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Week 7 · Lecture outline

Week 7 — Lecture Outline · Intervals II

Music Theory I · MUS 156 Fictional sample

Course: MUS 156 Music Theory I · Kenosis College
Instructor: Professor Hemsworth
Unit: Learning Unit 7 of 16 (Week 7) · two sessions per week
Objectives: SLO 3 (identify, spell, and invert intervals, simple and compound) · SLO 7 (translate what you hear into names and notation — the spine)
Sessions: session 1 — teach · session 2 — studio + cumulative midterm review (double-header; see the timing note below)

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

Sung in Aural Skills I: tritone and compound-interval echo, plus transcription warm-ups — MUS-155 sings the pull you'll name here this morning, and its dictation drills run the same leap-mapping you'll race with in the second session.

Week at a Glance

The table below summarizes the unit in one screen.
The unit's big question "One piano key to the next same-sounding key can carry two different interval names. If the sound is identical, what is the spelling actually telling you — and how does knowing it let you transcribe a whole melody in minutes?"
By the end of the unit, students can… (1) name and spell compound intervals (9ths through 13ths) as simple intervals plus an octave; (2) spell the tritone both ways — A4 and d5 — above any pitch, and explain why they are two different intervals with one sound; (3) sort intervals into consonant and dissonant, and state why the perfect fourth is context-dependent; (4) show that enharmonic intervals (m3 vs. A2, M3 vs. d4) share a sound but not a name or a job; (5) transcribe a short melody by leap-mapping — naming each interval out loud and spelling the next note from the last one.
Key vocabulary compound interval, ninth, tenth, eleventh, twelfth, thirteenth, tritone, augmented fourth, diminished fifth, consonance, dissonance, context-dependent (the perfect fourth), enharmonic intervals, resolution, leap-mapping
Materials Deck 7 · the Week 7 chapter · paper keyboards from Week 1 · transcription race sheets (the second session) · a piano or keyboard in the room · timers (phones work) · the Week 8 midterm study guide, open since two weeks ago, for the the second session review block
Timing note 8 segments ≈ 150 min. Session 1 = Segments 1–6 (75). Session 2 = Segments 7–8 (75: studio ≈ 45 + cumulative midterm review ≈ 30). This week's second session is a double-header — the midterm runs next week, in exam week's single session, so the cumulative review lives here. Protect the last half hour.

Segment 1 — Ear first: the itch (8 min) · Session 1 opens

Hook (no notation on screen yet). Play B3 and F4 together and just… stop. Let it hang. Ask: "Does the music feel finished?" Every head shakes no. Now resolve it — C4 and E4. Watch the shoulders drop. Play the pair again; ask the room to sing where the two notes want to go. They will find C and E without being told.

  • "Your ear just did voice leading. It heard a six-half-step itch and knew the cure. What it doesn't have yet is the name of that itch — and the news that the same sound has two different names depending on which way it's leaning."
  • The promise (say it, then put it on the board): "By the end of this week you can transcribe a whole melody by ear in minutes — not by magic, but by naming each leap as it lands. And you'll know why the itchy interval you just heard resolves where it does."
  • Say the week's shape out loud, early: the second session is the transcription race plus the start of midterm review; the exam itself runs next week, in exam week's single session. The study guide, prep tutorial, and practice exam have been open since two weeks ago. Foundations' finish line is now visible at street level.

Memory hook: "Dissonance is not a mistake. It's the music leaning."

Segment 2 — Compound intervals: the same ladder, upstairs (10 min)

Plain language first. Last unit's intervals all fit inside one octave. But a bass player and a singer are rarely that polite — the gap between a low E and a melody note is often an octave and change. Intervals wider than an octave are compound intervals, and here's the whole trick: nothing new is happening. A tenth is just a third wearing an octave like a coat.

  • The rule: simple size + 7 = compound size. A M3 plus an octave is a M10 (3 + 7 = 10). A P4 plus an octave is a P11. A P5 plus an octave is a P12. The quality never changes — major stays major, perfect stays perfect.
  • Worked example (walk it at the piano): C4 up to E4 is a M3. Push the E up an octave to E5: C4 up to E5. Letters still C-to-E — a third's letters — but the span is a tenth: M10. Same two letter names, same quality, one octave more air.
  • Interaction (2 min): call compounds, class strips the coat: "M9?" → "M2 plus an octave." "P12?" → "P5." "m10?" → "m3." Then reverse: "a m6 plus an octave?" → "m13."

