assignment 5.2 key signatures

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I. Fundamentals

12 Major Scales, Scale Degrees, and Key Signatures

Chelsey Hamm and Bryn Hughes

Key Takeaways

A major scale is an ordered collection of half and whole steps with the ascending succession W‑W‑H‑W‑W‑W‑H.
Major scales are named for their first note (which is also their last note), including any accidental that applies to the note.
Scale degrees are solmization syllables notated by Arabic numerals with carets above them. The scale degrees are [latex]\hat1-\hat2-\hat3-\hat4-\hat5-\hat6-\hat7[/latex].
Solfège solmization syllables are another method of naming notes in a major scale. The syllables are do , re , mi , fa , sol , la , and ti .
Each note of a major scale is also named with scale-degree names : tonic, supertonic, mediant, subdominant, dominant, submediant, and leading tone.
A key signature, consisting of either sharps or flats , appears at the beginning of a composition, after a clef but before a time signature.
The order of sharps in key signatures is F, C, G, D, A, E, B, while the order of flats is the opposite: B, E, A, D, G, C, F. In sharp key signatures, the last sharp is a half step below the tonic (the first note of a scale). In flat key signatures, the second-to-last flat is the tonic.
The circle of fifths is a convenient visual for remembering major key signatures. All of the major key signatures are placed on a circle in order of number of accidentals.

A scale is an ordered collection of half and whole steps (see Half and Whole Steps and Accidentals to review).

Major Scales

A major scale is an ordered collection of half- (abbreviated H) and whole steps (abbreviated W) in the following ascending succession: W-W-H-W-W-W-H. Listen to Example 1 to hear an ascending major scale. Each whole step is labeled with a square bracket and “W,” and each half step is labeled with an angled bracket and “H.”

https://musescore.com/user/32728834/scores/6815731/embed

Example 1. An ascending major scale.

A major scale always starts and ends on notes of the same letter name, one octave apart, and this starting and ending note determines the name of the scale. Therefore, Example 1 depicts a C major scale because its first and last note is a C.

The name of a scale includes any accidental that applies to the first and last note. Example 2 shows a B♭ (B-flat) major scale—not a B major scale, which would use a different collection of pitches. Note that the pattern of half and whole steps is the same in every major scale, as shown in Example 1 and Example 2 .

https://musescore.com/user/32728834/scores/6823280/embed

Example 2. A B-flat major scale.

Scale Degrees, Solfège, and Scale-Degree Names

Musicians name the notes of major scales in several different ways. Scale degrees are solmization syllables notated by Arabic numerals with carets above them. The first note of a scale is [latex]\hat{1}[/latex] and the numbers ascend until the last note of a scale, which is also [latex]\hat{1}[/latex] (although some instructors prefer [latex]\hat{8}[/latex]). Example 3 shows a D major scale with each scale degree labeled with an Arabic numeral and a caret.

https://musescore.com/user/32728834/scores/8452298/embed

Example 3. A D major scale.

Below the scale degrees, Example 3 also shows another method of naming notes in a major scale: solfège solmization syllables. Solfège (a system of solmization syllables) are another method of naming notes in a major scale. The syllables do , re , mi , fa , sol , la , and ti can be applied to the first seven notes of any major scale; these are analogous to the scale degrees [latex]\hat{1}[/latex], [latex]\hat{2}[/latex], [latex]\hat{3}[/latex], [latex]\hat{4}[/latex], [latex]\hat{5}[/latex], [latex]\hat{6}[/latex], and [latex]\hat{7}[/latex]. The last note is do ([latex]\hat{1}[/latex]) because it is a repetition of the first note. Because do ([latex]\hat{1}[/latex]) changes depending on what the first note of a major scale is, this method of solfège is called movable do . This is in contrast to a fixed do solmization system, in which do ([latex]\hat{1}[/latex]) is always the pitch class C.

Each note of a major scale is also named with scale-degree names : tonic, supertonic, mediant, subdominant, dominant, submediant, leading tone, and then tonic again. Example 4 shows how these names align with the scale-degree number and solfège systems described above.

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Example 4. Scale-degree numbers, solfège syllables, and scale-degree names.

Example 5 shows these scale-degree names applied to an A♭ major scale:

https://musescore.com/user/32728834/scores/8452340/embed Example 5. An A♭ major scale with scale-degree names.

Example 6 shows the notes and scale-degree names of the A♭ major scale in an order that shows how the names of the scale degrees were derived. The curved lines above the staff show the intervallic distance between each scale degree and the tonic.

The word dominant is inherited from medieval music theory, and refers to the importance of the fifth above the tonic in diatonic music.
The word mediant means “middle,” and refers to the fact that the mediant is in the middle of the tonic and dominant pitches.
The Latin prefix super means “above,” so the supertonic is a second above the tonic. This is the only “super-” interval.
The Latin prefix sub means “below”; the subtonic, submediant, and subdominant are the inverted versions (i.e., below the tonic) of the supertonic, mediant, and dominant respectively. (Note that in this text, we prefer the term leading tone instead of “subtonic” when referring to the scale-degree that is a half step below tonic, so named because it is often thought of as “leading” toward the tonic.)

Lines show that a fifth relates D♭–A♭ and A♭–E♭; a third relates F–A♭ and A♭–C, and a second relates G–A♭ and A♭–B♭.

Key Signatures

A key signature, consisting of either sharps or flats , appears at the beginning of a composition, after a clef but before a time signature. You can remember this order because it is alphabetical: clef, key, time. Example 7 shows a key signature in between a bass clef and a time signature.

A bass clef is shown on a staff, followed by a three-flat key signature, and a 4/4 time signature.

Key signatures collect the accidentals in a scale and place them at the beginning of a composition so that it is easier to keep track of which notes have accidentals applied to them. In Example 7 , there are flats on the lines and spaces that indicate the notes B, E, and A (reading left to right). Therefore, every B, E, and A in a composition with this key signature will be flat, regardless of octave. In Example 8 both of these Bs will be flat because B♭ is in the key signature.

Flat key signatures have a specific order in which flats are added, and the same is true of the sharps in sharp key signatures. These orders apply regardless of clef. Example 9 shows the order of sharps and flats in all four clefs that we have learned:

The order of sharps and flats in treble, bass, alto, and tenor clefs.

