Building on the half steps and whole steps we learned in Chapter 2, we will explore a new scale called the major scale. From this scale, we will learn about major keys and their key signatures.

4.1   Diatonic Scale

In Chapter 2, we learned that a scale is a convenient way to organize notes alphabetically from one pitch to another pitch an octave away. The chromatic scale uses all twelve keys on the keyboard by combining chromatic and diatonic half steps.

• Recall that a half step is the smallest distance between two keys on the piano. Half steps can be chromatic (same note name, such as D and D♯D sharp) or diatonic (different note name, such as D and E♭E flat).
• Two half steps make a whole step.

There are other scales besides the chromatic scale, but only the chromatic scale uses chromatic steps. The other scales are diatonic scales, which have several characteristics:

• Diatonic scales use only diatonic half and whole steps. In other words, they do not include any chromatic steps.
• Diatonic scales include each letter name once and only once.
• Diatonic scales cannot omit a letter name.

Observe the diatonic scales in Example 4.1.

Example 4.1. Diatonic scales

Notice how both diatonic scales above contain the same keys on the keyboard. However, because you must use every letter name once and only once, the scales use different sets of pitches.

• Look at the first two keys on the keyboard:
  • If the first note is C♯C sharp, the second note must be D-something, since we cannot use C again, and we cannot skip a letter name. Therefore, the second note is D♯D sharp.
  • If the first note is E♭E flat, the second note must be E-something, since we cannot use D again and we cannot skip a letter name. Therefore, the second note is E♭E flat.
  • While the second note in the first collection was D♯D sharp, it is incorrect to call the second note D♯D sharp in the second collection; it must be called E♭E flat.
• Look at the last two keys on the keyboard:
  • If the last note is C♯C sharp, the penultimate (second-to-last) note must be B-something, since we cannot use C again and we cannot skip a letter name. Therefore, the penultimate note is B♯B sharp.
    • Although it seems like C would be much easier to read than B♯B sharp, in the context of scales, it is easier to read the penultimate note as B♯B sharp. It would be incorrect to write B♯B sharp as C, no matter how much you think it is better.
  • If the last note is D♭D flat, the penultimate note must be C-something, since we cannot use D again and we cannot skip a letter name. Therefore, the penultimate note is C.

Directions:

• Write the diatonic scales indicated by the selected notes on the keyboard as note names in the spaces below. Be sure to use each letter name once and only once. See Example 4.1 for a sample.

4.2   Tetrachords

“Tetra” comes from the Greek meaning “four” and tetrachords refer to a group of four notes that are melodic, meaning that each note is played one at a time. The major tetrachord consists of the following pattern: whole step (w) – whole step (w) – half step (h).

To create major tetrachords, write the notes diatonically (that is, write each letter name once and only once), then add the appropriate accidentals.

Note that each letter name is used only once and cannot be skipped. For example, the second note in the F♯F sharp major tetrachord must be G♯G sharp and not A♭A flat.

If you have been to a baseball game, you might have heard the major tetrachord played by the organist, as everyone cheers, “charge!” (Example 4.2.1).

Example 4.2.1. Major tetrachord: Baseball Cheer

In Example 4.2.1, there are three major tetrachords. Each labeled major tetrachord is a half step higher than the previous one.

The major tetrachord is fairly common in music. Krumpholtz uses the major tetrachord four times in Example 4.2.2.

Example 4.2.2. Major tetrachord: Krumpholtz^[1], “The Favorite Air of Robin Adair”

Although Krumpholtz uses the major tetrachord G-A-B-C four times in Example 4.2.2, the major tetrachord is not as obvious as the baseball cheer in Example 4.2.1 because Krumpholtz varies each occurrence.

• The notes of the major tetrachord in measures 1-2 are immediately preceded by other notes.
• In measures 3-4, other notes immediately follow the notes of the major tetrachord.
• In the second system, the major tetrachord appears across two different octaves, placed above rolled chords.

Directions:

• Based on the given first note, fill in the blanks to complete major tetrachords.
• Write “w” to indicate whole steps and “h” to indicate half steps.
• You may use the keyboard below for help.

Directions:

• Identify the given tetrachords as either “major” or “X” if it is not a major tetrachord.

A. Farrenc^[2], Cello Sonata, Op. 46, i – Allegro moderato

B. Farrenc, Cello Sonata, Op. 46, iii – Finale. Allegro

4.3   Major Scales

When we take a major tetrachord and connect it to another major tetrachord by a whole step, the result is a major scale.

Example 4.3.1. Major scale

• Major tetrachord #1 consists of C-D-E-F (whole-whole-half).
• Major tetrachord #2 consists of G-A-B-C (whole-whole-half).
• When the two tetrachords are connected by a whole step, the outcome is a major scale.
• The example above is called a C major scale because C is the first and last note of the scale.

Although the major scale itself is not a very melodic tune, we often find the major scale used to create emphasis, give rise to tension, or serve as filler, as in Examples 4.3.2 and 4.3.3.

Example 4.3.2. Major scale: Beethoven^[3], Symphony No. 5 in C Minor, Op. 67, iv – Allegro

The orchestra features the main melody in Example 4.3.2. However, the piccolo’s repeated ascending C major scale adds to the excitement. The descending major scale can be used similarly (Example 4.3.3).