Misconception + cure:

  • ❌ "Compound intervals are a new system to memorize."
    ✅ Cure: they're the Week 6 system plus seven. If you can spell a M3, you can spell a M10 — spell the third, raise the top note an octave, done. The only genuinely new fact this segment teaches is the number 7.

Segment 3 — The tritone: one sound, two intervals (14 min)

Ear first. Replay Segment 1's itch. Now spell it, twice, at the board.

  • F4 up to B4. Letters F–G–A–B: four names, so it's a fourth. Six half steps — one more than the perfect fourth's five. A fourth stretched a half step past perfect: augmented fourth (A4).
  • B3 up to F4. Letters B–C–D–E–F: five names, so it's a fifth. Six half steps — one less than the perfect fifth's seven. A fifth squeezed a half step short: diminished fifth (d5).
  • Same six half steps. Same sound. Two different intervals. The pair even gets a nickname for its sound — the tritone, three whole steps — but the nickname is not a spelling. On paper it is always either A4 or d5, and which one it is tells you which way the music is leaning: the A4 (F4–B4) tends to expand outward (to E4 and C5, a sixth); the d5 (B3–F4) tends to contract inward (to C4 and E4, a third). The itch from Segment 1 resolved inward because it was spelled as a d5.
  • Show both resolutions at the piano, slowly, and have the room sing each. The fence for the deck and chapter:
METER: 4/4    CLEF: treble
| <B3,F4>/h <C4,E4>/h | <F4,B4>/h <E4,C5>/h |

Two half-note pairs per bar on the treble staff: first the diminished fifth B3–F4 melting inward to C4–E4 (each voice moving by half step), then the augmented fourth F4–B4 opening outward to E4–C5. One sound, two spellings, two opposite destinations.

  • Every major key has exactly one tritone built in — in C major it lives between F and B (fa and ti). That's why V7 chords pull so hard toward home; you'll shake hands with that fact properly in the harmony units.

Misconception + cure:

  • ❌ "The tritone is always an augmented fourth."
    ✅ Cure: "tritone" names the sound; the interval on paper is A4 or d5, decided by the letter names. F4–B4 is an A4; B3–F4 is a d5. Count the letters before you speak.

Segment 4 — Consonance and dissonance: the sort your ear already runs (12 min)

Ear first. Play pairs of long intervals; the class votes with thumbs: settled or leaning. P5 — settled. m2 — leaning, hard. M6 — settled. m7 — leaning. A4 — leaning, deliciously. Their votes will match five centuries of consensus, because their ears run the same firmware.

  • Name the sort: consonant (settled, stable, could end a piece): unisons, octaves, fifths, thirds, sixths — P1, P8, P5, M3, m3, M6, m6. Dissonant (leaning, wants to move): seconds, sevenths, and the tritone — M2, m2, M7, m7, A4/d5.
  • The odd one out: the perfect fourth. Melodically, and between the upper parts of a texture, it sounds perfectly stable. But against the bass in two-voice writing, centuries of practice treat it as a dissonance that needs to resolve. So this course's honest answer is: the P4 is context-dependent — consonant in some settings, treated as dissonant in others. When we write two voices in Week 13, the fourth-against-the-bass rule becomes practical; for now, know that "is a fourth consonant?" is a where question, not a yes/no question.
  • Interaction — the gig framing (3 min): "Your duo ends a song. Which do you hold: the sixth or the seventh?" Then invert it: "Your bridge needs tension before the last chorus — which do you write?" Dissonance isn't failure; it's fuel. Every song they love leans before it lands.

Misconception + cure:

  • ❌ "The perfect fourth is always consonant — it's called perfect!"
    ✅ Cure: "perfect" describes its quality family, not its manners. Between upper voices: stable. Against the bass: treated as needing resolution. Context decides — and knowing that puts you ahead of half the chatbots on the internet, which flatten this to a yes or a no.

Segment 5 — Enharmonic intervals: same sound, different name, different job (13 min)

Plain language first. Week 1 taught that G♯4 and A♭4 share a key but are two written notes. The same idea now climbs to intervals: two intervals can share a sound and not be the same interval.

