Week 9 — Chapter · Triads

Course: MUS 156 Music Theory I · Kenosis College
Instructor: Professor Hemsworth
Unit: Learning Unit 9 of 16 (Week 9) · two sessions per week
The unit's primary reading · ~30–40 minutes · SLOs 4 and 7 · Read this before the first session if you can, or right after — everything else in the module builds on it.

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The chord you've been singing since week 4

Every week since unit 4, this course has warmed up on the same three syllables: do, mi, sol. You've sung them climbing, falling, stacked against your neighbors' voices. Nobody ever told you what they were. That was deliberate.

Here is the reveal: do–mi–sol is a chord. Specifically, it's a major triad — the single most common chord in the music you play, the sound under the first word of nearly every song your congregation or your cover band opens with. Your ear has owned this sound for years; your voice has rehearsed it for five weeks. Today it gets its name, its spelling, and its whole family.

That's this course's spine working exactly as designed — you already hear this; we're going to name what you already know — and it's worth pausing on where you stand. The midterm is behind you. Foundations is certified: nobody is checking anymore whether you can read notes, count rhythms, spell scales, or name intervals. You can. From this unit to the end of the course, we take that certified vocabulary and start building with it — chords this week, richer chords next week, then progressions, cadences, and finally whole charts. Unit 9 is the ground floor of harmony, and you arrive at it already fluent in everything the floor is made of.

By the end of this chapter you will be able to: build a triad as a stack of thirds and name its three members; spell all four qualities — major, minor, diminished, augmented — on any root from their interval recipes; read and write the four triad chord symbols (C, Cm, Cdim, Caug); harmonize any major scale into its seven diatonic triads with a Roman numeral and quality for each; do the same for minor, including the two chords harmonic minor upgrades; and identify root position, first inversion, and second inversion by the bass note, labeling them with the figures 6 and 6/4.

Where we are

Units 1–7 built the vocabulary: addresses, rhythm, scales, keys, and — critically for this unit — intervals, with size measured by letters and quality measured by half steps, each on its own ruler. Unit 8 certified all of it. This unit stacks intervals into chords, and every spelling move you make here is a unit-6 move wearing new clothes: a triad's quality is the pair of intervals it's built from. If intervals felt like abstract bookkeeping when you first met them, this is the week they start paying rent.

The stack: root, third, fifth

A triad is three notes stacked in thirds — built on every-other-letter, the way C skips D to reach E and skips F to reach G.

The three members have names, counted from the bottom of the packed stack:

• The root — the note the chord is named after and grows from.
• The third — a third above the root.
• The fifth — a fifth above the root.

On the staff, a triad packed in thirds is a snowman: three noteheads sitting on three adjacent lines, or three adjacent spaces. Line–line–line or space–space–space, no gaps, no overlaps. It's the fastest visual identification in all of music reading, and after this week your eye will find snowmen in every chart you open.

The every-other-letter rule is the definition, not a suggestion. C–E–G is a triad. C–D–G is not — D is only a second above C, so the stack breaks the pattern. That doesn't make C–D–G useless or illegal; it's a real sound, and your guitarist plays something like it every time a chart says "sus." It just isn't a triad, because "triad" is a spelling claim: three notes, stacked in thirds, root–third–fifth. Three random notes make a sound; three thirds-stacked notes make a triad.

Misconception check. "Any three notes played together are a triad." Count the letters. If you can't arrange the three notes as an every-other-letter stack, no triad exists — whatever the sound. The word works exactly like "interval" did in unit 6: it names a spelled relationship, not a headcount.

Four flavors on one root

Play a C major chord on any keyboard, then slide the middle note down one half step. Same root, same fifth — and the whole emotional weather changes. Your ear caught that flip years before this course existed. What changed is the chord's quality, and quality is not magic: it's the interval recipe above the root, measured with unit 6's two rulers.

