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Week 13 · Chapter

Week 13 — Chapter · Progression, and Two Independent Voices

Music Theory I · MUS 156 Fictional sample

Course: MUS 156 Music Theory I · Kenosis College
Instructor: Professor Hemsworth
Unit: Learning Unit 13 of 16 (Week 13) · two sessions per week
The unit's primary reading · ~30–40 minutes · SLOs 6 and 7 · Read this before the first session if you can, or right after — everything else in the module builds on it.

You already sing this

Somewhere in your musical life you have sung a round. Frère Jacques at a campfire, Row, Row, Row Your Boat in a minivan — half the group starts, the other half comes in late, and suddenly there are two melodies in the air at once. Nobody got a lecture first. Nobody read a rule. And yet you held your line while a different line moved against it, and the whole thing locked together like it was designed to. It was.

That experience is this unit's subject. Until now, this course's harmony has been vertical — chords as stacks, named and spelled. This week harmony goes horizontal: two independent lines sounding at once, each with its own shape, each worth singing alone. Working musicians build this texture constantly and call it ordinary names: a harmony vocal that doesn't melt into the lead, a countermelody that answers the tune, a bass line that stands on its own instead of shadowing the melody. The craft behind all three is the same short list of habits, and — this course's favorite sentence — your ear already enforces most of them. You can hear when a harmony part "disappears into" the melody. You can hear when two lines tangle. This chapter names what your ear is reacting to.

By the end you will be able to: use the functional cycle as a working map for diatonic progressions; name the four motion types between two voices; explain what parallel fifths and octaves actually do to a texture (hint: the problem is not ugliness); tell a direct fifth from a parallel one; keep two lines out of each other's lanes (crossing, overlap, range); resolve the two tendency tones every key contains; and write a second voice against a given line that passes the same voice-leading check this course's own materials must pass.

Where we are

Units 9–11 built chords and gave them jobs; unit 12 showed where the jobs land. This unit and the next are a pair: first two clean lines (now), then the decorations that make lines sing (next unit). After that, unit 15 cashes everything in on the real-world chart — including yours. Your Chart project hits milestone 3 this week: the lead sheet, drafted. One more zoom-out, for honesty's sake: the skills in this unit — independent lines, parallel-hunting, tendency tones — are the entry hall of a whole discipline. Counterpoint proper waits for MUS 158; what you build here is the musician's working version, the part you'll use on a bandstand this month.

The engine, in practice

Before adding a second line, know what the first line is riding on. Unit 11's functional cycle — T → PD → D → T — isn't just an analysis label; it's how diatonic progressions actually behave, and a second voice that fights the engine sounds wrong no matter how clean its intervals are. The working norms:

  • Tonic is free. I, and its family members vi and iii, can move anywhere: to a predominant, straight to the dominant, off on a detour. Home has all the exits.
  • Predominant leans forward. ii and IV have packed the bags; their normal destination is the dominant — V or viio. In C major that's D–F–A or F–A–C heading for G–B–D.
  • Dominant goes home. V and V7 resolve to I — or make unit 12's deceptive swerve to vi and pay the promise off a phrase later.

Run a lap in C: I – IV – V7 – I (C–E–G, F–A–C, G–B–D–F, C–E–G). Another: I – vi – ii – V7 – I (C–E–G, A–C–E, D–F–A, G–B–D–F, C–E–G). You have heard both laps ten thousand times; that's what makes them norms.

Misconception check. "So V can never move to IV?" Norms are gravity, not law. Songs bend them constantly and on purpose — much of the rock and gospel canon runs V–IV–I as a signature move. The norm matters because it's what your ear predicts; deviations work precisely because the norm exists. This week, practice the norm; bend it later, on purpose, like the pros do.

Two lines, four relationships

Freeze any moment where two voices move, and their motion is one of exactly four kinds. Four names, four behaviors — this is the unit's alphabet.

Contrary motion — the voices move in opposite directions. Maximum independence: the lines literally cannot be mistaken for each other.

KEY: C major    METER: 4/4    CLEF: grand
U: | E4/h G4/h |
L: | C3/h A2/h |

On the grand staff: the upper voice climbs E4 to G4 while the lower voice descends C3 to A2 — a major tenth opening out to a minor fourteenth. Two voices, two directions, no possible confusion about who is who.

Oblique motion — one voice holds while the other moves. The moving line gets the spotlight; the holding line anchors it.

