Week 10 — Chapter · Seventh Chords

Course: MUS 156 Music Theory I · Kenosis College
Instructor: Professor Hemsworth
Unit: Learning Unit 10 of 16 (Week 10) · 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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Two chords, one note apart

Sit at any keyboard — or open the keyboard app on your phone — and play these four notes together: C4, E4, G4, B4. Let it ring. That shimmer, that floating almost-finished feeling: you've heard it open a hundred ballads and close a thousand jazz tunes. Now lower just the top note a half step and play C4, E4, G4, B♭4. Completely different animal: bluesy, restless, leaning hard on the next chord like a runner leaning off first base.

One note changed. Your ear never once confused the two sounds — not today, not ever. What you may not have had, until this morning, is the news that those are Cmaj7 and C7, that the difference between them is the entire plot of this unit, and that by the end of the week you'll spell both of them — plus three more flavors — on any root, on demand.

Unit 9 built triads: three notes, stacked thirds. This unit stacks one more. Seventh chords are the working currency of every chart you'll ever be handed — worship slides, jazz lead sheets, the chord names floating over tabs on the internet — and this is the week they stop being decoration you skip over and start being words you read. It's also the week your term project begins: inside this week's assignment sits The Chart, milestone 1 — choose your song. The symbols you learn in the next twenty minutes are the notation your own Chart will be written in.

Where we are

Foundations is certified, and unit 9 spent that capital immediately: triads in four qualities, root position and two inversions, the figures 6 and 6/4, triad chord symbols. This unit is unit 9's second story — one move: add another third on top. Next, unit 11 gives the chords jobs. Every section below runs the same direction as always: sound first, name second, notation third.

The recipe: one more third

A triad is a stack of thirds three notes deep: root, third, fifth. Keep stacking. One more third above the fifth lands a seventh above the root — count the letters: C to B is C-D-E-F-G-A-B, seven names. The four-note result is a seventh chord, and the new note is called the chordal seventh (or just "the seventh").

On the staff, a triad in root position is three noteheads snowmanned line-to-line or space-to-space. A seventh chord is four — the snowman gets a hat, sitting one third above the fifth.

Everything new this week lives in that top note. The triad underneath can be major, minor, or diminished (unit 9's inventory), and the seventh above the root can be major (11 half steps — the leaning, one-shy-of-an-octave interval from unit 6), minor (10 half steps), or diminished (9 half steps, and spelled as a seventh — hold that thought; it matters in a page). Combine a triad with a seventh and you get the chord's quality.

Misconception check. "Any four notes played together make a seventh chord." The stacking law from unit 9 still governs: thirds, all the way up. Root–third–fifth–seventh, each a third above the last. C–E–G–A is a perfectly good sound (you'll meet it in living rooms and jazz clubs alike), but the A is a sixth above C, not a seventh — different chord, different name, different job. Thirds are what make chords spellable at all.

The five qualities

Here is the whole inventory, built on C. Five rows, five sounds you already know by feel:

Quality	Recipe	On C	Typed symbol
Major seventh (MM7)	major triad + major seventh	C E G B	Cmaj7
Dominant seventh (Mm7)	major triad + minor seventh	C E G B♭	C7
Minor seventh (mm7)	minor triad + minor seventh	C E♭ G B♭	Cm7
Half-diminished (ø7)	diminished triad + minor seventh	C E♭ G♭ B♭	Cm7b5
Fully diminished (°7)	diminished triad + diminished seventh	C E♭ G♭ B𝄫	Cdim7

METER: free    CLEF: treble
| <C4,E4,G4,B4>/w <C4,E4,G4,Bb4>/w <C4,Eb4,G4,Bb4>/w <C4,Eb4,Gb4,Bb4>/w <C4,Eb4,Gb4,Bbb4>/w |

Five whole-note stacks on the treble staff, every one rooted on C4: C–E–G–B (major seventh chord), C–E–G–B♭ (dominant seventh), C–E♭–G–B♭ (minor seventh), C–E♭–G♭–B♭ (half-diminished), and C–E♭–G♭–B𝄫 (fully diminished). Read left to right, exactly one note changes at each step — the whole quality system is a staircase, descending one half step at a time.