There are four triad qualities. Here they are on the root C — and every one of these spellings comes straight from the course theory reference:

Quality	Recipe above the root	On C	Symbol
Major	M3 + P5	C E G	C
Minor	m3 + P5	C E♭ G	Cm
Diminished	m3 + d5	C E♭ G♭	Cdim
Augmented	M3 + A5	C E G♯	Caug

METER: free    CLEF: treble
| <C4,E4,G4>/w | <C4,Eb4,G4>/w | <C4,Eb4,Gb4>/w | <C4,E4,G#4>/w |

Four whole-note chords on the treble staff, every one rooted on C4: C–E–G (major), then C–E♭–G (minor — only the third moved), then C–E♭–G♭ (diminished — third and fifth both pulled down), then C–E–G♯ (augmented — the fifth pushed up). One root, four flavors, and each flavor is exactly one interval recipe.

Hear the architecture in the table. Major and minor share a perfect fifth — a stable frame — and differ only in the third. That's why they feel like siblings: same body, different paint. Diminished squeezes the frame: the fifth itself shrinks to d5, and the chord sounds pulled-in, restless. Augmented stretches it: the fifth grows to A5, and the chord sounds like it's leaning off the top of a ladder. Frame and paint: fifths set the stability, thirds set the color.

Two spelling disciplines carry over from unit 6, and both will be tested by your chatbot's mistakes this week:

• Letters first. The fifth of any C-rooted triad is a G-something, because C up to G is a fifth by letters. Spell C diminished as C–E♭–F♯ and you've written the right piano keys with a wrong letter — F♯ names the same key as G♭, but a C-to-F stack is a fourth, and the triad collapses. Same sound, different spelling, different chord: the enharmonic rule of unit 1, now bearing weight.
• The recipe is exact. Diminished is m3 + d5 — not "minor but weirder." Augmented is M3 + A5 — not "major but extra." Check both intervals, every time, until the recipes run automatically.

Chord symbols. Charts don't write "a major triad rooted on G" — they write G. The four symbols this unit owns, typed exactly this way in every quiz and AI session: a bare letter means major (C); m means minor (Cm); dim means diminished (Cdim); aug means augmented (Caug). Out in the wild you'll also meet ° for diminished and + for augmented — read them as the same two recipes. What you will not meet this week: symbols with 7 in them, and slashes like C/E. Those are unit 10's whole subject, and they're worth the wait.

Misconception check. "Quality = mood. Major is happy, minor is sad — done." The mood words are a decent first handle and a terrible final answer. Some of the saddest songs you know sit entirely on major triads; whole genres dance for joy in minor. Quality is an interval fact — which third, which fifth — that your ear perceives as color. The recipes let you spell the color; the mood is the song's business, not the chord's.

One key, seven chords: harmonizing the major scale

Now take the four flavors into a key. Build a snowman on every degree of the C major scale, using only C major's own notes — no accidentals, just the scale harmonizing itself:

METER: 4/4    CLEF: treble
| <C4,E4,G4>/q <D4,F4,A4>/q <E4,G4,B4>/q <F4,A4,C5>/q | <G4,B4,D5>/q <A4,C5,E5>/q <B4,D5,F5>/q <C5,E5,G5>/q |

Eight quarter-note chords climbing the treble staff — a triad on every step of the C major scale: C–E–G, D–F–A, E–G–B, F–A–C, G–B–D, A–C–E, B–D–F, and the octave C–E–G to close. Nothing but white keys; the qualities change anyway.

These seven are the diatonic triads of C major — the chords the key contains natively — and their qualities land in a pattern:

Degree	Chord	Quality	Roman numeral
^1	C E G	major	I
^2	D F A	minor	ii
^3	E G B	minor	iii
^4	F A C	major	IV
^5	G B D	major	V
^6	A C E	minor	vi
^7	B D F	diminished	vii°

Read the quality column downward: M m m M M m d. Memorize that ladder once and you own it in all fifteen major keys, because the pattern comes from the scale's step structure, not from C. In G major the same ladder gives G–B–D (I), A–C–E (ii), B–D–F♯ (iii), C–E–G (IV), D–F♯–A (V), E–G–B (vi), F♯–A–C (vii°). New key signature, same M m m M M m d.

