4 Major Scales and Keys

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

DIATONIC SCALE  4.1

In Chapter 2, we learned that a scale was a convenient way to organize notes alphabetically from one pitch to another pitch an octave away. The chromatic scale used all twelve keys on the keyboard by using a combination of 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-sharp) or diatonic (different note name, such as D and E-flat).
  • Two half steps create a whole step.

There are other scales in addition to the chromatic scale, but only the chromatic scale uses chromatic steps. All other scales are diatonic scales, which have several characteristics:

  • Diatonic scales use only diatonic half steps and diatonic whole steps. In other words, diatonic scales do not contain any chromatic half steps or whole steps.
  • Diatonic scales must use each letter name once and only once.
  • Diatonic scales cannot skip a letter name.

Observe the diatonic scales in Example 4.1.

Example 4.1. Diatonic scales

Two different diatonic scales on the same notes of the keyboard. Diatonic scale #1 contains C-sharp, D-sharp, E-sharp, F-sharp, G-sharp, A-sharp, B-sharp, and C-sharp. Diatonic scale #2 contains D-flat, E-flat, F, G-flat, A-flat, B-flat, C, and D-flat.

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-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-sharp.
    • If the first note is D-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-flat.
    • While the second note in the first collection was D-sharp, it is incorrect to call the second note D-sharp in the second collection; you must call it E-flat.
  • Look at the last two keys on the keyboard:
    • If the last note is 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-sharp.
      • Although it seems like C would be much easier to read than B-sharp, in the context of scales, it is easier to read the penultimate note as B-sharp. It would be incorrect to write B-sharp as C, no matter how much you think it is better.
    • If the last note is 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.

Diatonic Scale

Unlike chromatic scales, which used all twelve keys on the keyboard, diatonic scales can only use each letter name once. As a result, diatonic scales only use diatonic steps and have seven different notes.

Practice 4.1

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.

Number 1 begins on B. Number 2 begins on F-sharp. Number 3 begins on A-flat. Number 4 begins on G-sharp.

Click here to watch the tutorial.

Solution
1)  B – C-sharp – D-sharp – E – F-sharp – G-sharp – A-sharp – B
2)  F-sharp – G-sharp – A – B – C-sharp – D-sharp – E-sharp – F-sharp
3)  A-flat – B-flat – C – D-flat – E-flat – F – G – A-flat
4)  G-sharp – A-sharp – B – C-sharp – D-sharp – E-sharp – F-double-sharp – G-sharp

TETRACHORDS  4.2

“Tetra” comes from the Greek meaning “four” and tetrachords refer to a collection 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).

Whole step, whole step, half step pattern.

In order to create major tetrachords, write notes diatonically (i.e., write each letter name once and only once) while adding the appropriate accidentals.

The major tetrachord pattern is whole step, whole step, half step. The major tetrachord beginning on C is C, D, E, F. The major tetrachord beginning on E-flat is E-flat, F, G, A-flat. The major tetrachord beginning on F-sharp is F-sharp, G-sharp, A-sharp, B.

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

If you have been to a baseball game, you may have heard the major tetrachord performed by the organist, as everyone cheers, “charge!”

Example 4.2.1. Major tetrachord: Baseball Cheer

Major tetrachords in the baseball cheer. The first major tetrachord is F, G, A, B-flat. The second major tetrachord is F-sharp, G-sharp, A-sharp, B. The third major tetrachord is G, A, B, C.

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

Major tetrachords in the baseball cheer. The first major tetrachord is F, G, A, B-flat. The second major tetrachord is F-sharp, G-sharp, A-sharp, B. The third major tetrachord is G, A, B, C.

The major tetrachord is not uncommon 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”

Major tetrachords in Krumpholtz, “The Favorite Air of Robin Adair." The major tetrachord G, A, B, C appears four times.


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.

  • In the first system, notes immediately preceding (measures 1-2) or following (measures 3-4) decorate the major tetrachord.
  • In the second system, the major tetrachord appears in two different octaves.

Major Tetrachord

The major tetrachord consists of four notes using the following diatonic steps: whole step – whole step – half step.

Practice 4.2A

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.

Fill in the major tetrachords with pitch names. The sample shows D, E, F-sharp, G. Number 1 begins on B-flat. Number 2 ends on A. The second pitch on number 3 is A-flat.

Click here to watch the tutorial.

Solution
1)  B-flat – C – D – E-flat
2)  E – F-sharp – G-sharp – A
3)  G-flat – A-flat – B-flat – C-flat

 

Practice 4.2B

Directions:

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

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

Farrenc, Cello Sonata, op. 46, first movement - Allegro moderato. Number 1 points to the pitches D-flat, C, B-flat, A. Number 2 points to the pitches F, G, A, B-flat. Number 3 points to the pitches C, D-flat, E-flat, F.

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

Farrenc, Cello Sonata, op. 46, third movement - Finale. Allegro. Number 1 points to the pitches A, B-flat, C, D. Number 2 points to the pitches C-sharp, D, E-flat, F. Number 3 points to the pitches D, E-flat, F, G. Number 4 points to the pitches E-flat, D, C, B-flat. Number 5 points to the pitches B-flat, A, G, F.

Click here to watch the tutorial.

Solution
A1)  X
A2)  major
A3)  X
B1)  X
B2)  X
B3)  X
B4)  major
B5)  major

MAJOR SCALES  4.3

When we take a major tetrachord and write another major tetrachord joined by a whole step, what results is a major scale.

Example 4.3.1. Major scale

Major scale built by combining two major tetrachords. Major tetrachord number 1 consists of C, D, E, and F. A whole step above F is G. Major tetrachord number 2 consists of G, A, B, and C. Joining the two major tetrachord together with a whole step in between creates a C 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 joined by a whole step, what results 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 tuneful melody, we often find the major scale to create emphasis, give rise to tension, or add 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

Beethoven, Symphony No. 5 in C Minor, Op. 67, fourth movement - Allegro. There are three ascending C-major scales in the piccolo.