Play the row and listen for the staircase. The names attach to sounds you've already sorted: the major seventh chord shimmers and floats (ballad intros, neo-soul, the last chord of bossa novas). The dominant seventh is the engine of blues and the lean of every "here comes the chorus" moment — it wants to go, and unit 7 already told you why: hiding between its third and seventh is a tritone (in C7, E up to B♭ — count it: six half steps), and that restless interval is what's begging to resolve. The minor seventh chord is velvet — smooth, unhurried, the wallpaper of R&B. The last two rows are the specialists, and they deserve their own paragraph.

Half-diminished versus fully diminished. Both sit on the diminished triad C–E♭–G♭. The difference is entirely in the seventh:

• Half-diminished (ø7): diminished triad + minor seventh — C E♭ G♭ B♭. Only half the chord's intervals are diminished; the seventh stayed minor. Chart name: Cm7b5 — "C minor seven, flat five" — which is literally the recipe read aloud: take Cm7, lower the fifth.
• Fully diminished (°7): diminished triad + diminished seventh — C E♭ G♭ B𝄫. Everything diminished, top to bottom. Chart name: Cdim7.

And yes: B double-flat, not A. Same piano key, two different written notes — unit 1's law, still load-bearing. The chord is stacked thirds, and the letter stack C–E–G–B must survive the accidentals: C to B𝄫 is a seventh (seven letter names), which is what the chord's own name claims. Write A instead and the "seventh" becomes a sixth on paper, the stack breaks, and the next musician reads a different chord. Nine half steps spelled as a seventh is a diminished seventh; the same nine half steps spelled C-to-A is a major sixth — same sound, different interval, exactly the unit 7 distinction, now with a paycheck attached.

Misconception check. "ø and ° are typographic variants — half-diminished and diminished are the same chord." One note apart, and audibly so: play Cm7b5 then Cdim7 and the second is distinctly darker, tenser, more horror-movie. Say "half-diminished" to a keys player and you'll be understood in two seconds; treat the symbols as interchangeable and someone plays the wrong chord in front of an audience.

Reading the symbols: what "7" really means

Chord symbols are how working musicians write harmony to each other — texted, scribbled, projected on a screen at rehearsal. This course types them the way charts do: Cmaj7, C7, Cm7, Cm7b5, Cdim7. One rule unlocks the whole system, and it's the one that traps everyone at their first jam session:

A plain 7 means the dominant recipe — major triad plus MINOR seventh.

C7 is C E G B♭. It is not "C major with a seventh on top" in the maj7 sense; that chord has its own symbol, Cmaj7, which spells out "maj" precisely because the plain 7 was already taken. History handed the naked numeral to the sound centuries of ears treated as the seventh chord — the dominant one — and every chart since has honored the deal.

Worked example. A chart says G7. Recipe: G major triad — G, B, D — plus a minor seventh above G. Count letters G up to F: seven names; ten half steps confirms minor. G B D F. Now the neighboring symbol Gmaj7: same triad, major seventh above G — G B D F♯. One accidental apart, a whole genre apart. Play F♯ over a blues in G because you misread the 7 and the whole band will hear it.

The rest of the family reads just as literally. Am7: A minor triad + minor seventh = A C E G. Em7b5: E minor seven with the fifth flattened = E G B♭ D — the half-diminished recipe wearing its street name. C#dim7: fully diminished on C♯ = C♯ E G B♭.

Misconception check. "7 by itself means major seventh — surely the plain number is the plain chord." Backwards, and expensively so. Plain 7 = dominant = minor seventh above the root, every time, on every chart in every genre. When someone wants the shimmer, the chart will say maj7 (or Δ7 in jazz handwriting — same meaning, different pen). This single reading rule is the difference between "read it right the first time" and "learned it in front of an audience."