Roman numerals are the analyst's chord symbols: the numeral names the scale degree the chord is built on, and the case carries the quality — upper case for major (I, IV, V), lower case for minor (ii, iii, vi), lower case with a small circle for diminished (vii°). It's a beautifully compact system, and it's also the seed of something bigger: because numerals name degrees instead of letters, a progression written in numerals transposes to any key instantly. Unit 11 builds that whole engine; this week you just need to read and write the seven.

Notice which chord got the strange quality. The triad on ^7 — B–D–F in C major — is the ladder's only diminished triad, and it's no accident: it's the only snowman whose frame lands on the scale's built-in tritone (unit 7's fa-to-ti itch, B-to-F seen from the other side). Play it and it squirms. It has a name for that squirm and a specific job, and unit 11 hands it both; for now, spell it correctly and enjoy that the weird chord is weird for a reason you can already explain with intervals.

And the naming ceremony completes itself here: do–mi–sol is ^1–^3–^5 — the I chord. The tonic triad. You've been singing the home chord of every key since week 4.

Misconception check. "Diminished means any dissonant chord." Diminished is one recipe — m3 + d5 — and nothing else qualifies, however crunchy it sounds. B–D–F is diminished because its two intervals say so. A cluster like C–D–G sounds far more abrasive and is not diminished (it's not even a triad). Let the spelling rule the word; the ear's job is to find the chord, not to define it.

Minor's grid — and the two chords worth upgrading

Harmonize natural minor the same way and seven more chords fall out. In A minor: i (A–C–E), ii° (B–D–F), III (C–E–G), iv (D–F–A), v (E–G–B), VI (F–A–C), VII (G–B–D). Quality ladder: m d M m m M M.

Look closely and you'll recognize every one of those chords — they're C major's seven, renumbered. Of course they are: relative keys share all seven notes (unit 5's oldest fact), so they must share all seven snowmen. What changes is which chord is home, and that changes everything about how the grid behaves.

But natural minor has a soft spot, and you already know where. Play i → v → i in pure natural minor: the v chord (E–G–B, minor) drifts home rather than driving home, because natural minor's ^7 is the subtonic — a whole step below tonic, no lean. Unit 5 taught the fix: harmonic minor raises ^7. Do that inside the chord grid and two chords upgrade:

• v becomes V: E–G–B turns into E–G♯–B — major — and suddenly the five chord pulls toward home like it means it. That pull has unit 7's tritone hiding in it (G♯ against D whenever the harmony thickens — next unit's territory).
• VII becomes vii°: the whole-step G–B–D on the subtonic gives way to G♯–B–D — diminished — built on the new leading tone, leaning hard on the tonic's doorstep.

(One more resident appears in harmonic minor's grid, for the curious: the triad on ^3 becomes III+ — C–E–G♯ in A minor — an honest-to-goodness augmented triad living diatonically. You'll spell it in exercises as a quality workout; music uses it sparingly, like hot sauce.)

So when you harmonize in minor, the practical answer to "which grid?" is: natural minor's chords, with V and vii° borrowed from harmonic minor whenever the music wants the pull home — which, in the songs you actually play, is most of the time. That's not a contradiction; it's the same choice you made melodically in unit 5, now made harmonically, and for the same reason.

Misconception check. "The five chord in a minor key is minor — the scale says so." Which scale? Natural minor says v (minor); harmonic minor — invented precisely for this moment — says V (major, with the raised ^7 as its third). Charts in minor keys overwhelmingly write the major V when they want motion home. Spell both, know why both exist, and read the chart in front of you.

Inversions: same chord, different floor

Sit at a keyboard and play C–E–G. Now move the bottom C up an octave and play E–G–C. Once more: G–C–E. Three sonorities, one chord — you can hear that the harmony never changed, only the floor under it did.

