Harmony from Scratch: Major & Minor Scales, Circle of Fifths, and Exercises

A practical, clear, no‑nonsense guide to why some notes love each other, others get along, and a few need couple’s therapy.

#Harmony #CircleOfFifths #Scales #Exercises #Beginner

Contents Goals Fundamentals Major scales Minor scales Circle of fifths Chords & functions Progressions Practice exercises 30‑day plan Extra fundamentals Glossary

Goals

• Understand the basics of note, interval, and scale.
• Build all major scales and the minor ones (natural, harmonic, melodic).
• Use the circle of fifths to read key signatures, find relatives, and do simple modulations.
• Stack triads and recognize tonal functions (Tonic, Subdominant, Dominant).
• Apply common progressions in major and minor on your instrument (piano, guitar, bandurria, lute…).
• Work through graded exercises with solutions for self‑assessment.

Recommended gear: pencil, staff paper (or notation app), metronome, and your instrument. Coffee optional, curiosity required.

Fundamentals: sound, notes, and intervals

Do–Re–Mi vs C–D–E

Latin solfège uses Do, Re, Mi, Fa, Sol, La, Si; letter names use C, D, E, F, G, A, B. Equivalences: Do=C, Re=D, Mi=E, Fa=F, Sol=G, La=A, Si=B.

Latin	Letter	Alterations
Do	C	C♯/D♭
Re	D	D♯/E♭
Mi	E	E♯/F, D♭♭
Fa	F	E♯, F♯/G♭
Sol	G	G♯/A♭
La	A	A♯/B♭
Si	B	B♯/C, C♭/B

Tone and semitone

A semitone is the smallest interval between adjacent notes (E–F, B–C or a ♯/♭ alteration). A tone equals two semitones. Scale formulas are built from tones (T) and semitones (S).

Diatonic intervals

We name intervals by number (2nd…8ve) and quality (major, minor, perfect, augmented, diminished). For starters, learn to hear steps of T and S, and to spot the perfect 5th (7 semitones) and perfect 4th (5 semitones) — both crucial for the circle of fifths.

Major scales

The universal major scale formula is T–T–S–T–T–T–S: two tones, a semitone, three tones, a semitone to the octave.

Example: C major

C–D (T) – E (T) – F (S) – G (T) – A (T) – B (T) – C (S). No accidentals.

Example: D major

D–E (T) – F♯ (T) – G (S) – A (T) – B (T) – C♯ (T) – D (S). Key: 2 sharps (F♯, C♯).

Quick rule: go up by 5ths from C (C→G→D→A→E→B→F♯→C♯) and you add one ♯ per step. Go the other way (C→F→B♭→E♭→A♭→D♭→G♭→C♭) and you add one ♭ per step.

Major key signatures

Major key	Signature	Order of ♯	Order of ♭
C	–	F♯, C♯, G♯, D♯, A♯, E♯, B♯	B♭, E♭, A♭, D♭, G♭, C♭, F♭
G	1 ♯ (F♯)	Always in that order	Always in that order
D	2 ♯ (F♯, C♯)
A	3 ♯
E	4 ♯
B	5 ♯
F♯	6 ♯
C♯	7 ♯
F	1 ♭ (B♭)
B♭	2 ♭
E♭	3 ♭
A♭	4 ♭
D♭	5 ♭
G♭	6 ♭
C♭	7 ♭

Minor scales

The minor mode is used in three practical variants:

• Natural minor (aeolian): T–S–T–T–S–T–T.
• Harmonic minor: like natural, but with a raised 7th (leading tone), creating a tone and a half gap between 6th and 7th.
• Melodic minor: raised 6th and 7th ascending; descending returns to the natural form.

Example: A minor (a)

Natural: A B C D E F G A (0 accidentals). Harmonic: A B C D E F G♯ A. Melodic asc.: A B C D E F♯ G♯ A; desc.: A G F E D C B A.

Relative major/minor

The relative minor of a major key is three semitones down (its 6th degree). Ex.: C major ↔ A minor. They share the key signature.