The order of sharps is always F, C, G, D, A, E, B. This can be remembered with the mnemonic “Fat Cats Go Down Alleys (to) Eat Birds.” The sharps form a zig-zag pattern, alternating going down and up. In the treble, bass, and alto clefs, this pattern “breaks” after D♯ and then resumes. In the tenor clef, there is no break, but F♯ and G♯ appear in the lower octave instead of the upper octave.

The order of the flats is the opposite of the order of the sharps: B, E, A, D, G, C, F. This makes the order of flats and sharps palindromes. The order of flats can be remembered with this mnemonic: “Birds Eat And Dive Going Copiously Far.” The flats always make a perfect zig-zag pattern, alternating going up and down, regardless of clef, as seen in Example 9 .

There are easy ways to remember which key signature belongs to which major scale. In sharp key signatures, the last sharp is a half step below the tonic (the first note of a scale). Example 10 shows three sharp key signatures in different clefs. Here’s how to identify each with this method:

1. A one-sharp key signature in treble clef, 2. a three-sharp key signature in bass clef, and 3. a six-sharp key signature in Alto Clef

The last sharp (in this case the only sharp), F♯, is a half step below the note G. Therefore, this is the key signature of G major.
The last sharp, G♯, is a half step below the note A. Therefore, this is the key signature of A major.
The last sharp, E♯, is a half step below the note F♯. Therefore, this is the key signature of F♯ major.

In flat key signatures, the second-to-last flat is the tonic (the first note of a scale). Example 11 shows three flat key signatures in different clefs. Here’s how to identify each with this method:

1. A two-flat key signature after a bass clef, 2. a four-flat key signature after a treble clef, and 3. a six-flat key signature after a tenor clef.

The second-to-last flat in this key signature is B♭. Therefore, this is the key signature of B♭ major.
The second-to-last flat is A♭. Therefore, this is the key signature of A♭ major.
The second-to-last flat is G♭. Therefore, this is the key signature of G♭ major.

A treble clef is shown with a blank key signature, and a one-flat key signature is shown after a bass clef.

There are two key signatures that have no “tricks” that you will simply have to memorize. These are C major, which has nothing in its key signature (no sharps or flats), and F major, which has one flat: B♭ ( Example 12 ).

Example 13 shows the key signature for C major (no sharps or flats) followed by all of the sharp key signatures in order in all four clefs: G, D, A, E, B, F♯, and C♯ major.

Example 13. The key signatures of C, G, D, A, E, B, F♯, and C♯ in all four clefs.

Example 14 first shows the key signature for C major (no sharps or flats), then all of the flat key signatures in order in all four clefs: F, B♭, E♭, A♭, D♭, G♭, and C♭ major.

All of the flat key signatures, first in treble, bass, alto, and tenor clefs.

Example 14 first shows the key signature of C major (with no sharps or flats), and then the key signatures of F, B♭, E♭, A♭, D♭, G♭, and C♭ in all four clefs.

There is one other “trick” that might make memorization of the key signatures easier: C major is the key signature with no sharps or flats, C♭ major is the key signature with every note flat (7 flats total), and C♯ major is the key signature with every note sharp (7 sharps total).

Major keys are said to be “real” if they correspond to one of the key signatures in Examples 13 or 14 . If a double sharp or double flat would be needed for a key signature, then that key signature would be “imaginary.” Occasionally, you may encounter music in an imaginary key. Example 15 shows an F♭ major scale; an F♭ major key signature is imaginary because it would need a B𝄫.

https://musescore.com/user/32728834/scores/6817049/embed

Example 15. An F♭ major scale in treble clef.

The Circle of Fifths

The circle of fifths is a convenient visual. In the circle of fifths, all of the major key signatures are placed on a circle in order of number of accidentals. The circle of fifths is so named because each key signature is a fifth away from the ones on either side of it. Example 16 shows the circle of fifths for major key signatures:

Major key signatures are placed around a circle in order of the number of their accidentals

If you start at the top of the circle (12 o’clock), the key signature of C major appears, which has no sharps or flats. If you continue clockwise, sharp key signatures appear, each subsequent key signature adding one more sharp. If you continue counter-clockwise from C major, flat key signatures appear, each subsequent key signature adding one more flat. The bottom three key signatures (at 7, 6, and 5 o’clock) in Example 16 are enharmonically equivalent . For example, the B major and C♭ major scales have different key signatures—five sharps and seven flats, respectively—but they sound the same because the notes B and C♭ are enharmonically equivalent.

Major Scales Tutorial (musictheory.net)
Major Scales (Practical Chords and Harmonies)
Major Scales (YouTube)
Scale Degree Names (musictheoryfundamentals.com)
Scale Degree Names (musictheory.net)
Solfège History and Tutorial (Earlham College)
Scale Degrees, Solfège, and Scale-degree Names (YouTube)
Major Key Signatures (musictheory.net)
Sharp Key Signatures (YouTube)
Flat Key Signatures (YouTube)
Major Key Signature Flashcards (music-theory-practice.com)
The Circle of Fifths (YouTube)
The Circle of Fifths (Classic FM)
Writing Major Scales ( .pdf ), from Tonic and Other Scale Degrees ( .pdf )
Writing Major Key Signatures ( .pdf )
Identifying Major Key Signatures ( .pdf )
Major Keys Worksheets for Children ( .pdf )
Scale Degrees or Solfège ( .pdf , .pdf )
Writing Major Scales ( .pdf , .mscx )
Key Signatures: Major ( .pdf , .mscx )

An ordered collection of half steps and whole steps.

The relative position of a note within a diatonic scale. Indicated with a number, 1–7, that indicates this position relative to the tonic of that scale.

A system that pairs each note of a scale with a particular syllable.

The numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

A symbol akin to an angled bracket, placed above Arabic numerals to indicate scale degrees; a circumflex symbol.

The application of solmization syllables (do, re, mi, fa, sol, etc.) to scale degrees.

A movable system of names for scale degrees based on their function within the scale, such as tonic (do, 1̂) and dominant (sol, 5̂).

Raises a note by a half step.

Lowers a note by a half step.

An ordered collection of half steps (H) and whole steps (W) as follows (ascending): W–W–H–W–W–W–H.

