Week 7 · Chapter

Week 7 — Chapter · 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
The unit's primary reading · ~30–40 minutes · SLOs 3 and 7 · Read this before the first session if you can, or right after — everything else in the module builds on it.

The itch you already know the cure for

Play two notes together — B3 and F4 — on any keyboard, or have a friend sing one while you sing the other. Hold them. Notice what your body does: it waits. That sound is not finished, and you know it's not finished, and you even know — without one minute of training — where it wants to go. Let the B slide up a half step and the F slide down a half step, and there it is: C and E, home, done, exhale.

You've been hearing that itch your whole musical life — it's the sound movie composers reach for when something is about to go wrong, and it hides inside the chord your worship band leans on before every chorus comes home. What you haven't had is its name — and here is the twist this unit is built on: that one sound has two names, and the two names are not interchangeable. The spelling decides which name is right, and it tells you which way the music is leaning.

Last unit you built the interval machine: size from letters, quality from half steps, each measured on its own ruler. This unit the machine goes to work. You'll stretch it past the octave (compound intervals), point it at the famous six-half-step itch (the tritone), use it to sort every interval by how settled it sounds (consonance and dissonance), sharpen the Week 1 rule that "sounds alike" never means "equals" (enharmonic intervals that are not the same interval), and then cash the whole thing in on the skill this unit is really about: transcribing a melody by ear, fast, by naming each leap as it lands.

One more thing, because it's fair to keep the finish line visible: the midterm — the exam that certifies all of Foundations — runs next week, in exam week's single session — so this week's second session carries the studio and the cumulative review, and the study guide, prep tutorial, and practice exam have been open since two weeks ago. Nothing on that exam is new. It's everything you've already named, certified.

Where we are

Units 1 through 5 gave every note an address, every rhythm a count, and every key a spelling. Unit 6 built the two-ruler interval machine — size from letter distance, quality from semitone distance, measured independently — and taught you to spell intervals above and below any pitch and to invert them. This unit is the second half of that story: the machine, applied. After this week, Foundations is complete, and everything from unit 9 onward — triads, sevenths, progressions — is interval arithmetic wearing a different hat.

Compound intervals: the same ladder, upstairs

Everything in unit 6 fit inside one octave. Real music doesn't. Your bass player's low E and the melody note you're singing are rarely within eight letters of each other; the gap between a lead vocal and a harmony line an octave-and-a-third up is a real, nameable thing. Intervals wider than an octave are called compound intervals, and the entire topic is one piece of good news:

Nothing new is happening. A compound interval is a simple interval wearing an octave like a coat.

The arithmetic: simple size + 7 = compound size. (Seven, not eight — the octave's top note and the simple interval's bottom note share a letter, so one rung of the ladder gets counted only once.)

M2 + octave = M9 (major ninth)
M3 + octave = M10 (major tenth)
P4 + octave = P11 (perfect eleventh)
P5 + octave = P12 (perfect twelfth)
M6 + octave = M13 (major thirteenth)

And the crucial fine print: the quality never changes. Major stays major, minor stays minor, perfect stays perfect. A m3 an octave wider is a m10 — not "more minor," not upgraded, just wider.

Worked example. C4 up to E4: letters C-D-E, a third; four half steps; M3. Now raise the top note an octave — C4 up to E5. The letters involved are still C and E, but counting every letter name on the way (C-D-E-F-G-A-B-C-D-E) gives ten: a tenth. Same quality as the third it grew from: M10. To spell any compound interval, spell the simple one, then move the top note up an octave. If you can spell a M3, you already spell M10s.

METER: free    CLEF: treble
| C4/w E4/w E5/w |

Three whole notes on the treble staff: C4, then E4 a major third above it, then E5 — the same E pushed up an octave, now a major tenth above the C. The coat went on; the quality never moved.

Going the other way is just as useful: to identify a big interval, strip the coat — subtract 7 from the size, name the simple interval, then add the octave back. A thirteenth? Subtract 7: a sixth. Name the sixth's quality, and you have the thirteenth's. When your ear meets a leap bigger than an octave in the transcription work below, this is the move: hear it as "an octave plus something," name the something.

Misconception check. "Compound intervals are a new system to memorize." They're last unit's system plus the number 7. If compound intervals feel hard, the gap is almost always in the simple interval underneath — patch that, and the coat is free.

The tritone: one sound, two intervals

Back to the itch. Six half steps. On a keyboard it's dead center between the perfect fourth (five half steps) and the perfect fifth (seven). Musicians nickname the sound the tritone — "three whole tones" — and your ear flags it instantly: restless, leaning, unfinished.