KEY: C major    METER: 4/4    CLEF: grand
U: | G4/h G4/h |
L: | E3/h C3/h |

The upper voice holds one G4 across the bar while the lower voice falls E3 to C3 — a minor tenth becoming a perfect twelfth. Notice something quietly important: this pair lands on a perfect interval and is completely legal, because of how it got there. Hold that thought two sections.

Similar motion — both voices move the same direction, but by different distances. Common, useful, and safe — with one caution coming below.

KEY: C major    METER: 4/4    CLEF: grand
U: | C4/h D4/h |
L: | A2/h F3/h |

Both voices rise together, but by different distances — the upper voice steps C4 to D4 while the lower voice leaps A2 up to F3. A minor tenth becomes a major sixth: same direction, different distances, and the imperfect landing keeps it friendly.

Parallel motion — both voices move the same direction at the same interval. In thirds, sixths, and tenths, this is the most beloved sound in popular music — the country duet, the gospel harmony line, the Beatles chorus:

KEY: C major    METER: 4/4    CLEF: grand
U: | E4/q F4/q G4/q A4/q |
L: | C4/q D4/q E4/q F4/q |

Four beats of parallel thirds: E4–F4–G4–A4 riding over C4–D4–E4–F4, a major third, two minor thirds, a major third. Sing either line alone — each is a real melody. Together they move as a lockstep pair and the ear loves it. Parallel motion is not the crime. The crime is parallel motion at three particular intervals — next section.

And one sound you already trust, holding two of these behaviors at once — the round, at the moment the second group enters:

KEY: C major    METER: 4/4    CLEF: grand
U: | E4/q F4/q G4/h |
L: | C3/q D3/q E3/q C3/q |

The upper voice sings "Dor-mez-vous?" (E4, F4, G4 held) while the lower voice, entering an octave down, walks "Frè-re Jac-ques" (C3–D3–E3–C3). Beats one through three: parallel tenths — major, minor, minor. Beat four: the upper voice holds while the lower falls away to C3 — oblique motion landing on a perfect twelfth. The round harmonizes itself, and it does it with this unit's two favorite motions.

Misconception check. "Parallel motion is banned in two-voice writing." Parallel what? Thirds, sixths, tenths: welcome everywhere. The ban has exactly three targets — and the next section says why.

The independence rules

Rule 1 — no parallel perfect fifths, octaves, or unisons

Here is the most famous rule in Western music theory, and the first thing to know about it is what kind of rule it is. It is not a beauty rule. Parallel perfect fifths do not sound ugly — play some and listen honestly:

```music counterexample
KEY: C major METER: 4/4 CLEF: grand
U: | C4/q D4/q E4/q D4/q |
L: | F3/q G3/q A3/q G3/q |


A deliberately broken passage — the course's checker flags all three moves. The upper voice walks C4–D4–E4–D4; the lower voice shadows it a perfect fifth below at every step: F3–C4, G3–D4, A3–E4, G3–D4. The sound is hollow, open, oddly ancient — medieval chant harmonization (organum) is *made* of this sound, and so is every power-chord riff in rock, where one guitarist plays fifths as a deliberately thickened single line.

That last phrase is the whole explanation: **a thickened single line.** A perfect interval is so acoustically stable — the sound waves nest so neatly — that two voices locked in parallel perfects stop registering as two voices. The ear welds them into one. In a style built on that weld (organum, power chords), wonderful. In a texture whose entire purpose is *two independent lines*, it is the one move that silently deletes a voice.

Octaves are the extreme case:

```music counterexample
KEY: C major    METER: 4/4    CLEF: grand
U: | G4/h A4/h |
L: | G3/h A3/h |

Another deliberate foul: G4 to A4 over G3 to A3 — a perfect octave gliding to another perfect octave. This isn't even a hollow harmony; it's the same line twice. Doubling a melody at the octave is a fine orchestration choice (every piano player's left hand knows it) — but it is one voice in boots, not a second voice, and in this unit's writing the checker flags it instantly. Parallel unisons are the same failure at zero distance.

Why your harmony vocal keeps "disappearing." If you've ever improvised a harmony part that mysteriously melted into the lead — congratulations, you found parallel perfects by ear. The fix is the fix professionals use: ride in thirds and sixths, and save the perfect intervals for arrivals.