An interval of twelve half steps between two notes with the same letter name. The frequencies of two notes related by octave form a 2:1 ratio. Abbreviated “8ve.”

A system of solfège in which do is the first scale degree in a scale; this is in contrast to fixed do, where do is always the pitch class C.

A system of solfège in which do is always the pitch class C, re the pitch class D, etc., regardless of scale.

1. A scale, mode, or collection that follows the pattern of whole and half steps W–W–H–W–W–W–H, or any rotation of that pattern. 2. Belonging to the local key (as opposed to "chromatic").

A 7̂ that is one half step below 1̂. The leading tone is diatonic in major keys, but requires an accidental in minor keys.

Raises a note by two half steps.

Lowers a note by two half steps.

A relationship between notes, intervals, or chords that sound the same but are spelled differently.

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I. Fundamentals

8. Major Keys and Key Signatures

8.1 introduction.

In tonal Western art music, when a piece tends primarily to use the pitches of a single major or minor scale, it is said to be in that major or minor key. Such pieces typically have groups of sharps or flats called key signatures . The following example has a D b -major key signature (five flats). It appears just after each clef on each staff:

These key signatures provide a convenient alternative to writing out all of the necessary accidentals for a given key. Instead of writing a b before every B, E, A, D, and G (as necessitated by the D b -major scale), the key signature instructs the performer that every B, E, A, D, and G on the staff are to be lowered a semitone unless otherwise noted. Compare Example 8–1 with the following, which writes out the required accidentals instead of using a key signature. Notice how much more cluttered the score appears:

In this chapter, we will discuss how a key is established using the pitches of a major scale, how to determine a major key from a given key signature, and how to write key signatures on bass and treble clefs. We will also look at relationships between major scales and how to organize them with regards to one another.

8.2 Major keys

Chapter 6 discusses the role of the tonic (the keynote) as the most prominent note of a major scale. When a piece is in a major key it takes the pitches from that major scale and gives the tonic a position of primary importance. The remaining scale degrees are treated according to a hierarchy relative to the tonic.

Consider the following melody:

As you can see, this melody uses the pitches C, D, E, F, G, and A. All of these pitches belong to the C major scale (C, D, E, F, G, A, and B). This is a very good indication that this melody is in the key of C major. But all of these pitches also belong to the F major scale (F, G, A , B b , C, D, and E). To determine the key of this melody—C major or F major—we need to decide which note sounds most like the tonic. Listen to the melody again and consider which pitch, C or F, sounds more stable—in other words, which pitch sounds more restful, more like a musical destination and less like an attraction along the way.

It is likely that you heard the pitch C as having greater stability. Simply looking at the melody, we can see that C occupies a more stable position than the pitch class F. The excerpt begins and ends on C, and C holds a prominent position at the end of m. 2 and the beginning of m. 5. Whenever F appears, on the other hand, it is given a shorter note-value, and is always within a descending stepwise passage toward C. Because the pitch class C is the most stable-sounding pitch in the melody, Example 8–3 is in the key of C major.

The melody from Example 8–3 can be written in any major key. The following example transposes it (rewrites it at a different pitch level) to E major by raising each note up two whole steps, putting E in the most stable position. The melody sounds the same, only higher:

Activity 8–1

Identify the key of each of the following melodies by considering which scale is represented by the present pitches and by looking for points of stability that might be the tonic note.

Exercise 8–1a:

In what key is the following melody?

Look for stable pitches that might be the tonic.

Exercise 8–1b:

Exercise 8–1c:.

Look for stable pitches that might be the tonic. (Note that the melody might not begin on the tonic!)

Exercise 8–1d:

Exercise 8–1e:, exercise 8–1f:, 8.3 key signatures.

Each major scale contains a distinct set of seven pitch classes. (Again, see Chapter 6 for a lengthier discussion of the major scale.) One major scale may share as many as six pitches with another, as we saw in Example 8–3, but not all. (Two major scales that share seven pitch classes in common are considered to be the same scale.) Since each major scale is unique in this way, a piece in a major key will draw from the same pitches as its corresponding major scale. These sharps and flats used in the corresponding major scale are usually written at the beginning of each line in a key signature .

The key signature is a collection of sharps or flats that indicates which notes should be raised or lowered so that they belong to the key. In C major, there are no sharps or flats in the key signature, just as there are no sharps or flats in the C major scale. In keys other than C major, the key signature is written to the right of the clef, just before the time signature, at the beginning of each line of music. In Example 8–4 we transposed “Ah! vous dirai-je, maman” (“Twinkle, Twinkle, Little Star”) to the key of E major. The following example shows the same melody in E major but here makes use of a key signature instead of writing out all the accidentals:

a. without key signature

b. with key signature

E major has four sharps (F # , C # , G # , and D # ), all of which appear in the key signature. (Even though D # is not used in this melody, the accidental is left in the key signature. Doing so makes it clear that this excerpt is in E major.) Sharps or flats in the key signature affect more than just the notes whose line or space they share:

The first sharp of the key signature in Example 8–6 (centered on the top line of the staff) applies to the note on the same line, making it F # . Likewise, the second sharp of the key signature (centered on the third space on the staff) applies to the note on the same space, making it C # . The accidentals appearing in the key signature apply to every instance of that pitch class. The F and C in the second half of Example 8–6 are both sharp even though the key signature does not include an accidental on their respective space and line.

Note: The sharps in the key signature are centered on the line or space of the note to which they apply. As you will see momentarily, the same is true of key signatures using flats. The head of the flat accidental is centered on the line or space of the note it affects.

Activity 8–2

Identify the major key represented by each of the following key signatures:

Exercise 8–2a:

Which major key does the following key signature represent?

Which major scale has two sharps?

Exercise 8–2b:

Which major scale has two flats?

Exercise 8–2c:

Which major scale has three sharps?

Exercise 8–2d:

Which major scale has three flats?

Pitches specified by the key signature can be canceled out by an accidental next to a note, as in the following example:

This piece is in E b major, which has three flats (B b , E b , and A b ) as specified by the key signature. The natural sign ( § ) next to the A on the last eighth note of the first measure cancels out the A b of the key signature. This canceling out of A b lasts only as long as the measure in which the accidental appears. By the second measure, all As should again be flatted according to the key signature.