Examples (common for plucked strings and keyboard)

Key	Natural	Harmonic	Melodic (asc.)
A minor	A B C D E F G	A B C D E F G♯	A B C D E F♯ G♯
E minor	E F♯ G A B C D	E F♯ G A B C D♯	E F♯ G A B C♯ D♯
D minor	D E F G A B♭ C	D E F G A B♭ C♯	D E F G A B C♯
G minor	G A B♭ C D E♭ F	G A B♭ C D E♭ F♯	G A B♭ C D E F♯
C minor	C D E♭ F G A♭ B♭	C D E♭ F G A♭ B	C D E♭ F G A B

Circle of fifths

The circle of fifths arranges the 12 keys by 5th relationships. Moving clockwise adds ♯; counter‑clockwise adds ♭. Relative majors/minors share positions.

Quick reading tips

• Clockwise (♯): C → G → D → A → E → B → F♯ → C♯ (1♯, 2♯, 3♯…)
• Counter‑clockwise (♭): C → F → B♭ → E♭ → A♭ → D♭ → G♭ → C♭ (1♭, 2♭, 3♭…)
• Relatives: each major shares its signature with a minor (C ↔ a, G ↔ e, etc.).
• Gentle modulations: moving to neighboring keys in the circle minimizes new accidentals.

Practical tip: imagine a capo in your mind: shifting a scale or chord pattern up the fretboard is like rotating around the circle.

Triads, tetrads, and tonal functions

Stacking in thirds

Triads are built by stacking thirds on each degree. In major we get: I major, ii minor, iii minor, IV major, V major, vi minor, vii° diminished.

Degree	Quality in Major	Function	Ex. in C
I	Major	Tonic (T)	C–E–G
ii	Minor	Subdominant (S)	D–F–A
iii	Minor	Tonic	E–G–B
IV	Major	Subdominant	F–A–C
V	Major	Dominant (D)	G–B–D
vi	Minor	Tonic	A–C–E
vii°	Diminished	Dominant	B–D–F

Common cadences

• Authentic: V–I (with leading tone rising to tonic). In minor (harmonic): V (or V7) → i.
• Plagal: IV–I (the “Amen” close).
• Deceptive: V–vi (major) or V–VI (minor).
• Half cadence: ending on V (comma, not period).

Tetrads and color

Adding the 7th to triads (tetrads) yields modern colors: ii⁷, V⁷, I^Δ7, etc. For beginners, ii–V–I (or ii°–V–i in minor) is the ultimate harmony gym.

Starter progressions (playable examples)

Pop in major

I–V–vi–IV. In C: C–G–Am–F. Strum 4 bars per chord at 80–96 BPM.

Degrees:  I   V   vi  IV
Key C:    C   G   Am  F

Folk/rock

I–IV–V–IV. In G: G–C–D–C. Feel the 5th pulling home.

ii–V–I in major

In D: Em7 – A7 – DΔ7. Practice 1–3–5–7 arpeggios and voice‑leading 7→3 (G→F♯ on resolution).

Minor (harmonic) flow

In A minor: Bm7♭5 – E7 – Am(Δ or m6). The G♯ creates a strong pull to A.

12‑bar blues (simplified)

Major (C): | C7 | F7 | C7 | C7 | F7 | F7 | C7 | C7 | G7 | F7 | C7 | G7 |
Minor (A): | Am7 | Dm7 | Am7 | Am7 | Dm7 | Dm7 | Am7 | Am7 | E7  | Dm7 | Am7 | E7  |

Great lab to internalize the dominant function and phrasing.

Practice exercises (with solutions)

1) Build five major scales

Write the notes of G, D, A, F and B♭ majors using T–T–S–T–T–T–S and add their signatures.

Solution

• G: G A B C D E F♯ (1♯)
• D: D E F♯ G A B C♯ (2♯)
• A: A B C♯ D E F♯ G♯ (3♯)
• F: F G A B♭ C D E (1♭)
• B♭: B♭ C D E♭ F G A (2♭)

2) Relative major/minor

Name the relative minor of E major, and the relative major of d minor.

Solution

E major ↔ C♯ minor; d minor ↔ F major.

3) Natural, harmonic and melodic minor

Write the three variants of e minor.

Solution

Natural: E F♯ G A B C D. Harmonic: E F♯ G A B C D♯. Melodic asc.: E F♯ G A B C♯ D♯ (desc.: natural).

