I. Fundamentals

# 6.1 Introduction

The example below shows the beginning of the first movement of a piano sonata.

Consider the gesture found in mm. 1–2. Starting on a low C, a series of sixteenth notes sweeps up through three full octaves, one staff position at a time (with an extra middle C halfway through). This type of figure is known as a scale—more specifically, a major scale.

The major scale is a cornerstone of pitch organization and structure in tonal music. It consists of an ordered collection of seven pitch classes. The sound of a major scale is one with which you are very likely quite familiar. The following example shows a reduced version of the scale found in Example 6–1:

The beginning (and end) of a scale is referred to as the tonic or keynote. We refer to the major scale found in these examples as a C-major scale because it begins and ends on the keynote C. All of the other notes in the scale are organized around this note.

The high C that ends the major scale in Example 6–2 can also act as the beginning of its own major scale. The following example demonstrates:

Like the scale in Example 6–1, this C-major scale begins on middle C and continues upwards beyond just a single octave. Similarly, middle C could also act as the high end of a C-major scale an octave below. The major scale (and other scales) can therefore continue indefinitely in both directions.

In this chapter, we will begin by examining how a major scale is organized and how to construct one. We will then go on to look at the relationships between its various members and how to refer to them individually.

# 6.2 Spelling a major scale

For study, scales are typically written in ascending order, spanning a single octave. When notating a scale, we begin with the keynote and use each of the seven note letter names (A, B, C, D, E, F, and G) until we return to the keynote. This is referred to as the spelling of the scale and is demonstrated in the following example:

As you can see from Example 6–4a, the only repeated note letter name is the keynote (in this case, C) for a single octave of a major scale. To repeat any other note letter name would be incorrect, as in Example 6–4b which uses the letter E twice.

Note: At this point, the specific spelling of a scale may seem arbitrary. After all, E# and F are enharmonically equivalent, and the two scales shown in Example 6–4 sound identical. However, the specific spelling of an individual pitch has a direct effect on the implied musical meaning of that note—a concept that will become clearer in later chapters.

Activity 6-1

Activity 6–1

### Question

Which of the following scales is spelled incorrectly?

This scale is spelled incorrectly. Although this scale is spelled in ascending order and begins and ends on the keynote, the letter G is used twice (G and G#).

# 6.3 Pitch relations in the major scale

Major scales—and minor scales, as we will discuss shortly—are named after their keynotes: C-major scales have C as their keynote, Ab-major scales have Ab as their keynote, and so on. While the keynote may be the most important and defining pitch of any given scale, it is the organization of the remaining notes—the other six scale degrees—that give each scale its unique identity.

In Chapter 5 we introduced the concept of an interval as the perceived distance between two pitches. There, we discussed two different intervals: semitones and octaves. An octave is the distance from one pitch to the next pitch above or below it that has the same letter name—for example, middle C to the next C above (or below) it. A semitone, on the other hand, is the distance between a pitch and the very next pitch above or below it—middle C and the B directly below it, for example. An octave is equal in size to twelve semitones.

Semitones are represented by adjacent keys on the piano keyboard:

Example 6–5 shows that semitones can be formed between two white keys (blue dots) or between a white key and a black key (red dots). In either case, the two pitches are right next to each other; there is no pitch in between.

An interval that is twice the size of a semitone is known as a whole tone (sometimes just tone). The following figure shows three examples of whole tones on a piano keyboard:

Every whole tone has exactly one key (pitch class) in the middle. Notice that a whole tone can occur between two black keys (blue dots), two white keys (red dots), or a black and a white key (green dots).

We refer to the intervals formed by consecutive scale degrees as steps. Some of the steps in a major scale are a semitone in size. Semitone steps are known as half steps. In the C-major scale from Example 6–2, the step from E up to F is a half step. The step from B up to the keynote C is also a half step. All of the remaining steps—C to D, D to E, etc.—are a whole tone in size and so these steps are known as whole steps.

Note: As implied by the preceding paragraph, the terms “half step” and “semitone” are not interchangeable. All half steps are one semitone in size, but not all semitones are half steps. Because a major scale must use all seven pitch letters, the two pitches forming a step must be spelled with consecutive letters. In other words, B and C are a half step apart, but F and F# are not because the names are not spelled with consecutive letters. (G and A are considered consecutive.)

Similarly, all whole steps are one whole tone in size, but not all whole tones are whole steps. If the blue dots in Example 6-5 were spelled as C# and D#, they would be considered a whole step apart. If, on the other hand, they were spelled C# and Eb, they would not be considered a whole step apart since C and E are not consecutive letters.

Every major scale features the exact same pattern of whole steps (W) and half steps (H): W-W-H-W-W-W-H.