Example 4.3.3. Descending major scale: Beethoven, Symphony No. 5 in C Minor, Op. 67, iv – Allegro

Listen to Example 4.3.3 and observe how the energy builds and peaks at the end of the descending C major scale.

For major scales, you can either think of two major tetrachords separated by a diatonic whole step, or you can think of the entire pattern of diatonic half steps and whole steps.

• Option 1: Two major tetrachords separated by a whole step:
  • whole – whole – half :: whole :: whole – whole – half
• Option 2: The entire major scale pattern:
  • whole – whole – half – whole – whole – whole – half

As musicians, you will be asked to write, identify, and perform ascending and descending major scales. For descending scales, make sure to use the pattern in reverse order.

Steps to Writing a Major Scale

Step one:

• Write all the notes diatonically: write each note only once in ascending or descending order (alternate line–space or space–line).
• Do not skip any notes, and be sure that the first and last notes are the same notes with the same accidentals (Example 4.3.4).

Example 4.3.4. Step one

Step two:

• Write in the pattern of whole steps and half steps.
• Do not forget that for descending major scales, the pattern must go in reverse (Example 4.3.5).

Example 4.3.5. Step two

Step three:

• Add accidentals. Major scales will only include sharps or flats—never both.

Example 4.3.6. Step three

Directions:

• Construct the following major scales on the staff using half notes. Be aware of stem direction.
• First write in all the pitches diatonically so you do not repeat or skip any note names. Then add accidentals.
• If it helps, write in “w” for whole steps and “h” for half steps.
• You may use the keyboard below for help.

Directions:

• Identify the given scales as either “major” or “X” if it is not a major scale.

4.4   Scale Degrees

Since the pattern of whole steps and half steps is the same for every major scale, each note is the same distance apart across different major scales. For example, the third note in every major scale is exactly two whole steps away from the first note. To clarify this relationship, we use scale degree numbers and scale degree names (Example 4.4.1).

Example 4.4.1. Scale degrees in a C-major scale

Scale degree numbers tell us which member of the major scale a particular note is. Scale degree numbers are Arabic numerals with a caret (^) written above, as shown in Example 4.4.1. We say, “Scale degree three.”

• Note that the last scale degree number is not scale degree 8^; instead, it repeats scale degree 1^ because they are the same note name.

Scale degree names also tell us which member of the major scale a particular note is. Scale degree names and numbers always match. The supertonic is always scale degree 2^, and the reverse is always true.

• The tonic (scale degree 1^) begins and ends the major scale.
• The supertonic (scale degree 2^) gets its name because it is a whole step above the tonic.
  • The prefix super means above, just as superscript refers to writing above regular text, like when you square something in math, such as x².
• The mediant (scale degree 3^) is positioned halfway between the tonic and the dominant when it ascends.
  • The prefix med- means middle, just as in the words median and medium.
• The subdominant (scale degree 4^) is a fifth below the tonic.
  • The prefix sub- means below, as seen in words like submarine and subway.
• The dominant (scale degree 5^) is a fifth above the tonic.
• The submediant (scale degree 6^) is located halfway between the tonic and the subdominant when it descends.
  • The prefix med- means middle and the prefix sub- means below. Together, submediant means halfway between the tonic and the subdominant when descending.
• The leading tone (scale degree 7^) gets its name because it is a diatonic half step below the tonic.
  • You might have assumed a whole step below the tonic would be the subtonic. However, there is no subtonic in major.
  • Instead, scale degree 7^ is a half step below the tonic in major. It gets its name because leads to the tonic. This book will often abbreviate the leading tone as LT.

We are familiar with whole steps and half steps, but we have not yet learned about fifths. A fifth is the distance between a note and another note five note names away.

• The dominant is a fifth above the tonic.
  • For example, to find a note a fifth above C, we count five note names up from C: C-D-E-F-G.
  • Therefore, the dominant of C is G.
• The subdominant is a fifth below the tonic.
  • For example, to find a note a fifth below C, we count five note names down from C: C-B-A-G-F.
  • Therefore, the subdominant of C is F.
  • Although the subdominant is technically a fifth below the tonic, many students find it easier to count up four note names since the subdominant is scale degree 4^: C-D-E-F.

Students often assume that the subdominant means “below dominant” because scale degree 4^ is below scale degree 5^. However, this is not correct. The subdominant actually refers to the dominant below the tonic. If the subdominant meant “below dominant,” it would mean that the submediant is “below mediant,” but the submediant is not scale degree 2^. The submediant is scale degree 6^ because it is located halfway between the tonic and subdominant when descending.

Sometimes students find it hard to remember scale degree names. However, a diagram like Example 4.4.2 can help make memorizing easier.

Example 4.4.2. Scale degrees

• The dominant is a fifth above the tonic.
  • When ascending from the tonic to the dominant, the mediant falls halfway between them.
• The subdominant is a fifth below the tonic.
  • When descending from the tonic to the dominant, the submediant falls halfway between them.
• A step away from the tonic:
  • The supertonic is a whole step above the tonic.
  • The leading tone is a half step below the tonic.

Whether ascending or descending, scale degree numbers always refer to the same notes in major scales. Compare the scale degrees in the next two major scales (Example 4.4.3).