  • Worked example, at the board: F4 up to A♭4 — letters F–G–A, a third; three half steps; m3. Now F4 up to G♯4 — letters F–G, a second; the same three half steps; A2 (a second stretched a half step past major). Same piano keys. Same sound. A third and a second — different sizes, different names, different intervals.
METER: free    CLEF: treble
| F4/w Ab4/w | F4/w G#4/w |

Two whole-note pairs on the treble staff: F4 rising to A♭4 — a minor third, letters F to A — then F4 rising to G♯4 — an augmented second, letters F to G. On a piano both pairs use the same two keys; on paper they are different sizes with different names.

  • Why anyone would write A2: context. In A harmonic minor, the scale walks F4 → G♯4 — ^6 up to the raised ^7 — and the letters must be F and G because a scale uses each letter once. The A2 isn't a spelling error; it's the honest name for that scale step (say it and move on — you sang this gap in Week 5). Where the notes come from and where they're going decides the spelling; the spelling then tells the next musician what's happening.
  • Generalize with Week 6's regression examples: C4→E♯4 is an A3, not a P4; C4→F♭4 is a d4, not a M3. Six half steps is not automatically "a tritone-spelled-A4"; three half steps is not automatically m3. Letters first, always.
  • Inversion callback (2 min): invert the tritone pair — A4 inverts to d5, d5 to A4; the pair swaps partners with itself. Invert the enharmonic pair: m3 → M6, but A2 → d7. Inversion preserves the spelling distinction — more evidence they were never the same interval.

Misconception + cure:

  • ❌ "If two intervals sound identical, they're the same interval — the names are decoration."
    ✅ Cure: same sound, different spelling, different function. The m3 F–A♭ sits still; the A2 F–G♯ is mid-climb to A. The names carry the direction of travel. Enharmonic means "sounds alike," never "equals" — same rule as Week 1, one floor up.

Segment 6 — Leap-mapping: intervals as a transcription tool + the AI-critique moment (18 min) · Session 1 closes (~75)

Plain language first. Here's the payoff machine. To transcribe a melody you do not need to recognize every note from silence. You need one starting pitch and the ability to name each move. That's leap-mapping: hear the next note, name the interval and direction out loud, spell it from the note you already trust, write it, repeat.

  • The five moves, on the board: (1) get the starting pitch (given, or found at a keyboard); (2) hear the next note — up or down? (3) step or leap, and how big? Name it: "up a P4." (4) spell it from the note you have — letters first, then quality; (5) write it and move on. Every new note is a spellable distance from an old one.
  • Fully worked example — the class does it together: When the Saints Go Marching In, which everyone can sing cold. Start given: C4. Sing the opening — "Oh, when the saints": the first move is up a M3 (C4 → E4), then up a m2 (E4 → F4), then up a M2 (F4 → G4). Three calls, three spellings, and the lick is on paper:
METER: 4/4    CLEF: treble
| C4/q E4/q F4/q | G4/w |

Three rising quarter notes — C4, E4, F4 — as a pickup bar, landing on a long G4: the Saints call, leap-mapped in three named moves (M3, m2, M2) from a single given starting note.

  • Point at the compound segment: when the gap is bigger than an octave — the bass player's E2 under a singer's G♯3 — the same machine works; you just add the coat: M3 + octave = M10.
  • AI-critique moment (3 min, live on the projector). Paste into a chatbot: "Is C4 up to D♯4 a minor third? One sentence." Read the answer aloud. Most tools will say yes — collapsing A2 into m3 exactly the way Segment 5 warned. Have the room fix it: C to D is a second; three half steps on a second is A2. "All term the tool drafts and you judge — and this week your tutorial's audit runs on your own knowledge for the second time. You're ready for that."

Why this makes you a better musician

This is the week transcription stops being an afternoon and becomes a coffee break. The song your worship leader wants "by Sunday, there's no chart" — you leap-map the melody in ten minutes: starting note, then named moves, each one spelled from the last. The horn line you need to teach the trumpet player lands in his text messages as five addresses instead of a hummed voice memo. And the tritone knowledge is a working tool, not trivia: when a chart hangs on a dominant seventh, you can hear the A4/d5 inside it leaning toward home, know the resolution before it arrives, and cue the band into it. The studio is literally a race — you against the clock, transcribing real tunes by ear — because on a gig, speed is the difference between useful and too late.