Rule 2 — no direct (hidden) fifths or octaves

The subtler cousin. A direct fifth (or octave) happens when both voices move in the same direction into a perfect interval, with the upper voice leaping. There was no fifth before — it materializes out of the similar motion, which is why the old books call it hidden:

```music counterexample
KEY: C major METER: 4/4 CLEF: grand
U: | E4/h A4/h |
L: | C3/h D3/h |


Deliberately broken: the voices open a friendly major tenth (C3–E4), then both rise — the lower stepping to D3, the upper *leaping* to A4 — and land on a perfect twelfth. The checker's verdict, verbatim: "direct (hidden) perfect twelfth — similar motion, leap in upper voice." The fused sound arrives with a thump because the leap spotlights it.

The rule's mirror image tells you what *is* allowed, and it matters more than the prohibition: **perfect intervals are welcome when you approach them by contrary or oblique motion** — or even in similar motion when the upper voice moves by step. Look back at the oblique example: it lands on a perfect twelfth and passes clean. The lesson of both rules together, on one line:

> **Perfect intervals are arrival points. Earn them from the opposite direction.**

> **Misconception check.** *"A direct fifth is just a parallel fifth with extra steps."* No — parallel means fifth **to** fifth; direct means *some other interval* into a fifth, in similar motion, upper voice leaping. They are different faults with different fixes (break the lockstep vs. change the approach), and the course checker prints different messages for them. On the studio's swap-hunt, quoting the right name is the difference between a catch and a guess.

## Stay in your lane: crossing, overlap, range

Independence has a second enemy besides fusion: **confusion**. The listener has to know, at every moment, which line is which.

**Voice crossing** — the lower voice sounds *above* the upper voice at the same moment:

```music counterexample
KEY: C major    METER: 4/4    CLEF: grand
U: | E4/h C4/h |
L: | C4/h E4/h |

Deliberately broken: the voices open a major third (C4 under E4), then trade places — the "upper" voice drops to C4 while the "lower" voice rises above it to E4. The checker flags the crossing at the second pair. For one beat, the listener's ear hands the melody to the wrong singer. In this unit's writing, each line keeps its lane: the upper voice stays on top, the lower voice underneath.

Voice overlap — sneakier. Nobody is above anybody at the same instant, but a voice moves past the note the other voice just sang. The ear tracks lines partly by memory, and overlap scrambles the memory. You met one without knowing it, in the round — stack its later phrases and watch:

```music counterexample
KEY: C major METER: 4/4 CLEF: grand
U: | C4/q G3/q C4/h |
L: | G3/e A3/e G3/e F3/e E3/q C3/q |


Deliberately colliding: the upper group's "do–so–do" tag (C4–G3–C4) rides over the lower group's running eighth-note line (G3–A3–G3–F3–E3–C3). When the tune dives to G3, it lands *below the A3 the lower voice sang a half-beat earlier* — the checker reports an overlap, plus a leap into a unison in similar motion (a direct unison) for good measure. Nothing sounds "wrong," exactly; the lines just briefly trade identities. A round gets away with it because everyone is singing the same tune anyway. Your engineered second voice doesn't get that alibi.

**Range** — the practical lane. Every voice and instrument has a comfortable register, and a line that lives at the edge of someone's range isn't independent — it's endangered. Before you write, name the lane; then stay in it. A gorgeous countermelody nobody can sing is a rough draft.

> **Misconception check.** *"Voices can never cross — I read it's a law."* It's a working rule for *this texture at this stage*, where two-line clarity is the entire assignment — not a law of music. What you should take with you forever isn't "never cross"; it's "always know which line the listener is following."

## Tendency tones: two notes whose next move is already decided

Every key contains two notes under contract. Unit 11 met them inside V7; this unit makes you responsible for them in your own lines.

**The leading tone rises to do.** Ti sits a half step under the tonic, and it *points*. In a two-voice close in C major, B goes to C — that's the pull that makes an authentic cadence feel like arriving. Leaving ti hanging, or dropping it away, is like ending a sentence on the word "the."

**The chordal seventh falls by step.** When a line carries the seventh of a chord — the F in G7 is the one you'll meet most — that note resolves *down* by step: F to E. Sevenths fall. Your ear has enforced this at every worship set and jukebox of your life; now it's your pencil's job too.