Example 4.4.3. Comparing scale degrees

• Scale degree numbers are assigned based on the ascending scale, not their sequence of appearance.
  • The second note in Example 4.4.3B is scale degree 7^, not scale degree 2^.
• The same pitch will be assigned a different scale degree number in another major scale.
  • The pitch A is scale degree 6^ in the C major scale (Example 4.4.3A), but is scale degree 4^ in the E major scale (Example 4.4.3B).

The penultimate notes in both scales in Example 4.4.3 are a step away from the tonic. In Example 4.4.3A, the penultimate note is the leading tone, while in Example 4.4.3B, it is the supertonic. Because they are so close to the tonic, both the supertonic and leading tone have a strong pull toward it. As shown by the diagram in Example 4.4.2, the tonic is the main focus. In fact, the C major scale is called so because its tonic is C. We can hear this musical pull to the tonic when we stop just short of reaching it. Listen to Example 4.4.4—do you notice how strongly the music is drawn toward the tonic?

Example 4.4.4. Pull to tonic: stopping short

• Example 4.4.4A: The descending C major scale ends too soon, on the supertonic (scale degree 2^).
• Example 4.4.4B: The ascending C major scale stops short at the leading tone (scale degree 7^).

Did you notice how both examples sounded unfinished? Did you get the feeling like you only needed one more note (the tonic) to feel closure? It may be helpful to sing Example 4.4.4 to feel the inconclusiveness. In aural training, you might learn solfège (e.g., do–re–mi) to help you sing (Example 4.4.5). Scale degrees are the same as solfège but are used in music theory.^[4]

Example 4.4.5. Solfège

The next two examples demonstrate the pull toward the tonic (Examples 4.4.6 and 4.4.7).

Example 4.4.6. Pull to tonic: Foster^[5], “Camptown Races”

• The first system ends on the supertonic (scale degree 2^). The music feels unresolved, as we yearn for tonic.
• The second system ends on the tonic (scale degree 1^). The music finally feels complete.

While Example 4.4.6’s first system lacks closure by ending on the supertonic, the first system of Example 4.4.7 ends on the leading tone.

Example 4.4.7. Pull to tonic: “Yankee Doodle”

• The first system ends on the leading tone (scale degree 7^). The music sounds unresolved because it leaves us craving the tonic. Imagine listening to this example and stopping after the first system.
• The second system concludes on the tonic (scale degree 1^). The music finally feels complete.

Scale degree numbers and scale degree names are important in music theory. Make sure you are comfortable with these terms before moving on.

Directions:

• Answer the following questions based on the given major scale. First write in the scale degree numbers to help.

1. Which note is the tonic?
2. Which note is the dominant?
3. Which note is scale degree 6^?
4. Which note is scale degree 2^?
5. What scale degree number is B?
6. What scale degree number is E♯E sharp?
7. Why is scale degree 4^ called the subdominant?
8. Why is scale degree 7^ called the leading tone?
9. Why is scale degree 3^ called the mediant?
10. Why is scale degree 2^ called the supertonic?

4.5   Major Keys

A major scale is more than just a systematic way to list notes alphabetically. More importantly, the major scale is an organized way of telling us the content of a musical key, which combines the tonal center and mode.

• The tonic is the tonal center, a note that tells us where “home” is. Music gravitates around the tonal center and feels most complete when we end there. The tonal center can be any pitch, such as C, F♯F sharp, or G♭G flat.
• The mode tells us the collection of pitches used based on a tonal center. The most common modes are the major mode and minor mode. Since these modes contain different notes, they sound distinct. The major mode is often linked to happy music, while the minor mode is usually associated with sad music.
• The key combines the tonal center and mode (for example, F♯F sharp major or F♯F sharp minor). As you will learn later in this chapter, not every tonal center can have keys in both major and minor (for instance, you can have the key of G♭G flat major but not G♭G flat minor).

Ideally, you should be able to hear a musical example and determine if it is in a major or minor key. Examples 4.5.1 and 4.5.2 are two well-known classical works in major keys.

Example 4.5.1. Major key: Mozart^[6], Eine kleine Nachtmusik, K. 525, i – Allegro

Example 4.5.2. Major key: Wagner^[7], Bridal Chorus from Lohengrin, Act III, Scene i – Mässig bewegt^[8]

Can you hear that the music in Examples 4.5.1 and 4.5.2 are in major (i.e. that is, sounds “happy”)? If you are not able to do so yet, do not worry. Understanding, writing, and hearing music all take time and practice. We will also learn how you can recognize if a piece is in major without having to listen to it.

We can determine a major key by its major scale (Example 4.5.3).

Example 4.5.3. From scale to key

The pitch collection along with the tonal center tells us the key.

• If we have a piece of music that centers around A♭A flat with four flats, it is in the key of A♭A flat major.
  • The tonal center is A♭A flat because A♭A flat is the tonic.
  • The mode is major because the notes form an A♭A flat major scale. The steps are W-W-H-W-W-W-H.
  • Together, the tonal center and mode form the key of A♭A flat major.
• Although five flats appear in the A♭A flat major scale, there are only four different flats (A♭A flat, B♭B flat, D♭D flat, E♭E flat) since the first and last flats apply to A♭A flats.
  • Remember that accidentals are localized, so you must rewrite them in a different octave.
• This means that if a piece is in the key of A♭A flat major, every time you see A, B, D, or E, they will be A♭A flat, B♭B flat, D♭D flat, or E♭E flat.