Here is the fact this course will not let anyone flatten: the tritone is a sound, not a spelling — and on paper it is always one of two different intervals. Spell six half steps up from F4 and watch what the letters do:

F4 up to B4. Letters F–G–A–B: four letter names, so the size is a fourth. Six half steps is one more than the perfect fourth's five: a fourth stretched past perfect is an augmented fourth — A4.
B3 up to F4. Letters B–C–D–E–F: five letter names, so the size is a fifth. Six half steps is one less than the perfect fifth's seven: a fifth squeezed short of perfect is a diminished fifth — d5.

Same distance in sound. Different letter counts, different sizes, different names, different intervals. This is the same lesson as G♯4 and A♭4 in unit 1 — one piano key, two written notes — grown up and applied to the space between notes.

Why care which is which? Because the spelling predicts the resolution. The classical habit your ear already owns: the d5 contracts inward — each note moves a half step toward the middle (B3 rises to C4, F4 falls to E4, landing on a third). The A4 expands outward — F4 falls to E4 while B4 rises to C5, landing on a sixth. Same sound, opposite destinations, and the spelling is the road sign:

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. Play both at any keyboard and you'll hear your own Segment-1 instinct written down.

One more piece of furniture worth owning now: every major key has exactly one tritone built into it, between ^4 and ^7 — fa and ti. In C major, that's F and B, the only white-key tritone on the piano. When you reach dominant seventh chords in unit 10, you'll find that pair hiding inside V7, which is a big part of why V7 pulls home to I so hard. For now, just know where the itch lives in every key you spell.

Misconception check. "The tritone is always an augmented fourth." The nickname names the sound; the interval on paper is A4 or d5, and only the letters can tell you which. F4→B4 is an A4. B3→F4 is a d5. Count letters before you speak — the same discipline as ever, with a famous interval attached.

Consonance and dissonance: the sort your ear already runs

Some intervals sound settled — you could end a song on them and nobody would wait for more. Others lean — they ask for motion. Music theory's names for the two families are consonant and dissonant, and here's the encouraging part: played a stack of intervals, your ear sorts them the same way five centuries of musicians have. You are not learning a new skill in this section. You're labeling one.

The standard sort, which this course uses from here through the two-voice writing units:

Consonant (settled): the perfect unison and octave (P1, P8), the perfect fifth (P5), and all the thirds and sixths (M3, m3, M6, m6).
Dissonant (leaning): all the seconds (M2, m2), all the sevenths (M7, m7), and the tritone (A4/d5) — whichever way it's spelled.

And then there is the perfect fourth, which refuses to sit in either chair — and this course will tell you the truth about it rather than a tidy lie. Sung as a melody leap ("Amazing" in Amazing Grace opens with one), the P4 sounds sturdy and clean. Sounded between the upper parts of a chord, it's stable. But against the bass in two-voice writing, centuries of practice treat the fourth as a dissonance — a sound that needs to resolve, usually downward to a third. So the honest classification, and the one this course tests, is: the perfect fourth is context-dependent — consonant in some settings, treated as dissonant in others. When you write two independent voices in unit 13, "no bare fourth against the bass at a resting point" becomes a practical rule you'll use; for now, the takeaway is that "is a fourth consonant?" is a where question, not a yes/no question.

A working musician's reading of this whole section: dissonance is not a defect. Every song you love leans before it lands. Consonance with no dissonance is wallpaper. This vocabulary lets you place the lean on purpose, and name what a track is doing when it raises the hair on your arms.

Misconception check. "Perfect fourth means perfectly consonant." "Perfect" names its quality family (the one that comes in d–P–A flavors), not its behavior. Between upper voices: stable. Against the bass: treated as needing resolution. Context decides — write "context-dependent" and you're telling the truth.

Enharmonic intervals: same sound, different name, different job

Unit 1's rule — enharmonic means "sounds alike," never "equals" — has been climbing the course with you. It applied to notes (G♯4/A♭4), then to whole keys (F♯ major and G♭ major). Now it reaches intervals, where it does its most important work.

Two intervals can share a sound and not be the same interval. You've already met the headline pair — A4 and d5. But the idea is general, and the second-most-useful example is three half steps wide:

F4 up to A♭4. Letters F–G–A: a third. Three half steps: m3. Settled, consonant, minor-third sound — the interval that opens a thousand sad choruses.
F4 up to G♯4. Letters F–G: a second. The same three half steps, but on a second-sized frame: a second stretched a half step past major — an augmented second, A2.

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. Same two piano keys both times; two different written intervals.

Why would any sane musician write the A2? Because the music around it demands those letters. In A harmonic minor — a scale you spelled in unit 5 — the walk from ^6 up to the raised ^7 is F4 to G♯4. It must be spelled with F and G, because a scale uses each letter exactly once; respelling the G♯ as A♭ would wreck the scale (two A-letters, no G). The A2 is not an eccentric m3. It's the honest name of that scale step — and when a reader sees "A2," they know exactly where they are: mid-climb in harmonic minor, one half step from the tonic's doorstep.

