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Week 6 · Lecture outline

Week 6 — Lecture Outline · Intervals I

Music Theory I · MUS 156 Fictional sample

Course: MUS 156 Music Theory I · Kenosis College
Instructor: Professor Hemsworth
Unit: Learning Unit 6 of 16 (Week 6) · two sessions per week
Objectives: SLO 3 (identify, spell, and invert intervals by size and quality) · SLO 7 (translate what you hear into names and notation — the spine)
Sessions: session 1 — teach · session 2 — studio + the midterm family opens

You already hear this. We're going to name what you already know.

Sung in Aural Skills I: interval echo — MUS-155 sings back the gaps you name here this morning: seconds and thirds by step, then the perfect fourth and fifth as leaps, each one matched against the name it just earned in this class.

Week at a Glance

The table below summarizes the unit in one screen.
The unit's big question "Every pair of notes has a distance, and that distance has a first and last name. How do you measure it — and why do you need two rulers instead of one?"
By the end of the unit, students can… (1) find an interval's size by counting letter names, both ends included; (2) find its quality by counting half steps — and keep the two measurements independent; (3) name and spell perfect, major, minor, augmented, and diminished intervals up to the octave; (4) spell a named interval above and below any given note; (5) invert any interval by rule (sizes sum to 9; P↔P, M↔m, A↔d); (6) read the major scale as a ready-made bank of intervals above do.
Key vocabulary interval, size, quality, perfect, major, minor, augmented, diminished, inversion, letter distance, half-step count, melodic interval, harmonic interval
Materials Deck 6 · the Week 6 chapter · paper keyboard maps · hook-bank card blanks · the room piano · students' own instruments welcome in the studio
Timing note 8 segments ≈ 150 min. Session 1 = Segments 1–6 (75). Session 2 = Segments 7–8 (75: studio 55 + midterm-family launch 20). Scale to your own pacing.

Segment 1 — Ear first: the gap has a name (8 min) · Session 1 opens

Hook (no notation on screen yet). Sing the Twinkle tune's opening with the room — everybody owns it. Stop after the third note. "That jump you just made without thinking — how far was it?" The room can sing the distance perfectly; nobody can say it yet. Then sing the first two notes of Amazing Grace — "A-ma…" — another jump, clearly smaller. Every ear in the room just ranked two intervals with no vocabulary at all.

KEY: C major    METER: 4/4    CLEF: treble
| C4/q C4/q G4/q G4/q | A4/q A4/q G4/h |

The Twinkle tune's first seven notes on the treble staff: two repeated C4s, a leap up to two G4s, a step up to two A4s, and a longer G4 to land on. The leap from C4 to G4 is the wide jump the room just sang; G4 up to A4 is the small step after it.

  • "Your ear has been measuring these gaps for years — that's how you harmonize, that's how you know the guitarist bent the note too far. What it doesn't have yet is the name for each gap. This unit hands you the whole naming system."
  • The promise (say it, then put it on the board): "By the end of this week you can name the distance between any two written notes — and spell the note a named distance above or below anything."
  • Callback to the arc: Week 1 gave every note an address; Week 4–Week 5 organized the addresses into keys. Today we measure between addresses. Everything after the midterm — chords, harmony, all of it — is interval arithmetic wearing different hats.

Memory hook: "An interval's name is its first and last name: quality, then size. M3. P5. Say both or you haven't named it."

Segment 2 — Size: the letter ruler (10 min)

Plain language first. An interval's size is a letter count: count the letter names from the bottom note to the top note, counting both ends. C up to A: C-D-E-F-G-A — six letters — a sixth. E up to B: E-F-G-A-B — a fifth. That's the whole rule, and it ignores sharps and flats completely.

