Week 4 — Chapter · Major

Course: MUS 156 Music Theory I · Kenosis College
Instructor: Professor Hemsworth
Unit: Learning Unit 4 of 16 (Week 4) · two sessions per week
The unit's primary reading · ~35–45 minutes · SLOs 2 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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You already hear this

Sing this out loud, right now, wherever you are: do re mi fa sol la ti do. You just performed the entire content of this unit. That ladder — the major scale — has been in your ear since childhood. It's the sound of Joy to the World coming down, the sound of a choir warming up, the sound of "happy" in almost every song you've ever played at a wedding, a worship set, or a karaoke night. You can sing it starting anywhere: hum any note and walk the ladder up from it, and it comes out right, automatically.

Here's what your ear has been doing without telling you: it has been enforcing a precise recipe of whole steps and half steps, the two distances you learned to measure in unit 1. This unit writes the recipe down. By the end of this chapter you will be able to: say the major scale's step pattern; spell all fifteen major scales using each letter name exactly once; write and read key signatures using the fixed orders of sharps and flats; place any key on the circle of fifths — and rebuild that circle from scratch, because it's generated, not memorized; number scale members ^1 through ^7; and sing any major scale on movable-do solfège. None of it is new hearing. All of it is new naming.

Where we are

Unit 1 gave every note an address. Units 2 and 3 gave every rhythm a count. This unit organizes the addresses into neighborhoods: a key is a family of notes that all belong to one ladder, and a piece "in G major" lives in the G neighborhood — its notes drawn from one scale, its home base the note G. Units 5 through 7 build directly on this one: minor keys next, then the precise names of every distance inside the ladder. The midterm — the finish line for all of Foundations — is three units away, and this unit is its center of gravity.

As always, the order is: sound first, name second, notation third. You could already sing the ladder; now we name its parts.

One pattern: W W H W W W H

Go to a keyboard — paper or real — and play the white keys from middle C up to the next C: C4, D4, E4, F4, G4, A4, B4, C5. That's a major scale, and because you built it on white keys only, its inner structure is sitting in plain sight. Measure each move:

• C to D: a black key sits between — whole step.
• D to E: whole step.
• E to F: nothing between — half step (one of unit 1's two built-in white-key half steps).
• F to G, G to A, A to B: whole steps.
• B to C: the other built-in half step — half step.

Read the column of moves top to bottom: whole, whole, half, whole, whole, whole, half — W W H W W W H. That is the entire recipe. Eight notes, seven moves, half steps falling between steps 3–4 and 7–8. Every major scale ever written, in every key, is this one pattern.

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

In plain English: the C major scale climbing one octave on the treble staff — eight notes walking stepwise from middle C up to C5, no sharps or flats anywhere, with the two half-step moves hidden between E4–F4 and B4–C5.

And when you reach C5? Nothing resets. C5 is step 8 of the lap you just finished and step 1 of the next lap; the recipe loops through every octave the instrument has. The pattern doesn't break at the octave — it breathes there.

Misconception check. "The octave restart breaks the pattern." It doesn't — the ladder is circular. Climb past C5 and the next moves are whole (to D5), whole (to E5), half (to F5)… the same seven moves per lap, forever, in both directions.

The spelling law: every letter, exactly once

Now move the front door. Your ear already knows the ladder from G sounds like the ladder from C — same tune, new starting note. Build it on paper and watch the recipe make a demand:

G to A: whole ✓. A to B: whole ✓. B to C: half ✓ (right on schedule — steps 3–4). C to D: whole ✓. D to E: whole ✓. E to F: only a half step, but the recipe wants a whole — so the seventh note must be F♯. Then F♯ to G: half ✓. The full spelling: G A B C D E F♯ G.

That F♯ is not decoration and not tradition. It's the pattern's demand at a specific rung. And notice what it can not be: G♭. Same lever on the piano, but the scale already has a G — the front door itself. Which brings us to the law that governs every spelling in this course:

Every letter name appears exactly once per octave. Seven letters, seven rungs, then the front-door letter returns. A "scale" with two kinds of G and no F isn't an alternative spelling — it's a misspelling, the way thier is a misspelling no matter how it's pronounced.

Build from F and the law pushes the other way: F, G, A ✓ — but A to B is a whole step and the recipe wants a half at 3–4, so the fourth note must be B♭: F G A B♭ C D E F. Sharps and flats are the same law answering the same recipe from different directions.