Play or listen to the two scales in Example 6–7. Notice how similar they sound even though they begin on different pitches and contain different pitch classes (C major has F, while G major uses F#). It is because both scales follow the same pattern of whole steps and half steps that they sound so similar.

If we divide the major scale into two tetrachords (groups of four consecutive notes), we find that each tetrachord follows the same pattern of whole steps and half steps:

As Example 6–8 demonstrates, the major scale can be divided into two tetrachords, each of which follows the W-W-H pattern. The two tetrachords are themselves separated by a whole step. In C major, the lower tetrachord contains C, D, E, and F, while the upper contains G, A, B, and C. (The triangular brackets in Example 6–8 are a common shorthand way of indicating half-steps.)

Activity 6-2

Activity 6–2

The exercises below refer to the following tetrachord:

### Question

For which major scale would these four notes form the lower tetrachord?

Hint

The lower tetrachord of any major scale has the keynote as its lowest pitch.

F major. F-G-A-Bb form the lower tetrachord of an F-major scale.

### Follow-up question

Complete the F-major scale by adding the upper tetrachord:

Hint

Remember to follow the correct pattern of whole steps and half steps starting with the keynote.

### Question

For which major scale would these four notes form the upper tetrachord:

Hint

The upper tetrachord of any major has the keynote as its highest pitch.

Bb major. F-G-A-Bb form the upper tetrachord of a Bb-major scale.

### Follow-up question

Complete the Bb-major scale by adding the lower tetrachord:

Hint

Remember to follow the correct pattern of whole steps and half steps starting with the keynote.

The half steps in a major scale are always found in the same place. One is found between the third and fourth scale degrees and the other between the seventh and eighth scale degrees. The following example shows a C-major scale on the piano keyboard:

Visualizing C major is particularly useful as it uses only white keys. This makes the two half-steps very easy to see. Notice that on the piano keyboard, the keys E and F (the third and fourth white keys) have no black key in between them. The same is true for B and C. These two pairs of notes correspond to the half steps shown in Example 6–5.

Activity 6-3

Activity 6–3

Every major scale has two half steps. Identify the half steps in the following G-major scale:

### Question

Name one pair of consecutive notes that form a half step in a G-major scale.

B/C or F#/G

### Question

Now identify the other pair of consecutive notes that form a half step in the G-major scale.

B/C or F#/G (the other answer from Exercise 6–3a)

# 6.4 Building a major scale

There are several ways of building a major scale like those we’ve discussed so far. One way is to take advantage of the fact that every major scale follows the same pattern of whole steps and half steps.

Let’s say you were asked to build an Ab-major scale (a major scale beginning on Ab). A good place to start would be to write Ab on the staff:

Note: When writing music on a staff, accidentals are always placed to the left of the note they’re applied to, as in Example 6–8. When referring to them in written prose—as in the text of this chapter—they are written as you would say them out loud, with the accidental coming just after the pitch-letter name: “Ab major.”

Since the major scale uses each of the pitch-letter names only once before reaching the tonic note again, we can fill in the rest of the noteheads to help ensure that we’re spelling the scale correctly. Don’t worry about accidentals yet—those will come in the next step.

As we’ve seen, every major scale follows the same pattern of whole steps and half steps. You may find it helpful at first to write the pattern above or below your scale:

Once the noteheads are in place, completing the major scale is simply a matter of working from left to right and making sure each note conforms to the pattern. The step from Ab to B is larger than it should be: Ab to B is three semitones instead of two. Since we can’t change the initial Ab, our only alternative is to lower the B to Bb. Ab to Bb—a whole step—is the first step of the Ab-major scale. Moving from Bb to C is already a whole step, so C needs no accidental. Then we see that C to D is a semitone larger than the half step we need it to be. Lowering D to Db will solve this problem. And so on, until we arrive back at the keynote (if your scale began with an accidental, don’t forget to put one on the ending keynote as well!):

As Example 6–13 shows, the Ab-major scale requires four flats (Bb, Eb, Ab, and Db) to conform to the pattern of whole steps and half steps. Other scales will require sharps to maintain the pattern, but major scales will never use both sharps and flats in the same scale.

Note: If you are already familiar with the concept of key signatures—a topic we will discuss in Chapter 8 and Chapter 9—you may find this method of building a scale to be tedious and inefficient. However, while it is true that key signatures provide a handy means of quickly determining all the notes in a scale, they do little to reinforce the structure of that scale. It is recommended that you use the method described above at least until you feel confident in your familiarity with the pattern of whole and half steps that define the scale at hand.

Activity 6-4

Activity 6–4

In each of the following exercises, you will be given the keynote of a major scale. Fill in the remaining seven scale degrees ( $\hat2$ through $\hat8$).