Look at the example below, which shows the end of “Twinkle, Twinkle, Little Star” in the key of A♭A flat major.

Example 4.5.4. “Twinkle, Twinkle, Little Star” with accidentals

When we last saw “Twinkle, Twinkle, Little Star,” it was in the key of C major (Example 3.9.5). There were no sharps or flats. In Example 4.5.4, we see flats. We can deduce that the key is A♭A flat major based on several factors.

• The piece ends on A♭A flat.
  • It is important to distinguish that Example 4.5.4 is the end of the entire piece, not only the end of an excerpt.
  • Although ending on the tonal center is not a requirement, it often occurs.
  • More importantly, listen to the example—do you hear how it sounds like the end when we reach the ending? This is because we have arrived at the tonal center.
• The four flats (A♭A flat, B♭B flat, D♭D flat, E♭E flat) tell us that we are in the major mode. We know this because the A♭A flat major scale has four flats.
  • All the flats found in the A♭A flat major scale appear in this example.
  • However, not every note of the major scale must appear to be in a key.
• Therefore, the tonal center of A♭A flat plus the major scale (four flats)results in the key of A♭A flat major.

Instead of constantly writing and rewriting accidentals in the score, musicians use key signatures to make writing (and reading) music easier. A key signature is a group of flats or sharps placed at the beginning of each system of music. The following example shows Example 4.5.4 rewritten with a key signature instead of accidentals. Example 4.5.5 sounds exactly the same as Example 4.5.4.

Example 4.5.5. “Twinkle, Twinkle, Little Star” with a key signature

The key signature tells us which notes always have accidentals. For musicians, seeing the key signature at the start is much simpler than reading many accidentals.

When we wrote the A♭A flat major scale, it contained four flats. Therefore, the key signature of A♭A flat major has four flats: Every B, E, A, and D will be B♭B flat, E♭E flat, A♭A flat, and D♭D flat unless there is a different accidental.

To label the major key, write an uppercase letter of the tonic (e.g., A♭A flat) followed by a colon. Alternatively, you can also write an uppercase “M” after the tonic (e.g., A♭A flatM).

We learned that time signatures are only written once at the beginning of the piece (Example 3.2.9). They are not rewritten at the start of every system. Unlike time signatures, key signatures are rewritten at the start of each system (Example 4.5.6).

Example 4.5.6. Key signature versus time signature

• Each system must begin with a clef.
• The key signature appears immediately after the clef, and each system must include the key signature.
• The time signature appears only at the start of the piece or when it changes. Do not rewrite the time signature at the start of each system.
• The order of appearance is clef, key signature, time signature. It may help you to memorize the order by remembering that the names are in alphabetical order (C – K – T).

The table in Example 4.5.7 summarizes how the clef, key signature, and time signature should appear at the beginning of each system.

Example 4.5.7. The beginning of each system

Unlike accidentals, which are localized, key signatures are global. This means that with a key signature of A♭A flat major, all Bs are B-flat. Compare the localized accidentals in Example 4.5.8A to the global accidentals in Example 4.5.8B.

Example 4.5.8. Accidentals versus key signatures

Notice some important differences between accidentals versus key signatures.

• Example 4.5.8A: Accidentals:
  • The third note is B (not B♭B flat) because the flat on the previous note only applied to B♭B flat₄.
  • The note after the bar line is B (not B♭B flat) because even though it is B♭B flat₄, the bar line cancels previous accidentals.
• Example 4.5.8B: Key signatures:
  • The third note is B♭B flat because the key signature says all Bs are B♭B flats.
  • The note after the bar line is B♭B flat because bar lines make no difference: the key signature says all Bs are B♭B flats.
  • The penultimate note requires a double flat when the intended note is B𝄫B double flat. Sometimes students think adding a flat lowers B♭B flat to B𝄫B double flat; however, adding a flat would only make the note B♭B flat.
  • The last note requires a natural sign if the desired note is B.

Example 4.5.9 shows how accidentals function within a key signature and how they interact with ties. The pitches are displayed above the cello’s part.

Example 4.5.9. Accidentals and key signature: Bosmans^[9], Impressions for Cello and Piano, I. Cortège

• The key signature shows that there are two flats in this key: every B and E are automatically B♭B flat and E♭E flat.
• There is a sharp on the downbeat of measure 97, which makes the note a C#. The other two Cs are also C# because the accidental continues within the bar, and they are in the same octave.
• The B♭B flat in measure 97 does not have an accidental because B♭B flat is in the key signature.
• The C♯C sharp across the bar line is tied, making the note on the downbeat of m. 98 also C♯C sharp. An accidental is unnecessary because of the tie.
• On the second half of measure 98, C♯C sharp returns and requires an accidental for several reasons.
  • The previous bar line canceled the previous natural sign.
  • The C is in a different octave (C₅ instead of C₄).

Directions:

• Identify the pitches on the staff in the blanks below.

Bosmans, Impressions for Cello and Piano, I. Cortège

Directions:

• Write the given pitches using correct rhythm.

