2/9 2. Pitch, Scales, and Key Signatures

Pitch, steps, and accidentals

Pitch describes how high or low a sound seems. Western music names pitches with A, B, C, D, E, F, and G; these letter names recur in higher and lower octaves.

An octave contains twelve equal semitone distances in the standard twelve-tone system. The basic distances used to measure movement between pitches are the half step and the whole step:

• A half step is the distance between adjacent pitches, such as $\mathrm{E}$ to $\mathrm{F}$ or $\mathrm{B}$ to $\mathrm{C}$.

• A whole step contains two half steps, such as $\mathrm{C}$ to $\mathrm{D}$, with $\mathrm{C\sharp}$ between them.

Accidentals modify pitch:

• A sharp, $\sharp$, raises a note by one half step.

• A flat, $\flat$, lowers a note by one half step.

• A natural, $\natural$, cancels a preceding sharp or flat.

• A double sharp, $\double sharp$, raises a note by two half steps.

• A double flat, $\flat\flat$, lowers a note by two half steps.

The natural-note pairs $\mathrm{E-F}$ and $\mathrm{B-C}$ are half steps because no intervening black key appears on a standard keyboard.

Takeaway: Identify the distance between pitches in half steps before applying scale patterns or interpreting accidentals.

Enharmonic spelling and musical context

Two written notes can have the same sounding pitch while using different letter names. Enharmonic equivalents include $\mathrm{C\sharp = D\flat}$, $\mathrm{D\sharp = E\flat}$, and $\mathrm{F\sharp = G\flat}$.

The spelling depends on musical function. A pitch between C and D may be written $\mathrm{C\sharp}$ when it functions as a raised C or $\mathrm{D\flat}$ when it functions as a lowered D. Scale spelling normally uses each letter name once, so the notation reveals the structure of the scale.

For example:

• D major is $\mathrm{D-E-F\sharp-G-A-B-C\sharp-D}$.

• E-flat major is $\mathrm{E\flat-F-G-A\flat-B\flat-C-D-E\flat}$.

These scales can contain some sounds that are equivalent in equal temperament, but their spellings show different tonal organizations.

Takeaway: Equivalent sound does not make spelling interchangeable; the correct notation depends on the scale and harmonic context.

Constructing the major scale

A major scale is a seven-note collection built from the pattern

Here, $\mathrm{W}$ means whole step and $\mathrm{H}$ means half step. The final note repeats the starting letter one octave higher.

To construct a major scale:

1. Write the seven letter names in order, using each letter once.

2. Compare adjacent notes with the major-scale pattern.

3. Add accidentals wherever necessary.

4. Check that the final interval returns to the tonic by a half step.

C major requires no accidentals:

D major begins with the letter sequence $\mathrm{D-E-F-G-A-B-C-D}$. To satisfy the pattern, it becomes

Scale degrees label the notes from the tonic:

• $\mathrm{1}$: tonic

• $\mathrm{2}$: supertonic

• $\mathrm{3}$: mediant

• $\mathrm{4}$: subdominant

• $\mathrm{5}$: dominant

• $\mathrm{6}$: submediant

• $\mathrm{7}$: leading tone when it lies a half step below the tonic

Takeaway: Build the letter sequence first, then adjust accidentals to produce the major-scale step pattern.

Natural, harmonic, and melodic minor

The three commonly taught minor forms begin from the same tonal material but alter different scale degrees.

Natural minor follows the pattern

A natural minor is

A minor key shares its key signature with its relative major. A minor is the relative minor of C major because A is scale degree $6$ in C major, and the two keys use the same pitch collection.

Harmonic minor raises scale degree $7$ of natural minor by one half step. A harmonic minor is

This raised seventh creates a leading tone and a strong pull toward the tonic. It also produces an augmented second between F and G-sharp.

Melodic minor traditionally raises scale degrees $6$ and $7$ in the ascending form and returns to natural minor when descending. A melodic minor is

In some modern styles, melodic minor uses the ascending form in both directions, so the convention should be identified before applying the pattern.

Takeaway: Natural minor preserves the basic minor collection, harmonic minor raises scale degree $7$, and traditional melodic minor raises scale degrees $6$ and $7$ while ascending.

Reading key signatures

A key signature is written immediately after the clef and displays the sharps or flats that normally apply throughout a passage. A signature can represent a major key or its relative minor.

The sharp order is

For a sharp signature, identify the last sharp and raise it by one half step to find the major key. For example, a signature ending with $\mathrm{C\sharp}$ indicates D major.

The flat order is

For a flat signature, the second-to-last flat names the major key. The exception is a signature with only $\mathrm{B\flat}$, which indicates F major.

Examples:

• One sharp indicates G major or E minor.

• Three sharps indicate A major or F-sharp minor.

• Two flats indicate B-flat major or G minor.

• Four flats indicate A-flat major or F minor.

Accidentals used for harmonic or melodic minor are generally written as they occur rather than added permanently to the key signature.

Takeaway: Use the order of sharps or flats to identify the major key, then check the musical center to determine whether the passage is major or relative minor.

The circle of fifths and tonal centers

The circle of fifths organizes keys by ascending perfect fifths:

Moving clockwise adds one sharp at each step. Moving counterclockwise adds one flat at each step. Neighboring keys therefore have closely related key signatures.

Relative keys share a key signature but have different tonics. The relative minor is three half steps below the major tonic, or scale degree $6$ of the major scale:

• C major and A minor

• G major and E minor

• E-flat major and C minor

Relative keys are different from parallel keys. C major and C minor are parallel because they share the tonic C, but they do not share the same key signature.

When identifying a key in practice:

1. Count the sharps or flats.

2. Apply the sharp or flat shortcut to find the possible major key.

3. Identify its relative minor.

4. Look for evidence of the tonal center, such as the final note, repeated pitches, or motion toward the tonic.

A key signature alone does not always establish whether a passage is major or minor; melody and harmony provide the additional evidence.

Takeaway: The circle of fifths links key signatures, neighboring keys, and major–relative-minor pairs, but the tonal center determines how a passage functions.