6.1   Introduction

Listen to “Dingy, Dingy, Little Star” in Example 6.1.

Example 6.1. “Dingy, Dingy, Little Star”

What do you notice about “Dingy, Dingy, Little Star”? How does it compare to “Twinkle, Twinkle, Little Star” in sound and appearance?

• “Dingy, Dingy” sounds gloomy.
• Although the tonal center seems to be C, there are two flats. C major has no sharps or flats.

The fact that the music sounds gloomy and its tonal center does not match its major key signature tells us that this example is in the minor mode. Like the major mode, the minor mode has a specific set of pitches centered around a tonal center. However, unlike the major mode, the pattern of steps that make up the collection differs.

6.2   Natural Minor Scale

The minor mode is built on the natural minor scale  which follows a completely different pattern than the major scale (Example 6.2.1).

• Major scale: whole – whole – half – whole – whole – whole – half
• Natural minor scale: whole – half – whole – whole – half – whole – whole

Example 6.2.1. Scales

Because the pattern differs, the natural minor scale has its own distinct sound. Notice that the scale is called the “natural minor scale,” not just the “minor scale.” This is because there are three different types of minor scales. We will learn about the other two later in this chapter.

You will be asked to write and perform ascending and descending natural minor scales. The instructions are the same for both.

Steps to Writing a Natural Minor Scale

Step one: Write all the notes diatonically. That is, write each note once and only once in ascending or descending order (alternating line–space or space–line). Do not skip any notes, and make sure the first and last notes are the same with the same accidentals (Example 6.2.2).

Example 6.2.2. Step one

Step two: Write in the pattern of whole steps and half steps. Remember that for descending natural minor scales, the pattern must be in reverse order (Example 6.2.3).

Example 6.2.3. Step two

Step three: Add accidentals. Natural minor scales will only include sharps or flats—never both (Example 6.2.4).

Example 6.2.4. Step three

Directions:

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

6.3   Minor Keys

A natural minor scale is not just a way to organize notes alphabetically. Like the major scale, the natural minor scale is a method of understanding the components of a musical key, which combines the tonal center and mode. We learned the following from Chapter 4:

• The tonic is the tonal center.
• The mode tells us the set of pitches used around a tonal center. The most common modes are the major and minor modes.
• The key combines the tonal center and the mode.

We can identify the minor key using its natural minor scale.

Example 6.3.1. Natural minor scales

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

• Example 6.3.1A: If a piece of music centers around G with two flats, it is in the key of G minor. This is because the G natural minor scale contains two flats.
• Example 6.3.1B: If we have a piece of music that centers around G♯G sharp with five sharps, it is in the key of G♯G sharp minor. This is because the G♯G sharp natural minor scale contains five sharps. Although there are six sharps in Example 6.3.1B, there are only five different sharps.

Ideally, you should be able to listen to a musical example and determine whether it is in a major or minor key. Example 6.3.2 and 6.3.3 are two well-known classical works in minor keys.

Example 6.3.2. Minor key: Tchaikovsky,^[1] Swan Lake, Act I, No. 9, Finale

Example 6.3.3. Minor key: Bizet,^[2] L’Arlésienne Suite No. 1, I. Overture

Can you hear that the music in Examples 6.3.2 and 6.3.3 are in minor (i.e., are “sad” or “angry”)? Even though one is slow and quiet while the other is fast and loud, they are both in minor. If you’re not able to identify that they are in minor yet, do not fret. Understanding, writing, and hearing music all require time and practice. We will also learn how you can tell if a piece is in minor without having to listen to it.

Just like in major keys, instead of constantly rewriting accidentals in the score, musicians use key signatures to make writing (and reading) music in minor keys easier. Similar to major keys, we can identify a minor key by its corresponding scale. The following examples show “Dingy, Dingy, Little Star” written with minor key signatures (Example 6.3.4).

Example 6.3.4. “Dingy, Dingy, Little Star” with key signatures

For musicians, seeing the key signature once at the start is much easier than reading many accidentals. Just like in major keys, accidentals in minor key signatures are applied globally.