One more worked spelling, from a flat-side front door:

KEY: Eb major    METER: free    CLEF: treble
| Eb4/q F4/q G4/q Ab4/q Bb4/q C5/q D5/q Eb5/q |

In plain English: the E♭ major scale on the treble staff, E♭4 up to E♭5 — three flats (E♭, A♭, B♭) doing exactly what W W H W W W H demands, each of the seven letters used once.

Misconception check. "A key's sharps or flats are random — you just memorize them." Nothing is random. Every accidental is generated by the pattern. If you forget E major's sharps on a desert island, you can rebuild them in thirty seconds from W W H W W W H. Memorization is a speed upgrade, not a foundation.

All fifteen major scales

There are fifteen spellable major keys: C in the middle, seven that use sharps, seven that use flats. Here they all are — this table is your reference for the whole course.

The table below lists every major scale with its signature.

Key	Scale	Signature
C major	C D E F G A B C	no sharps or flats
G major	G A B C D E F♯ G	1 sharp: F♯
D major	D E F♯ G A B C♯ D	2 sharps: F♯ C♯
A major	A B C♯ D E F♯ G♯ A	3 sharps: F♯ C♯ G♯
E major	E F♯ G♯ A B C♯ D♯ E	4 sharps: F♯ C♯ G♯ D♯
B major	B C♯ D♯ E F♯ G♯ A♯ B	5 sharps: F♯ C♯ G♯ D♯ A♯
F♯ major	F♯ G♯ A♯ B C♯ D♯ E♯ F♯	6 sharps: F♯ C♯ G♯ D♯ A♯ E♯
C♯ major	C♯ D♯ E♯ F♯ G♯ A♯ B♯ C♯	7 sharps: F♯ C♯ G♯ D♯ A♯ E♯ B♯
F major	F G A B♭ C D E F	1 flat: B♭
B♭ major	B♭ C D E♭ F G A B♭	2 flats: B♭ E♭
E♭ major	E♭ F G A♭ B♭ C D E♭	3 flats: B♭ E♭ A♭
A♭ major	A♭ B♭ C D♭ E♭ F G A♭	4 flats: B♭ E♭ A♭ D♭
D♭ major	D♭ E♭ F G♭ A♭ B♭ C D♭	5 flats: B♭ E♭ A♭ D♭ G♭
G♭ major	G♭ A♭ B♭ C♭ D♭ E♭ F G♭	6 flats: B♭ E♭ A♭ D♭ G♭ C♭
C♭ major	C♭ D♭ E♭ F♭ G♭ A♭ B♭ C♭	7 flats: B♭ E♭ A♭ D♭ G♭ C♭ F♭

Two residents of this table deserve a wave from unit 1: E♯ (in F♯ and C♯ major) and C♭ (in G♭ and C♭ major — where F♭ also lives). They're played on white keys, they looked exotic four weeks ago, and here they are doing honest work — because the spelling law demands some kind of E at that rung, and the recipe makes it E♯.

Key signatures: the scale, filed

A song in A♭ major uses B♭, E♭, A♭, and D♭ constantly. Writing a flat in front of every one would bury the page. So notation files the key's accidentals once, at the start of every line — the key signature. A signature adds no new information: it is the scale's accidentals, collected and posted like a neighborhood sign.

What makes signatures readable at a glance is that accidentals always join in one fixed order:

• Order of sharps: F C G D A E B.
• Order of flats: B E A D G C F — the same list read backward.

So one sharp is always F♯. Three sharps are always F♯ C♯ G♯. Four flats are always B♭ E♭ A♭ D♭. No key signature ever mixes sharps and flats, and none ever skips around in the order. When you see a signature, you're seeing the front of one of these two lists, cut off at some length — nothing else is possible.

Reading a signature back into a key name. Two tricks, one per side:

• Sharps: the last sharp sits a half step below home. Last sharp G♯? A half step up is A — A major. Last sharp A♯? B major.
• Flats: the next-to-last flat names the key. See B♭ E♭ A♭? The next-to-last is E♭ — E♭ major. See B♭ E♭ A♭ D♭ G♭? D♭ major. One edge case: a single B♭ has no next-to-last, so that signature (F major) is simply learned — the only special case on the flat side.

Misconception check. "The signature tells you what note the piece starts on." No — it names the neighborhood, not the first house you visit. Pieces in G major start on all sorts of notes. The signature's promise is different: every F on the page is sharp until further notice, and the ladder underneath everything is G's.