4) Cadences in C major

Write V–I, IV–I and V–vi (American chord symbols) and record 8 bars at ♩=72.

Solution

• V–I: G → C (or G7 → C)
• IV–I: F → C
• V–vi: G → Am

5) Diatonic triads

List the triads of G major by degree.

Solution

I: G, ii: Am, iii: Bm, IV: C, V: D, vi: Em, vii°: F♯°.

6) Reading the circle

How many ♯ in B major? Which major sits to the left of E♭?

Solution

B major: 5♯. To the left of E♭ (counter‑clockwise) lies B♭.

7) ii–V–I

Write ii–V–I in D major and in a minor (harmonic).

Solution

D major: Em7 – A7 – DΔ7. a minor: Bm7♭5 – E7 – Am.

8) Practical transposition

Transpose I–V–vi–IV from C to E.

Solution

C→E (up 4 semitones): C–G–Am–F → E–B–C♯m–A.

9) Aural recognition (no instrument)

Hum a perfect 5th from C (C→G), a perfect 4th from G (G→C), and a major 3rd from A (A→C♯). Describe their character.

Hints/Solution

• Perfect 5th: stable, open.
• Perfect 4th: stable but with tendency depending on bass context.
• Major 3rd: bright color typical of major mode.

10) Melodic minor in action

Write 4 bars in e minor using ascending melodic minor in the tune and harmonize with iiø–V–i.

Suggested answer

Melody around E–F♯–G–A–B–C♯–D♯–E; harmony: F♯m7♭5 – B7 – Em(Δ or m6).

30‑day study plan

1. Days 1–5: intervals; C, G, D majors; memorize T–T–S–T–T–T–S.
2. Days 6–10: circle of fifths (up to 3♯/3♭), relatives, V–I and IV–I cadences.
3. Days 11–15: minors: natural/harmonic/melodic in a, e, d.
4. Days 16–20: diatonic triads; I–V–vi–IV and I–IV–V–IV in two keys.
5. Days 21–25: ii–V–I in three keys; 3–5 note dictations.
6. Days 26–30: write two 16‑bar mini pieces (one major, one minor) applying the above.

Glossary

Key signature: the set of ♯/♭ at the staff’s start affecting the whole piece.

Tonal function: the role of a chord relative to the tonic (T, S or D).

Relative: a major/minor pair sharing a signature.

Leading tone: the raised 7th a semitone below the tonic; drives the authentic cadence.

Extra harmony fundamentals (early‑intermediate)

1) Secondary dominants

A secondary dominant is a V (or V7) chord pointing to a degree other than I. In C major: V/V = D7 (resolves to G), V/ii = A7 (→ Dm), etc. They add direction and strengthen inner cadences.

Quick drill

Write V/ii, V/iii, V/IV, V/V and V/vi in C major and show their natural resolutions.

Solution

A7→Dm, B7→Em, C7→F, D7→G, E7→Am.

2) Modal interchange

Borrow from the parallel mode (C major ↔ C minor) for color: ♭III, ♭VI, ♭VII and iv are frequent. Classic pop: I–♭VII–IV–I.

3) Voice‑leading and guide tones

In V7→I: the 3rd of V falls to the 3rd of I; the 7th of V steps down. Favor contrary motion; avoid parallel 5ths/8ves for a classical blend.

4) Tetrads, extensions and suspensions

Add 7ths to triads (Δ7, m7, 7, m7♭5). Common tensions: 9, 11, 13 (context‑dependent). sus4 asks to resolve to the 3rd.

5) Modes at a glance

Handy recap: Ionian (major), Dorian (minor with major 6th), Phrygian (minor with ♭2), Mixolydian (major with ♭7). Great for color without leaving tonality.

6) Short modulations

By pivot chord (common to both keys) or chaining secondary dominants. Ex.: C→G via Am (pivot) or V/V (D7) → V (G7) → I (G).

Mini challenge

Write 8 bars in C major including: a V/ii and a ♭VI (borrowed). End with an authentic cadence.

Did this help? Bookmark, share with your ensemble, and return whenever the perfect 5th wants to hug the tonic (spoiler: always).

© 2025 • Beginner’s guide to harmony • Feel free to cite with a link.