• Example 6.3.4A: At first glance, one might think the example is in B♭B flat major.
  • However, when we hear the example, it sounds gloomy.
  • The final double bar line tells us that the piece ends on G. When we write out the collection of notes starting and ending on G, we recognize that we are in G minor rather than B♭B flat major.
  • Below the staff, write the minor key using a lowercase ‘g.’
• Example 6.3.4B: Notice that the note letters are the same in Example 6.3.4A and B. However, due to the key signature, Example 6.3.4B is in G♯G sharp minor, not G minor.
  • o Below the staff, you can also write the key with an uppercase letter followed by a lowercase m: G♯G sharpm.

When writing sentences, always spell out the word “minor” and capitalize the name of the key: G minor, not g minor.

6.4   Minor Key Signatures with Flats

Similar to major key signatures, accidentals in minor key signatures must follow a specific order and be placed in precise locations on the staff. Often, students memorize major key signatures but overlook minor key signatures, which puts them at a disadvantage. If you can quickly identify and write all the major and minor key signatures, understanding music theory will become much easier for you.

Key signatures have either flats or sharps, not both. We will start with minor key signatures with flats. Flats in minor key signatures always follow the same order as in major keys.

Fortunately, the placement of flats in a key signature is the same for both major and minor keys. Since there are seven different note names, a key signature can have up to seven flats. The example below shows all the minor key signatures with flats (Example 6.4.1).

Example 6.4.1. Minor key signatures from zero to seven flats

Notice that A minor has zero flats while A♭A flat minor has seven flats. While we could look at the penultimate flat for major keys with flats, there is no simple shortcut for minor keys with flats.

Now we will combine everything we have learned to determine the key of a musical example in minor (Example 6.4.2).

Example 6.4.2. Finding the key: Montgeroult,^[3] Piano Sonata, Op. 5, No. 2, iii – Allegro agitato con fuoco

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

1. Listen to the example: Does it sound like it’s in major (happy) or minor (sad or angry)?
   • Example 6.4.2 seems to be in minor.
2. Look at the key signature.
   • The key signature has four flats, which belongs to the key of F minor.
3. Look at the first lowest note.
   • The first lowest note is F.
4. Look at the last lowest note.
   • The last lowest note is A♭A flat.

The first three steps point to F minor. In this case, relying on the last lowest note was not dependable. However, since three of the four steps led to F minor, the key is F minor. The steps are more reliable when combined.

Relative Keys

In Example 6.4.2, the last lowest note was A♭A flat. Looking at the key signature, we see that the two options with four flats are F minor and A♭A flat major. Luckily, the music sounds like it’s in minor, and the first lowest note is F, so we know the excerpt is in F minor.

When a major key signature and minor key signature are the same, such as A♭A flat major and F minor, those major and minor keys are called relative keys.

• A♭A flat major is the relative major of F minor because both keys have four flats.
• F minor is the relative minor of A♭A flat major because both keys have four flats.

Counting Diatonic Steps to Find the Relative Key

Let’s find the relative major of E♭E flat minor.

1. Count up three diatonic steps (i.e., letter names). Do not worry about accidentals for the first step. Simply count up three letter names.
   • E♭E flat up to F up to G
2. Match the accidentals to figure out the relative major. Is the relative major G major, G♭G flat major, or G♯G sharp major?
   • G major: No, because G major is a key with sharps, and E♭E flat minor has flats.
   • G♭G flat major: Yes.
   • G♯G sharp major: Impossible, because there is no such key as G♯G sharp major.
3. Therefore, the relative major of E♭E flat minor is G♭G flat major. Both keys have six flats.

Let’s try one going the other way: Find the relative minor of E♭E flat major.

1. Count down three diatonic steps (i.e., letter names). Do not worry about accidentals for the first step. Simply count down three letter names.
   • E♭E flat down to D down to C
2. Match the accidentals to figure out the relative minor. Is the relative major C minor, C♭C flat minor, or C♯C sharp minor?
   • C minor: Yes.
   • C♭C flat minor: Impossible, because there is no such key as C♭C flat minor.
   • C♯C sharp minor: No, because C♯C sharp minor has sharps and E♭E flat major has flats.
3. Therefore, the relative minor of E♭E flat major is C minor. Both keys have three flats.

Another method involves counting half steps.^[4]

Counting Half Steps to Find the Relative Key

Let’s find the relative major of F minor.