The circle of fifths: the map of every key

Line up three facts from earlier in this chapter: C major has no sharps. G major — whose front door is the fifth note of C's scale — has one. D major — the fifth note of G's scale — has two. Every time the front door moves up a fifth (five letter names up; the do-to-sol distance; you'll learn this distance's full name in unit 6), exactly one sharp joins the signature, in order.

Chain that single move and the entire key system unrolls:

• Sharp side (up a fifth each stop): C → G → D → A → E → B → F♯ → C♯. Zero sharps to seven, one new sharp per stop.
• Flat side (down a fifth each stop): C → F → B♭ → E♭ → A♭ → D♭ → G♭ → C♭. Zero flats to seven, one new flat per stop.

Bend the two arms around and they meet at the bottom: the circle of fifths, the map of all fifteen major keys. And hiding inside it, a bonus: the order of sharps — F C G D A E B — is itself a chain of fifths, and the order of flats is the same chain run backward. The whole apparatus is one distance, applied over and over. This is why the circle never needs to be taken on faith: anyone who can count up five letter names can rebuild the entire thing on a napkin.

Misconception check. "The circle of fifths is a poster to memorize." It's a machine to operate. Memorize it too, eventually — speed matters on a gig — but the difference between memorizing and generating is the difference between hoping you remember D♭'s flats and being able to derive them while the drummer counts off.

Fifteen homes, twelve levers: enharmonic keys

Count the circle's stops: eight on the sharp arm (C through C♯) and seven more on the flat arm — fifteen major keys. But unit 1 told you a piano octave has only twelve levers. The books balance because three pairs of keys share sound:

B / C♭ · F♯ / G♭ · C♯ / D♭.

These are enharmonic keys — the whole-key version of unit 1's G♯4/A♭4 twins. F♯ major and G♭ major are played on the same twelve levers and sound identical, and they are two different keys: one is spelled with six sharps (F♯ G♯ A♯ B C♯ D♯ E♯), the other with six flats (G♭ A♭ B♭ C♭ D♭ E♭ F). Both spellings are complete, lawful, and in real use — charts arrive written both ways, depending on the instruments in the room and the arranger's habits.

METER: free    CLEF: treble
| F#4/w Gb4/w |

In plain English: one piano lever written twice on the treble staff — first as F♯4, then as G♭4. In unit 1 this was a fact about two notes. This week each spelling opens onto an entire key: six sharps behind the first, six flats behind the second.

The course rule, unchanged since unit 1 and now operating at full scale: enharmonic means "sounds alike," never "equals." A chatbot that tells you "F♯ major and G♭ major are the same key, just use whichever" has collapsed exactly the distinction this course pays you to keep.

Scale degrees ^1–^7, and the syllables you'll sing in Aural Skills I

Once a key is chosen, its rungs get numbers: ^1 ^2 ^3 ^4 ^5 ^6 ^7, and then ^1 again at the octave. The numbers are portable across every key: the ^5 of E♭ major is B♭; the ^5 of D major is A; the ^4 of G major is C. When this course writes "^6," read it out loud as "scale degree six." (The degrees also carry traditional names — those arrive in unit 5, where minor keys make them earn their keep. This week, numbers only.)

The singable version of the numbers is movable-do solfège:

do (^1) · re (^2) · mi (^3) · fa (^4) · sol (^5) · la (^6) · ti (^7) · do (^8).

"Movable" is the key word: do is not a fixed pitch — do is ^1 of whatever key you're in. In G major, do is G and ti is F♯; in E♭ major, do is E♭ and fa is A♭. Its paired course, MUS-155 Aural Skills I, sings this ladder the same weeks this course spells it — including do–mi–sol echo patterns, a shape your ear will come to know cold long before unit 9 gives it a formal name. What you write here you'll sing there; the two courses are one system on purpose.

Hear the ladder in the wild — the most famous descending major scale in the repertoire:

KEY: D major    METER: free    CLEF: treble
| D5/q C#5/q B4/q A4/q G4/q F#4/q E4/q D4/q |

In plain English: the D major scale falling one octave, D5 down to D4 — which is note-for-note the opening phrase of Joy to the World. Sing "Joy to the world, the Lord is come" down it and you've sung ^8 ^7 ^6 ^5 ^4 ^3 ^2 ^1: do ti la sol fa mi re do. You have known this unit's material, at performance quality, for most of your life.