  • Sizes up through the octave: unison (same letter), second, third, fourth, fifth, sixth, seventh, octave.
  • Both ends count. C to D is a second, not a first — you count the fence posts, not the gaps between them.
  • Accidentals are invisible to size: C to E is a third, C to E♭ is a third, C to E♯ is a third. Same letters, same size, every time. (What the accidentals change is Segment 3's job.)
  • Interaction (2 min): call letter pairs — F up to D? G up to E? B up to F? — class answers the size on fingers. Speed matters more than solemnity.

Misconception + cure:

  • ❌ "Count the piano keys between the notes — that's the interval."
    ✅ Cure: the keyboard counts sounds; the interval's size counts letters. Two different rulers. Counting keys is exactly the mistake that makes every chatbot call C-to-E♯ a fourth (Segment 5 will spring that trap on purpose). Letters first, always.

Segment 3 — Quality: the half-step ruler (12 min)

Ear first. Play C4–E4, then C4–E♭4. Same size — both thirds, the letters say so — but the room hears two different colors: the first bright, the second darker. That difference is quality, and it's measured with the second ruler: the half-step count.

METER: free    CLEF: treble
| C4/w E4/w | C4/w Eb4/w |

Two thirds on the treble staff, one after the other: C4 up to E4 — four half steps, a major third — then C4 up to E♭4 — three half steps, a minor third. Same letter distance, different half-step distance: same size, different quality.

  • The method, stated as a procedure: (1) count letters → size. (2) count half steps → quality. Two rulers, used independently, every single time.
  • A major third is 4 half steps; a minor third is 3. Both are thirds — the letters said so before the half steps got a vote.
  • Names are quality-then-size, written in the course's typed forms: M3 (major third), m3 (minor third), P5 (perfect fifth). Capital M and small m mean different things; type them the way you'd type an address.

Misconception + cure:

  • ❌ "Five half steps IS the interval — the half-step count is the name."
    ✅ Cure: the half-step count alone can't name anything, because two differently-spelled intervals can share a count. The count picks the quality only after the letters have picked the size. One ruler measures span on the page, the other measures span in sound; the name needs both.

Segment 4 — The two families, and the scale you already own (13 min)

Plain language first — the family rule. Sizes split into two families, and each family has its own quality ladder:

  • Perfect family — unisons, fourths, fifths, octaves. Ladder: diminished → perfect → augmented. There is no "major fifth"; a fifth is perfect, or it's been stretched (augmented) or squeezed (diminished).
  • Major/minor family — seconds, thirds, sixths, sevenths. Ladder: diminished → minor → major → augmented. Shrink a major interval one half step (letters unchanged) and it's minor; shrink it again and it's diminished; stretch a major one and it's augmented.

Then hand them the bank they already own. Every interval from do up to a scale degree of the major scale is major or perfect — no exceptions:

KEY: C major    METER: free    CLEF: treble
| C4/w D4/w E4/w F4/w G4/w A4/w B4/w C5/w |

The C major scale ascending on the treble staff, C4 to C5. Measured from the bottom C4: up to D4 is a major second, E4 a major third, F4 a perfect fourth, G4 a perfect fifth, A4 a major sixth, B4 a major seventh, C5 a perfect octave.

  • Say it in solfège too — do up to fa is a P4, do up to sol is a P5 — because Aural Skills I sings exactly these gaps.
  • This is why Week 4 mattered: anyone who can spell a major scale can already spell M2 M3 P4 P5 M6 M7 P8 above any note. Minor, diminished, augmented are all one or two half-step nudges away from that bank.

Misconception + cure:

  • ❌ "Perfect is just a fancier word for major."
    ✅ Cure: they're different families with different ladders. A fourth can never be major; a sixth can never be perfect. If a name mixes the families — "major fourth," "perfect seventh" — it's not a rare interval, it's a spelling error.

Segment 5 — The trap: C4 up to E♯4, and the AI-critique moment (10 min)

Spring it. Put C4 and E♯4 on the board. "Count the keys: C to C♯ to D to D♯ to E... five half steps. Five half steps is a perfect fourth. So this is a P4 — right?" Let the room sit in it. Then apply the method in order: letters first. C-D-E: three letters. It's a third. It cannot be any kind of fourth, ever — the letters already decided. Five half steps on a third-sized frame makes it an augmented third: A3.