1. Count up three half steps.
   • F up to F♯F sharp up to G up to G♯G sharp/A♭A flat
2. There are two options: G♯G sharp or A♭A flat. Choose the key that shares the same accidentals.
   • G♯G sharp major: Impossible, because there is no such key as G♯G sharp
   • A♭A flat major: Yes.
3. Therefore, the relative major of F minor is A♭A flat major. Both keys have four flats.

To find the relative minor of a given major key, follow the same steps but count down three half steps instead of up three. Now, let’s find the relative minor of G♭G flat major.

1. Count down three half steps.
   • G♭G flat down to F down to E down to D♯D sharp/E♭E flat
2. There are two options: D♯D sharp or E♭E flat. Choose the key that shares the same accidentals.
   • D♯D sharp minor: No, because D♯D sharp minor has sharps and E♭E flat major has flats.
   • E♭E flat minor: Yes.
3. Therefore, the relative minor of G♭G flat major is E♭E flat minor. Both keys have six flats.

When we first analyzed music in Chapter 4 (Major Scales and Keys), the initial step was “Listen to the example: Does it sound like it’s in major (happy)?” That question makes more sense now that we are learning about minor keys. With any given key signature, we have two options, so the new first question becomes, “Listen to the example: Does it sound like it’s in major (happy) or minor (sad or angry)?”

Try to identify the key to Example 6.4.3.

Example 6.4.3. Identifying the key: Chopin,^[5] Piano Sonata No. 2 in B Minor, Op. 35, iii – Marche funèbre 

Now that we understand that music can be in major or minor, the first step is slightly different.

1. Listen to the example: Does it sound like it’s in major (happy) or minor (sad or angry)?
   • Example 6.4.3 sounds very somber—indeed, it is a funeral march (Marche funèbre). This example seems to be in minor.
2. Look at the key signature.
   • The key signature has five flats. What is the minor key with five flats?
   • If you don’t know your minor key signatures yet, find the relative major, then count down three diatonic steps.
     • The major key with five flats: D♭D flat major.
     • Find the relative minor: D♭D flat down to C down to B♭B flat.
       • We know the relative minor can’t be B minor, because the first flat in the key signature is B♭B flat.
       • We know the relative minor can’t be B♯B sharp minor, because there is no such key.
     • The minor key with five flats is B♭B flat minor.

3. Look at the first lowest note.
   • The first lowest note is B♭B flat.
4. Look at the last lowest note.
   • The last lowest note is D♭D flat.

The answers to three of the four questions point to B♭B flat minor. If you didn’t know the minor key signature for five flats, finding the key for Example 6.4.3 might have been time-consuming. This is why it’s best to have your minor key signatures memorized.

Directions:

• Identify the minor keys. For minor keys, you only need to write a lowercase letter (e.g., d).

Directions:

• Write the given key signatures on the staff.

Directions:

• Write the relative major or minor key in the table.

6.5   Minor Key Signatures with Sharps

Just like sharps in major key signatures, sharps in minor key signatures always follow this order:

Fortunately, the placement of sharps in a key signature is identical for both major and minor keys. Since there are seven different note names, the maximum number of sharps in a key signature is seven. The example below displays all the minor key signatures with sharps (Example 6.5.1).

Example 6.5.1. Minor key signatures from zero to seven sharps

Remember how A minor had zero flats, and A♭A flat minor had seven flats? A♯A sharp minor has seven sharps. One method you can use to identify minor key signatures with sharps on the staff is that the last sharp is a whole step above the key. To find the name of the key, count down a diatonic whole step from the last sharp.

• Two sharps:
  • The last sharp in the key signature with two sharps is C♯C sharp.
  • A whole step below C♯C sharp is B.
  • Therefore, the minor key with two sharps is B minor.
• Seven sharps:
  • The last sharp in the key signature with seven sharps is B♯B sharp.
  • A whole step below B♯B sharp is A♯A sharp.
  • Therefore, the minor key with seven sharps is A♯A sharp minor.

Relative Keys

As we did with minor keys with flats, understanding how to find relative keys is useful. We will use both methods.

Counting Diatonic Steps to Find the Relative Key

Let’s go through the steps to find the relative major of C♯C sharp minor.