4.6   Major Key Signatures with Flats

Accidentals in key signatures must follow a specific order and be placed at exact locations on the staff. Quickly identifying and writing key signatures is one of the biggest hurdles for students. However, if you can easily recognize and write all the major and minor key signatures, music theory will become much easier. Key signatures will contain either flats or sharps, but not both. We will start with major key signatures with flats.

Flats in major (and minor) key signatures always appear in this order:

B♭B flat – E♭E flat – A♭A flat – D♭D flat – G♭G flat – C♭C flat – F♭F flat

One of the easiest ways to remember the order of flats is that it spells “BEAD” followed by “GCF” (“Greatest Common Factor”). You can also use other mnemonics to help you memorize the order of flats, such as “Before Eating A Donut Get Coffee First.” Ultimately, you just need to memorize the order of flats.

The order of flats is very important. For example, if there are three flats, the following statements will always be true:

• The three flats are always B♭B flat, E♭E flat, and A♭A flat.
• The three flats will never be other pitches. For example, they will never be B♭B flat, E♭E flat, and D♭D flat.
• The three flats will never be in any other order. For example, they will never be B♭B flat, A♭A flat, then E♭E flat.

Once you memorize the order of flats, learn their exact placement on the grand staff. Each flat appears on a specific line or space in both the treble and bass clefs. For example, the first flat is always written on B₄ in the treble clef and B₂ in the bass clef. It is incorrect to write them anywhere else.

The major key with three flats is E♭E flat major. Example 4.6.1 shows both correct and incorrect ways of writing the key signature for E♭E flat major.

Example 4.6.1. Key signature for E♭E flat major

Start by identifying the parts that are correctly written (shown in blue in the first measure).

• The key signature is accurately written on the staff in both the treble and bass clefs.
• The key signature always appears before the time signature. An easy way to remember the order is that alphabetically, the word “key” comes before the word “time.”

Now, focus on the second measure, which highlights two of the most common key signature mistakes students make (in red).

• In the treble clef, the order of flats is correct, but E♭E flat, which should be written at E♭E flat₅, is incorrectly written at E♭E flat₄.
• In the bass clef, the key signature is correctly written for the treble clef. Based on the bass clef, the placement of the flats indicates that the three flats are D♭D flat, G♭G flat, and C♭C flat.

Since there are seven different note names, the maximum number of flats in a key signature is seven. The example below shows all the major key signatures with flats (Example 4.6.2).

Example 4.6.2. Major key signatures from zero to seven flats

There are multiple hints that can assist you in quickly memorizing the major key signatures with flats.

• C major has zero flats, while C♭C flat major has seven flats.
• All the major keys with flats have a tonal center with a flat except for F (e.g., B-flat major and G-flat major).
  • In other words, all keys with flats include “flat” in their names except for F major.
• Notice the pattern of flats: flats alternate between moving up and down to create descending pairs.
  • Accidentals in the treble clef start on B♭B flat₄, with the pattern ascending then descending.
  • Accidentals in the bass clef begin on B♭B flat₂, and the pattern remains the same: up–down.
  • For C♭C flat major, the pattern of flats is 2+2+2+1.

One of the best ways to practice memorizing the proper placement of key signatures on the staff is to be able to write C♭C flat major quickly from memory. If you can correctly write all seven flats in both treble and bass clefs, then writing fewer flats should be easy.

Directions:

• Write the key signature for C♭C flat major until you are able to do so quickly and by memory.

Until you memorize all seven major key signatures with flats, you can use a shortcut. Except for F major, the shortcut is that the key is the penultimate (second-to-last) flat (Example 4.6.3).

Example 4.6.3. Penultimate flat = key

• Example 4.6.3A: The penultimate flat is B♭B flat, so the key is B♭B flat major.
• Example 4.6.3B: The penultimate flat is D♭D flat, so the key is D♭D flat major.
• Example 4.6.3C: The penultimate flat is C♭C flat, so the key is C♭C flat major.
  • Sometimes students call this B major because B and C♭C flat are enharmonically equivalent (i.e., the same key on the piano). However, calling it B major would be incorrect since the first flat in the key signature is B♭B flat. It would be impossible for B major to have any flats because the first flat is always B♭B flat.

The reason we could not use the shortcut for F major is that F major has only one flat, so there is no penultimate flat.

Now we will combine everything we have learned to identify the key of a musical example (Example 4.6.4).

Example 4.6.4. Finding the key: Szymanowska^[10], March No. 5

When determining the key of a musical example, follow these steps:

1. Listen to the example: Does it sound like it’s in major (happy)?
   • Yes, Example 4.6.4 sounds like it is in major.
2. Look at the key signature.
   • The key signature has two flats, which is the key of B♭B flat major.
3. Look at the first lowest note.
   • The first lowest note is B♭B flat.
4. Look at the last lowest note.
   • The last lowest note is B♭B flat.

In Example 4.6.4, all four steps point to B♭B flat major. Using the first lowest note and the last lowest notes is not always reliable, but they become more dependable when combined with the other steps.

Directions:

• Identify the major keys. For major keys, you only need to write an uppercase letter (e.g., F).

Directions:

• Write the given key signatures on the staff.

Directions:

• In the given keys, write the pitch of the given scale degree number.

