Introduction to Music Theory by Catherine Schmidt-Jones - HTML preview

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Chapter 2

Keys and Scales

2.1 Major Keys and Scales1

The simple, sing-along, nursery rhymes and folk songs we learn as children; the "catchy" tunes used in advertising jingles; the cheerful, toe-tapping pop and rock we dance to; the uplifting sounds of a symphony: most music in a major key has a bright sound that people often describe as cheerful, inspiring, exciting, or just plain fun.

How are these moods produced? Music in a particular key tends to use only some of the many possible notes available; these notes are listed in the scale associated with that key. In major keys, the notes of the scale are often used to build "bright"-sounding major chords (Section 3.2). They also give a strong feeling of having a tonal center (p. 30), a note or chord that feels like "home", or "the resting place", in that key. The "bright"-sounding major chords and the strong feeling of tonality are what give major keys their happy, pleasant moods. This contrasts with the moods usually suggested by music that uses minor (Section 2.2) keys, scales, and chords. Although it also has a strong tonal center (the Western2 tradition of tonal harmony3 is based on major and minor keys and scales), music in a minor key is more likely to sound sad, ominous, or mysterious. In fact, most musicians, and even many non-musicians, can distinguish major and minor keys just by listening to the music.

Exercise 2.1.1

(Solution on p. 42.)

Listen to these excerpts. Three are in a major key and two in a minor key. Can you tell which is which simply by listening?

NOTE: If you must determine whether a piece of music is major or minor, and cannot tell just by listening, you may have to do some simple harmonic analysis (Section 3.3.5: Minor Keys) in order to decide.

2.1.1 Tonal Center

A scale starts with the note that names the key. This note is the tonal center of that key, the note where music in that key feels "at rest". It is also called the tonic, and it's the "do" in "do-re-mi". For example, music in the key of A major almost always ends on an A major chord, the chord9 built on the note A. It often also begins on that chord, returns to that chord often, and features a melody and a bass line that also return to the note A often enough that listeners will know where the tonal center of the music is, even if they don't realize that they know it. (For more information about the tonic chord and its relationship to other chords in a key, please see Beginning Harmonic Analysis (Section 3.3).)

Example 2.1

Listen to these examples. Can you hear that they do not feel "done" until the final tonic is played?

Example A10
Example B11

2.1.2 Major Scales

To find the rest of the notes in a major key, start at the tonic and go up following this pattern: whole step, whole step, half step, whole step, whole step, whole step, half step. This will take you to the tonic one octave higher than where you began, and includes all the notes in the key in that octave.

Example 2.2

These major scales all follow the same pattern of whole steps and half steps. They have different sets of notes because the pattern starts on different notes.

Listen to the difference between the C major12, D major13, and B at major14 scales.

Exercise 2.1.2

(Solution on p. 42.)

For each note below, write a major scale, one octave, ascending (going up), beginning on that note. If you're not sure whether a note should be written as a at, sharp, or natural, remember that you won't ever skip a line or space, or write two notes of the scale on the same line or space. If you need help keeping track of half steps, use a keyboard, a picture of a keyboard (Figure 1.6: Keyboard), a written chromatic scale (p. 7), or the chromatic scale fingerings for your instrument. If you need more information about half steps and whole steps, see Half Steps and Whole Steps (Section 1.2).

If you need staff paper for this exercise, you can print out this staff paper15 PDF file.

In the examples above, the sharps and flats are written next to the notes. In common notation, the sharps and flats that belong in the key will be written at the beginning of each staff, in the key signature. For more practice identifying keys and writing key signatures, please see Key Signature16. For more information about how keys are related to each other, please see The Circle of Fifths (Section 2.3).

NOTE: Do key signatures make music more complicated than it needs to be? Is there an easier way? Join the discussion at Opening Measures17 .

2.1.3 Music in Different Major Keys

What difference does key make? Since the major scales all follow the same pattern, they all sound very much alike. Here is the tune "Row, Row, Row Your Boat", written in G major and also in D major.

Listen to this tune in G major18 and in D major19. The music may look quite different, but the only difference when you listen is that one sounds higher than the other. So why bother with different keys at all? Before equal temperament20 became the standard tuning system, major keys sounded more different from each other than they do now. Even now, there are subtle differences between the sound of a piece in one key or another, mostly because of differences in the timbre21 of various notes on the instruments or voices involved. But today the most common reason to choose a particular key is simply that the music is easiest to sing or play in that key. (Please see Transposition22 for more about choosing keys.)