Here's the vocabulary, and the rule that governs it: a triad's identity comes from its root — the bottom of the stack when it's packed in thirds. Which member actually sounds lowest in a given voicing is a separate fact, called the bass note. When they match, the chord is in root position; when they don't, the chord is inverted:

• Root position — root in the bass: C–E–G.
• First inversion — third in the bass: E–G–C.
• Second inversion — fifth in the bass: G–C–E.

METER: 4/4    CLEF: treble
| <C4,E4,G4>/h <E4,G4,C5>/h | <G4,C5,E5>/h <C4,E4,G4>/h |

Four half-note chords on the treble staff: C major in root position (C4 lowest), then first inversion (E4 lowest), then second inversion (G4 lowest), then root position again to close the loop. Same three letter names throughout — one chord visiting its three floors.

Each floor has a label, borrowed from a shorthand system that continuo keyboardists have used since the 1600s. The figures count intervals above the bass note:

• Root position: a fifth and a third above the bass — figures 5/3, which are so completely the default that nobody writes them.
• First inversion: a sixth and a third above the bass — abbreviated to the figure 6.
• Second inversion: a sixth and a fourth above the bass — the figure 6/4.

Type the figures with a slash — 6/4, never 6-4. This course reserves the hyphen for a different job arriving in unit 14, and keeping the two marks separate now saves a real headache later.

How do you identify an inverted chord in the wild? Re-stack it in thirds. Given E–G–C: try E as root (E to G is a third… G to C is a fourth — the snowman breaks). Slide C to the bottom: C–E–G — thirds all the way up. Root C, quality major, and the sounding bass was E, the third: C major, first inversion, figure 6. The re-stack move works on every triad you will ever meet, and it takes about four seconds once it's a habit.

Why do musicians invert chords at all? Because the bass line is a melody too. Keep every chord in root position and your bass player leaps around like a kangaroo; let the chords invert and the bass can walk — C down to B under a G chord... which is a first-inversion move, and exactly the kind of sound you've admired in every well-arranged record you own.

Misconception check. "6/4 is a fraction." Nothing is being divided. The figures are two separate interval counts above the bass note — a sixth, and a fourth — stacked typographically the way the notes stack musically. And they're not a time signature either, despite the costume. Apartment labels, not arithmetic.

Why this makes you a better musician

Count what this unit just handed you, in gig terms. You can spell the call. When the leader says "it goes to F sharp minor," that's F♯–A–C♯ in your head before the count-off — no app, no hunting. You can name the flavor change. The moment a song darkens, you can say "that's the minor four" instead of "it gets sad there," and a thing you can name is a thing you can play into, anticipate, and reuse in your own writing. You can talk to the rhythm section like an arranger. "Keys, hold the chord; bass, give me the third on the bottom" is a first-inversion instruction, and it's the difference between five people playing the same chord and a band playing an arrangement. And you finally know what you've been singing: do–mi–sol was the tonic triad all along, which means every warm-up since week 4 has been chord practice in disguise. The studio cashes all of it: you'll sort flavors by ear, spell them on any root at relay speed, and voice a triad across the room — then hand the bass singer the third, and hear the room turn into an arrangement.

Key terms

• Triad — three notes stacked in thirds: root, third, fifth.
• Root — the note a triad is built from and named after; the bottom of the stack when packed in thirds.
• Third (chord member) — the member a third above the root; carries most of the chord's color.
• Fifth (chord member) — the member a fifth above the root; frames the chord's stability.
• Quality — a triad's flavor, determined by its interval recipe: major (M3+P5), minor (m3+P5), diminished (m3+d5), augmented (M3+A5).
• Chord symbol — chart shorthand for a chord: C (major), Cm (minor), Cdim (diminished), Caug (augmented).
• Diatonic triad — a triad built on a scale degree using only that key's own notes.
• Roman numeral — the analyst's chord label: degree number as numeral, with case carrying quality (I major, ii minor, vii° diminished).
• Quality ladder (major) — M m m M M m d: the diatonic qualities of every major key, in degree order.
• Bass note — the lowest sounding note of a voicing; not necessarily the root.
• Root position — root in the bass; figures 5/3, left unwritten.
• First inversion — third in the bass; figure 6.
• Second inversion — fifth in the bass; figure 6/4.
• Figures — interval counts above the bass, typed with slashes (6, 6/4), that label a chord's inversion.