The diatonic sevenths — and the spelling everyone prints wrong

Unit 9 harmonized the major scale in triads. Same exercise, one story taller: build a seventh chord on every degree of C major using only the key's own notes — white keys only. The qualities sort themselves:

Degree	Chord	Spelled	Quality
^1	IM7	C E G B	major seventh
^2	ii7	D F A C	minor seventh
^3	iii7	E G B D	minor seventh
^4	IVM7	F A C E	major seventh
^5	V7	G B D F	dominant seventh
^6	vi7	A C E G	minor seventh
^7	viiø7	B D F A	half-diminished

The pattern is worth saying out loud: two major sevenths (I and IV), three minor sevenths (ii, iii, vi), and exactly one dominant seventh — V7. The key manufactures precisely one, on ^5, and that scarcity is why the V7 sound points home so unmistakably: hear a dominant seventh and your ear already knows which chord is being promised. (The tritone inside it — B up to F in G7 — is unit 7's restless interval doing the pointing. Unit 11 gives this pull its official vocabulary; your ear has had it for years.)

And then there's the last row — the most commonly misprinted chord in amateur theory content, and this course's flagged regression. Read this paragraph twice.

The seventh chord on ^7 in a major key is half-diminished — viiø7 — never fully diminished. Build it slowly: B–D–F–A. B to D, minor third. B to F, diminished fifth — so far, the diminished triad, as unit 9 promised. Now B to A: seven letter names, ten half steps — a minor seventh. Diminished triad + minor seventh = half-diminished.

Why can't it be viio7, the fully diminished version? Because that chord is B–D–F–A♭, and A♭ is not in C major. Run the same test in any major key you like: the fully diminished seventh on ^7 always demands a note the key signature doesn't own — the diminished seventh above ^7 is always the flatted ^6, and major keys don't flat their ^6. That is exactly what "not diatonic" means. viio7 is not diatonic to any major key. It does have a home — harmonic minor, where the raised ^7 makes it genuinely diatonic, and unit 11 hands it those keys — but in major, the honest chord on ^7 is viiø7, every time, in all fifteen keys.

This error is everywhere: blog posts, video thumbnails, and — reliably — chatbots. Paste "spell the seventh chord on B in C major" into an AI and a startling fraction of the time you'll get B–D–F–A♭ delivered with total confidence: a "diatonic" chord containing a note the key doesn't have. Your tutorial audit this week hunts exactly this. Catching it is not pedantry; it's the difference between an answer that survives the key-membership test and one that just sounds authoritative.

Misconception check. "Diminished triad on ^7, so the seventh chord there must be fully diminished." The triad is diminished; the seventh above the root is whatever the key supplies — and the key supplies A natural, a minor seventh. Half of the stack is diminished: half-diminished. The fully diminished version needs an accidental in every major key on the circle.

Inversions and the figures: 7 · 6/5 · 4/3 · 4/2

Four notes means four candidates for the bass — root position plus three inversions, one more floor than triads had. Unit 9's law carries up a story unchanged: inversion changes the color and the bass line, never the chord's identity. G7 with F in the bass is still G7 — same four names, new floor.

The shorthand, one figure per floor — written with slashes, always:

Bass note	Position	Figure
root	root position	7
third	first inversion	6/5
fifth	second inversion	4/3
seventh	third inversion	4/2

METER: free    CLEF: treble
| <G3,B3,D4,F4>/w <B3,D4,F4,G4>/w <D4,F4,G4,B4>/w <F4,G4,B4,D5>/w |

Four whole-note stacks on the treble staff: G7 in root position (G3 at the bottom — figure 7), then first inversion (B in the bass — 6/5), second inversion (D in the bass — 4/3), and third inversion (F in the bass — 4/2). Play them in a row and sing the bass line as it climbs: same chord all four times; your ear signs off on the identity rule.

A memory hook for the sequence: the figures count down as the bass climbs up — 7, then 6/5, then 4/3, then 4/2. (Each figure is really naming the intervals sounding above the bass note, which is where the numbers come from; you don't need to derive them, just to read them.)