```music
KEY: C major    METER: 4/4    CLEF: grand
U: | B3/h C4/h | F4/h E4/h |
L: | G2/h C3/h | G2/h C3/h |

Both contracts honored, over a sol–do bass, and the checker passes it clean. Bar one: ti rises — B3 to C4 — while the bass climbs G2 to C3; a major tenth opens onto an octave, approached with the upper voice stepping. Bar two: the dominant's seventh — F4 over the G2 bass, a minor fourteenth — falls by step to E4 as the bass lands on C3: a major tenth, the sound of a promise kept. (G2–B3–F4 spells the working skeleton of G7 across the two bars; the full four-note chord is G–B–D–F.)

Misconception check. "The leading tone thing is optional — singers resolve wherever." Great singers delay and decorate resolutions (next unit is entirely about how); they don't cancel them. In plain two-voice writing, ti rises and sevenths fall. Break the contract and every ear in the room hears the promise go unpaid — including yours.

Writing the second voice: the procedure

Now the deliverable. Someone hands you a line — a melody, a hook, the tune your worship leader hums — and you write the line that goes with it. Here is the working procedure, the same one the studio and this week's assignment walk you through:

  1. Read the engine first. What progression is the tune implying (tonic opening? predominant lean? dominant close)? Your line should agree with the harmony, not fight it.
  2. Default to imperfect. Thirds, sixths, and tenths are the workhorses — full harmony, zero fusion. When in doubt, a third or a sixth below the tune is never embarrassing.
  3. Spend perfects at arrivals. An octave on the final note, a fifth at a phrase joint — approached by contrary or oblique motion — sounds like architecture. Perfect intervals mid-phrase in parallel sound like a deleted voice.
  4. Vary the motion. Tune steps up? Try stepping down. Tune leaps? Hold your note and let it pass (oblique motion is free independence). A line that only shadows in one direction is a shadow.
  5. Honor the tendency tones. If either line touches ti or a chordal seventh, the next note is spoken for. Write it that way.
  6. Run the two-rules pass before anyone hears it. Scan every consecutive pair: two perfect intervals in a row moving the same direction? Similar-motion leap into a perfect? Lower line above upper at any instant? Fix now, thank yourself later.

Watch the whole procedure land on a real line — a given tune in G major, and a written lower voice that passes the checker with zero findings:

KEY: G major    METER: 4/4    CLEF: grand
U: | B4/h A4/h | G4/h B4/h | C5/h A4/h | F#4/h G4/h |
L: | G3/h C4/h | B3/h D4/h | E4/h C4/h | D4/h G3/h |

The given tune (upper voice) arcs B4 down to A4, dips to G4, leaps back to B4, peaks at C5, and closes ti–do: F♯4 rising to G4. The written line under it answers with its own shape — G3 up to C4, B3 up to D4, E4 falling to C4, D4 falling home to G3. Read the intervals: a major tenth, then sixths nearly wall-to-wall (C4–A4 major sixth, B3–G4 minor sixth, D4–B4 major sixth, E4–C5 minor sixth, C4–A4 again), a major third at the cadence (D4–F♯4), and one perfect octave — the last one, G3 under G4, arrived at by contrary motion while ti rises above. Imperfect workhorses, perfects spent at the arrival, motion varied, tendencies honored. Sing the lower line alone: it's a melody. That's the test.

Why this makes you a better musician

Count the gigs hiding in this one unit. The harmony vocal: you can now write — or improvise, because the habits become reflexes — the part that rides in thirds and sixths, holds while the lead runs, and lands the octave only at the button, approached from below while the melody floats down. That part sounds produced; singers will assume you arranged professionally, because you did. The bass line: instead of pumping roots, you can hand your bass player contrary motion under the tune's climb — the single cheapest trick in arranging, and the one that makes a two-instrument gig sound like a band. The fix-it vocabulary: "your part's fusing with the lead — slide to the sixth" and "you crossed above her in bar two" are ten-second rehearsal repairs that used to take four frustrating run-throughs of something's off. And the second session, your table writes a line, swaps sheets with the next table, hunts their parallels, and checks every verdict against the course's own software gate — the exact quality-control loop a professional copyist runs, at gig speed, with your name on the part.