Summary

• A triad is a three-note stack of thirds — root, third, fifth; every-other-letter or it isn't a triad, whatever it sounds like.
• Four qualities, four recipes above the root: M3+P5 major · m3+P5 minor · m3+d5 diminished · M3+A5 augmented — on C: C–E–G, C–E♭–G, C–E♭–G♭, C–E–G♯. Symbols: C, Cm, Cdim, Caug. Letters first, always: the fifth of a C chord is a G-something.
• Harmonizing any major scale yields the diatonic triads with the quality ladder M m m M M m d — numerals I ii iii IV V vi vii°, case carrying quality. Do–mi–sol is ^1–^3–^5: the I chord, sung since week 4.
• Natural minor's ladder is m d M m m M M (i ii° III iv v VI VII — the relative major's chords renumbered); harmonic minor upgrades two: major V and diminished vii°, via the raised ^7. III+ is the diatonic home of the augmented triad.
• Inversion changes the bass, not the identity: root position (root in bass), first inversion (third in bass, figure 6), second inversion (fifth in bass, figure 6/4). Figures count intervals above the bass and take slashes, never hyphens. Re-stack in thirds to find the root.

Check your understanding

Work these before peeking — they're ungraded, and worked answers follow at the bottom of the page.

1. Your bandmate plays B♭–D♭–F and asks what chord it is. Name the quality and the chord symbol — and explain, using letters, why the middle note must be spelled D♭ rather than C♯.
2. Spell the diminished triad on E, and name the major key in which that triad is diatonic on ^7.
3. In F major, give the Roman numeral, spelling, and quality of the triads on ^5 and on ^6.
4. A chart in A minor shows an E–G♯–B chord. Which minor-scale form put the G♯ there, what Roman numeral does the chord get, and what would the chord be if the song had stayed in pure natural minor?
5. You hear a D major triad with F♯ as the lowest sounding note. Name the inversion, the figure, and the bass member — then re-stack it in thirds to prove the root is still D.

Answers (worked reasoning — read after attempting)

1. B♭ minor — symbol B♭m (typed Bbm): B♭ up to D♭ is a m3 (letters B–C–D, a third; three half steps), and B♭ up to F is a P5. The third of a B♭-rooted triad must be a D-something, because B to D is a third by letters — C♯ names the same piano key as D♭ but makes B♭-to-C♯ a second, and the snowman collapses. Same sound, wrong letter, no triad.
2. E–G–B♭ (m3 + d5 above E). It sits on ^7 of F major — F major's quality ladder puts its one diminished triad on the leading tone, spelled E–G–B♭ from the key's own notes.
3. In F major: V = C–E–G, major (the triad on ^5) and vi = D–F–A, minor (the triad on ^6). The ladder M m m M M m d hands you both qualities before you spell a note.
4. The raised ^7 of harmonic minor put the G♯ there. The chord is V — E–G♯–B, major, ^5's triad with the leading tone as its third. In pure natural minor it would be v — E–G–B, minor — with the soft subtonic G instead of the leaning G♯. The chart chose the pull home; now you can name the choice.
5. F♯ lowest = the third in the bass: first inversion, figure 6. Re-stack in thirds: F♯-to-A is a third, A-to-D is a fourth — broken; put D on the bottom instead: D–F♯–A, thirds all the way, root D, quality major. Same chord on a different floor — D major in first inversion.

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Next in this module: the Readings & Resources page if you want other angles on triads (including two excellent drill machines), then Tutorial 9 — your AI tutor session, due before Week 9's second session so the studio's quality sort can build on it.

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