Note: You will frequently come across accidentals that may seem unnecessary. The flat next to the A on the fourth beat of m. 2, for instance, seems superfluous, given the A b in the key signature. Such accidentals are referred to as courtesy accidentals . They occur after a previous accidental altered a given pitch (in this case, the A § at the end of the first measure) to remind the performer that a scale degree has gone back to normal as specified by the key signature. Courtesy accidentals are sometimes placed in parentheses, although you will see that this practice is far from consistent as you go from one score, composer, or publisher to the next.

8.4 Writing key signatures

In Chapter 6 we discussed how one octave of a major scale can be divided into two tetrachords, an upper and a lower, each of which follows the same a W-W-H step pattern. In C major, for example, the lower tetrachord would be (C, D, E, F) and the upper (G, A, B, C). Since the pattern of whole steps and half steps is identical in each major tetrachord, they can both be used interchangeably as either the upper or lower tetrachord of a major scale. The upper tetrachord of a C-major scale (G, A, B, C) could, for example, also serve as the lower tetrachord of a G-major scale:

Notice how similar these two scales are. They have six pitch classes in common (G, A, B, C, D, and E), differing in only one note: C major has F, while G major has F # . Scales like these that share six out of their seven pitch classes are referred to as closely-related . Their key signatures, therefore, will differ by only one accidental. (C major has no sharps, G major has one sharp.)

The following example shows the key signatures for C and G major, and takes the process one step further, using the upper tetrachord of G major (D, E, F # , G) as the lower tetrachord of D-major. Each subsequent scale, in other words, begins on the fifth degree of the scale before it (as shown by the arrows):

a. sharp key signatures

b. sharp key scales

We can see a pattern beginning to emerge. G major is built on scale degree [latex]\hat5[/latex] of C major and has one sharp (F # ). D major is built on scale degree [latex]\hat5[/latex] of G major and has two sharps (F # and C # ). We could continue the pattern by building a major scale on scale degree [latex]\hat5[/latex] of D major (A) and would arrive at A major, which has three sharps (F # , C # , and G # ). And so on…

The following example shows all of the sharp key signatures up through seven sharps—from C major, in which none of the notes require an accidental, to C # major, in which every note is sharped:

The sharps or flats in a key signature must be written in a particular order and position on the staff. Notice how none of the sharps are written on ledger lines and that the key signatures are adjusted depending on which clef is assigned to the staff. It is important that you memorize not only the order in which particular sharps are added to the key signature (F # , C # , G # , D # , A # , E # , B # ), but also the pattern in which they are added on the staff.

Note: You may find it helpful to come up with mnemonic devices to help remember these patterns. The order of sharps as they are added to a key signature, for example, can be remembered by the sentence: “ F at C ats G o D own A lleys E ating B irds.”

There is also a useful, quite easy trick for determining the tonic of a sharp key. In every sharp key, the right-most accidental of the key signature is the leading tone of the key. Say the key signature has five sharps: F # , C # , G # , D # , A # . A # is the leading tone for the B major scale. Therefore, the key is B major.

Activity 8–3

Write out each of the following sharp key signatures on the staff provided. Be sure to write each sharp on the appropriate line and in the correct order.

Exercise 8–3a:

Write out a G-major key signature:

G major has one sharp.

Exercise 8–3b:

Write out an F # -major key signature:

F # major has six sharps.

Exercise 8–3c:

Write out a D-major key signature:

D major has two sharps.

Exercise 8–3d:

Write out an E-major key signature:

E major has four sharps.

Flat key signatures can be determined similarly, though here, the lower tetrachord of each scale becomes the upper tetrachord of the next closely-related key. Instead of going up four steps from the tonic to begin each subsequent key on scale degree [latex]\hat5[/latex] , we must go down four steps from the tonic and start on scale degree [latex]\hat4[/latex] . F major, for example, begins on scale degree [latex]\hat4[/latex] of C major and has one flat (B b ). B b major begins on scale degree [latex]\hat4[/latex] of F major and has two flats (B b and E b ). If we were to continue, the next key would be E b major which would have three flats (B b , E b , and A b ). And so on…

a. flat key signatures

b. flat key scales

The following example shows all of the flat key signatures up to seven flats:

Again, it is essential that you remember the order in which flats are added to key signatures and the pattern in which they are notated on the staff.

Note: The order of flats as they are added to a key signature can be reversing the mnemonic for sharp keys: “ B efore E ating A D onut, G et C offee F irst.”

The second to last accidental in a flat key signature will tell you the key. E b major, for example, has three flats: B b , E b , and A b . The second to last (E b ) is the tonic of the key!

Activity 8–4

Write out each of the following flat key signatures. Be sure to write each flat on the appropriate line and in the correct order.

Exercise 8–4a:

Write out an A b -major key signature:

A b major has four flats.

Exercise 8–4b:

Write out an F-major key signature:

F major has one flat.

Exercise 8–4c:

Write out a D b -major key signature:

D b major has five flats.

Exercise 8–4d:

Write out an E b -major key signature:

E b major has three flats.

Although treble and bass clefs are the most commonly encountered, it is also helpful to be able to write and recognize key signatures written next to other clefs. The following example shows where each sharp and flat would be written in a key signature next to treble, bass, alto, and tenor clefs. For key signatures requiring less than seven sharps or flats, simply follow the pattern as far as needed:

Notice that, for the most part, the placement pattern of sharps and flats remains the same, regardless of the clef. The symbols are simply moved up or down to match the arrangement of pitch letter names on the lines and spaces of the staff as indicated by the clef. The only exception is the set of sharp key signatures written beside a tenor clef (the last key signature on the first line). Here a small adjustment is made: the first and third sharps are shifted down an octave to avoid using ledger lines in the key signature.

As we saw in Example 8–10 and Example 8–12, we typically divide keys into two categories: “sharp keys” (those whose key signatures consist of sharps) and “flat keys” (those whose key signatures consist of flats). In tonal music, you will never see a key signature with a mixture of sharps and flats. You may, however, encounter natural signs in a key signature when the accidentals of a previous key signature must be canceled out as in the following excerpt where the key changes to E major in m. 17:

8.5 Summary

A piece that draws primarily from the pitches of a single major scale is said to be in that major key. Within a key, pitch classes are organized hierarchically—primarily around the tonic which is heard as the most stable and grounding degree of the scale. A piece in G major, for example, will use pitch classes from the G major scale but will treat the pitch class G as the most conclusive sounding resting point. Other scale degrees will be treated accordingly, relative to the tonic.