The orchestra has 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 the same way.

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

Descending major scale in Beethoven's Symphony No. 5 in C Minor, Op. 67, fourth movement - Allegro. The example closes with a descending C-major scale.

Listen to Example 4.3.3 and how the energy builds and climaxes 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 diatonic 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, be sure to use the pattern in reverse order.

Steps to Writing a Major Scale

Step one: Write in all the notes diatonically: write each note once and 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. Step one

Example A shows pitches written out diatonically from A-flat2 to A-flat3. Be sure the accidentals match for notes an octave apart. Example B shows pitches written out diatonically from B3 to B2.

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. Step two

Example A adds the steps for writing an ascending major scale: whole, whole, half, whole, whole, whole, half. Examples B adds the steps fro writing a descending major scale. Be sure the steps are in reverse order: half, whole, whole, whole, half, whole, whole.

Step three: Add accidentals. Major scales will only contain sharps or flats—never both.

Example 4.3.6. Step three

Example A shows the added accidentals after applying the whole steps and half steps from the previous steps. Added accidentals include B-flat, D-flat, and E-flat. Added accidentals for Example B include A-sharp, G-sharp, F-sharp, D-sharp, and C-sharp.

Writing Major Scales

1.   Write in all the note names diatonically (once and only once) in ascending or descending order.
2.   Write in the pattern of whole steps and half steps: whole-whole-half-whole-whole-whole-half.
3.   Add accidentals. Major scales will only contain sharps or flats–never both.

Practice 4.3A

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.

Number 1 is a descending major scale beginning on A3. Number 2 is an ascending major scale beginning on B-flat2. Number 3 is an ascending major scale beginning on E-flat4. Number 4 is a descending major scale beginning on F-sharp5.

Click here to watch the tutorial.

Practice 4.3B

Directions:

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

Number 1 contains E, F-sharp, G-sharp, A, B, C-sharp, D-sharp, and E. Number 2 contains D-flat, C, B-flat, A-flat, G-flat, F, E-flat, D. Number 3 contains D, D-flat, B, A, G, F-sharp, E, and D. Number 4 contains G-flat, A-flat, B-flat, C-flat, D-flat, E-flat, F, and G-flat.

Click here to watch the tutorial.

Solution
1)  major
2)  X
3)  X
4)  major

SCALE DEGREES  4.4

Because the pattern of whole steps and half steps is the same for every major scale, every note is exactly the same distance apart between different major scales. For example, the third note in every major scale is exactly two whole steps away from the first note. To make this relationship clear, we use scale degree numbers and scale degree names.

Example 4.4.1. Scale degrees in a C-major scale

Scale degree names and numbers in a major scale. Scale degree 1 is the tonic. Scale degree 2 is the supertonic. Scale degree 3 is the mediant. Scale degree 4 is the subdominant. Scale degree 5 is the dominant. Scale degree 6 is the submediant. Scale degree 7 is the leading tone.

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.”

  • Notice that the last scale degree number is not [latex]\hat8[/latex]. Instead, it repeats [latex]\hat1[/latex]. This is 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 are synonymous. The supertonic is always [latex]\hat2[/latex] and vice versa.

  • The tonic ([latex]\hat1[/latex]) begins and ends the major scale.
  • The supertonic ([latex]\hat2[/latex]) is so named because it is a whole step above the tonic (e.g., superscript is writing above the regular text).
  • The mediant ([latex]\hat3[/latex]) is halfway between the tonic ascending to the dominant.
  • The subdominant ([latex]\hat4[/latex]) is a fifth below the tonic (e.g., subscript is writing below the regular text).
  • The dominant ([latex]\hat5[/latex]) is a fifth above the tonic.
  • The submediant ([latex]\hat6[/latex]) is halfway between the tonic descending to the subdominant.
  • The leading tone ([latex]\hat7[/latex]) is so named because it is a diatonic half step below the tonic. It leads to the tonic. This book often abbreviates 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.

  • For example, a fifth above C is G because there are five note names from C to G (C-D-E-F-G). The dominant is a fifth above the tonic, so the dominant of C is G.
  • The subdominant is a fifth below the tonic. If we count five note names below C, we get F (C-B-A-G-F). Therefore, the subdominant of C is F.

A visualization of the scale degree names may be helpful.

Example 4.4.2. Scale degrees

Diagram of scale degree names and numbers. Details of diagram given in text below.

Sometimes students struggle with remembering scale degree names. However, if you use a diagram such as Example 4.4.2, it may be easier to memorize scale degree names.

  • The dominant is a fifth above the tonic.
    • The mediant is halfway between the tonic ascending to the dominant.
  • The subdominant is a fifth below the tonic.
    • The submediant is halfway between the tonic descending to the subdominant.
  • 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.

The last two bullet points describe scale degrees that are a step away from the tonic. Being only a step away from the tonic, the supertonic and leading tone have a strong pull to the tonic. As shown by the diagram in Example 4.4.2, the tonic is the focal point. Indeed, the C-major scale is so named because its tonic is C. We can hear the musical pull to the tonic when we stop short before arriving to the tonic. Listen to Example 4.4.3—do you hear how strongly the music wants to reach the tonic?

Example 4.4.3. Pull to tonic: stopping short

Major scales stopping before reaching tonic. Example A is a descending C major scale that stops on scale degree 2. Example B is an ascending C major scale that stops on degree 7.

  • The descending C-major scale stops short on the supertonic ([latex]\hat2[/latex]).
  • The ascending C-major scale stops short on the leading tone ([latex]\hat7[/latex]).

The next two examples illustrate the pull to tonic.

Example 4.4.4. Pull to tonic: Foster[4], “Camptown Races”

Pull to tonic: Foster's "Camptown Races." Measure 4 ends on scale degree 2, the supertonic. Measure 8 ends on scale degree 1, the tonic.