4.7   Major Key Signatures with Sharps

Just as flats in key signatures must appear in a specific order and be placed at specific locations on the staff, so must sharps in key signatures. Sharps in major (and minor) key signatures always appear in this order:

F♯F sharp – C♯C sharp – G♯G sharp – D♯D sharp – A♯A sharp – E♯E sharp – B♯B sharp

One of the simplest ways to remember the order of sharps is that it is the reverse of the order of flats (Example 4.7.1).

Example 4.7.1. Relationship between flats and sharps

You can also use other mnemonic devices to help you memorize the order of sharps, such as “Fat Cats Get Drunk And Eat Birds.” In the end, you just need to memorize the order of sharps.

The order of sharps shows that if there are six sharps, they are always F♯F sharp, C♯C sharp, G♯G sharp, D♯D sharp, A♯A sharp, and E♯E sharp in that order. Once you memorize the order of sharps, you need to know their exact placement on the grand staff. Each sharp is placed on a specific line or space in the treble clef and the bass clef. For example, the first sharp is always written on F₅ in the treble clef and F₃ in the bass clef. It is wrong to write them anywhere else.

The major key with six sharps flats is F♯F sharp major. Example 4.7.2 shows correct and incorrect ways to write key signatures.

Example 4.7.2. Key signature for F♯F sharp major

The first measure shows the key signature correctly written (in blue). The second measure highlights some of the most common key signature errors students make (in red):

• The time signature always follows the key signature. Remember that the word “key” comes before the word “time” alphabetically.
• In the treble clef, the last sharp is E♯E sharp, not F. Sometimes students think it is easier to write F, but that is incorrect.
  • F♯F sharp is already the first sharp in the key signature.
  • The enharmonic equivalent of E♯E sharp is actually F♮F natural, not F♯F sharp.
• In the bass clef, the key signature is written in pairs, as if for treble clef. The pattern for key signatures with sharps is different.

Since there are seven different note names, a key signature can have up to seven sharps. Example 4.7.3 below shows all the major key signatures with sharps.

Example 4.7.3. Major key signatures from zero to seven sharps

There are several clues that can assist you in quickly memorizing the major key signatures with sharps.

• C major has no sharps, while C♯C sharp major has seven sharps.
• The only major keys with “sharp” in their names are F♯F sharp and C♯C sharp major.
  • All other major keys with sharps do not have “sharp” in their names (e.g., G major and B major).
  • Remember that F major was the only major key without “flat” in its name that had a flat.
  • If there is one sharp, it is F♯F sharp, so F major cannot have any sharps.
• The pattern of sharps is different from the pattern of flats.
  • The treble clef starts on F♯F sharp₅, and the bass clef starts on F♯F sharp₃.
  • The pattern begins down–up, but then is followed by down–down–up.
  • For C♯C sharp major, the pattern of sharps is 2+3+2.

One of the best ways to practice memorizing the correct placement of key signatures on the staff is to quickly write C♯C sharp major from memory. If you can correctly write all seven sharps in both treble and bass clefs, then writing fewer sharps should be easy.

Directions:

• Write the key signature for C-sharp major until you are able to do so quickly and by memory.

Until you memorize all seven major key signatures with sharps, you can use a shortcut. For all the major keys with sharps, the last sharp is a diatonic half step below the tonic. In other words, the last sharp is the leading tone (LT) of the key (Example 4.7.4).

Example 4.7.4. Last sharp = leading tone

• In the first measure, the last sharp is C♯C sharp. C is a diatonic half step below D, so the key is D major.
• In the second measure, the last sharp is G♯G sharp. G-sharp is the leading tone of A major, so the key is A major.
• In the final measure, the last sharp is B♯B sharp. B♯B is a diatonic half step below C♯C sharp, not C. Therefore, the key is C♯C sharp major.
  • Remember that every note in  C♯C sharp major has a sharp.

Apply the steps we learned in the previous section to determine the key of a musical example (Example 4.7.5).

Example 4.7.5. Find the key: Szymanowska, March No. 3^[11]

1. Listen to the example: Does it sound like it’s in major (happy)?
   • Yes, Example 4.7.5 sounds like it is in major.
2. Look at the key signature.
   • The key signature has two sharps, which is the key of D major.
3. Look at the first lowest note.
   • The first lowest note is A.
4. Look at the last lowest note.
   • The last lowest note is D.

In Example 4.7.5, step 3 conflicts with D major. However, when analyzing the music, the initial lowest note (A) is an anacrusis. We understand that the anacrusis leads into the downbeat, which is much stronger. If we focus on the downbeat instead, we see that the first lowest note is actually D. Example 4.7.5 is in D major.

Directions:

• Identify the major keys. For major keys, you only need to write an uppercase letter (e.g., G).

Directions:

• Write the given key signatures on the staff.

Directions:

• In the given keys, write the pitch of the given scale degree number.

Notice the pattern between major keys with flats and major keys with sharps (Example 4.7.6).

Example 4.7.6. Major keys comparison

• Reading across, the letter names of the keys are the same, but one has an accidental. For example:
  • F and F♯F sharp
  • D♭D flat and D
• The number of accidentals equals seven. For example:
  • 1 flat + 6 sharps = 7 accidentals
  • 5 flats + 2 sharps = 7 accidentals
• C is the only note name that appears three times.
  • C major = 0
  • C♭C flat major = 7 flats
  • F♯F sharp major = 7 sharps
• F is the only flat key without “flat” in its name.