Why this makes you a better musician

Keys are the difference between reading warnings and reading a map. The player who doesn't know this unit sees a D♭ chart as five separate flats to dodge, line after line; the player who does sees one key — B♭ E♭ A♭ D♭ G♭, filed in order, done — and spends the ten minutes before downbeat on the music instead of the accidentals. When the singer says "too low, take it up to E," you know instantly that's four sharps and which four. When the guitarist calls "it's in A," every C, F, and G in your part is already sharp in your mind before beat one. And when a chart shows up spelled in G♭ because the horn parts wanted flats, you read it without blinking, because you can spell both twins. This is the arithmetic every transposing, sitting-in, key-changing working musician runs silently all night — the studio exists to make yours fast.

Key terms

• Major scale — the eight-note ladder built by the step recipe W W H W W W H; half steps fall between ^3–^4 and ^7–^8.
• Key — the family of notes belonging to one scale, named for its home note (^1): music "in E♭ major" draws from the E♭ major scale.
• Spelling law — every letter name appears exactly once per octave in a correctly spelled scale.
• Key signature — the key's accidentals, collected at the start of each line instead of written per note.
• Order of sharps — F C G D A E B; sharps always join a signature in this order.
• Order of flats — B E A D G C F; the order of sharps reversed.
• Circle of fifths — the map of all fifteen major keys generated by moving up a fifth per stop (sharp side) or down a fifth per stop (flat side), adding one accidental each time.
• Enharmonic keys — key pairs that sound identical but are spelled differently: B/C♭, F♯/G♭, C♯/D♭.
• Scale degree — a scale member's number within its key, written ^1 through ^7.
• Movable-do solfège — the sung syllables do re mi fa sol la ti do, where do is always ^1 of the current key.

Summary

• One recipe builds every major scale: W W H W W W H, half steps between ^3–^4 and ^7–^8. The pattern loops at the octave; nothing resets.
• Spell with each letter exactly once. The accidentals a key needs are the recipe's demands, not random facts: G major needs F♯; F major needs B♭; D♭ major needs five flats.
• The key signature files the scale's accidentals at the line's start, always in fixed order — sharps F C G D A E B, flats B E A D G C F, never mixed. Read signatures backward: last sharp + half step = home; next-to-last flat = home (single-flat F major is the learned exception).
• The circle of fifths is generated, not decreed: up a fifth per stop adds one sharp; down a fifth per stop adds one flat. Fifteen stops, and the orders of sharps and flats are themselves chains of fifths.
• Fifteen keys, twelve sounds: B/C♭, F♯/G♭, and C♯/D♭ are enharmonic keys — same levers, different spellings, never "the same key."
• Rungs are numbered ^1–^7 and sung do re mi fa sol la ti — movable do, where do is ^1 of the key you're in. Degree names arrive in unit 5.

Check your understanding

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

1. Spell the A major scale, and explain why its sixth-to-seventh rung is G♯ and cannot be written A♭.
2. Write the signature of A♭ major — how many of what, in exactly what order — and name the tool you used to order them.
3. A signature shows five sharps. Name the key, and show the trick that gets you there.
4. Your bandmate says, "F♯ major and G♭ major are the same key, so learning both spellings is busywork." What's right and what's wrong in that sentence?
5. In E♭ major, which notes are ^4 and ^7 — and which solfège syllables sing them?

Answers (worked reasoning — read after attempting)

1. A B C♯ D E F♯ G♯ A. Walking W W H W W W H from A forces C♯ at rung 3, F♯ at rung 6, and G♯ at rung 7. The seventh rung must be some kind of G — the spelling law gives each letter exactly one rung per octave, and A is already taken by the front door (^8). A♭ names the right lever and the wrong letter: same sound, misspelled scale.
2. Four flats: B♭ E♭ A♭ D♭. The tool is the order of flats — B E A D G C F — cut off after four. Flats never join a signature in any other sequence, so "four flats" fully determines which four and in what order.
3. B major. The last of five sharps (F♯ C♯ G♯ D♯ A♯) is A♯; the last sharp sits a half step below home, and a half step up from A♯ is B.
4. Right: the two keys share all twelve levers — they sound identical, and that's real. Wrong: they are two different keys with two complete spellings (F♯: six sharps, ending E♯; G♭: six flats, including C♭), and charts genuinely arrive in both. Enharmonic means "sounds alike," never "equals" — and the player who can only read one twin is helpless on the other's chart.
5. E♭ major runs E♭ F G A♭ B♭ C D E♭, so ^4 = A♭ and ^7 = D. Solfège: ^4 is fa, ^7 is ti — and do, throughout, is E♭, because movable do parks on ^1 of the current key.

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Next in this module: the Readings & Resources page if you want other angles on keys and the circle, then Tutorial 4 — your AI tutor session, due before Week 4's second session so the studio can build on it.

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