  • The first system ends on the supertonic ([latex]\hat2[/latex]). The music does not sound conclusive, as we yearn for tonic.
  • The second system ends on the tonic ([latex]\hat1[/latex]). The music finally sounds complete.

Example 4.4.5. Pull to tonic: “Yankee Doodle”

Pull to tonic in "Yankee Doodle." Measure 4 ends on scale degree 7, the leading tone. Measure 8 ends on scale degree 1, the tonic.

  • The first system ends on the leading tone ([latex]\hat7[/latex]). The music does not sound conclusive, as we yearn for tonic.
  • The second system ends on the tonic ([latex]\hat1[/latex]). The music finally sounds complete.

Compare the scale degrees in the next two major scales.

Example 4.4.6. Comparing scale degrees

Comparing scale degrees in two different major scales. Example A shows a C major scale, where scale degree 1 is C, scale degree 2 is D, scale degree 3 is E, scale degree 4 is F, scale degree 5 is G, scale degree 6 is A, scale degree 7 is B, and scale degree 1, C, returns. Example B shows a descending E-major scale, where scale degree 1 is E, scale degree 7 is D-sharp, scale degree 6 is C-sharp, scale degree 5 is B, scale degree 4 is A, scale degree 3 is G-sharp, scale degree 2 is F-sharp, and scale degree 1, E, returns at the end.

  • Scale degree numbers are based on the ascending scale, not the order in which they appear.
    • The second note in Example 4.4.6B is [latex]\hat7[/latex], and not [latex]\hat2[/latex].
  • The same note varies in scale degree depending on the scale.
    • A is [latex]\hat6[/latex] in the C major scale (Example 4.4.6A), but is [latex]\hat4[/latex] in the E major scale (Example 4.4.6B).

In aural training, you may learn solfège (e.g., do–re–mi) to help you sing. Scale degrees are the same thing as solfège, but are used in music theory.[5]

Scale degree numbers with solfège. Scale degree 1 is doe, scale degree 2 is ray, scale degree 3 is me, scale degree 4 is fa, scale degree 5 is sol, scale degree 6 is la, scale degree 7 is tee, and scale degree 1 once again is doe.

Scale Degrees

Each member of a major scale has a scale degree number and scale degree name. The scale degrees help show the relationship between notes within the major scale, and the relationship between different major scales.

Practice 4.4

Directions:

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

The given pitches descend in the bass clef, beginning on F-sharp3. The pitches are F-sharp, E-sharp, D-sharp, C-sharp, B, A-sharp, G-sharp, and F-sharp.

  1. Which note is the tonic?
  2. Which note is the dominant?
  3. Which note is [latex]\hat6[/latex]?
  4. Which note is [latex]\hat2[/latex]?
  5. What scale degree number is B?
  6. What scale degree number is E-sharp?
  7. Why is [latex]\hat4[/latex] called the subdominant?
  8. Why is [latex]\hat7[/latex] called the leading tone?
  9. Why is [latex]\hat3[/latex] called the mediant?
  10. Why is [latex]\hat2[/latex] called the supertonic?

Click here to watch the tutorial.

Solution
1)  F-sharp
2)  C-sharp
3)  D-sharp
4)  G-sharp
5)  [latex]\hat4[/latex]
6)  [latex]\hat7[/latex]
7)  fifth below tonic
8)  leads to tonic
9)  halfway between tonic ascending to dominant
10)  whole step above tonic

MAJOR KEYS  4.5

A major scale is not only an organized way to write notes in alphabetical order. More importantly, the major scale is an organized way of telling us the contents of a musical key, which combines the tonal center and mode.

  • The tonic is the tonal center. It is a note that tells us where “home” is; the music gravitates around the tonal center and does not feel complete unless we end at home. The tonal center can be any pitch, such as C, F-sharp, or 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 the major mode and minor mode contain different notes, they sound different. The major mode is often associated with happy music, while the minor mode is often associated with sad music.
  • The key combines the tonal center and mode (e.g., F-sharp major or F-sharp minor). As you will learn later in this chapter, not every tonal center can have keys in both major and minor (e.g., you can have the key of G-flat major but not G-flat minor).

Ideally, you will be able to hear a musical example and tell if it is in major or minor. Examples 4.5.1. and 4.5.2 are two famous classical works that are in major keys.

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

An example of a major key is Mozart's Eine kleine Nachtmusik, Kurshell 525, first movement - Allegro. Listen to the recording below.

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

An example of a major key is Wagner's Bridal Chorus from Lohengrin, Act III, Scene i - Mässig bewegt. Listen to the recording below.

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

We can figure out a major key by its major scale.

Example 4.5.3. From scale to key

A-flat major scale with accidentals. The notes are A-flat, B-flat, C, D-flat, E-flat, F, G, and A-flat.

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

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

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

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

"Twinkle Twinkle Little Star" with accidentals A-flat, E-flat, D-flat, and B-flat.

  • 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, the tonal center is A-flat because it ends on A-flat. 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-flat, B-flat, D-flat, E-flat) tell us that we are in the major mode. We know this because the A-flat-major scale has four flats.
    • All the flats found in the A-flat major scale appear in this example. However, this is not a requirement.
  • Therefore, the tonal center of A-flat + the major scale (four flats) = the key of A-flat major.

Rather than constantly writing and rewriting accidentals within the score, musicians use key signatures to simplify writing (and reading) music. A key signature is the group of flats or sharps located at the start of every system of music. The following example shows Examples 4.5.4 rewritten with a key signatures 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

"Twinkle Twinkle Little Star" with a key signature rather than accidentals. Below the score, the major key is shown by an uppercase letter followed by a colon.

The key signature tells us which notes always have accidentals. For musicians, seeing the key signature once at the beginning is much easier than reading numerous accidentals.

