Advanced theory
The next layer after Western foundations.
Foundations covered pitch through chords, Roman numerals, and inversions.
This page starts with cadences and functional harmony,
then how chords connect, how melodies decorate them, how pieces are shaped,
and tools for keys, arranging, and feel.
Mirror: advancedtheory.md.
The full path
- Cadences — how phrases end
- Functional harmony — chord jobs
- Smooth chord changes (voice leading)
- Old bass shorthand (figured bass)
- Temporary “V of …” chords (secondary dominants)
- Melody notes that aren’t in the chord
- Phrases and song shapes
- Viola / cello clefs
- How many melodies at once?
- Turning a lead sheet into an arrangement
- Moving a piece to a new key
- Nearby vs distant keys
- Roman numerals in minor
- Fully diminished 7th chords
- Swing vs straight eighths
1 · Cadences (how phrases end)
In one line: a cadence is the chord motion that ends a phrase — harmonic punctuation (period, comma, question mark).
You already know the chord letters from foundations · chords in a key. Here the labels matter: they tell you whether the phrase closed, hung open, or surprised you.
The four everyday cadences (major)
| Cadence | Motion | In C | Feel |
|---|---|---|---|
| Authentic | V → I (or V7 → I) | G → C | strong close — the “period” |
| Half | … → V | … → G | hangs open on the dominant — a “comma / question” |
| Plagal | IV → I | F → C | “Amen” — soft close, no leading-tone push |
| Deceptive | V → vi | G → Am | expects I, lands on vi — delayed home |
Perfect vs imperfect authentic (PAC / IAC)
Both are V → I (or V7 → I). The labels refine how closed it feels:
- PAC (perfect authentic) — both chords in root position, and the melody (top voice) ends on the tonic note. Strongest “done.”
- IAC (imperfect authentic) — still V→I, but something is softer: an inversion, or the melody ends on 3 or 5 instead of 1. Still a close, less final.
Try it: play G–C with C in the top voice (PAC feel), then G–C with E on top (IAC feel). Same roots; different finality.
Why V→I feels so strong
- Roots fall a fifth (or rise a fourth) — neighbours on the circle of fifths.
- The leading tone (B in C major) wants to resolve up to C.
- In V7 (G–B–D–F), the tritone B–F wants to collapse inward to C–E.
Minor-key extras
- Authentic close is usually V → i (E → Am) — raise the leading tone so V is major (see minor numerals).
- Phrygian half cadence — iv6 → V in minor (e.g. Dm/F → E in A minor): bass steps down by half step into V; common “open” ending in minor phrases.
- Plagal and deceptive still exist (iv → i, V → VI).
How to practise hearing them
- Play a short I–… progression and stop on V (half) vs finish on I (authentic).
- Swap the last chord: V→I vs V→vi (deceptive) — notice the “almost home.”
- In a song you know, mark where the harmony feels like a sentence end — label it.
Cadences feed phrases & form: periods are often half cadence (question) then authentic (answer).
2 · Functional harmony (chord jobs)
In one line: Roman numerals name which chord; function names its job in the key — home, leave-home, or pull-home.
Three jobs (major)
| Job | Typical chords | Role |
|---|---|---|
| Tonic (T) | I · vi · (iii) | home / rest — stable |
| Predominant (PD) | IV · ii · (vi) | leave home; point toward the dominant |
| Dominant (D) | V · V7 · vii° | tension that wants tonic |
Classic sentence: T → PD → D → T (I–IV–V–I or I–ii–V–I). That order is the backbone of a huge amount of tonal music.
Same job, different chord (substitutes)
- vi can stand in for I (softer tonic) — deceptive cadence is V→vi.
- ii often replaces IV as predominant (ii–V–I vs IV–V–I).
- vii° shares dominant function with V (both contain the leading tone).
- iii is the weakest tonic cousin — used less as a “home” stop.
Map a pop loop to jobs
| Loop | In C | Jobs (rough) |
|---|---|---|
| I–V–vi–IV | C–G–Am–F | T → D → T(soft) → PD — spins without a full stop |
| I–IV–V–I | C–F–G–C | T → PD → D → T — textbook sentence |
| ii–V–I | Dm–G–C | PD → D → T — jazz/pop turnaround |
| I–vi–IV–V | C–Am–F–G | T → T(soft) → PD → D — ends ready to loop or cadence |
Loops can avoid a PAC for minutes; function still explains why a bar feels like departure, hanging, or return — even when letter names change with the key.