A key signature is a symbol—a collection of sharps or flats—that indicates the key of a particular piece or passage. Key signatures are written just to the right of the clef and appear at the beginning of each line of music. A sharp or flat indicated by the key signature applies to every instance of that pitch-letter name, not just those on the line or space on which it is written. They remain in effect throughout the entire piece unless they are canceled out by an accidental or a new key signature. Key signatures are always written in a particular pattern on the staff and must be adjusted to match the clef.

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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.

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.
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.

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.

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

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.

Practice 4.2B

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.

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.

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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:

whole – whole – half :: whole :: whole – whole – half
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.

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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

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.

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.

Practice 4.3B

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.

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 mediant is halfway between the tonic ascending to the dominant.
The submediant is halfway between the tonic descending to the subdominant.
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.

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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.

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.

The second note in Example 4.4.6B is [latex]\hat7[/latex], and not [latex]\hat2[/latex].
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

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.

Which note is the tonic?
Which note is the dominant?
Which note is [latex]\hat6[/latex]?
Which note is [latex]\hat2[/latex]?
What scale degree number is B?
What scale degree number is E-sharp?
Why is [latex]\hat4[/latex] called the subdominant?
Why is [latex]\hat7[/latex] called the leading tone?
Why is [latex]\hat3[/latex] called the mediant?
Why is [latex]\hat2[/latex] called the supertonic?

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.

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

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.

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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.
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.
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.

The third note is B (not B-flat) because the flat on the previous note only applied to B-flat 4 .
The note after the bar line is B (not B-flat) because even though it is B-flat 4 , the bar line cancels previous accidentals.
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.
The previous bar line canceled the previous natural sign.
The C is in another octave (C 5 instead of C 4 ).

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

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.

Practice 4.5B

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.

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 B 4 in the treble clef and B 2 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-flat 5 , is written incorrectly at E-flat 4 .
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.
In other words, all keys with flats have “flat” in their names except for F major.
Treble clef begins on B-flat 4 and the pattern is up–down.
Bass clef begins on B-flat 2 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

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.

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.
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:

Yes, Example 4.6.4 sounds like it is in major.
The key signature has two flats, which is the key of B-flat major.
The first lowest note is B-flat.
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

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.

Practice 4.6C

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.

Practice 4.6D

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.

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 F 5 in the treble clef and F 3 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.
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.
In other words, none of the keys with sharps have “sharp” in their names except for F-sharp major and C-sharp major.
The treble clef begins on F-sharp 5 and the bass clef begins on F-sharp 3 .
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

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.

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.
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.

Yes, Example 4.7.4 sounds like it is in major.
The key signature has two sharps, which is the key of D major.
The first lowest note is A.
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

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.

Practice 4.7C

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.

Practice 4.7D

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.

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.

e.g., F and F-sharp or D-flat and D
e.g., 1 flat + 6 sharps or 5 flats + 2 sharps
C = 0; C-flat = 7 flats; C-sharp = 7 sharps
F is the only flat key without “flat” in its name.

Practice 4.7E

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.

Practice 4.7F

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.

Practice 4.7G

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.

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.

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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.
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.

A fifth above E is B.
E major has 4 sharps and B major has 5 sharps.
C (no sharps, no flats) moves clockwise to C-sharp major (7 sharps).
A fifth below E-flat is 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

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.

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.

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Example 4.9.1A: First figure out the key the original melody is in and write scale degree numbers above.
Write the clef and key signature of the new key. Rewrite the same scale degree numbers as the original melody above the blank staff.
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.

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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.

The original melody is in C major.
Scale degree numbers are shown above the melody.
The melody reappears at measure 42. However, this time it is in F 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

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.
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.

A major tetrachord consists of three diatonic steps: whole – whole – half. [4.1]
A major scale is made of two major tetrachords joined by a diatonic whole step: whole – whole – half :: whole :: whole – whole – half. [4.2, 4.3]
[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
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. [4.5]
The penultimate flat in the key signature is the key.
The exception is F major, which has one flat.
The last sharp in the key signature is the leading tone of the key.
Moving clockwise, the key ascends by five and adds a sharp.
Moving counterclockwise, the key descends by five and adds a flat.
Melodic transposition is the act of rewriting a melody in a different key. [4.9]
circle of fifths
diatonic scale
enharmonically equivalent keys
key signature
major scale
major tetrachord
melodic contour
melodic transposition
tonic ([latex]\hat1[/latex])
supertonic ([latex]\hat2[/latex])
mediant ([latex]\hat3[/latex])
subdominant ([latex]\hat4[/latex])
dominant ([latex]\hat5[/latex])
submediant ([latex]\hat6[/latex])
leading tone ([latex]\hat7[/latex])
scale degree number
tonal center
Anne-Marie Krumpholtz (1766-1813) was a French composer and harpist. ↵
Louise Farrenc (1804-1875) was a French composer. ↵
Ludwig van Beethoven (1770-1827) was a German composer. ↵
Stephen C. Foster (1826-1864) was an American composer known as “The Father of American Music.” ↵
In later chapters, we will use solfège periodically to clarify ambiguous scale degree numbers. ↵
Wolfgang Amadeus Mozart (1756-1791) was an Austrian composer. ↵
Richard Wagner (1813-1883) was a German composer. ↵
Not all tempo markings are in Italian. Wagner chooses German for the tempo marking. Mässig bewegt means "moderately moving." ↵
Hanriëtte Bosmans (1895-1952) was a Dutch composer and pianist. ↵
Maria Szymanowska (1789-1831) was a Polish composer and pianist. ↵
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. ↵
Helena Munktell (1852-1919) was a Swedish composer. ↵

Scale that uses every letter name once and only once.

Collection of four notes.

When notes are sounded one at a time.

Four notes with the pattern whole - whole - half.

Scale with the pattern WWHWWWH. Major keys are based on their major scales.

Arabic numeral with a caret above it that says which member of a scale a note is.

Names of members of a scale ( or names of scale degree numbers).

^1. This is considered the "home." Scales begin and end with tonic.

^2. "Above tonic."

^3. Halfway between tonic (^1) and dominant (^5).