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

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

Summary box on how to write "B-flat major." First, you can write an uppercase B followed by a flat symbol and the word major with a lowercase m or an uppercase B with a dash and the word flat and the word major with a a lowercase m. Use these when describing the key within the text. It is common to write out the word flat when describing the key within the text, especially if you cannot make the flat symbol. Avoid using an italicized lowercase B for the flat symbol. Do not capitalize the letter m when major is being used in a sentence. For example, in the sentence Brahms's First String Sextet begins in B-flat major, the word major would use a lowercase m. Second, you can write B-flat major with an uppercase M when you are writing the title of a piece. For example, "The program opens with Brahms's String Sextet No. 1 in B-flat Major" would use an uppercase M since it is the title of the piece. Third, you can abbreviate an uppercase B followed by a flat symbol or an uppercase B followed by a flat symbol and an uppercase M when you are labeling the key in analysis. See Example 4.5.5.

Unlike time signatures, key signatures are rewritten at the start of each system.

Example 4.5.6. Key signature versus time signature

How to correctly write key signatures and time signatures on a staff. The example shows two staves of blank music. The first line is called the first system and the second line is called the second system. Rewrite the clef at the start of each section. Write the time signature only once at the beginning, after the clef. Rewrite the key signature at the start of each system. The key signature is written before the time signature.

  • Each system must begin with a clef.
  • The key signature appears immediately after the clef and each system must have the key signature (if there is one).
  • The time signature only appears at the start of the composition or when the time signature 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).

Unlike accidentals, which were localized, key signatures are globalized. This means that with a key signature of A-flat major, all Bs are B-flat.

Example 4.5.7. Accidentals versus key signatures

Differences between using accidentals and using a key signature. Example A shows accidentals. The first pitch is B-flat4 with a flat symbol. The third pitch is B5 not B-flat5 because the note is in a different octave. After the bar line, the first note is B4, not B-flat4, because the bar line cancels all accidentals. It would be better to use a courtesy accidental. Example B uses a key signature of four flats. The first pitch is B-flat4 because of the key signature. The third pitch is B-flat5 because of the key signature. After the bar line, the pitch is still B-flat4 because of the bar line. The third pitch after the bar line is B-double flat4 because of the double flat accidental. Even though there is a B-flat in the key signature, a double flat is required to lower B-flat. The last pitch is B-natural3. The natural sign is required because of the key signature.

Notice some important differences between accidentals versus key signatures.

  • Accidentals (Example 4.5.7A):
    • The third note is B (not B-flat) because the flat on the previous note only applied to B-flat4.
    • The note after the bar line is B (not B-flat) because even though it is B-flat4, the bar line cancels previous accidentals.
  • Key signatures (Example 4.5.7B):
    • The third note is B-flat because the key signature says all Bs are B-flats.
    • The note after the bar line is B-flat because bar lines make no difference: the key signature says all Bs are B-flats.
    • The penultimate note requires a double flat when the desired note is B-double-flat. Sometimes students think adding a flat lowers B-flat to B-double-flat; however, adding a flat would only make the note B-flat.
    • The last note requires a natural sign if the desired note is B.

Example 4.5.8 illustrates how accidentals work within a key signature, as well as how they work with ties. The pitches are shown above the cello’s part.

Example 4.5.8. Accidentals and key signature: Bosmans[9], Impressions for Cello and Piano, I. Cortège

Example of accidentals and key signature in Bosman's Impressions for Cello and Piano, First movement Cortège. The key signature has two flats. The first pitch is C-sharp4 with an added sharp. The second pitch is D. The third pitch is also C-sharp4 although there is no added sharp. The fourth pitch is B-flat3 although there is no added flat because of the key signature. The fifth pitch is C-sharp4 because of the earlier accidental. That fifth pitch C-sharp4 is tied across the bar line where C-sharp4 continues to be held out. The last pitch is C-sharp5 which requires an accidental because it is in a different octave.

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

Accidentals Versus Key Signatures

•  Accidentals are localized, meaning that they only apply to a specific octave designation and do not last past the bar line.
•  Key signatures are global, meaning notes have the accidental in any octave designation and despite any bar lines.

Practice 4.5A

Directions:

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

Bosmans, Impressions for Cello and Piano, I. Cortège

The example begins in the treble clef with two flats. The sample shows F. Number 1 looks like E. There is a bar line. Number 2 looks like D-flat. Number 3 looks like E. Number 4 looks like D. Number 5 looks like C. Number 6 looks like D and is tied across the bar line to number 7. There is another bar line and the clef changes to bass clef. Number 8 looks like A. Number 9 looks like B. Number 10 looks like A. Number 11 looks like G. Number 12 looks like A and is tied across the bar line to number 13.

Click here to watch the tutorial.

Solution
1)  E-flat
2)  D-flat
3)  E-flat
4)  D-flat
5)  C
6)  D-flat
7)  D-flat
8)  A-flat
9)  B-flat
10)  A-flat
11)  G
12)  A-flat
13)  A-flat

 

Practice 4.5B

Directions:

  • Write the given pitches using correct rhythm.

The clef is bass clef, the key signature has three sharps, and the time signature is 3-4. Measures 1 and 2 have 3 pitches. Measure 3 has one pitch. Number 1 is G-sharp2. Number 2 is G-sharp3. Number 3 is G2. There is a bar line. Number 4 is G2. Number 5 is G-double sharp3. Number 6 is G-sharp 3. There is a bar line. Number 7 is G2.

Click here to watch the tutorial.

MAJOR KEY SIGNATURES WITH FLATS  4.6

Accidentals in key signatures must appear in a specific order and they must be placed on specific locations within the staff. This is one of the biggest hurdles for students to memorize and be able to identify and write quickly. However, if you are able to quickly identify and write all the major and minor key signatures, music theory will be much easier for you. Key signatures will have either flats or sharps, not both. We will begin with major key signatures with flats.

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

The order of flats is always B-flat, E-flat, A-flat, D-flat, G-flat, C-flat and 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 need to just simply memorize the order of flats.