Where this page goes next
- Smooth chord changes — how voices move between jobs.
- Secondary dominants — borrow dominant function for a non-tonic chord (V/V, etc.).
- Minor numerals — same jobs in minor (i, iv, V→i).
3 · Smooth chord changes (voice leading)
In one line: when chords change, each note should have a sensible path to the next chord — like four singers who don’t jump randomly.
Classical writing often imagines four parts stacked high→low: Soprano · Alto · Tenor · Bass (SATB). The same ideas work with four fingers on a keyboard or with guitar and bass roles.
What “good” usually means
- Keep shared notes. C major (C E G) → F major (F A C): the C can stay put.
- Move the others by step when you can (E→F, G→A), not big leaps.
- Outer voices (highest + lowest) often move in opposite directions (contrary motion) so the change feels balanced.
- Bass is allowed bigger leaps (4ths/5ths) because roots often move that way (C→G, G→C).
What strict classical style avoids
- Two voices sliding in parallel perfect 5ths or octaves (sounds hollow / “stuck together”).
- Voices crossing (alto above soprano) or leaving the leading tone (B in C major) hanging without resolving to C.
On your instrument: “change the chord with the fewest finger moves” is voice leading. Pop and jazz break the strict rules all the time — the ear still likes smooth connections.
4 · Old bass shorthand (figured bass)
In one line: numbers under a bass note tell you which intervals to stack above that bass — an older way to write the same idea as modern slash chords.
Today we write C/E (“C major with E in the bass”). In figured bass you might only see a bass note E with a 6 under it — meaning “put a 6th above this E,” which lands on C (the root). Same chord, different notation.
| Numbers under the bass | What it means | Today’s writing |
|---|---|---|
| nothing (or 5 / 3) | ordinary triad, root in the bass | C |
| 6 | 1st inversion — root is a 6th above the bass | C/E |
| 6 4 | 2nd inversion — 6th and 4th above the bass | C/G |
| 7 | 7th chord, root in the bass | G7 |
| 6 5 | 7th chord, 1st inversion | G7/B |
| 4 3 | 7th chord, 2nd inversion | G7/D |
| 4 2 (or 2) | 7th chord, 3rd inversion (7th in the bass) | G7/F |
Accidentals on the numbers raise or lower that interval. For song charts, slash chords on the foundations page are enough; figured bass matters when you read older classical scores.
5 · Temporary “V of …” chords (secondary dominants)
In one line: the V→I “pull home” trick applied to a chord that is not the home tonic — a short visit that makes that chord feel like a temporary home.
In C major, plain V→I is G → C. Now suppose you want a stronger arrival on G (the V chord). The V of G is D major (or D7). So D7 → G → C is “five of five, then five, then one.” Notation: V/V → V → I (read “five of five”).
These chords usually add a sharp or flat that is not in the home key (D7 needs F♯ in C major). That chromatic note is the clue you’re hearing a secondary dominant.
| Label | Meaning | In C major | Then often goes to |
|---|---|---|---|
| V/V or V7/V | dominant of V | D or D7 | G |
| V/ii | dominant of ii | A or A7 | Dm |
| V/vi | dominant of vi | E or E7 | Am |
| V/IV | dominant of IV | C7 (with B♭) | F |
Try it: play C → D7 → G → C. The D7 “points at” G harder than a plain Am or Dm would. That pointing is the whole idea.
6 · Melody notes that aren’t in the chord
In one line: if the band plays C (C–E–G) but the singer hits a D, that D is a non-chord tone — decoration around the harmony.
These get names from how you arrive and how you leave:
| Name | Plain English | Tiny example over C |
|---|---|---|
| Passing | step through on the way somewhere | C–D–E (D fills C→E) |
| Neighbor | step away and back | E–F–E |
| Suspension | hold an old note into a new chord, then fall | hold G while chord becomes F, then resolve G→F |
| Appoggiatura | leap in, then step to a chord tone | leap to A, step to G |
| Escape | step away, then leap away | E–F then leap down |
| Anticipation | play the next chord’s note early | sing F before the F chord arrives |
You do not need every label to play — use them when you want to describe why a melody feels smooth or spicy against the chords.
