chords are constructed, how Roman numeral analysis labels any progression, how cadences punctuate phrases, and how the seven modes recolor a key. Master this and a beginner can take any chord progression — pop loop, folk song, film cue — and name exactly what every chord is doing and why.
## Overview
Tonal music organizes pitches around a **tonic** (home note). Everything else is measured as distance and function relative to that center. Three layers do all the work: (1) **pitch collections** — scales, key signatures, modes; (2) **vertical structures** — intervals stacked into chords; (3) **syntax** — chord functions (tonic, predominant, dominant) moving through progressions and closing with cadences. Roman numeral analysis is the shorthand that compresses all three layers into labels like `I–V–vi–IV`, which is why the same four chords can be recognized instantly in any key.
## Core Principles
- **Intervals are the atoms.** Count letter names for the number, semitones for the quality. From C: C–D = major 2nd (2 semitones), C–E♭ = minor 3rd (3), C–E = major 3rd (4), C–F = perfect 4th (5), C–G = perfect 5th (7), C–A = major 6th (9), C–B = major 7th (11), C–C = octave (12). Perfect intervals (unison, 4th, 5th, octave) invert to perfect; major/minor swap; augmented ↔ diminished.
- **The major scale is one fixed pattern:** W–W–H–W–W–W–H (whole = 2 semitones, half = 1). Natural minor is W–H–W–W–H–W–W. Every key signature is just that pattern starting on a new tonic.
- **Key signatures follow the circle of fifths.** Order of sharps: F♯ C♯ G♯ D♯ A♯ E♯ B♯ ("Father Charles Goes Down And Ends Battle"). Order of flats is the reverse: B♭ E♭ A♭ D♭ G♭ C♭ F♭. Sharp keys ascend by fifths (G=1♯, D=2♯, A=3♯…); flat keys by fourths (F=1♭, B♭=2♭…). Minor keys sit a minor 3rd below their relative major (3♯ = A major / F♯ minor).
- **Chords are stacked thirds.** A triad = root + 3rd + 5th. Major (4+3 semitones), minor (3+4), diminished (3+3), augmented (4+4). Add another third for 7th chords: major 7, dominant 7 (major triad + minor 7th — the tension engine of tonal music), minor 7, half-diminished (ø7), fully diminished (vii°7).
- **Function beats identity.** Every diatonic chord acts as **tonic** (I, vi — rest), **predominant** (ii, IV — preparation), or **dominant** (V, vii° — tension demanding resolution). Progressions overwhelmingly flow T → PD → D → T.
## Techniques
**Building diatonic chords.** Spell the scale, stack thirds on each degree. Major key pattern: I (major), ii (minor), iii (minor), IV (major), V (major), vi (minor), vii° (diminished). In C: C, Dm, Em, F, G, Am, B°. Natural minor: i, ii°, III, iv, v, VI, VII. In practice minor keys raise scale degree 7 (harmonic minor) so v becomes **V** and VII becomes vii° — that raised leading tone is what makes minor cadences bite.
**Roman numeral analysis, step by step.** (1) Find the tonic — check the key signature, then confirm with the first/last chords and where phrases resolve. (2) For each chord, identify its root and quality. (3) Locate the root's scale degree; write the numeral in uppercase for major, lowercase for minor, ° for diminished, ø for half-diminished. (4) Add inversion figures: root position = no figure, first inversion (3rd in bass) = 6, second inversion (5th in bass) = 6/4; seventh chords use 7, 6/5, 4/3, 4/2. (5) Mark accidentals that break the key (e.g., ♭VI) and slash labels for secondary functions (V/V = "five of five").
**Cadence recognition.** Cadences are harmonic punctuation at phrase ends:
- **Perfect authentic (PAC):** V–I, both root position, scale degree 1 in the melody. Full stop; strongest close.
- **Imperfect authentic (IAC):** V–I with any condition broken (inversion, melody ending on 3 or 5), or vii°–I. Comma-like.
- **Half (HC):** phrase ends on V. A question mark — demands continuation.
- **Deceptive (DC):** V–vi (or V–VI in minor). The expected resolution swerves; used to extend form.