The order of flats is very important as they tell us the following things:

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

Once you have the order of flats memorized, you need to learn their exact placement on the grand staff. Each flat sits on a specific line or space in the treble clef and in the bass clef. 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-flat major. Example 4.6.1 illustrates correctly- and incorrectly-written key signatures.

Example 4.6.1. Key signature for E-flat major

Correct and incorrect ways to write a key signature. Accidentals must be written in a specific order in both clefs. In the first measure, accidentals are correctly written. The key signature always appears before the time signature. In the second measure, accidentals are incorrectly written. In the treble clef, the order of flats is correct but E-flat is on the wrong octave of the staff. It is written at E4 as opposed to E5. The key signature in the bass clef appears correct, but it is how the flats are written in the treble clef not the bass clef.

First, notice the parts that are correctly written (in blue).

  • The key signature is correctly written on the staff in both the treble clef and bass clef.
  • 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 shows two of the most common key signature errors students make (in red).

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

Since there are seven different note names, there can be a maximum of seven flats in a key signature. The example below shows all the major key signatures with flats.

Example 4.6.2. Major key signatures from zero to seven flats

All major key signatures with flats. C major has zero flats. F major has 1 flat. B-flat major has 2 flats. E-flat major has 3 flats. A-flat major has 4 flats. D-flat major has 5 flats. G-flat major has 6 flats. C-flat major has 7 flats.

There are several clues that can help you quickly memorize the major key signatures with flats:

  • C major has zero flats while C-flat major has seven flats.
  • All the major keys with flats have a flatted tonal center except for F (e.g., B-flat major and G-flat major).
    • In other words, all keys with flats have “flat” in their names except for F major.
  • Notice the pattern of flats: flats alternate up–down to create descending pairs.
    • Treble clef begins on B-flat4 and the pattern is up–down.
    • Bass clef begins on B-flat2 and the pattern is the same: up–down.
    • For C-flat major, the pattern of flats is 2+2+2+1.

One of the best ways to practice memorizing the correct placement of key signatures on the staff is to be able to write C-flat major quickly by memory. If you can write all seven flats correctly in both treble clef and bass clef, writing fewer flats should be a cinch.

Practice 4.6A

Directions:

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

The empty grand staff allows you to practice writing the key signature for C-flat major four times.

Click here to watch the tutorial.

 

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

Example 4.6.3. Penultimate flat = key

Shortcut for identifying major keys with flats. In Example A, the penultimate flat is B-flat, so the key is B-flat major. In Example B, the penultimate flat is D-flat, so the key is D-flat major. In Example C, the penultimate flat is C-flat, so the key is C-flat major.

  • Example 4.6.3A: The penultimate flat is B-flat, so the key is B-flat major.
  • Example 4.6.3B: The penultimate flat is D-flat, so the key is D-flat major.
  • Example 4.6.3C: The penultimate flat is C-flat, so the key is C-flat major.
    • Sometimes students call this B major because B and 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-flat. It would be impossible for B major to have any flats since the first flat is always B-flat.

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

Now we will put together everything we have learned to figure out the key of a musical example.

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

Finding the key in Szymanowska's March No. 5. The key signature has two flats. The first lowest note is B-flat. The last lowest note is B-flat.

When figuring out the key of a given musical example, follow these steps:

  1. Listen to the example: Does it sounds 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-flat major.
  3. Look at the first lowest note.
    • The first lowest note is B-flat.
  4. Look at the last lowest note.
    • The last lowest note is B-flat.

In Example 4.6.4, all four steps point to B-flat major. Using the first lowest note and the last lowest notes are not always reliable, but are more dependable when put together with the other steps.

Summary box of strategies for major key signatures with flats. First, memorize the order of flats: B-flat, E-flat, A-flat, D-flat, G-flat, C-flat, and F-flat. Second, memorize the key signature for all the major keys with flats. Be able to quickly identify major keys by their key signatures. The penultimate flat is the key. Finally, be able to quickly write the key signature for C-flat major for treble clef and bass clef. If you can write the key signature for all seven flats, then you can write all the major key signatures with flats.

Practice 4.6B

Directions:

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

Number 1, 4 flats. Number 2, 7 flats. Number 3, 2 flats. Number 4, 5 flats. Number 5, 1 flat. Number 6, 6 flats. Number 7, 1 flat. Number 8, 6 flats. Number 9, zero flats. Number 10, 3 flats. Number 11, 4 flats. Number 12, 7 flats.

Click here to watch the tutorial.

Solution
1)  A-flat
2)  C-flat
3)  B-flat
4)  D-flat
5)  F
6)  G-flat
7)  F
8)  G-flat
9)  C
10)  E-flat
11)  A-flat
12)  C-flat

 

Practice 4.6C

Directions:

  • Write the given key signatures on the staff.

Number 1 through 6 are in treble clef. Number 1, C-flat major. Number 2, B-flat major. Number 3, E-flat major. Number 4, F major. Number 5, D-flat major. Number 6, G-flat major. Numbers 7 to 12 are in bass clef. Number 7, E-flat major. Number 8, C major. Number 9, G-flat major. Number 10, C-flat major. Number 11, F major. Number 12, A-flat major.

Click here to watch the tutorial.

Practice 4.6D

Directions:

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

The sample shows that scale degree 7 in A-flat major is G. Number 1, scale degree 5 in E-flat major. Number 2, scale degree 3 in B-flat major. Number 3, scale degree 4 in F major. Number 4, scale degree 6 in G-flat major. Number 5, scale degree 2 in D-flat major.

Click here to watch the tutorial.

Solution
1)  B-flat
2)  D
3)  B-flat
4)  E-flat
5)  E-flat

MAJOR KEY SIGNATURES WITH SHARPS  4.7

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

The order of sharps is always F-sharp, C-sharp, G-sharp, D-sharp, A-sharp, E-sharp, and B-sharp.

One of the easiest ways to remember the order of sharps is that it is the order of flats backwards.

The order of sharps is the reverse of order of flats.