1. Count up three diatonic steps (i.e., letter names). Don’t worry about accidentals for the first step. Just count up three letter names.
   • C♯C sharp up to D up to E.
2. Match the accidentals to figure out the relative major. Is the relative major E major, E♭E flat major, or E♯E sharp major?
   • E major: Yes.
   • E♭E flat major: Not possible, because E♭E flat major is a key with flats, and C♯C sharp minor has sharps.
   • E♯E sharp major: Impossible, because there is no such key as E♯E sharp major.
3. Therefore, the relative major of C♯C sharp minor is E major. Both keys have four sharps.

Now let’s go through the steps to find the relative minor of B major.

1. Count down three diatonic steps using letter names. Don’t worry about accidentals for the first step. Just count down three letter names.

• B down to A down to G.

2. Match the accidentals to figure out the relative minor. Is the relative major G minor, G♭G flat minor, or G♯G sharp minor?
   • G minor: No, because B major has five sharps including G♯G sharp.
   • G♭G flat minor: Impossible, because there is no such key as G♭G flat minor.
   • G♯G sharp minor: Yes.
3. Therefore, the relative minor of B major is G♯G sharp minor. Both keys have five sharps.

The second method involves counting half steps.

Counting Half Steps to Find the Relative Key

Let’s find the relative major of F♯F sharp minor.

1. Count up three half steps.

• • F♯F sharp up to G up to G♯G sharp up to A

2. Therefore, the relative major of F♯F sharp minor is A major. Both keys have three sharps.

To find the relative minor of a given major key, follow the same steps but count down three half steps instead of up three. Now, let’s find the relative minor of F# major.

1. Count down three half steps.

• • F♯F sharp down to F down to E down to E♭E flat/D♯D sharp

2. There are two options:
   • E♭E flat minor: No, because E♭E flat minor has flats and F# major has sharps.
   • D♯D sharp minor: Yes, because both F♯F sharp major and D♯D sharp minor have sharps.
3. Therefore, the relative minor of F♯F sharp major is D♯D sharp minor. Both keys have six sharps.

Again, although understanding relative keys is important, you should ultimately memorize the fifteen minor keys just as you did with the fifteen major keys.

Now we will put together everything we have learned to figure out the key of a musical example in minor (Example 6.5.2).

Example 6.5.2. Finding the key: Smetana,^[6] Má Vlast

When figuring out the key of a single line, the steps are a little different.

1. Listen to the example: Does it sound like it’s in major (happy) or minor (sad)?
   • Example 6.5.2 sounds like it is in minor.
2. Look at the key signature.
   • The key signature has one sharp, which is the key of E minor.

Since there is only a single line, we cannot look for the first lowest note and last lowest note. Instead, we must rely on our ears and the key signature.

Directions:

• Identify the minor keys. For minor keys, you only need to write a lowercase letter (e.g., b).

Directions:

• Write the given key signatures on the staff.

Directions:

• Write the relative major or minor key in the table.

Notice the pattern between minor keys with flats and minor keys with sharps (see Example 6.5.3).

Example 6.5.3. Minor keys comparison

• Looking across, the note names are identical, but only one includes an accidental.
  • For example, D minor and D♯D sharp, minor or E♭E flat minor and E minor.
• The number of accidentals equals seven.
  • For example, 1 flat + 6 sharps, or 5 flats + 2 sharps.
• The only note name that appears three times is A.
  • A minor = 0; A♭A flat minor = 7 flats; A♯A sharp minor= 7 sharps

Example 6.5.4. Memorizing up to three accidentals

To use this tip, you need to know which keys have sharps and which have flats.

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

You can also use this method when identifying key signatures.

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

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

Directions:

• Identify the minor keys. For minor keys, you only need to write a lowercase letter (e.g., e).

Directions:

• Write the given key signatures on the staff.

Directions:

• Write the relative major or minor key in the table.

6.6   Circle of Fifths

In Chapter 4, we learned about the circle of fifths: a diagram that shows how all major keys are related by ascending or descending fifths. Now that we know that every major key has a relative minor, we can use the same circle of fifths diagram for minor keys (Example 6.6.1).