Key terms

  • Contrary motion — two voices moving in opposite directions; the strongest independence.
  • Oblique motion — one voice holding while the other moves.
  • Similar motion — both voices moving the same direction by different intervals.
  • Parallel motion — both voices moving the same direction at the same interval; welcome in thirds/sixths/tenths, banned at perfect intervals.
  • Parallel fifths / parallel octaves — consecutive perfect fifths (or octaves/unisons) between the same two voices in parallel motion; they fuse two lines into one.
  • Direct (hidden) fifth/octave — similar motion into a perfect interval with a leap in the upper voice.
  • Voice crossing — the lower voice sounding above the upper voice at the same moment.
  • Voice overlap — a voice moving past the note the other voice just left.
  • Range — the comfortable register of a voice or instrument; a line's lane.
  • Tendency tone — a note whose resolution is stylistically decided: the leading tone rises to do; the chordal seventh falls by step.
  • Second voice — an independent line written against a given line: a harmony vocal, a countermelody, a bass line that stands on its own.
  • Round — a tune written to harmonize with itself at staggered entries; the ear's oldest proof that two-voice independence is singable by anyone.

Summary

  • Progressions run on the functional engine — tonic free, predominant to dominant, dominant home (or the deceptive detour). Norms, not laws: your second voice rides this engine.
  • Every two-voice moment is one of four motions: contrary, oblique, similar, parallel. Parallel thirds/sixths/tenths are beloved; contrary and oblique are independence on tap.
  • No parallel perfect fifths, octaves, or unisons — not because they're ugly (they're hollow, ancient, and power chords are built from them) but because they weld two voices into one. No direct fifths/octaves — similar motion into a perfect with an upper-voice leap. Perfect intervals are arrival points: earn them by contrary or oblique approach.
  • Keep lanes: no crossing (lower above upper), no overlap (past the note the other just sang), and respect range.
  • Two notes are under contract: ti rises to do; the chordal seventh falls by step.
  • Write the second voice by procedure: read the engine → default to imperfect → spend perfects at arrivals → vary motion → honor tendencies → run the two-rules pass. Then sing your line alone; if it survives, it's a voice.

Check your understanding

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

  1. The upper voice steps up from E4 to F4 while the lower voice steps down from C4 to B3. Name the motion type — and name the two harmonic intervals the voices make.
  2. A friend proudly harmonizes a whole chorus in parallel motion and asks if that breaks "the rule." What one question do you ask before answering, and why?
  3. Lower voice F3 under upper voice C4, then both voices step up: G3 under D4. What exactly has gone wrong — name it precisely — and offer one fix that keeps the same upper line.
  4. Both voices rise and land on a perfect octave: the lower steps E3→F3 while the upper leaps C4→F4. Is this the same fault as question 3? Name it, and name the approach that would have made the same octave legal.
  5. In a two-voice close in G major, the tune sings F♯4 on the dominant chord, and your lower line carries C4 — the seventh of D7 — at the same moment. Write the next note of each voice, and say whose contract each note honors.

Answers (worked reasoning — read after attempting)

  1. Contrary motion — the voices move in opposite directions. The intervals: C4 up to E4 is a major third; B3 up to F4 is… count it — B to F is a fifth by letters, and B3–F4 spans six semitones: a diminished fifth. (A d5 between voices is fine here — it isn't a perfect interval, and unit 14 shows how such tensions lean and resolve.)
  2. "Parallel what?" The ban covers perfect intervals only — fifths, octaves, unisons. If the chorus rides thirds or sixths, it's not just legal, it's the most-loved harmony sound in popular music. If it rides fifths or octaves, the two parts have fused into one thickened line — which might even be the sound they want, but it isn't a second voice.
  3. Parallel perfect fifths: F3–C4 is a P5, G3–D4 is a P5, and the voices moved to it in parallel. Two fixes that keep the same upper line: hold the F3 — oblique motion, and the second pair becomes F3–D4, a major sixth; or send the lower voice down to B2 — contrary motion into a minor tenth. Either way the fifth-to-fifth lockstep is broken, which was the whole problem.
  4. Not the same fault. Question 3 was fifth to fifth: parallel. This is some-other-interval into an octave, in similar motion, with the upper voice leaping — a direct (hidden) octave. The same arrival octave is perfectly legal approached by contrary or oblique motion (or with the upper voice stepping): let the upper voice step down into it, or hold one voice still.
  5. F♯4 is ti in G major: it rises to G4 — the leading tone's contract. C4 is the chordal seventh of D7 (D–F♯–A–C): it falls by step to B3 — the seventh's contract. Together they land G4 over B3, a minor sixth: a close that keeps both promises. (And notice what you just did: resolved a dominant seventh in two voices, by contract alone.)

Next in this module: the Readings & Resources page if you want other angles on two-voice writing, then Tutorial 13 — your AI tutor session, due before Week 13's second session so the second session's writing and hunting can build on it.

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