Why slashes and never hyphens — this course means it. You will someday see "4-3" in a piece of music, and it will not mean an inversion. A hyphen in figures marks a suspension: one interval resolving to another over a single held bass note — a leaning-and-landing event, not a chord position. That tool arrives in unit 14. Until then (and forever after), the lanes stay clean: 6/5, 4/3, 4/2 with slashes are chord positions; 4-3 with a hyphen is a different sentence entirely. Writing one when you mean the other says something you don't mean, to exactly the readers who know the difference.

Misconception check. "Putting the seventh in the bass makes it a new chord." Same test as unit 9: name the four letters. F–G–B–D from the bass up still contains exactly G, B, D, F — it's G7, third inversion, figure 4/2. The bass note is the address of the floor you entered on, not a new building.

Slash chords: the letter after the slash is the bass you actually hear

Charts have their own way of ordering a bass note, and you've been squinting at it for years: C/E. G7/D. Am7/G. Read the slash as the word "over": C over E — play the C major triad, put E on the bottom. The letter after the slash is the bass note you actually hear.

• C/E = C major triad, E in the bass. E is the chord's third — this is the triad's first inversion (unit 9's figure 6), spelled gig-style.
• G7/D = G7 with D in the bass. D is the fifth — the 4/3 position, wearing street clothes.
• Am7/G = A minor seven with G in the bass. G is the chordal seventh — a 4/2 in the wild, and a staple of every descending-bass worship progression you've ever played.

Figures and slashes are two dialects for one idea: figures are how analysts write the bass choice; slashes are how charts order it. You now read both.

Misconception check. "C/E is C divided by E — or maybe just the two notes C and E." It's an instruction, not arithmetic: whole chord on the left, bass note on the right. Your bass player reads the right side of the slash; everyone else reads the left. (If the letter after the slash isn't a member of the chord, that's an advanced flavor you'll meet in later courses — in this course's charts, the slash bass is always a chord member.)

Why this makes you a better musician

Count what this unit just handed you, in gig currency. The lead sheet a music director slides across the piano — Gmaj7 · Em7 · Am7 · D7 — you now read correctly on the first pass, because D7 and Dmaj7 are different words to you now, not fuzzy variants of "D-something." The moment in rehearsal when the keys player asks "what's that chord in bar 12?" you can answer "half-diminished" — two seconds, zero ambiguity, and the person on the other end knows exactly which four notes to play. The pull your ear has always felt right before a chorus lands: you can now name the machinery — that's the key's one dominant seventh, tritone inside, begging its way home — which means you can build that lean into your own arrangements on purpose. Slash chords stopped being typos: C/E and Am7/G are now precise instructions you can write for your own bass player, in your own charts. And "your own chart" is no longer hypothetical: The Chart launched this week. Milestone 1 is choosing the song — one you love, one you can hum the bass of — and every symbol you drill this week is a symbol you'll shortly be writing over your own melody, in your own hand.

Key terms

• Seventh chord — a four-note chord built in stacked thirds: root, third, fifth, seventh.
• Chordal seventh — the fourth note of the stack, a seventh above the root; the note whose size (major, minor, or diminished) helps define the chord's quality.
• Major seventh chord (MM7) — major triad + major seventh (Cmaj7 = C E G B).
• Dominant seventh chord (Mm7) — major triad + minor seventh (C7 = C E G B♭); the only seventh quality a major key builds diatonically on ^5, and the one a plain 7 always names.
• Minor seventh chord (mm7) — minor triad + minor seventh (Cm7 = C E♭ G B♭).
• Half-diminished seventh chord (ø7) — diminished triad + minor seventh (Cm7♭5 = C E♭ G♭ B♭); the diatonic seventh on ^7 in every major key (viiø7).
• Fully diminished seventh chord (°7) — diminished triad + diminished seventh (C°7 = C E♭ G♭ B𝄫); not diatonic to any major key — its diatonic home is harmonic minor (unit 11).
• Diatonic sevenths — the seven seventh chords a key builds from its own notes; in major: IM7 · ii7 · iii7 · IVM7 · V7 · vi7 · viiø7.
• Third inversion — the seventh chord position with the chordal seventh in the bass; figure 4/2.
• Figures (7 · 6/5 · 4/3 · 4/2) — the shorthand for a seventh chord's four bass positions, written with slashes; a hyphen in figures means a suspension (unit 14), never an inversion.
• Chord symbol — chart shorthand for a chord's root, quality, and (after a slash) bass note: Cmaj7, C7, Cm7, Cm7b5, Cdim7, C/E.
• Slash chord — a chord symbol with a specified bass note after a slash; the letter after the slash is the bass note you actually hear (G7/D = G7, D on the bottom).