Example 6.6.1 Circle of fifths

Each key in Example 6.6.1 shows the major key and its relative minor. We can find the same information from the circle of fifths for minor keys as we did with major keys.

• Moving clockwise from A minor:
  • Each key is a fifth higher.
    • A fifth above B minor is F♯F sharp minor.
  • Each key adds a sharp.
    • B minor has two sharps, and F♯F sharp minor has three sharps.
  • A minor (no sharps, no flats) moves clockwise to A♯A sharp minor (seven sharps).
  • If the key signature has flats, each key removes a flat.
    • G minor has two flats, and D minor has one flat.
• Moving counterclockwise from A minor:
  • Each key is a fifth lower.
    • A fifth below C minor is F minor.
  • Each key adds a flat.
    • C minor has three flats and F minor has four flats.
  • A minor (no sharps, no flats) moves counterclockwise to A♭A flat minor (seven flats).
  • If the key signature has sharps, each key removes a sharp.
    • G♯G sharp minor has five sharps, and C♯C sharp minor has four sharps.

We learned that the three keys at the bottom of the circle of fifths are enharmonically equivalent. There are also three minor keys that are enharmonically equivalent (Example 6.6.2).

Example 6.6.2. Enharmonically equivalent keys in minor

• The pitch span aria-hidden=”true”>E♭E flat is enharmonically equivalent to D♯D sharp.
• Therefore E♭E flat minor is enharmonically equivalent to D♯D sharp minor.
• The key of Therefore E♭E flat minor must have flats because its tonic is Therefore E♭E flat, and the key of D♯D sharp minor must have sharps because its tonic is D♯D sharp.

Directions:

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

6.7   Scale Degrees

We learned about scale degrees in Chapter 4. Each note of a major scale has a scale degree number and name. Similarly, each note of a natural minor scale also has a scale degree number and name.

In Example 6.7.1, the differences between the major scale and the natural minor scale are highlighted in boxes and shown in blue.

Example 6.7. Scale degrees

Although three pitches differ in Examples 6.7A and B, their scale degree numbers remain the same. Additionally, only one of them has a different scale degree name.

• The mediant (scale degree 3^) has the same scale degree name and number in both major and minor keys, even though they are different pitches.
• The submediant (scale degree 6^) shares the same scale degree name and number in both major and minor keys, even though they have different pitches.
• Note that scale degree 7^ has the same scale degree number but different scale degree names and pitches in major and minor.
  • In the major scale, scale degree 7^ is the leading tone.
  • In the natural minor scale, scale degree 7^ is the subtonic.

The difference between the leading tone and the subtonic cannot be overstated.

• As we learned, the leading tone leads to the tonic: it is only a half step below the tonic.
• The subtonic appears only in minor keys and is a whole step below the tonic.
  • Remember that the supertonic is a whole step above the tonic.

We will later discover that the leading tone exists in both major and minor keys. However, the subtonic is exclusive to minor keys.

In Chapter 4, we learned that solfège (e.g., do–re–me) is often used in aural training. The three notes that differ between the major scale and natural minor scale use different solfège syllables.

The differences between the major scale and the natural minor scale include the following:

• In major, scale degree 3^ is mi; in minor, it is me.
• In major, scale degree 6^ is la; in minor, it is le.
• In major, scale degree 7^ is ti; in the natural minor scale, it is te.

Because scale degree 3^ has the same scale degree name and number in major and minor, we often differentiate between the two by referring to “lowered scale degree three” or “raised scale degree three.” However, it is often easier to distinguish between the two by using solfège. Scales with me gives minor its “sad” or “angry” sound. Listen to Example 6.7.2 while asking yourself these questions: Does the example sound sad or angry at the start? What about at the end?

Example 6.7.2. Listening for major or minor: Ponce,^[7] Preludio Trágico

The excerpt begins with a sense of tension, conveying anger. By the end, the music shifts to an optimistic mood that feels resolved and hopeful. The main factor driving this transition is the use of scale degree 3^. Initially, me, or E, is prominently heard in the highest voice. The pitch E belongs to the key of C♯C sharp minor. The music creates tension and reaches a climax at measure 98. Ponce builds tension in several ways:

• The music accelerates (accel.).
• The music becomes louder (cresc. molto) until it is extremely loud (fff).
• The music expands outward from F♯F sharp₅ up to E♯E sharp₆ in the right hand, and from D♯D sharp₃ down to C♯C sharp₁ in the left hand.