7 · Phrases and song shapes
In one line: form is how long ideas are grouped — from a tiny hook up to whole sections of a piece.
- Motive — a short recognizable cell (rhythm + shape). Think of a famous four-note opening: tiny, but you know it instantly.
- Phrase — a complete musical sentence, often ending with a cadence.
- Period — two phrases as question + answer (antecedent ends open, consequent ends more closed).
- Binary = A then B · Ternary = A B A · Strophic = same music, new words each verse (many folk songs).
- Sonata form (big classical shape, overview only): exposition (themes — home key, then usually a new key) → development (themes get twisted) → recapitulation (themes return in the home key).
8 · Viola & cello clefs (C clefs)
In one line: treble and bass aren’t the only clefs — a C clef pins Middle C to a chosen line so mid-range instruments avoid endless ledger lines.
- Alto clef (viola) — Middle C on the middle line of the staff.
- Tenor clef (high cello / bassoon / trombone) — Middle C on the second line from the top.
If you only play piano, guitar, or voice from treble/bass / TAB, skip this until a score needs it.
9 · How many melodies at once? (texture)
In one line: texture describes the relationship between lines — one tune, tune+chords, or several independent tunes.
| Word | Means | Everyday example |
|---|---|---|
| Monophony | one melodic line | solo voice, or everyone on the same tune |
| Homophony | melody + chords | almost every pop song |
| Polyphony | independent melodies together | a round / fugue |
| Heterophony | same melody with simultaneous variants | some folk / traditional ensembles |
10 · Turning a lead sheet into an arrangement
In one line: a lead sheet gives you melody + chord symbols (+ lyrics). Arranging means choosing bass, voicings, and rhythm so it sounds like a band.
- Read the symbol — C, Am7, G7/B mean specific pitch sets (see foundations · chords / inversions).
- Give the bass a job — usually the root, or the note after the slash.
- Fill the middle — on piano/guitar, play enough chord tones under the melody. In jazz, the 3rd and 7th (guide tones) often define the quality more than the root.
- Leave the melody space — don’t cover the singer/lead with thick chords in the same register.
- Optional color (9ths, 13ths) comes after the basic spelling is clear.
11 · Moving a piece to a new key (transposition)
In one line: shift every pitch by the same interval so the song fits a new key (singer’s range, or a Bb instrument part).
Keep the interval quality the same; change the key signature to match. On fretted instruments, sliding a shape up or down the neck is physical transposition.
Example: a song in C that is too low for a singer might move up a whole step to D — every C becomes D, every G becomes A, and so on.
12 · Nearby vs distant keys
In one line: keys that share almost the same signature sound “nearby”; keys with many different sharps/flats sound “far.”
From C major, close neighbours include Am (relative minor), F (1♭), G (1♯), and their relatives — next-door slices of the circle of fifths. Jumping from C major to F♯ major is distant. Moving to a nearby key usually feels smoother.
13 · Roman numerals in minor
From foundations: major-key chords in a key (Roman numerals). Minor keys use different triad qualities — and raising the leading tone makes a real V chord that pulls to i.
A common map (with that raised 7th on V and vii°):
In A minor: Am · B° · C · Dm · E · F · G♯°. Real music freely mixes natural / harmonic / melodic choices — label what you actually hear.
14 · Fully diminished 7th chords
In one line: stack minor thirds (C♯–E–G–B♭) and you get a tense chord that can tip into several resolutions — useful as tension or a chromatic connector.
It is symmetric (every note is a minor 3rd from the next), so any tone can act like a leading tone up a half step. Different from the foundations half-diminished chord (m7♭5), which has a minor 7th on top, not a diminished 7th.
15 · Swing vs straight eighths
In one line: straight eighths are even; swing makes the first part of the beat longer and the second shorter (a long–short feel).
Charts often still draw equal eighths and just write the word swing. How uneven depends on tempo and style. Theory names the contrast; grooves in the rooms teach the feel.