Summary

• A seventh chord is a triad plus one more third: root, third, fifth, seventh — four notes, still stacked thirds, still spellable by law.
• Five qualities: maj7 = M triad + M7 (C E G B) · dominant 7 = M triad + m7 (C E G B♭) · m7 = m triad + m7 (C E♭ G B♭) · half-diminished = d triad + m7 (C E♭ G♭ B♭) · fully diminished = d triad + d7 (C E♭ G♭ B𝄫 — double-flat spelled, because the stack is thirds).
• Symbols: plain 7 = dominant recipe, always; maj7 = the major seventh; m7b5 = half-diminished; dim7 = fully diminished. One accidental often separates two different genres.
• Diatonic sevenths in major: IM7 · ii7 · iii7 · IVM7 · V7 · vi7 · viiø7. The key builds exactly one dominant seventh (on ^5) — and the chord on ^7 is half-diminished, never viio7: the fully diminished version needs a note no major key owns.
• Inversions: four floors, figures 7 · 6/5 · 4/3 · 4/2 — slashes, never hyphens (the hyphen belongs to suspensions, unit 14). Inversion never changes a chord's identity.
• Slash chords: the letter after the slash is the bass note — C/E is C over E; G7/D is 4/3 in street clothes.

Check your understanding

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

1. Spell Bbmaj7 and Bb7, and name the one note that differs.
2. A chart in a minor-ish ballad shows F#m7b5. Spell it, and explain to a bandmate — one sentence — how it differs from F#dim7.
3. Your chatbot says the seventh chord on ^7 in G major is "F♯ diminished seventh: F♯–A–C–E♭." Run the key-membership test and give the corrected chord, spelled, with its honest quality.
4. Am7/G: name the four notes, say which chord member is in the bass, and give the figure that position would carry in analysis.
5. Why does this course write the third-inversion figure as 4/2 and never 4-2? One sentence.

Answers (worked reasoning — read after attempting)

1. Bbmaj7 = B♭ D F A (major triad + major seventh). Bb7 = B♭ D F A♭ (major triad + minor seventh). The difference is the seventh: A versus A♭ — one half step, and the whole difference between shimmer and lean.
2. F#m7b5 = F♯ A C E — a diminished triad (F♯–A–C) plus a minor seventh (E). F#dim7 would flatten that seventh to E♭: F♯–A–C–E♭. One sentence for the bandmate: "Half-diminished keeps the natural seventh (E); fully diminished drags it down another half step (E♭) — one note, two different chords."
3. Key-membership test: is E♭ in G major? No — G major's only accidental is F♯. The key offers E natural, making F♯ up to E a minor seventh. Corrected chord: F♯–A–C–E, half-diminished (viiø7). The fully diminished version is not diatonic to G major — or to any major key; its diatonic home is harmonic minor, coming in unit 11.
4. Am7/G: the chord is A–C–E–G; the bass is G, the chordal seventh; a seventh chord with its seventh in the bass is third inversion, figure 4/2.
5. Because the hyphen already has a different job in figures — it marks a suspension (one number resolving to another over a single bass note, arriving in unit 14) — so 4/2 with a slash names a chord position while 4-2 with a hyphen would claim a resolution you don't mean.

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Next in this module: the Readings & Resources page if you want other angles on sevenths, then Tutorial 10 — your AI tutor session, due before Week 10's second session so the studio can build on it. And start turning over candidate songs for The Chart — milestone 1 lives inside this week's assignment.

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