Scales & Key Signatures: Major and Minor

Music Theory Fundamentals

Chapter 3 · Scales & Key Signatures: Major and Minor

A scale is simply a real, fixed pattern of whole and half steps applied starting from any note. Learn the pattern once, and you can build the same scale starting anywhere — which is exactly how this chapter's own key signatures work.

The Major Scale

Every major scale follows the exact same real interval pattern: whole, whole, half, whole, whole, whole, half — usually written W-W-H-W-W-W-H. Applied starting on C, this produces C-D-E-F-G-A-B-C, using only the white keys on a piano — the only major scale that needs no sharps or flats at all, which is exactly why C major is the standard reference point for everything else in this chapter.

The Natural Minor Scale

The natural minor scale follows a genuinely different real pattern: whole, half, whole, whole, half, whole, whole — W-H-W-W-H-W-W. Applied starting on A, this produces A-B-C-D-E-F-G-A — also using only the white keys, with no sharps or flats.

Relative Major and Minor

That's not a coincidence — C major and A minor share the exact same key signature (no sharps, no flats), because they contain exactly the same seven notes, just starting from a different point in the pattern. A minor's own tonic sits on the sixth scale degree of C major (C-D-E-F-G-A), a real, fixed relationship that holds for every major/minor pair: the relative minor's tonic is always the sixth degree of its relative major, three semitones below it.

Key Signatures and the Circle of Fifths

Key signatures don't accumulate sharps or flats randomly — they follow directly from Chapter 1's own real perfect fifth (the 3:2 frequency ratio). Stack real perfect fifths upward from C — C, G, D, A, E, B, F♯ — and each new key in that sequence gains exactly one more sharp than the last, in a fixed real order: F♯-C♯-G♯-D♯-A♯-E♯-B♯. Stack perfect fifths downward instead, and each new key gains one more flat, in the exact reverse order: B♭-E♭-A♭-D♭-G♭-C♭-F♭.

Key	Sharps/flats	Relative minor
C major	None	A minor
G major	1 sharp (F♯)	E minor
D major	2 sharps (F♯, C♯)	B minor
F major	1 flat (B♭)	D minor

A genuinely surprising real limit

Stacking twelve real, exact 3:2 perfect fifths (per Chapter 1's own ratio) should eventually return exactly to the starting pitch, seven octaves up — but it doesn't. The real gap is called the Pythagorean comma, about 23.46 cents (roughly a quarter of a semitone), and it's a genuine mathematical fact, not a tuning error: (3/2)¹² is not exactly equal to 2⁷. This real discrepancy is the actual reason equal temperament — the tuning system that very slightly adjusts every interval so the circle of fifths closes cleanly — was developed, and it's covered in depth later in this course.

The circle of fifths itself, as a real teaching diagram, isn't a modern invention either — the earliest documented version appears in Mykola Dyletsky's 1677 Grammatika, written to teach a Russian audience how to compose Western-style polyphonic music.

Hands-On Exercises

Exercise 1

Using the real W-W-H-W-W-W-H major scale pattern, build the G major scale starting on G, and identify which single note requires a sharp.

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Exercise 2

D major has 2 sharps. Using the real relative-minor relationship from this chapter (the sixth scale degree of the major scale), identify D major's relative minor key.

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Exercise 3

Explain, in your own words, why the Pythagorean comma shows that a perfectly "pure" (exact 3:2 ratio) circle of fifths cannot actually close into a real circle at all.

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Chapter 3 Quick Reference

Major scale pattern: W-W-H-W-W-W-H (e.g. C major: C-D-E-F-G-A-B-C)
Natural minor scale pattern: W-H-W-W-H-W-W (e.g. A minor: A-B-C-D-E-F-G-A)
Relative major/minor — share the same key signature; the minor's tonic is the major's own 6th scale degree
Circle of fifths — built from real 3:2 perfect fifths (Ch.1); sharps add in the order F-C-G-D-A-E-B, flats in the reverse order
The real Pythagorean comma (~23.46 cents) is the genuine mathematical reason twelve exact perfect fifths don't close the circle, motivating equal temperament
Next chapter: Intervals — The Building Blocks of Harmony