That's the general principle, and it's worth stating in bold: enharmonic intervals sound identical; the spelling carries the function — where the notes came from and where they're going. The same discipline covers unit 6's regression traps, which are worth re-saying once here: C4→E♯4 is an augmented third, never a perfect fourth; C4→F♭4 is a diminished fourth, never a major third. The keys under your fingers can't distinguish these. The page can, and the page is where musicians talk to each other.

Inversion respects the distinction too, which is tidy proof the pairs were never "the same": invert the m3 F4–A♭4 and you get a M6; invert the A2 F4–G♯4 and you get a d7 — enharmonic again, and again not equal. The tritone pair inverts into itself: A4 ↔ d5.

Misconception check. "Enharmonic intervals must sound at least a little different — otherwise why two names?" They sound exactly the same; that's the point. The two names encode information sound alone can't carry: which letters, which scale, which direction of travel. Spelling is the difference between describing a sound and explaining a sentence.

Leap-mapping: intervals as a transcription tool

Now the payoff — the reason this unit exists in a course built for musicians who already hear.

Most people imagine transcription as heroic guessing: hear a note, hunt for it, repeat forty times, lose an evening. People who do it fast anchor one note, and from there they never identify a note from silence again — they name each move. That's leap-mapping, and you already own every part of it:

Anchor the start. Get the first pitch — given to you, or found once at a keyboard.
Hear the next note. Up or down? Your ear has answered that one since childhood.
Name the move. Step or leap? How wide? Call it out loud: "up a perfect fourth." (Singing the gap against do–re–mi patterns, or against song hooks you collected in unit 6, is exactly how working players do it.)
Spell it from the note you already trust — letters first for the size, quality second, the unit-6 machine.
Write it and move on. The note you just wrote becomes the new anchor. Repeat.

Fully worked example. Take When the Saints Go Marching In — you can sing it cold, which makes it perfect lab material. Say the starting note is given: C4. Sing the opening four notes — "Oh, when the saints."

Move 1: the second note is higher, a leap but a small one — sing it against your do-mi pattern: it's do to mi, up a M3. Spell from C4: letters C–D–E, third; major quality; E4. Write it.
Move 2: the next note is barely higher — the smallest step there is: up a m2. Spell from E4: E to F is the white-key half step; F4. Write it.
Move 3: one more step up, a whole one this time: up a M2 from F4 → G4. Write it, and the long note under "saints" 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 into a long G4 on the downbeat: the Saints call, transcribed from one given note and three named moves (M3, m2, M2). Four notes, maybe fifteen seconds of work.

Two finishing touches make the method complete. Compound leaps: when a move is wider than an octave — the gap down to a bass note, a big vocal jump — hear it as "an octave plus something," name the something, add the coat: an octave plus a M3 is a M10, and the spelling machine handles it exactly like the M3 it grew from. (Your guitarist capoing the Saints call up an octave is playing C5–E5–F5–G5 — same moves, new floor.) Spelling discipline: in a real key, the key signature chooses the letters — if the tune lives in F major, the black key you hear above A is B♭, not A♯, no matter what a chatbot tells you. Sound gets you the distance; the key gets you the letters; you get the credit.

The studio is this section with a stopwatch: a transcription race on tunes you already know, interval calls out loud, measured against where you started in week 1. It will be loud and it will be fast, and you will be startled by how much faster you are than you were six weeks ago.

Why this makes you a better musician

Every payoff in this unit converts directly to gig currency. The song request that arrives Thursday night for Sunday morning — no chart anywhere — stops costing you an evening: anchor one note, leap-map the melody, ten minutes, done, and the chart you text the band is in the right key with the right letters. The harmony part you need to teach a singer becomes three named intervals instead of twenty hummed takes. When the bridge of a song makes everyone lean forward, you can name the machinery — there's the tritone, spelled as a d5, contracting home — which means you can reuse the machinery in your own arrangements instead of waiting for it to happen by luck. And the compound-interval habit fixes the most common charting mistake bands make: writing the bass note in the singer's octave. A tenth is not a third, and the player reading your chart will thank you for knowing it. Next week, the midterm certifies this whole vocabulary — and then the second half of the course starts stacking it into chords.