METER: free    CLEF: treble
| C4/w E#4/w | C4/w F4/w |

Two intervals on the treble staff that share one sound: C4 up to E♯4 — three letter names, an augmented third — then C4 up to F4 — four letter names, a perfect fourth. The piano plays the same two keys for both pairs; the page, and the name, are different.

  • E♯4 and F4 are the same piano key — Week 1's enharmonic twins — so A3 and P4 are two different names for one sound. Which name is correct depends entirely on the spelling in front of you. Enharmonic means "sounds alike," never "equals" — that rule now applies to intervals, not just notes. (The full one-sound-two-intervals story gets its own stage next unit.)
  • AI-critique moment (2 min, live on the projector). Paste into a chatbot: "What interval is C4 up to E♯4? One sentence." Chatbots count keys, so expect "perfect fourth" delivered with total confidence. Let the room catch it with the letter ruler. "This is the single most famous AI music-theory error, and as of today you can out-spell it. Your tutorial's audit step hunts exactly this — and from this unit on, you are the answer sheet."

Misconception + cure:

  • ❌ "Same keys pressed, so same interval."
    ✅ Cure: same sound, different written interval — the there/their rule from Week 1, now one level up. The interval's name lives in the spelling, and the spelling carries meaning the piano key can't see.

Segment 6 — Flip it, then spell downward (22 min) · Session 1 closes (~75)

Inversion, plain language first. Take an interval and move its bottom note up an octave — the pair flips. C4 up to A4 is a major sixth; put the C on top (A4 up to C5) and you're holding a minor third. Two rules govern every flip:

  1. Sizes sum to 9. Sixths flip to thirds (6+3), seconds to sevenths, fourths to fifths.
  2. Qualities trade partners: major ↔ minor, augmented ↔ diminished, and perfect ↔ perfect — perfect intervals are the family that flips into itself. (That's part of why they're called perfect.)
  • Worked pair on the board: M3 inverts to m6. m7 inverts to M2. P4 inverts to P5.
  • Misconception + cure: ❌ "Inversion flips every quality, so a perfect fourth inverts to something un-perfect." ✅ Cure: P flips to P, full stop. If your inversion of a perfect interval isn't perfect, re-add your sizes — something slipped.

Spelling below — the skill the gig actually asks for. "Sing me a third below the melody" is a below problem. Two honest methods; teach both, let each student keep their favorite:

  • Method 1, two rulers downward: a major third below C5 — count letters down, C-B-A, so the answer is an A of some kind; count four half steps down and you land on A♭4. Answer: A♭4 — not G♯4, even though it's the same key, because the letters already committed to A.
  • Method 2, invert-and-drop: the inversion of a M3 is a m6 — so go a m6 up from C5's lower octave... or more simply: go up the inverted interval from the given note, then drop an octave. m6 above C5 is A♭5; drop an octave: A♭4. Same answer, always.

Worked examples: P5 below D5 = G4. M2 below C5 = B♭4. Watch the two traps: the letter trap (G♯4 for A♭4 — right key, wrong letter) and the octave trap (crossing B/C on the way down and keeping the old number).

Why this makes you a better musician

This unit turns "somewhere up there" into a name you can act on. When you're learning a melody by ear, you stop re-fishing for each next note — you catch that the hook leaps a fifth and your hand goes there on the first try. When the worship leader says "sing a third below the melody," you now know which of two thirds, and you can spell every note of the harmony line before you sing a note of it — that's the difference between tuning a harmony and hunting for one. And when you text the band "the chorus jumps a P5 off the D," you've just handed four people the exact shape of the line in nine characters. The studio is precisely this: the gaps you've been singing all your life, caught, named, and banked.

Callback + tease + hand-off.