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

The order of sharps tells us that if there are six sharps, they are always F-sharp, C-sharp, G-sharp, D-sharp, A-sharp, and E-sharp in that order. Once you have the order of sharps memorized, you need to learn their exact placement on the grand staff. Each sharp sits on a specific line or space in the treble clef and in 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 incorrect to write them anywhere else.

The major key with six sharps flats is F-sharp major. Example 4.7.1 illustrates correctly- and incorrectly-written key signatures.

Example 4.7.1. Key signature for F-sharp major

Correct and incorrect way to write a key signature. The first measure shows the correct way to write a key signature. There are 6 sharps in the grand staff. The order of correct appearance is the clef, key signature, then time signature. The second measure shows mistakes. The time signature appears before the key signature, which is incorrect. In the treble clef, the last sharp appears on F5. However, the last sharp must be E-sharp5 since the first sharp appears on F4. In the bass clef, the pattern of sharps appears as the pattern of flats. The pattern of sharps is different.

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

  • The time signature always comes after the key signature. Remember that the word “key” comes before the word “time” alphabetically.
  • In the treble clef, the last sharp is E-sharp, not F. Sometimes students think it is easier to write F, but that is incorrect.
    • F-sharp is already the first sharp in the key signature.
    • The enharmonic equivalent of E-sharp is actually F-natural, and not 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, there can be a maximum of seven sharps in a key signature. The example below shows all the major key signatures with sharps.

Example 4.7.2. Major key signatures from zero to seven sharps

All key signatures with sharps. C major has zero sharps. G major has 1 sharp. D major has 2 sharps. A major has 3 sharps. E major has 4 sharps. B major has 5 sharps. F-sharp major has 6 sharps. C-sharp major has 7 sharps.

There are several clues that can help you quickly memorize the major key signatures with sharps:

  • C major has zero sharps while C-sharp major has seven sharps.
  • All the major keys with sharps do not have a sharped tonal center except for F-sharp and C-sharp major (e.g., G major and B major).
    • In other words, none of the keys with sharps have “sharp” in their names except for F-sharp major and C-sharp major.
  • The pattern of sharps is different than the pattern of flats.
    • The treble clef begins on F-sharp5 and the bass clef begins on F-sharp3.
    • The pattern begins down–up, but is then followed by down–down–up.
    • For 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 be able to write C-sharp major quickly by memory. If you can write all seven sharps correctly in both treble clef and bass clef, writing fewer sharps should be easy.

Practice 4.7A

Directions:

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

Blank grand staff to practice writing C-sharp major four times.

Click here to watch the tutorial.

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 4.7.3. Last sharp = leading tone

Strategy for identifying major key signatures with sharps. In the first measure, there are two sharps. The last sharp is C-sharp. C-sharp is the leading tone of D major. Thus, the key is D major. In the second measure, the last sharp is G-sharp. G-sharp is the leading tone of A. Thus, the key is A major. In the last measure, the last sharp is B-sharp. B-sharp is the leading tone of C-sharp major. Thus, the key is C-sharp major.

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

Apply the steps we learned in the last section to figure out the key of a musical example.

Example 4.7.4. Find the key: Szymanowska, March No. 3[11]

The first four bars of Szymanowska's March No. 3 for piano. The steps for finding the key are in the text below.

  1. Listen to the example: Does it sounds like it’s in major (happy)?
    • Yes, Example 4.7.4 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 4.7.4, step 3 does not agree with D major. However, if we look at the music, the first lowest note (A) is an anacrusis. We know that the anacrusis leads into the downbeat and the downbeat is much stronger. If we take the downbeat into consideration instead, we see that the first lowest note is actually D. Example 4.7.4 is in D major.

Summary box for strategies to identify major key signatures with sharps. First, memorize the order of sharps: F-sharp, C-sharp, G-sharp, D-sharp, A-sharp, E-sharp, and B-sharp. Second, memorize the key signatures for all the major keys with sharps. Be able to quickly identify major keys by their key signature. The last sharp is the leading tone of the key. Third, be able to quickly write the key signature for C-sharp major for treble clef and bass clef. If you can write the key signature for all seven sharps, then you can write all the major key signatures with sharps.

Practice 4.7B

Directions:

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

Number 1, 3 sharps. Number 2, 5 sharps. Number 3, zero sharps. Number 4, 1 sharp. Number 5, 7 sharps. Number 6, 2 sharps. Number 7, 6 sharps. Number 8, 3 sharps. Number 9, 1 sharp. Number 10, 7 sharps. Number 11, 5 sharps. Number 12, 4 sharps.

Click here to watch the tutorial.

Solution
1)  A
2)  B
3)  C
4)  G
5)  C-sharp
6)  D
7)  F-sharp
8)  A
9)  G
10)  C-sharp
11)  B
12)  E

 

Practice 4.7C

Directions:

  • Write the given key signatures on the staff.

Exercise to write the given major key signatures. Numbers 1-6 are in the bass clef. Number 1, A major. Number 2, C-sharp major. Number 3, F-sharp major. Number 4, D major. Number 5, B major. Number 6, G major. Numbers 7-12 are in treble clef. Number 7 is E major. Number 8 is C major. Number 9 is A major. Number 10 is B major. Number 11 is F-sharp major. Number 12 is D major.

Click here to watch the tutorial.

Practice 4.7D

Directions:

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

Exercise asking to write the correct pitch for the given scale degrees numbers in the given keys. Number 1 is scale degree 3 in G major. Number 2 is scale degree 5 in B major. Number 3 is scale degree 4 in A major. Number 4 is scale degree 6 in C-sharp major. Number 5 is scale degree 7 in F-sharp major. Number 6 is scale degree 2 in E major.

Click here to watch the tutorial.

Solution
1)  B
2)  F-sharp
3)  D
4)  A-sharp
5)  E-sharp
6)  F-sharp

 

Notice the pattern between major keys with flats and major keys with sharps.