^4. Five below tonic.

^5. Five above tonic.

^6. Halfway between the tonic descending to the subdominant.

^7. Diatonic half step below tonic and "leads" to tonic.

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.

Tells us the collection of pitches used based on a center pitch. The major mode and minor mode are the most common modes.

Mode that is often associated with happy music; based on the major scale.

Mode that is often associated with sad music; based on the natural minor scale.

Tonal center and mode combined, such as C major.

Group of flats or sharps located at the start of every system that says what the key may be.

Graphic representation of how all the major and minor keys are built by moving up or down by fifths. Each key either gains a sharp (clockwise) or gains a flat (counterclockwise).

Keys that share the same pattern of white and black keys on the piano, but are spelled differently (e.g., G-flat and F-sharp major).

Changing all pitches by the same proportion; when you write or perform the same melody in a different key.

The direction the melody ascends or descends.

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I. Fundamentals

Minor Scales, Scale Degrees, and Key Signatures

Chelsey Hamm and Bryn Hughes

Key Takeaways

A minor scale's third note is always a half step lower than the third note of the major scale with the same name.
There are three variations on the minor scale: natural minor , harmonic minor , and melodic minor .
Natural minor: W‑H‑W‑W‑H‑W‑W (ascending)
Harmonic minor: W‑H‑W‑W‑H‑3Hs‑H (ascending)
Melodic minor: W‑H‑W‑W‑W‑W‑H (ascending) and W‑W‑H‑W‑W‑H‑W (descending).
While there are three minor scales, minor keys and minor key signatures are always identified as simply “minor” (“A minor,” “D minor,” etc.) and are based on the natural minor scale.
Scale degrees in minor are the same as those in major. There are a few new solfège syllables in minor including me ([latex]\downarrow\hat3[/latex]), le ([latex]\downarrow\hat6[/latex]), and te ([latex]\downarrow\hat7[/latex]).
Each note of a minor scale is also named with scale-degree names . These are largely the same in minor as they are in major, except for the subtonic ( te or [latex]\downarrow\hat7[/latex]).
Major and minor keys share two different relationships. The parallel relationship is when a major and minor key share a tonic note, while the relative relationship is when a major and minor key share a key signature.
Each major key signature has a corresponding relative minor key signature whose tonic is three half steps below the relative major’s tonic. The orders of sharps and flats in major and minor key signatures are the same.

Chapter Playlist

The Minor Scale

A minor scale's third note is always a half step lower than the third note of the major scale with the same name (e.g., B major and B minor). There are three different types of minor scales: natural minor , harmonic minor , and melodic minor . These three types of minor scales should be thought of like flavors of ice cream; ice cream is still ice cream regardless of whether it is chocolate, vanilla, strawberry, etc. Likewise, a work is simply “minor” or “in minor”; musicians do not consider music to be “in” a specific type of minor scale (i.e., natural, harmonic, or melodic). In other words, while there are three minor scales, minor keys and minor key signatures are always identified as simply “minor” (“A minor,” “D minor,” etc.) and are based on the natural minor scale.

The three different types of minor scales are useful categories primarily for instrumental performers. Learning to play the different types of minor scales on instruments allows performers to become familiar with the minor patterns most commonly used in Western classical music. Just like major scales, minor scales are named for their first note (including the accidental, if any), which is also their last note.

Natural Minor

The natural minor form of the minor scale consists of an ordered collection of half and whole steps with the ascending succession W‑H‑W‑W‑H‑W‑W, as shown in Example 1 . Each whole step is labeled with a square bracket and “W,” and each half step is labeled with an angled bracket and “H.” Listen carefully to Example 1 and notice that the half and whole step pattern of the natural minor form of the minor scale is the same ascending and descending.

Example 1. A G natural minor scale. (Sounding scale is F natural minor.)

Harmonic Minor

The harmonic minor form of the minor scale consists of an ordered collection of half and whole steps in the ascending succession W‑H‑W‑W‑H‑3Hs‑H (“3Hs” = 3 half steps), as shown in Example 2 . The curved bracket represents a distance of three half steps (or a whole step plus a half step). Listen carefully to Example 2 and notice that the half and whole step pattern of the harmonic minor form of the minor scale is the same ascending and descending.

Example 2. A G harmonic minor scale. (Sounding scale is F harmonic minor.)

Melodic Minor

The melodic minor form of the minor scale consists of an ordered collection of half and whole steps in the ascending succession W‑H‑W‑W‑W‑W‑H and the descending succession W‑W‑H‑W‑W‑H‑W, as shown in Example 3 . When you listen to Example 3 , notice that the melodic minor form has different ascending and descending patterns: the ascending pattern is unique to the melodic minor form, while the descending pattern is the same as the natural form.

Example 3. A G melodic minor scale. (Sounding scale is F melodic minor.)

Example 4 shows four versions of a C scale— major , natural minor , harmonic minor , and melodic minor—with the scale degrees indicated. Listen to this example carefully, noting the aural differences between the scales.

Minor Scale Degrees, Solfège, and Scale-Degree Names

Minor scale degrees , solfège , and scale-degree names are similar to, but not exactly the same as, their major-scale counterparts. Example 5 summarizes the three types of minor scale, and shows the scale degrees and solfège for each. Note that the scale degrees are the same as in a major scale. The bottom line shows the solfège syllables, which differ from the major-scale syllables in several places to reflect the minor scale’s pattern of whole and half steps.

Example 5. Scale degrees and solfege for all three types of minor scales: a) natural minor; b) harmonic minor, and c) melodic minor.

In natural minor ( Example 5a ), mi ([latex]\hat{3}[/latex]) becomes me ([latex]\downarrow\hat3[/latex]) (pronounced “may”), la ([latex]\hat{6}[/latex]) becomes le ([latex]\downarrow\hat6[/latex]) (pronounced “lay”), and ti ([latex]\hat{7}[/latex]) becomes te ([latex]\downarrow\hat7[/latex]) (pronounced “tay”). If you sing or play through the above example, you’ll notice that the ending lacks the same sense of closure you heard in the major scale. In the major scale, this closure is created in part by the ascending semitone between ti ([latex]\hat{7}[/latex]) and do ([latex]\hat{1}[/latex]).