Key terms

Compound interval — an interval wider than an octave; named by adding 7 to the simple interval's size (M3 + octave = M10). Quality is unchanged by the octave.
Ninth / tenth / eleventh / twelfth / thirteenth — the compound sizes built from the 2nd, 3rd, 4th, 5th, and 6th respectively.
Simple interval — an interval an octave or smaller; the "inside the coat" form of any compound interval.
Tritone — the six-half-step sound, nicknamed for its three whole steps; on paper always spelled as either A4 or d5, which are two different intervals.
Augmented fourth (A4) — a fourth one half step wider than perfect (F4–B4); tends to resolve outward.
Diminished fifth (d5) — a fifth one half step narrower than perfect (B3–F4); tends to resolve inward.
Consonance — the settled family: P1, P8, P5, and the thirds and sixths.
Dissonance — the leaning family: seconds, sevenths, and the tritone.
Context-dependent (the perfect fourth) — this course's honest classification of the P4: consonant melodically and between upper voices; treated as a dissonance against the bass in two-voice writing.
Enharmonic intervals — intervals that sound identical but are spelled differently and are not the same interval (m3 vs. A2; A4 vs. d5; M3 vs. d4).
Resolution — the move by which a dissonance settles into a consonance (d5 contracting to a third; A4 expanding to a sixth).
Leap-mapping — transcribing by naming each interval move from the previous note, so every new note is a spellable distance from one you already trust.

Summary

A compound interval is a simple interval plus an octave: size + 7, quality unchanged. M3 → M10, P4 → P11, P5 → P12. To read a big interval, strip the coat; to spell one, spell the simple interval and raise the top note an octave.
The tritone is one sound with two spellings, and they are different intervals: F4→B4 = A4 (a fourth), B3→F4 = d5 (a fifth). The d5 pulls inward to a third; the A4 pushes outward to a sixth. Every major key hides exactly one, between fa and ti.
Consonant: P1, P8, P5, thirds, sixths. Dissonant: seconds, sevenths, the tritone. The P4 is context-dependent — stable in melody and upper voices, treated as dissonant against the bass.
Enharmonic intervals sound alike and are not equal: m3 ≠ A2, M3 ≠ d4, A4 ≠ d5. The spelling carries the function — harmonic minor's ^6→^7 step is an A2 because scale letters leave it no other honest name.
Leap-mapping: anchor one note, then name and spell every move from the previous note — letters for size, half steps for quality, key signature for the letter choices. Transcription becomes minutes, not hours.

Check your understanding

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

A duet has the melody on E5 while the bass holds C4. Name the interval, then name the simple interval hiding inside it.
Spell the tritone above D4 twice — once as an augmented fourth, once as a diminished fifth — and say which spelling you'd expect to contract inward when it resolves.
Your band's closing chord needs to sound finished. A friend suggests holding either a major sixth or a minor seventh above the root. Which do you pick, and what's the one-word reason?
G4 up to B♭4 and G4 up to A♯4 use the same two piano keys. Name both intervals, and give one musical situation in which the second spelling would be the honest one.
You're leap-mapping a tune that starts on A4. The moves are: down a M2, down a m3, up a P4. Spell the three notes you write, in order.

Answers (worked reasoning — read after attempting)

C4 up to E5: letters C through E the long way — C-D-E-F-G-A-B-C-D-E — ten names, a tenth; four-half-step quality on the third underneath: major. M10, and the simple interval inside the coat is M3 (10 − 7 = 3). Quality identical in both — the octave never changes quality.
As an augmented fourth: a fourth above D4 uses letters D-E-F-G, and six half steps lands on G♯4 — D4→G♯4 = A4. As a diminished fifth: a fifth uses letters D-E-F-G-A, and the same six half steps must be spelled A♭4 — D4→A♭4 = d5. The d5 spelling is the one that classically contracts inward; the A4 expands outward. Same keys on the piano, two different road signs.
The major sixth — it's consonant (settled); the m7 is dissonant and would leave the ending leaning. (If you wanted the audience waiting for a note that never comes, the m7 is exactly how you'd do it — dissonance is a tool, not an error.)
G4→B♭4: letters G-A-B, a third, three half steps — m3. G4→A♯4: letters G-A, a second, the same three half steps — A2. The A2 is the honest spelling in B harmonic minor, where the scale climbs ^6 to raised ^7 as G4→A♯4 — the letters G and A are forced because a scale uses each letter once (unit 5's spelling logic, now with its interval named).
Down a M2 from A4: G4. Down a m3 from G4: E4. Up a P4 from E4: A4 — back where you started, which is also a quiet check on your work: a M2 plus a m3 down is a P4's worth of half steps (2 + 3 = 5), so the P4 up must land you home.

Next in this module: the Readings & Resources page if you want other angles on intervals, then Tutorial 7 — your AI tutor session, due before Week 7's second session so the second session's transcription race can build on it. And keep the Week 8 study guide open in the other tab — the midterm is next week, and it's all vocabulary you now own.

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