2.2 Minor Keys and Scales23

2.2.1 Music in a Minor Key

Each major key (Section 2.1) uses a different set of notes24 (its major scale (Section 2.1.2: Major Scales)). In each major scale, however, the notes are arranged in the same major scale pattern and build the same types of chords that have the same relationships with each other. (See Beginning Harmonic Analysis (Section 3.3) for more on this.) So music that is in, for example, C major, will not sound significantly different from music that is in, say, D major. But music that is in D minor will have a different quality, because the notes in the minor scale follow a different pattern and so have different relationships with each other. Music in minor keys has a different sound and emotional feel, and develops differently harmonically. So you can't, for example, transpose25 a piece from C major to D minor (or even to C minor) without changing it a great deal. Music that is in a minor key is sometimes described as sounding more solemn, sad, mysterious, or ominous than music that is in a major key. To hear some simple examples in both major and minor keys, see Major Keys and Scales (Exercise 2.1.1).

2.2.2 Minor Scales

Minor scales sound different from major scales because they are based on a different pattern of intervals (Section 1.3). Just as it did in major scales, starting the minor scale pattern on a different note will give you a different key signature26, a different set of sharps or flats. The scale that is created by playing all the notes in a minor key signature is a natural minor scale. To create a natural minor scale, start on the tonic note (p. 30) and go up the scale using the interval pattern: whole step, half step, whole step, whole step, half step, whole step, whole step.

Listen27 to these minor scales.

Exercise 2.2.1

(Solution on p. 43.)

For each note below, write a natural minor scale, one octave, ascending (going up) beginning on that note. If you need staff paper, you may print the staff paper28 PDF file.

2.2.3 Relative Minor and Major Keys

Each minor key shares a key signature29 with a major key. A minor key is called the relative minor of the major key that has the same key signature. Even though they have the same key signature, a minor key and its relative major sound very different. They have different tonal centers (p. 30), and each will feature melodies, harmonies, and chord progressions30 built around their (different) tonal centers. In fact, certain strategic accidentals31 are very useful in helping establish a strong tonal center in a minor key. These useful accidentals are featured in the melodic minor (Section 2.2.3: Relative Minor and Major Keys) and harmonic minor (Section 2.2.3: Relative Minor and Major Keys) scales.

It is easy to predict where the relative minor of a major key can be found. Notice that the pattern for minor scales overlaps the pattern for major scales. In other words, they are the same pattern starting in a different place. (If the patterns were very different, minor key signatures would not be the same as major key signatures.) The pattern for the minor scale starts a half step plus a whole step lower than the major scale pattern, so a relative minor is always three half steps lower than its relative major. For example, C minor has the same key signature as E at major, since E at is a minor third higher than C.

Exercise 2.2.2

(Solution on p. 44.)

What are the relative majors of the minor keys in Figure 2.5?

2.2.4 Harmonic and Melodic Minor Scales

NOTE: Do key signatures make music more complicated than it needs to be? Is there an easier way? Join the discussion at Opening Measures32 .

All of the scales above are natural minor scales. They contain only the notes in the minor key signature. There are two other kinds of minor scales that are commonly used, both of which include notes that are not in the key signature. The harmonic minor scale raises the seventh note of the scale by one half step, whether you are going up or down the scale. Harmonies in minor keys often use this raised seventh tone in order to make the music feel more strongly centered on the tonic (p. 30). (Please see Beginning Harmonic Analysis (Section 3.3.5: Minor Keys) for more about this.) In the melodic minor scale, the sixth and seventh notes of the scale are each raised by one half step when going up the scale, but return to the natural minor when going down the scale. Melodies in minor keys often use this particular pattern of accidentals33, so instrumentalists find it useful to practice melodic minor scales.

Listen to the differences between the natural minor34, harmonic minor35, and melodic minor36 scales.

(Solution on p. 44.)

Exercise 2.2.3

Rewrite each scale from Figure 2.5 as an ascending harmonic minor scale.

Exercise 2.2.4

(Solution on p. 45.)

Rewrite each scale from Figure 2.5 as an ascending and descending melodic minor scale.

2.2.5 Jazz and "Dorian Minor"

Major and minor scales are traditionally the basis for Western Music37, but jazz theory also recognizes other scales, based on the medieval church modes38, which are very useful for improvisation. One of the most useful of these is the scale based on the dorian mode, which is often called the dorian minor, since it has a basically minor sound. Like any minor scale, dorian minor may start on any note, but like dorian mode, it is often illustrated as natural notes beginning on d.

Comparing this scale to the natural minor scale makes it easy to see why the dorian mode sounds minor; only one note is different.