### Question

Build a Bb-major scale:

Hint

Use the pattern of whole steps and half steps to determine each consecutive step of the scale.

### Question

Build a D-major scale:

Hint

Use the pattern of whole steps and half steps to determine each consecutive step of the scale.

### Question

Build an E-major scale:

Hint

Use the pattern of whole steps and half steps to determine each consecutive step of the scale.

### Question

Build an F#-major scale:

Hint

Use the pattern of whole steps and half steps to determine each consecutive step of the scale.

# 6.5 Scale degree labels

Because the pattern of whole steps and half steps discussed above is the same for every major scale, we can use labels to identify each scale degree with respect to a given keynote. The three main types of labels that we will give scale degrees in this chapter are scale degree numbers, solfège syllables, and scale degree names.

Labeling with scale degree numbers is the most straightforward systems: each scale degree is given a number 1 through 8. Scale degree numbers are distinguished from other types of numbers by the caret (^) that appears above each digit: $\hat1$, $\hat2$, $\hat3$, $\hat4$, $\hat5$, $\hat6$, $\hat7$, and $\hat8$. The following example demonstrates:

As we saw earlier, the keynote can function as the beginning of a scale or the end. Hence, $\hat8$ and $\hat1$ are used interchangeably, depending on the context.

Activity 6-5

Activity 6–5

For each of the following exercises you will be given a pitch and told what major scale degree it represents. It is up to you to fill in the remainder of the scale. The keynote of the scale may or may not have an accidental.

### Question

Build a major scale in which G is $\hat3$:

Hint

Keep in mind that the keynote of the scale may or may not have an accidental.

G is the third degree of an Eb-major scale.

### Question

Build a major scale in which G is $\hat4$:

Hint

Keep in mind that the keynote of the scale may or may not have an accidental.

G is the fourth degree of a D-major scale.

### Question

Build a major scale in which Eb is $\hat2$:

Hint

Keep in mind that the keynote of the scale may or may not have an accidental.

Eb is the second degree of a Dbmajor scale.

### Question

Build a major scale in which G# is $\hat6$:

Hint

Keep in mind that the keynote of the scale may or may not have an accidental.

G# is the sixth degree of a B-major scale.

When singing, it is convenient to give each scale degree a single-syllable name. Solfège syllables, as they are commonly called, are most often used when practicing vocal performance, but can also be used to refer to scale degrees in general.

As popularized by the Broadway musical The Sound of Music, solfège syllables are particularly useful for how they help familiarize us with the relationships between various scale degrees. Becoming acquainted with solfège syllables will be a tremendous help in memorizing and performing music.

Our final system for labeling scale degrees gives each a name according to its position relative to the keynote and its function within the scale:

The tonic—another, common name for the keynote—is central to this system. In other words, all of the other labels indicate the position of the scale degrees relative to the tonic. The dominant is four steps above the tonic, the subdominant is four steps below the (upper) tonic. The mediant is two steps above the tonic, the submediant is two steps below the (upper) tonic. The supertonic, as the name implies, is just above the tonic, while the leading tone is a semitone below. These names will be particularly useful when it comes to discussing functional harmony.

It may seem redundant to have three labeling systems for the scale degrees, but each has a different and useful purpose. It is essential that you familiarize yourself with all three and be able to use them interchangeably.

Activity 6-6

Activity 6–6

Identify the solège syllable, scale degree number, or scale degree name as specified for each of the following scales:

### Question

What is the scale degree number for the note indicated by the arrow in the following Eb-major scale?

7

### Question

What is the solfège syllable for the note indicated by the arrow in the following A-major scale?

re

### Question

What is the solfège syllable for the note indicated by the arrow in the following D-major scale?

mi

### Question

What is the scale-degree name for the note indicated by the arrow in the following F-major scale?

dominant

# 6.6 Summary

The major scale, one of the most important building blocks of tonal music, consists of seven distinct pitch classes called scale degrees arranged in a specific pattern. It begins and ends with the most important pitch, the keynote (or tonic), by which we name the scale. Each pitch letter name is used only once (except for the keynote, which is typically repeated at the end of the scale).

Every major scale is built of two tetrachords separated by a whole step, each of which follows the same pattern of whole steps and half steps internally: W-W-H. The overall pattern of a major scale, therefore, is: W-W-H-W-W-W-H. Every major scale follows this same pattern and it is this specific pattern that gives the major scale its unique sound.

There are three common systems for labeling scale degrees: scale degree numbers ( $\hat1$, $\hat2$, $\hat3$, etc.), solfège syllables (do, re, mi, etc.), and scale degree names (tonic, supertonic, mediant, etc.). Each system has a different purpose and you should be able to use all three interchangeably.