If you understand this pattern, focus on memorizing only major keys with three accidentals as a starting point. Then follow these steps:

1. Subtract the number of accidentals from seven.
2. Flip the accidentals (i.e. that is, flats become sharps and sharps become flats).
3. Add or remove the accidental of the key.

The table in Example 4.7.7 summarizes the key signatures you need to memorize and the three steps.

Example 4.7.7. Memorizing up to three accidentals

Using this method, you can determine how many accidentals are in each major key.

• If you memorize that D major has two sharps:
  1. 7 – 2 = 5
  2. Flip the accidentals: 5 flats
  3. Add or remove the accidental of the key: D becomes D♭D flat
     • The new key cannot be D♯D sharp major because there is no such key as D♯D sharp major, and the new key signature has flats.
  4. Therefore, if D major has two sharps, D♭D flat major has five flats.
• If you memorize that F major has one flat:
  1. 7 – 1 = 6
  2. Flip the accidentals: 6 sharps
  3. Add or remove the accidental of the key: F becomes F♯F sharp
     • The new key cannot be F♭F flat major because there is no such key as F♭F flat major, and the new key signature has sharps.
  4. Therefore, if F major has one flat, F♯F sharp major has six sharps.
• If you memorize that E♭E flat major has three flats:
  1. 7 – 3 = 4
  2. Flip the accidentals: 4 sharps
  3. Add or remove the accidental of the key: E♭E flat becomes E
     • The new key cannot be E♯E sharp major because there is no such key as E♯E sharp major.
  4. Therefore, if E♭E flat major has three flats, E major has four sharps.

You can also apply this method when identifying key signatures.

• If you are given six flats, but cannot remember the key.
  • 7 – 6 = 1
  • Flip the accidentals: 1 sharp
  • G major has one sharp. Now add or remove the accidental of the key: G becomes G♭G flat.
    • The key cannot be G♯G sharp major because there is no such key as G♯G sharp major, and the given key signature has flats.
  • Therefore, six flats is the key of G♭G flat major because G major has one sharp.
• If you see five sharps, but cannot remember the key.
  • 7 – 5 = 2
  • Flip the accidentals: 2 flats
  • B♭B flat major has two flats. Now add or remove the accidental of the key: B♭B flat becomes B.
    • The key cannot be B♯B sharp major because there is no such key as B♯B sharp major.
  • Therefore, five sharps is the key of B major because B♭B flat major has two flats.

Although you can use this tip when you are starting out, your goal is to confidently know all the major key signatures without relying on any tricks or steps.

Directions:

• Identify the major keys. For major keys, you only need to write an uppercase letter (e.g., E).

Directions:

• Write the given key signatures on the staff.

Directions:

• In the given keys, write the pitch of the given scale degree number.

4.8   Circle of Fifths

Recall that we can create major scales by writing two major tetrachords with a whole step in between. Notice what happens when we use the second major tetrachord of a C major scale as the first major tetrachord of another major scale. It creates the G major scale (Example 4.8.1).

Example 4.8.1. Forming a new major scale

• Example 4.8.1A:
  • Major tetrachord #1 begins on C. After a whole step, major tetrachord #2 begins on G and ends on C.
  • The result is a C major scale.
  • There are no accidentals in the C major scale, so the key of C major has no sharps or flats.
• Example 4.8.1B:
  • Major tetrachord #2 from Example 4.8.1A now becomes major tetrachord #1.
  • Major tetrachord #1 begins on G, which is a fifth higher than Example 4.8.1A’s major tetrachord #1. After a whole step, major tetrachord #2 begins on D and ends on G.
  • The result is a G major scale.
  • There is one sharp (F♯F sharp) in the G major scale, so the key of G major has one sharp.

We can continue this pattern by transforming Example 4.8.1B’s major tetrachord #2 into major tetrachord #1 to form a D major scale, and so on (Example 4.8.2).

Example 4.8.2. Continuation of Example 4.8.1

Each new major scale is a fifth higher and has one more sharp. In fact, we can continue this pattern until we circle back to C major. Each subsequent scale will be a fifth higher than the last. This key relationship is well illustrated by the circle of fifths.

Example 4.8.3. Circle of fifths

There is a wealth of information in the circle of fifths.

• Moving clockwise from C:
  • Each key is a fifth higher.
    • A fifth above E is B.
    • A fifth above A♭A flat is E♭E flat.
  • Each key adds a sharp or removes a flat.
    • E major has 4 sharps and B major has 5 sharps.
    • A♭A flat major has 4 flats and E♭E flat major has 3 flats.
  • C (no sharps, no flats) moves clockwise to C♯C sharp major (7 sharps).
• Moving counterclockwise from C:
  • Each key is a fifth lower.
    • A fifth below D♭D flat is G♭G flat.
    • A fifth below E is A.
  • Each key adds a flat or removes a sharp.
    • D♭D flat major has 5 flats and G♭G flat major has 6 flats.
    • E major has 4 sharps and A has 3 sharps.
  • C (no sharps, no flats) moves counterclockwise to C♭C flat major (7 flats).