- **Plagal (PC):** IV–I. The "Amen" cadence — conclusive but gentler.
- **Phrygian half:** iv6–V in minor, bass descending by half step (♭6–5). Baroque-flavored half close.
**The seven modes.** Rotations of the major scale, ordered brightest → darkest: **Lydian** (♯4 — floating, dreamy; *The Simpsons* theme), **Ionian** (major itself), **Mixolydian** (♭7 — bluesy rock; "Sweet Home Alabama," "Norwegian Wood"), **Dorian** (♭3, ♭7, natural 6 — hopeful minor; "Scarborough Fair," Miles Davis's "So What"), **Aeolian** (natural minor; "House of the Rising Sun"), **Phrygian** (♭2 — dark, Spanish/metal color), **Locrian** (♭2, ♭5 — tonic chord is diminished, so it rarely sustains a whole piece). Practical method: play the parent major scale starting on the mode's degree — D Dorian = C major's notes heard from D.
## Worked Examples
**Analyzing a pop loop.** Chords: C – G – Am – F. Key signature: none. C major fits; C sounds like home. Roots are scale degrees 1, 5, 6, 4; qualities major, major, minor, major → **I–V–vi–IV**, the "Axis" progression. Functions: T–D–T–PD, a self-renewing loop that never fully cadences — which is why it can repeat for an entire song (U2's "With or Without You," in D: D–A–Bm–G).
**Analyzing in minor.** Chords: Am – F – C – G. Relative major of A minor is C major (no sharps/flats), and phrases resolve to Am → key is A minor: **i–VI–III–VII**. Note VII is G major, not the dominant — pop minor loops often avoid V entirely, trading cadential drive for endless rotation.
**Spotting the cadence.** A phrase in G major ends …D7 → Em. V7 moving to vi instead of I = **deceptive cadence**. Expect the phrase to continue — the composer just bought another four bars.
## Common Pitfalls
- Confusing relative major/minor: C major and A minor share a key signature; the tonic is decided by resolution, not by the signature alone.
- Labeling a major II chord in a major key as "II" — a raised chord usually functions as **V/V**; label the function, not just the quality.
- Calling any V–I a PAC: if either chord is inverted or the melody ends on 3 or 5, it is an IAC.
- Forgetting that minor-key dominants are major (V, vii°) thanks to the raised leading tone — v and VII have different, weaker functions.
- Treating the cadential 6/4 (I6/4–V) as a tonic arrival; it is dominant function in disguise.
## Practice Drills
1. **Fifths fluency:** recite the order of sharps and flats daily until automatic; name any key signature's major and minor keys in under 3 seconds.
2. **Chord spelling sprints:** in a random key, spell all seven diatonic triads, then all seventh chords.
3. **Loop labeling:** take five songs you know, write out their verse progressions in Roman numerals, and mark each chord's function (T/PD/D).
4. **Cadence dictation:** play or listen to phrase endings and classify PAC / IAC / HC / DC / PC before checking.
5. **Mode A/B:** improvise over a Dm vamp first in D Aeolian, then D Dorian — the raised 6th (B natural vs B♭) is the whole lesson in one note.
## When to Use and Limits
- **Use it when:** a task calls for music theory foundations, as laid out in the Techniques and Worked Examples above.
- **Watch first for:** (see Common Pitfalls).
- **Limits:** this is a general reference drawn from public sources; it is a starting point for practice, not a full course, and attributions and dates should be checked against the cited sources before quoting them.
## Quick Reference
- Major scale: W W H W W W H · Diatonic triads: I ii iii IV V vi vii°
- Sharps order: F C G D A E B · Flats order: B E A D G C F
- Cadences: PAC V–I (root pos., melody 1) · IAC V–I (weakened) · HC ends on V · DC V–vi · PC IV–I · Phrygian iv6–V
- Modes bright→dark: Lydian, Ionian, Mixolydian, Dorian, Aeolian, Phrygian, Locrian
- Functions: Tonic I/vi · Predominant ii/IV · Dominant V/vii°
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