In harmonic minor ( Example 5b ) , mi ([latex]\hat{3}[/latex]) becomes me ([latex]\downarrow\hat3[/latex]) and la ([latex]\hat{6}[/latex]) becomes le ([latex]\downarrow\hat6[/latex]). Having ti ([latex]\hat{7}[/latex]) creates the sense of closure that is absent in the natural minor scale.

As noted above, the melodic minor scale has different ascending and descending patterns ( Example 5c ) . In the ascending form of melodic minor, mi ([latex]\hat{3}[/latex]) becomes me ([latex]\downarrow\hat3[/latex]), but the rest of the solfège syllables are the same as in major. In the descending form of melodic minor, mi ([latex]\hat{3}[/latex]) becomes me ([latex]\downarrow\hat3[/latex]), la ([latex]\hat{6}[/latex]) becomes le ([latex]\downarrow\hat6[/latex]), and ti ([latex]\hat{7}[/latex]) becomes te ([latex]\downarrow\hat7[/latex]), like natural minor. Therefore, the ascending version of melodic minor has the sense of closure associated with the major scale, while the descending version follows the pattern of the natural minor scale.

As in major scales, each note of a minor scale is also named with scale-degree names . Example 6 shows the scale-degree names used in minor scales alongside the corresponding scale-degree numbers and solfège syllables.

Scale Degree Number	Solfège	Scale Degree Names
[latex]\hat1[/latex]		Tonic
[latex]\hat2[/latex]		Supertonic
[latex]\downarrow\hat3[/latex]		Mediant
[latex]\hat4[/latex]		Subdominant
[latex]\hat5[/latex]		Dominant
[latex]\downarrow\hat6[/latex]		Submediant
[latex]\downarrow\hat7[/latex]		Subtonic
[latex]\hat7[/latex]		Leading Tone

Example 6. Scale-degree names in minor scales.

As the chapter on major scales discussed, the Latin prefix sub means “under”—the submediant is a third below the tonic, and the subdominant is a fifth below. To this, we can now add one new scale degree name: the subtonic, for lowered [latex]\downarrow\hat7[/latex]. The supertonic is one whole step above the tonic, while the subtonic is one whole step below the tonic.

Example 7 shows a B melodic minor scale, ascending and descending, with scale-degree names labeled. As you can see, the melodic minor scale utilizes the leading tone in its ascending form, and the subtonic in its descending form.

A B melodic minor scale, ascending and descending in bass clef, with half and whole steps labeled as well as scale-degree names.

Example 8 is a helpful visual for learning about the three forms of the minor scale. The order reflects the number of lowered scale degrees (compared to a major scale starting on the same note).

Form of Minor Scale	Lowered Scale Degrees
Natural	[latex]\downarrow\hat{3},\downarrow\hat{6}, \downarrow\hat{7}[/latex]
Harmonic	[latex]\downarrow\hat{3},\downarrow\hat{6}[/latex]
Melodic (ascending)	[latex]\downarrow\hat{3}[/latex]

Example 8. Lowered scale degrees of minor.

As you can see, natural minor scales have three lowered scale degrees, harmonic minor scales have two, and melodic minor scales have one in the ascending version. Remember, the descending version of melodic minor is the same as natural minor, with three lowered scale degrees.

The Parallel and Relative Relationships

When comparing major and minor keys, there are two relationships that are important. The parallel relationship is when a major key shares a tonic (do, [latex]\hat{1}[/latex]) with a minor key. For example, C major and C minor (or A♭ major and A♭ minor, or F♯ major and F♯ minor) are parallel keys. We use the terms “parallel minor” and “parallel major” to describe this relationship: C major is the parallel major of C minor, and C minor is the parallel minor of C major.

The relative relationship is when a major key shares a key signature with a minor key. For example, C major does not have any sharps or flats in its key signature, and neither does A minor. We use the terms “relative minor” and “relative major” to describe this relationship: C major is the relative major of A minor, and A minor is the relative minor of C major. The tonic of a minor key is always three half steps below the tonic of its relative major: if you count three half steps below C, you will get A (C–B, B–B♭, B♭–A). Likewise, to find the relative major key of a given minor key, count three half steps up.

When counting half steps to determine the relative major or minor of a given key, keep in mind that relative keys have the same key signature. A sharp key cannot share a relative relationship with a flat key (and vice versa), which means you need to select the correct enharmonic key. For example, although the pitch three half steps down from D♭ could be written as either B♭ or A♯, only B♭ minor (five flats) is the relative minor of D♭ major (also five flats), because A♯ minor has a different key signature (seven sharps).

Minor Key Signatures

Minor key signatures , like major key signatures, go after a clef but before a time signature. Each major key has a corresponding relative minor key signature; therefore, the orders of the sharps and flats are the same in minor key signatures as they are in major key signatures, placed on the same lines and spaces. Example 9 , reproduced from the previous chapter, shows the order of sharps and flats in all four clefs:

The order of the seven sharps and seven flats of key signatures are shown in treble, bass, alto, and tenor clefs.

As previously mentioned, if you know the major key associated with a given key signature, you can go down three half steps from the tonic to find the minor key for that key signature. Example 10 shows all of the sharp minor key signatures in order, and Example 11 depicts all of the flat minor key signatures in order.

Minor keys can also be imaginary (like imaginary major keys) if they contain double accidentals.

You can practice identifying minor key signatures in the following exercise:

Minor Keys and the Circle of Fifths

The circle of fifths can be used as a visual for minor key signatures as well as major key signatures. Each key signature is placed alongside the corresponding major and minor keys. Example 12 shows the circle of fifths for minor and major keys:

keys arranged by fifth: C–G–D–A–E–B–F♯–D♭–A♭–E♭–B♭–F–C (repeating in a circle).

In Example 12 , major keys are in blue uppercase letters around the outside of the circle, while minor keys are in red lowercase letters around the inside of the circle. Once again, key signatures appear in order of their number of accidentals. If you start at the top of the circle (12 o’clock) and continue clockwise, key signatures add sharps, while if you start at the top of the circle and continue counterclockwise, they add flats. The bottom three key signatures can be written in sharps or flats, and so are enharmonic .

Major or Minor?