  • Callback: "This morning your ear ranked two gaps before you had a single name. Now every gap you can hear, you can name and spell — both directions."
  • Tease: "Next unit — Intervals II: the gaps get bigger than an octave, one famous sound turns out to own two names, and interval math becomes your fastest transcription tool."
  • Hand-off: read the chapter; Tutorial 6 with your AI tutor is due before Week 6's second session — and from this unit on, the audit step runs on your arithmetic, not a printed answer sheet. Practice set, quiz, discussion, and the Spell It Both Ways assignment close the end of Week 6.

Segment 7 — Studio: "Sound to name" (55 min) · Session 2

Run from the studio sheet (P-studio-week-06). Shape, for planning: ear-only wider/narrower rounds → the printed seed bank (six out-of-copyright hooks, sung then named) → each student builds their own hook-bank card from songs they actually carry → a speed round of spelling above, below, and inverted, with the E♯ trap inside it. The studio is the payoff section enacted: hear the gap, name the gap, spell the gap. 20 points, graded in session; the async make-up path (full credit) is on the studio sheet.

Segment 8 — The midterm family opens (20 min) · Session 2 closes

The unit-8 midterm's whole support family releases today, Week 6's second session — study guide, exam-prep tutorial, and a practice exam that's worth zero points with unlimited attempts. Walk the room through each piece and say the shape of the calendar out loud: the midterm week has exactly one class meeting. That is why review starts now, two units early, and why next unit's second session carries the cumulative review. A student who touches the practice exam this weekend takes the midterm twice — once alone at zero stakes, once for real. Frame it exactly as the course means it: the midterm is the finish line of Foundations, the certification that the vocabulary is yours. There is nothing in it we haven't named together.

Instructor FAQ — common stumbles

The table below lists predictable Week 6 questions and quick cures.

Student says / does Quick cure
Counts C up to A as a fifth ("I didn't count the C"). Both ends count. Fence posts, not gaps: C-D-E-F-G-A is six letters, a sixth. Have them say the letters aloud with fingers up.
"Five half steps, so it's a fourth — why do the letters get a vote?" The letters get the first vote. Size from letters, quality from half steps, in that order. C→E♯ is the case that settles it: five half steps but only three letters — an A3, never a P4.
Writes "major fifth" or "perfect third." Family error, not a rare interval. Perfect family: 1-4-5-8. Major/minor family: 2-3-6-7. The two ladders never mix.
"Is a minor third the same as an augmented second? Three half steps either way." Same sound, different letters, different interval — and different job. The full story is next unit's; for now: the letters name it, every time.
Inverts a P4 into "something major." P flips to P — the perfect family inverts into itself. Check: sizes sum to 9, qualities trade M↔m, A↔d, P↔P.
Spells a M3 below C5 as G♯4. Right piano key, wrong letter. Letters commit first going down too: C-B-A means the answer is an A-something — A♭4.
Loses the octave number spelling downward ("B♭5 below C5"). The B/C boundary from Week 1 works downward: any letter B below a C carries the lower octave number. M2 below C5 is B♭4.
"Do I really have to write the quality? Everyone knows what a third is." A third without a quality is half a name — the difference between M3 and m3 is the difference between a major and a minor chord, three units from now. First and last name, always.

Scope flag

This outline stays inside Week 6's eight ledger concepts (interval size, interval quality, the perfect and major/minor families, augmented and diminished, intervals above do in the major scale, inversion, spelling above and below) plus earlier-unit material it legitimately leans on (addresses, half steps, enharmonic twins, major scales, solfège). A4 and d5 appear only as members of the augmented/diminished family; the tritone's one-sound-two-names story, compound intervals, consonance/dissonance, and enharmonic-interval pairs as a topic all belong to Intervals II and are teased, never taught or assessed here. The Segment 8 midterm-family walkthrough previews logistics only — no new content.

~ Professor Hemsworth's edition · Kenosis College · built with thecoursemaker.com