Callback + tease + hand-off.

  • Callback: "In week 1 you needed a keyboard map to name two notes. This morning you spelled a six-half-step itch two different ways and mapped a melody from one given note. Same ears — richer vocabulary."
  • Tease: "Next unit — the midterm — the literacy gate: one session, one exam, all of Foundations certified. Everything from C4 to this morning's tritone, and you've been ready longer than you think."
  • Hand-off: read the chapter if you haven't; Tutorial 7 is due before Week 7's second session — the studio's race assumes its leap-mapping reps. Practice set, quiz, discussion, and the Ten-Minute Transcription assignment close the end of Week 7. The midterm study guide and practice exam have been open in the Week 8 module since two weeks ago — bring one question about them to the studio.

Segment 7 — Studio: "Figure it out fast" (≈45 min) · Session 2

Run from the studio sheet (P-studio-week-07). Shape, for planning: baseline warm-up on the Twinkle tune (the Week 1 callback) → "call the leap" rounds by ear → the transcription race, two timed heats on out-of-copyright tunes with interval reasoning called out loud → the tritone corner, both spellings resolved by ear. The studio is the payoff enacted: hear it, name the move, write it, beat the clock. 20 points, graded in session; async make-up path (full credit) on the studio sheet. Keep it at 45 minutes — the review block needs the rest.

Segment 8 — Cumulative midterm review (≈30 min) · Session 2 closes

The midterm runs next week, in Week 8's single session — so this half hour is the whole-class review slot. Run it from the Week 8 review outline and study guide (open since two weeks ago, with the prep tutorial and practice exam): rapid-fire spelling rounds across Week 1–Week 7, the two or three misconceptions the room still trips on (expect the octave boundary, compound-meter beats, and today's A2-vs-m3), and five minutes of "ask me anything on the guide." Students who've started the practice exam get their sticking points aired here; students who haven't leave knowing exactly what to do this weekend. Frame it the spine's way: nothing on session 1 is new — it's everything you've already named, certified.

Instructor FAQ — common stumbles

The table below lists predictable Week 7 questions and quick cures.

Student says / does Quick cure
"Is a ninth just a second? Why two names?" Same letters, different air. Name what's actually written: within an octave, second; octave-plus, ninth. The +7 rule converts instantly, so know both and read the staff honestly.
Calls every six-half-step gap "an augmented fourth." Count the letters first. F up to B (F-G-A-B) is a fourth → A4. B up to F (B-C-D-E-F) is a fifth → d5. The sound can't tell you; the letters can.
"Why would anyone ever write an augmented second?" Harmonic minor forces it: ^6 to raised ^7 (F4→G♯4 in A minor) must use F and G because scales use each letter once. The A2 is the honest name of that step.
"So is the perfect fourth consonant or not? Just tell me." Both, honestly: stable between upper voices and in melody; treated as a dissonance against the bass in two-voice writing. Write "context-dependent" and mean it — the two-voice units make it practical.
Hears the race melody perfectly but spells leaps from scratch each time. Leap-map: every new note is spelled from the previous note, not from silence. One trusted note plus named moves beats ten guesses.
In the race, writes the right keys but the wrong letters (A♯4 for B♭4 in an F-major tune). Same key, wrong address — the key signature picks the letters. Ask: which letters does this tune's scale use? (Week 4–Week 5 earning rent.)
"Compound quality changes too, right? A tenth is bigger, so… more major?" Quality never changes with the octave coat. M3 → M10, m3 → m10, P4 → P11. Only the size number moves, and only by 7.
Panics about next week's session. Point at the study guide (open two weeks now), the practice exam (unlimited attempts, zero points), and the in-class review block. Nothing on the midterm is new; it's the vocabulary they've been using out loud for seven weeks.

Scope flag

This outline stays inside Week 7's five ledger concepts (compound intervals, the tritone, consonance/dissonance with the context-dependent P4, enharmonic-distinct intervals, interval reasoning as a transcription tool), drawing freely on Week 6's interval machinery and earlier scale/key vocabulary. The V7-pulls-home remark in Segment 3 is a forward-reference by name only — dominant-seventh spelling belongs to Week 10–Week 11 and is not taught or assessed here. Segment 8 reviews previously introduced Week 1–Week 7 material for the midterm and introduces nothing new by design.

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