You might wonder when and how to switch from sharps to flats, or vice versa. To do this, we can use one of the three keys at the bottom of the circle of fifths that have two keys. This is because these keys are enharmonically equivalent keys. The three pairs of enharmonically equivalent keys are shown in the table in Example 4.8.4.

Example 4.8.4. Enharmonically equivalent keys

• The first row of the table shows that B major is enharmonically equivalent to C♯C sharp major.
  • Although they are enharmonically equivalent keys, B major (with 5 sharps) is much more commonly used than C♭C flat major (with 7 flats).
• The second row of the table shows that F♯F sharp major is enharmonically equivalent to G♭G flat major.
• The third row of the table shows that C♯C sharp major is enharmonically equivalent to D♭D flat major.
  • Example 4.8.5 revisits Example 4.1, demonstrating how each member of these keys is enharmonically equivalent.

Example 4.8.5. Enharmonically equivalent keys: C♯C sharp major and D♭D flat major

If we move along the circle of fifths beyond C♯C sharp major, the next key a fifth above would be G♯G sharp major. However, G♯G sharp major does not exist. Instead, the next key after C♯C sharp major is A♭A flat major, which exists and is enharmonically equivalent to G♯G sharp major. Therefore, the circle of fifths continues from C♯C sharp major to A♭A flat major, with A♭A flat major being enharmonically equivalent.

If you wanted to switch to flats earlier, you could. A fifth above B major is F♯F sharp major. However, you might decide to go to G♭G flat major instead, since they are enharmonically equivalent keys.

Although the circle of fifths contains a lot of information, students sometimes rely on it rather than memorize key signatures. I have seen students waste five valuable minutes of exam time recreating the entire circle of fifths. As musicians, it’s more helpful for you to spend that time now memorizing the fifteen major key signatures quickly.

Directions:

• Using the circle of fifths, fill in the table. If you do not need the circle of fifths and already have the key signatures memorized, even better.

4.9   Transposition: Melodic

We already learned about rhythmic transposition when we rewrote a rhythm by the same proportion to fit into a different time signature. There is also melodic transposition, which involves writing or performing the same melody in a different key. For example, imagine you’re playing the flute with a vocalist. The piece is in B♭B flat major, but the melody is too low for the singer. The vocalist can easily change keys using solfège, but for instrumentalists, it isn’t as simple unless you’re fluent in key signatures. Since all major scales share the same pattern of whole and half steps, you can easily transpose melodies by using scale degree numbers (Example 4.9.1).

Example 4.9.1. Steps to melodic transposition

• Example 4.9.1A: First, identify the key of the original melody and then write in the scale degree numbers.
• Example 4.9.1B: Transposing involves two steps.
  1. Write the clef and key signature of the new key. Rewrite the same scale degree numbers as in the original melody above the blank staff.
  2. Write the correct pitches on the staff, ensuring the rhythm, dynamics, and articulation marks are accurate.
• Example 4.9.1C: You can transpose either higher or lower. In this case, the melody has been transposed one octave lower and requires a change of clef.
• Note that stem direction varies based on placement on the staff.

An important thing to remember when transposing is that melodic contour matters. Melodic contour is the direction the melody ascends or descends. If the original melody leaps up from scale degree 1^ to scale degree 3^, you cannot leap down. Listen to Examples 4.9.1A and B and how they sound the same. Now listen to Examples 4.9.2A and B.

Example 4.9.2. Incorrect contour

The reason why Example 4.9.2B sounds so different is because the melodic contour is incorrect, as shown by the circled red arrows.

Composers often repeat the same melody in different keys to add variety. Example 4.9.3 shows the music from Example 4.9.1 in C major and F major.

Example 4.9.3. Melodic transposition: Mozart, Piano Sonata No. 16 in C Major, K. 545, i – Allegro

A. Original melody in C major

B. Transposed melody in F major

• Example 4.9.3.A:
  • The original melody is in C major.
  • Scale degree numbers are displayed above the melody.
• Example 4.9.3B:
  • The melody returns at measure 42, this time in F major.
  • Although the key signature remains the same, there are two ways to see that this is no longer in C major.
    • By writing the same scale degree numbers, you can see that scale degree 1^ is now F.
    • If you analyze the music, every B has a flat. Therefore, even if the key signature does not show a flat, we know we are in F major because F major has one flat.

Directions:

• For A, write the key of the example, then write the scale degree numbers above the given melody.
• For B, write the key signature of the new key and add the same scale degree numbers above.
• Write the melody in the new key and add all appropriate musical symbols.

1. Munktell^[12], Violin Sonata, i – Allegro non tanto, vigoroso

2.   Munktell, Violin Sonata, ii – Moderato energico

Terms

• circle of fifths
• diatonic scale
• enharmonically equivalent keys
• key
• key signature
• major scale
• major tetrachord
• melodic contour
• melodic transposition
• mode
  • major mode
  • minor mode
• scale degree names
  • tonic (scale degree 1^)
  • supertonic (scale degree 2^)
  • mediant (scale degree 3^)
  • subdominant (scale degree 4^)
  • dominant (scale degree 5^)
  • submediant (scale degree 6^)
  • leading tone (scale degree 7^)
• scale degree number
• tetrachord
• tonal center