You may find it helpful to notice that the "relative major" of the Dorian begins one whole step lower. (So, for example, D Dorian has the same key signature as C major.) In fact, the reason that Dorian is so useful in jazz is that it is the scale used for improvising while a ii chord (Section 3.3.2: Basic Triads in Major Keys) is being played (for example, while a d minor chord is played in the key of C major), a chord which is very common in jazz. (See Beginning Harmonic Analysis (Section 3.3) for more about how chords are classified within a key.) The student who is interested in modal jazz will eventually become acquainted with all of the modal scales. Each of these is named for the medieval church mode39 which has the same interval pattern, and each can be used with a different chord within the key. Dorian is included here only to explain the common jazz reference to the "dorian minor" and to give notice to students that the jazz approach to scales can be quite different from the traditional classical approach.

2.3 The Circle of Fifths40

2.3.1 Related Keys

The circle of fifths is a way to arrange keys to show how closely they are related to each other. 40This content is available online at <http://cnx.org/content/m10865/2.17/>.

Keys are not considered closely related to each other if they are near each other in the chromatic scale (p. 7) (or on a keyboard). What makes two keys "closely related" is having similar key signatures41. So the most closely related key to C major, for example, is A minor, since they have the same key signature (no sharps and no flats). This puts them in the same "slice" of the circle. The next most closely related keys to C major would be G major (or E minor), with one sharp, and F major (or D minor), with only one at. The keys that are most distant from C major, with six sharps or six flats, are on the opposite side of the circle.

The circle of fifths gets its name from the fact that as you go from one section of the circle to the next, you are going up or down by an interval (Section 1.3) of a perfect fifth (Section 1.3.3.1: Perfect Intervals). If you go up a perfect fifth (clockwise in the circle), you get the key that has one more sharp or one less at; if you go down a perfect fifth (counterclockwise), you get the key that has one more at or one less sharp. Since going down by a perfect fifth is the same as going up by a perfect fourth (p. 14), the counterclockwise direction is sometimes referred to as a "circle of fourths". (Please review inverted intervals (Section 1.3.4: Inverting Intervals) if this is confusing.)

Example 2.3

The key of D major has two sharps. Using the circle of fifths, we find that the most closely related major keys (one in each direction) are G major, with only one sharp, and A major, with three sharps. The relative minors of all of these keys (B minor, E minor, and F sharp minor) are also closely related to D major.

Exercise 2.3.1

(Solution on p. 46.)

What are the keys most closely related to E at major? To A minor? Exercise 2.3.2

Exercise 2.3.2

(Solution on p. 46.)

Name the major and minor keys for each key signature.

2.3.2 Key Signatures

If you do not know the order of the sharps and flats, you can also use the circle of fifths to find these. The first sharp in a key signature is always F sharp; the second sharp in a key signature is always (a perfect fifth away) C sharp; the third is always G sharp, and so on, all the way to B sharp.

The first at in a key signature is always B at (the same as the last sharp); the second is always E at, and so on, all the way to F at. Notice that, just as with the key signatures, you add sharps or subtract flats as you go clockwise around the circle, and add flats or subtract sharps as you go counterclockwise. Adding Sharps and Flats to the Key Signature

Exercise 2.3.3

(Solution on p. 47.)

Figure 2.12 (Circle of Fifths) shows that D major has 2 sharps; Figure 2.14 (Adding Sharps and Flats to the Key Signature) shows that they are F sharp and C sharp. After D major, name the next four sharp keys, and name the sharp that is added with each key.

Exercise 2.3.4

(Solution on p. 47.)

E minor is the first sharp minor key; the first sharp added in both major and minor keys is always F sharp. Name the next three sharp minor keys, and the sharp that is added in each key.

Exercise 2.3.5

(Solution on p. 47.)

After B at major, name the next four at keys, and name the at that is added with each key.

Solutions to Exercises in Chapter 2

Solution to Exercise 2.1.1 (p. 29)

1. Major

2. Major

3. Minor

4. Major

5. Minor

Solution to Exercise 2.1.2 (p. 31)

Notice that although they look completely different, the scales of F sharp major and G at major (numbers 5 and 6) sound exactly the same when played, on a piano as shown in Figure 2.16 (Enharmonic Scales), or on any other instrument using equal temperament42 tuning. If this surprises you, please read more about enharmonic43 scales.

Figure 2.16: Using this figure of a keyboard, or the fingerings from your own instrument, notice that the notes for the F sharp major scale and the G at major scale in Figure 2.15, although spelled differently, will sound the same.

Solution to Exercise 2.2.1 (p. 33)