Example 4.7.5. Major keys comparison

Table comparing major keys with flats and major keys with sharps. C major has zero flats and C-sharp major has 7 sharps. F major has 1 flat and F-sharp major has 6 sharps. B-flat major has 2 flats and B major has 5 sharps. E-flat major has 3 flats and E major has 4 sharps. A-flat major has 4 flats and A major has 3 sharps. D-flat major has 5 flats and D major has 2 sharps. G-flat major has 6 flats and G major has 1 sharp. C-flat major has 7 flats and major has zero sharps.

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

Practice 4.7E

Directions:

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

Number 1 has 1 sharp. Number 2 has 4 flats. Number 3 has 3 sharps. Number 4 has 7 sharps. Number 5 has 5 sharps. Number 6 has 3 flats. Number 7 has 4 sharps. Number 8 has 6 flats. Number 9 has 2 sharps. Number 10 has 1 flat. Number 11 has 2 flats. Number 12 has 5 flats.

Click here to watch the tutorial.

Solution
1)  G
2)  A-flat
3)  A
4)  C-sharp
5)  B
6)  E-flat
7)  E
8)  G-flat
9)  D
10)  F
11)  B-flat
12)  D-flat

Practice 4.7F

Directions:

  • Write the given key signatures on the staff.

Exercise asking to write the given major key signatures. Numbers 1-6 are in treble clef. Number 1, A-flat major. Number 2, F-sharp major. Number 3, E-flat major. Number 4, A major. Number 5, C-sharp major. Number 6, B major. Numbers 7-12 are in the bass clef. Number 7, D major. Number 8, C-flat major. Number 9, E major. Number 10, G-flat major. Number 11, F major. Number 12, D-flat major.

Click here to watch the tutorial.

Practice 4.7G

Directions:

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

Number 1, scale degree 2 in B-flat major. Number 2, scale degree 7 in A major. Number 3, scale degree 5 in B major. Number 4, scale degree 3 in E-flat major. Number 5, scale degree 1 in C-flat major. Number 6, scale degree 6 in D major. Number 7, scale degree 7 in G-flat major. Number 8, scale degree 4 in F major. Number 9, scale degree 2 in D-flat major.

Click here to watch the tutorial.

Solution
1)  C
2)  G-sharp
3)  F-sharp
4)  G
5)  C-flat
6)  B
7)  F
8)  B-flat
9)  E-flat

CIRCLE OF FIFTHS  4.8

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

New major scales being built from the second tetrachord of a major scale. Example A shows major tetrachord #1 consisting of C-D-E-F and major tetrachord #2 consisting of G-A-B-C. Together, they create the C-major scale. Example B takes major tetrachord #2 from Example A and makes it major tetrachord #1. From there, a new major tetrachord #2 is added with pitches D, E, F-sharp, G. Together these two major tetrachords create the G-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, thus 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-sharp) in the G-major scale, thus the key of G major has one sharp.

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

Example 4.8.2. Continuation of Example 4.8.1

Second major tetrachord of a D-major scale becomes the first major tetrachord of an A-major scale.

Each new major scale is a fifth higher and contains one more sharp. In fact, we can continue this pattern until we return to C major. Each new scale will be a fifth higher than the previous. This important relationship can be illustrated by the circle of fifths.

Example 4.8.3. Circle of fifths

Diagram of the circle of fifths. Moving clockwise from C, each key is a fifth higher and adds a sharp. Moving counterclockwise from C, each key is a fifth lower and adds a flat.

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.
    • Each key adds a sharp.
      • E major has 4 sharps and B major has 5 sharps.
    • C (no sharps, no flats) moves clockwise to C-sharp major (7 sharps).
  • Moving counterclockwise from C:
    • Each key is a fifth lower.
      • A fifth below E-flat is A-flat.
    • Each key adds a flat.
      • E-flat major has 3 flats and A-flat major has 4 flats.
    • C (no sharps, no flats) moves counterclockwise to C-flat major (7 flats).

There are three keys on the bottom of the circle of fifths that have two keys. This is because these keys are enharmonically equivalent keys.

Example 4.8.4. Enharmonically equivalent keys

Table illustrating three enharmonically equivalent keys. D-flat major has 5 flats and C-sharp major has 7 sharps. G-flat major has 6 flats and F-sharp major has 6 sharps. C-flat major has 7 flats and B major has 5 sharps.

D-flat is enharmonically equivalent to C-sharp so the key of D-flat major is also enharmonically equivalent to the key of C-sharp major. However, since D-flat must have flats (because its tonic is D-flat) and C-sharp must have sharps (because its tonic is C-sharp), D-flat has five flats and C-sharp has seven sharps. You can refer back to Example 4.1 to see how every member of these keys are enharmonically equivalent.

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

Although there is a wealth of information in the circle of fifths, sometimes students depend on it rather than simply memorizing key signatures. Indeed, I have often witnessed students wasting five precious minutes of exam time recreating the entire circle of fifths. It is more beneficial as musicians for you to take the time now to memorize the fifteen major key signatures as quickly as possible.

Circle of Fifths

The circle of fifths is a graphic representation of how all the major keys are built by moving up or down by five. Each key either gains a sharp (clockwise) or gains a flat (counterclockwise).

Practice 4.8

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.

Number 1, zero sharps and flats. Number 2, 1 sharp. Number 3, 2 sharps. Number 4, 3 sharps. Number 5, 4 sharps. Number 6, 5 sharps. Number 7, 6 sharps. Number 8, 7 sharps. Number 9, zero flats and sharps. Number 10, 1 flat. Number 11, 2 flats. Number 12, 3 flats. Number 13, 4 flats. Number 14, 5 flats. Number 15, 6 flats. Number 16, 7 flats.

Click here to watch the tutorial.