When you are given a piece of music to play or sing, the notation will often include a key signature, which will help you to narrow down the key of the work to two options: a major key and its relative minor. [1] But how can you tell which one the work is in? One thing that can help is to listen to and look at the first and last notes of the work—pieces often start and end on the tonic, so this can help you determine whether a work is major or minor.

Example 13 shows the first three measures of a song by Louise Reichardt (1779–1826) titled “Durch die bunten Rosenhecken” (“Through the colorful rose hedges”):

This example shows a vocal line (the top staff) and a piano part (the grand staff underneath the vocal part). The key signature contains four flats, which means we can narrow down the key of this work to A♭ major or F minor. In Example 13 , the first note that is circled in the highest part (the vocalist) is is F, as is the first note that is circled in the lowest part (the lowest note played by the piano). Therefore, it is likely that the key of this work is F minor instead of A♭ major.

Minor Scales Tutorial (musictheory.net)
Minor Scales (Practical Chords and Harmonies)
Minor Scales (YouTube)
Scale Degree Names in Major and Minor (musictheory.net)
Minor and Major Key Signatures (musictheory.net)
Minor Key Signatures (YouTube)
Minor Key Signature Flashcards (music-theory-practice.com) (be sure to click “minor” in the menu)
The Circle of Fifths for Minor and Major (YouTube)
The Circle of Fifths (Classic FM)
Natural Minor Scales ( .pdf )
Harmonic Minor Scales ( .pdf )
Melodic Minor Scales ( .pdf )
Writing Minor Scales ( .pdf , .pdf )
Writing Minor Key Signatures ( .pdf)
Writing and Identifying Minor Key Signatures ( .pdf )
Parallel and Relative Minor Questions ( .pdf )
Scale Degree Names and Scale Degrees ( .pdf )
Writing Minor Scales ( .pdf , .mscz ). Asks students to write minor scales. All clefs.
Writing Minor Scales (Treble and Bass Clef) ( .pdf , .mscz ). Asks students to write minor scales. Treble and bass clef only.
Key Signatures: Minor ( .pdf , .mscz ). Asks students to write and identify minor key signatures. All clefs.
Key Signatures: Minor (Treble and Bass Clef) ( .pdf , .mscz ). Asks students to write and identify minor key signatures. Treble and bass clef only.

Media Attributions

Minor Circle of Fifths © Wiki Commons adapted by Bryn Hughes is licensed under a CC BY-SA (Attribution ShareAlike) license
Durch die bunten Rosenhecken © Louise Reichardt is licensed under a CC BY-NC-SA (Attribution NonCommercial ShareAlike) license
The vast majority of Western classical works from 1700–1900 are in either major or minor. But outside of this time period and cultural context, you should also consider if the piece may be in a diatonic mode . This would expand the number of possible tonics indicated by a key signature. ↵

An ordered collection of half steps and whole steps.

An ordered collection of half steps (H) and whole steps (W) with the ascending succession W–H–W–W–H–W–W.

An ordered collection of half and whole steps with the ascending succession W–H–W–W–H–3Hs–H. Like natural minor, but with a raised 7̂.

An ordered collection of half steps (H) and whole steps (W) with the ascending succession W–H–W–W–W–W–H and the descending succession W–W–H–W–W–H–W.

The relative position of a note within a diatonic scale. Indicated with a number, 1–7, that indicates this position relative to the tonic of that scale.

The application of solmization syllables (do, re, mi, fa, sol, etc.) to scale degrees.

A movable system of names for scale degrees based on their function within the scale, such as tonic (do, 1̂) and dominant (sol, 5̂).

When two keys/scales share the same tonic, such as C major and C minor.

When two keys/scales share the same pitches.

In music notation, a collection of sharps or flats written at the beginning of each line (immediately after the clef) to signal that certain notes are always sharp/flat.

An ordered collection of half steps (H) and whole steps (W) as follows (ascending): W–W–H–W–W–W–H.

A relationship between notes, intervals, or chords that sound the same but are spelled differently.

A graphic that shows the relationship between major (and/or minor) key signatures by placing the key signatures around a circle in order of number of accidentals.

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COMMENTS

Chapter 5: Major Scales and Keys Flashcards - Quizlet
key signature. a pattern of sharps or flats (or no sharps or flats) that appears immediately following the clef on a staff, showing which notes, in any octave, are to be sharped or flatted consistently throughout the piece; it helps identify the key of the piece; each one is used for two keys--one major and one minor. major key.
Chapter 5. Key Signatures - G Major Music Theory
key signature is a group of sharps or flats at the beginning of a staff which indicates the notes which are to be played sharp or flat in the following music. See the illustration above.
Major Scales, Scale Degrees, and Key Signatures – Open Music ...
A key signature, consisting of either sharps or flats, appears at the beginning of a composition, after a clef but before a time signature. The order of sharps in key signatures is F, C, G, D, A, E, B, while the order of flats is the opposite: B, E, A, D, G, C, F.
Key signatures Flashcards - Quizlet
Study with Quizlet and memorize flashcards containing terms like G flat major, c major, g major and more.
Major Scales, Scale Degrees, and Key Signatures – CMUS 120 ...
A key signature, consisting of either sharps or flats, appears at the beginning of a composition, after a clef but before a time signature. The order of sharps in key signatures is F, C, G, D, A, E, and B, while the order of flats is the opposite: B, E, A, D, G, C, F.
Major Scales and Key Signatures - University of Puget Sound
Chapter 2 Major Scales and Key Signatures. 2.1 Half Steps and Whole Steps; 2.2 The Major Scale; 2.3 Major Key Signatures; 2.4 Practice Exercises <
8. Major Keys and Key Signatures – Fundamentals, Function ...
In this chapter, we will discuss how a key is established using the pitches of a major scale, how to determine a major key from a given key signature, and how to write key signatures on bass and treble clefs.
Major Scales and Keys – Steps to Music Theory
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.
Minor Scales, Scale Degrees, and Key Signatures
When you are given a piece of music to play or sing, the notation will often include a key signature, which will help you to narrow down the key of the work to two options: a major key and its relative minor. [1]
Answers to Practice Exercises - University of Puget Sound
3 Minor Scales and Key Signatures. 3.1 Minor Scales. 3.2 Minor Key Signatures. 3.3 Scale Degree Names. 3.4 Practice Exercises. ... 14.5.2.2 Reggae. 14.6 The 3–2 Son ...