Music Theory Scales, Keys, and Intervals Syllabus

What is a relative minor key?

The minor key that shares the exact same key signature as a given major key but has a different tonic (e.g., A minor is the relative minor of C major — both have no sharps or flats).

How do you find the relative minor of a major key?

Go to the 6th degree of the major scale, or equivalently descend a minor 3rd ($3$ half steps) from the major tonic. Example: G major $\to$ E minor; Eb major $\to$ C minor.

What is a parallel minor key?

The minor key that shares the same tonic as a given major key but has a different key signature (e.g., C minor is the parallel minor of C major; C minor carries three flats while C major has none).

Compare: what are the relative minor and the parallel minor of C major?

Relative minor: A minor (same key signature — no sharps/flats — different tonic). Parallel minor: C minor (same tonic C, different key signature — three flats: Bb, Eb, Ab).

What is the order of sharps as they appear in key signatures? Give a mnemonic.

F#, C#, G#, D#, A#, E#, B# — each new sharp is a perfect 5th above the previous. Mnemonic: "Father Charles Goes Down And Ends Battle."

What is the order of flats in key signatures, and how does it relate to the order of sharps?

Bb, Eb, Ab, Db, Gb, Cb, Fb — exactly the reverse of the order of sharps, each new flat a perfect 4th above the previous. Mnemonic: "Battle Ends And Down Goes Charles' Father."

What is the rule for identifying a major key from a sharp key signature?

Take the last (rightmost) sharp and go up a half step: that note is the tonic. Example: last sharp C# $\to$ D major; last sharp A# $\to$ B major.

What is the rule for identifying a major key from a flat key signature, and what is the exception?

The second-to-last flat names the major key (e.g., flats Bb–Eb–Ab $\to$ Eb major). Exception: one flat (Bb only) is F major, which must simply be memorized.

Which major and minor keys have a key signature of no sharps and no flats?

C major and its relative, A minor.

Which major key has four sharps, and what are they?

E major, with F#, C#, G#, D# (following the order of sharps).

How do you identify the minor key indicated by a key signature? Apply it to three flats.

First identify the major key, then descend a minor 3rd ($3$ half steps) to find the relative minor. Three flats $\to$ Eb major $\to$ C minor.

What is the circle of fifths?

A circular diagram of all 12 keys arranged so each key is a perfect 5th from its neighbors: C at the top (no accidentals), sharp keys proceeding clockwise, flat keys counterclockwise, with relative minors usually shown inside the circle.

On the circle of fifths, what happens with each clockwise step?

The tonic rises a perfect 5th and the key signature gains one sharp (or loses one flat): C $\to$ G $\to$ D $\to$ A $\to$ E $\to$ B $\to$ F# $\to$ C#.

On the circle of fifths, what happens with each counterclockwise step?

The tonic rises a perfect 4th (equivalently, falls a perfect 5th) and the key signature gains one flat: C $\to$ F $\to$ Bb $\to$ Eb $\to$ Ab $\to$ Db $\to$ Gb $\to$ Cb.

Which three pairs of enharmonically equivalent major keys overlap at the bottom of the circle of fifths?

B major ($5$ sharps) = Cb major ($7$ flats); F# major ($6$ sharps) = Gb major ($6$ flats); C# major ($7$ sharps) = Db major ($5$ flats).

How do you determine the number (size) of an interval?

Count the letter names from the lower note to the upper note inclusively, ignoring accidentals. Example: C to G spans C–D–E–F–G $= 5$ letter names, so it is some kind of 5th regardless of sharps or flats.

What are the five qualities an interval can have?

Perfect (P), major (M), minor (m), augmented (A), and diminished (d).

Which interval numbers can be perfect, and which can be major or minor?

Perfect applies only to unisons, 4ths, 5ths, and octaves ($1, 4, 5, 8$). Major/minor applies only to 2nds, 3rds, 6ths, and 7ths ($2, 3, 6, 7$). The two families never mix: there is no "major 5th" or "perfect 3rd."

How many half steps are in a minor 2nd, major 2nd, minor 3rd, and major 3rd?

m2 $= 1$ half step, M2 $= 2$, m3 $= 3$, M3 $= 4$ half steps.

How many half steps are in a perfect 4th, perfect 5th, and perfect octave?

P4 $= 5$ half steps, P5 $= 7$, P8 $= 12$ half steps.

How many half steps are in a minor 6th, major 6th, minor 7th, and major 7th?

m6 $= 8$ half steps, M6 $= 9$, m7 $= 10$, M7 $= 11$ half steps.

How is an augmented interval formed?

By widening a perfect or major interval by $1$ chromatic half step without changing the letter names (e.g., C–G is a P5; C–G# is an augmented 5th, $8$ half steps).

How is a diminished interval formed, and how many half steps smaller than a major interval is it?

By narrowing a perfect or minor interval by $1$ chromatic half step (e.g., C–Gb is a diminished 5th). A diminished interval is $2$ half steps smaller than the corresponding major interval, since major must first shrink to minor, then to diminished.

What is the tritone, what are its two spellings, and how does it divide the octave?

The tritone spans $6$ half steps (three whole tones) and is spelled either as an augmented 4th (e.g., F–B) or a diminished 5th (e.g., B–F). It divides the octave exactly in half: $6 + 6 = 12$ half steps.

What is interval inversion, and what is the numerical rule for inverted intervals?

Inversion moves the lower note up an octave (or the upper note down an octave). The original and inverted numbers always sum to $9$: the inversion of an interval of size $n$ is $9 - n$ (2nds↔7ths, 3rds↔6ths, 4ths↔5ths, unisons↔octaves).

How do interval qualities change under inversion?

Major becomes minor and minor becomes major; augmented becomes diminished and diminished becomes augmented; perfect remains perfect.

C up to E is a major 3rd. What interval results when it is inverted (E up to C)?

A minor 6th: the number becomes $9 - 3 = 6$ and major inverts to minor. Check: M3 $(4) +$ m6 $(8) = 12$ half steps, a full octave.

Which intervals are classified as consonant, divided into perfect and imperfect consonances?

Perfect consonances: unison (P1), perfect 5th, and octave (P8) — the octave has frequency ratio $2:1$ and the perfect 5th $3:2$. Imperfect consonances: major and minor 3rds and 6ths (M3, m3, M6, m6).

Which intervals are classified as dissonant, and what is special about the perfect 4th?

Dissonant: all 2nds (m2, M2), all 7ths (m7, M7), and the tritone (A4/d5), plus every augmented or diminished interval. The perfect 4th is contextual: dissonant against the bass in traditional two-voice counterpoint, but consonant in other contexts.

What is a compound interval, and how do you simplify one? Give an example.

A compound interval is larger than an octave. Simplify by subtracting $7$ from its number (its quality is unchanged): a 9th $= $ compound 2nd, a 10th $=$ compound 3rd, an 11th $=$ compound 4th. Example: C4 up to E5 is a major 10th, i.e., a compound major 3rd, since $10 - 7 = 3$.