Solution
1)  C
2)  G
3)  D
4)  A
5)  E
6)  B
7)  F-sharp
8)  C-sharp
9)  C
10)  F
11)  B-flat
12)  E-flat
13)  A-flat
14)  D-flat
15)  G-flat
16)  C-flat

TRANSPOSITION: MELODIC  4.9

We already learned about rhythmic transposition when we rewrote a rhythm by the same proportion to fit in a different time signature. There is also melodic transposition, when you write or perform the same melody in a different key. Suppose you are playing the flute with a vocalist. The piece is in B-flat major, but the melody is too low for the singer. The vocalist is easily able to change keys using solfège, but for instrumentalists, it is not as easy unless you are fluent in key signatures.  Since all major scales contain the same series of whole steps and half steps, you can easily transpose melodies by using scale degree numbers.

Example 4.9.1. Steps to melodic transposition

Steps to melodic transposition. Example A shows the melody in B-flat major. Example B shows the melody transposed up to D major. Example C shows the melody transposed down to D major.

  • Example 4.9.1A: First figure out the key the original melody is in and write scale degree numbers above.
  • Example 4.9.1B: Transposing requires two steps.
    1. Write the clef and key signature of the new key. Rewrite the same scale degree numbers as the original melody above the blank staff.
    2. Write the correct pitches on the staff, making sure the rhythm, dynamics, and articulation marks are the same.
  • Example 4.9.1C: You can transpose higher or lower. Here, the melody has been transposed over an octave lower and requires a change of clef.
  • Notice that stem direction will change depending 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 ^1 to ^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 transposition

Examples showing to keep melodic contour while transposing. Example A shows scale degree 1 ascending to scale degree 3 and scale degree 5 then descending to scale degree 7. Example B is incorrect because scale degree 3 ascends to scales degree 5 and scale degree 5 ascends to scale degree 7.

The reason why Example 4.9.2B sounds so different is because the melodic contour is not correct (shown with red arrows).

Composers will often repeat the same melody but in another key to give it variety. Example 4.9.3 illustrates 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

Original melody of Mozart's Piano Sonata No. 16 in C Major, Kurshell 545, first movement - Allegro

B. Transposed melody in F major

Mozart's Piano Sonata No. 16 in C Major, Kurshell 545, first movement - Allegro transposed to F major.

  • Example 4.9.3.A:
    • The original melody is in C major.
    • Scale degree numbers are shown above the melody.
  • Example 4.9.3B:
    • The melody reappears at measure 42. However, this time it is in F major.
    • Although the key signature does not change, 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 [latex]\hat1[/latex] is now F.
      • If you look at the music, every B has a flat. Therefore, even though the key signature does not have a flat, we know we are in F major because F major has one flat.

Melodic Transposition

Melodic transposition is the act of rewriting music in a different key. Be sure to maintain the melodic contour, rhythm, articulation marks, and dynamics.

Practice 4.9

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

Transposing Munktell's Violin Sonata, first movement - Allegro non tanto, vigoroso. Example A is in treble clef in a key with 3 flats and you are to transpose to A major also in treble clef.

2.   Munktell, Violin Sonata, ii – Moderato energico

Transposing Munktell's Violin Sonata, second movement - Moderato energico. Example A is in treble clef with two sharps. You are to transpose to Example B in bass clef and B-flat major.

Click here to watch the tutorial.

SUMMARY

      1. A major tetrachord consists of three diatonic steps: whole – whole – half.
      2. A major scale is made of two major tetrachords joined by a diatonic whole step: whole – whole – half :: whole :: whole – whole – half.
      3. Scale degree numbers are numbers with carets that represent members of the scale. Scale degree names also represent members of the scale.
        • [latex]\hat1[/latex]: tonic
        • [latex]\hat2[/latex]: supertonic
        • [latex]\hat3[/latex]: mediant
        • [latex]\hat4[/latex]: subdominant
        • [latex]\hat5[/latex]: dominant
        • [latex]\hat6[/latex]: submediant
        • [latex]\hat7[/latex]: leading tone
      4. The collection of flats or sharps in any major scale can be reduced to a key signature. Flats and sharps in key signatures are global, meaning they apply to notes in every octave.
      5. The flats in major key signatures always go in this order: B-flat – E-flat – A-flat – D-flat – G-flat – C-flat – F-flat.
        • The penultimate flat in the key signature is the key.
        • The exception is F major, which has one flat.
      6. The sharps in major key signatures always go in this order: F-sharp – C-sharp – G-sharp – D-sharp – A-sharp – E-sharp – B-sharp.
        • The last sharp in the key signature is the leading tone of the key.
      7. The circle of fifths is a diagram that shows the relationship between keys.
        • Moving clockwise, the key ascends by five and adds a sharp.
        • Moving counterclockwise, the key descends by five and adds a flat.
      8. Melodic transposition is the act of rewriting a melody in a different key.

TERMS

  1. Anne-Marie Krumpholtz (1766-1813) was a French composer and harpist. ↵
  2. Louise Farrenc (1804-1875) was a French composer. ↵
  3. Ludwig van Beethoven (1770-1827) was a German composer. ↵
  4. Stephen C. Foster (1826-1864) was an American composer known as “The Father of American Music.” ↵
  5. In later chapters, we will use solfège periodically to clarify ambiguous scale degree numbers. ↵
  6. Wolfgang Amadeus Mozart (1756-1791) was an Austrian composer. ↵
  7. Richard Wagner (1813-1883) was a German composer. ↵
  8. Not all tempo markings are in Italian. Wagner chooses German for the tempo marking. Mässig bewegt means "moderately moving." ↵
  9. Hanriëtte Bosmans (1895-1952) was a Dutch composer and pianist. ↵
  10. Maria Szymanowska (1789-1831) was a Polish composer and pianist. ↵
  11. Example 4.7.4 includes an unfamiliar articulation marking: rf. Rinforzando, which comes from the Italian “reinforcing” or “strengthening,” is similar to sforzando but not as accented. ↵
  12. Helena Munktell (1852-1919) was a Swedish composer. ↵
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