Although the music heightens suspense, the climax at measure 98 does not sound apocalyptic or horrifying; rather, it feels uplifting and glorious. Note that Ponce changes me (E) to mi (E♯E sharp) at this point. Coming from the C♯C sharp major scale, E♯E sharp dramatically shifts the mood from gloom to radiance.

Directions:

• Answer the following questions based on the given natural minor scale. If it helps, write in the scale degree numbers first.

1. Which note is the tonic?
2. Which note is the dominant?
3. Which note is the subdominant?
4. Which note is scale degree 6^?
5. Which note is scale degree 3^?
6. Why is scale degree 2^ called the supertonic?
7. Why is scale degree 7^ called the subtonic?
8. Which scale degree numbers have different pitches from this scale and the F major scale?

6.8   Parallel Keys

We learned that relative keys are major and minor keys that share the same key signature. Parallel keys are major and minor keys that share the same tonic (i.e. that is, note name).

• The parallel minor of C major is C minor.
• The parallel major of F♯F sharp minor is F♯F sharp major.
• The parallel major of F♯F sharp minor is not G♭G flat major. The tonic, or note name, must be the same, and not an enharmonic equivalent.

We can determine the relationship between the key signatures of parallel keys by comparing their scales (Example 6.8.1).

Example 6.8.1. Scales of parallel keys

All the pitches are identical except for the three pairs of boxed notes, which we discussed in the last section about scale degree numbers. The relationship between parallel keys is that they differ by three accidentals.

• Starting from a major key, add three flats (or the equivalent) to identify the parallel minor.
• Start from a minor key and add three sharps (or the equivalent) to find the parallel major.

Since most students are more familiar with major key signatures, we will identify minor key signatures based on the parallel major.

• What is the key signature of F minor?
  • The key signature of F major has one flat.
  • To identify the parallel minor, add three flats (or the equivalent):
    • One flat + three flats = four flats.
  • Therefore, the key signature of F minor has four flats.
• What is the key signature of F♯F sharp minor?
  • The key signature of F♯F sharp major has six sharps.
  • To find the parallel minor, add three flats (or the equivalent). Since there are already six sharps, we cannot add three flats. Instead, we remove three sharps:
    • Six sharps – three sharps = three sharps.
  • Therefore, the key signature of F♯F sharp minor has three sharps.
• What is the key signature of G minor?
  • The key signature of G major has one sharp.
  • To find the parallel minor, add three flats (or the equivalent). Since G major only has one sharp, we cannot simply add three flats. Instead, we remove one sharp and add two flats:
    • One sharp – one sharp + two flats = two flats
  • Therefore, the key signature of G minor has two flats.

While some students find using parallel keys a great shortcut for figuring out minor keys, the problem is that not all keys exist when using parallel keys (Example 6.8.2). DNE refers to “Does Not Exist.”

Example 6.8.2. Key signatures of parallel keys

Notice that some keys exist in major but not in minor (e.g., D♭D flat major but not D♭D flat minor), and some keys exist in minor but not in major (e.g., G♯G sharp minor but not G♯G sharp major).

Composers sometimes exploit the parallel relationship between keys, as shown in Example 6.8.3.

Example 6.8.3. Parallel keys: Szymanowska,^[8] Dances for Piano, Cotillon

The cotillion dance in Example 6.8.3A begins in A♭A flat major. At measure 73 (Example 6.8.3B), Szymanowska changes the key signature to A♭A flat minor and writes a variation of the opening melody. She even labels the section “Mineur,” or “Minor” in French. Notice that although the notes look the same on the page, the music sounds very different because of the key signatures.

In summary, there are four ways to figure out minor key signatures:

1. Determine the relative major, which shares the same key signature.
2. Identify the parallel major and add three flats (or its equivalent).
3. Memorize the minor keys with up to three accidentals, then use this information to determine the rest of the keys.
4. Memorize all 15 minor key signatures. This is ultimately the best option.

Directions:

• In the blank, identify the parallel key and in the staff above, write the key signature for both keys.
  • For key signatures that do not exist, write DNE.

6.9   Harmonic Minor Scale

Example 6.9.3. Harmonic minor scales with key signatures

When we write a natural minor scale with a key signature, there is no need for accidentals. However, when we write the harmonic minor scale with a key signature, it will still require an accidental on scale degree 7^. The accidental can be a natural (Example 6.9.3B), a sharp (Example 6.9.3A), or a double sharp (Example 6.9.3C).

Composers will sometimes use the harmonic minor scale in their music (Example 6.9.4).

Example 6.9.4. Harmonic minor scale: Liebmann,^[9] Piano Sonata No. 3, i – Allegro moderato

• The key signature tells us the key is C minor.
• Liebmann uses a C harmonic minor scale from E♭E flat5 to E♭E flat4 (labeled above).

Sometimes composers do not use the entire harmonic minor scale but only the part that makes it different from the natural minor scale (i.e., the submediant and the leading tone, or le and ti) (Example 6.9.5).

Example 6.9.5. Ti and le: Dusikova,^[10] A Second Set of Airs and a March Arranged as Rondos for Pianoforte, No. 1, Minore

Example 6.9.5 is in D minor. Notice that not only is the C in the treble clef raised with a sharp, but all Cs in the bass clef are also raised. Although every C has a sharp, the key signature does not change: D minor has one flat. In fact, the raised leading tone will never change the key signature. For example, the key signature of F minor has four flats. If we raise the leading tone, E♭E flat becomes E♮E natural, resulting in three flats. However, the key signature of F minor has four flats, not three.

Although not part of the key signature, the raised leading tone is used in most minor key pieces. This is because of the strong pull toward the tonic. As a result, we can add another question to our list on how to analyze music (Example 6.9.6).

Example 6.9.6. Analysis: Dussek,^[11] Harp Sonata, Op. 3, No. 3, iii – Rondo. Allegro

1. Listen to the example: Does it sound like it’s in major (happy) or minor (sad or angry)?
   • Example 6.9.6 sounds like it is in minor.
2. Look at the key signature.
   • The key signature has three flats, which is the key of C minor.
3. Do you see the raised leading tone?
   • In C minor, the raised leading tone is B♮B natural. Yes, there are two B♮B naturals in measure 69.
4. Look at the first lowest note.
   • The first lowest note is C.
5. Look at the last lowest note.
   • The last lowest note is C.

The third step is new: Do you see the raised leading tone? While this step is generally reliable, the excerpt might include a section that uses only the natural minor scale or omits scale degree 7^ (see Example 6.3.2 and 6.3.3). As always, the combination of steps from the list produces the most convincing analysis.

Directions:

• Complete the table.

Directions:

• What is the key of the given excerpt? Use the steps we learned.

Vespermann,^[12] Bunte Reihen, op. 6, I. Charakterstück

1. Listen to the example: Does it sounds like it’s in major (happy) or minor (sad or angry)?
2. Look at the key signature. What is the key signature?
3. Do you see the raised leading tone? If so, what is it?
4. Look at the first lowest note. What is it?
5. Look at the last lowest note. What is it?
6. In what key is this excerpt?

Directions:

• Identify and label the key followed by a colon.
• Label the types of G scales indicated by the brackets.

Mozart,^[13] Piano Quartet in G Minor, K. 478,  i – Allegro

When we learned how to write the natural minor scale, we wrote the scale two different ways: one without a key signature, and one with a key signature. We will do the same for writing the harmonic minor scale, and we will use the natural minor scale as a starting point.

Step one (Example 6.9.7): Write all the notes diatonically once, in either ascending or descending order (alternate line–space or space–line). Do not skip any notes, and make sure the first and last notes are the same with the same accidentals.

Example 6.9.7. Step one

Step two (Example 6.9.8): Write in the accidentals that belong to its minor key. In other words, think of the minor key signature and apply every accidental from that key signature. This creates the natural minor scale. C minor has three flats, and C♯C sharp minor has four sharps.

Example 6.9.8. Step two

Step three (Example 6.9.9): Raise the leading tone: you may need to remove a flat, add a sharp, or add a double sharp.

Example 6.9.9. Step three

• In Example 6.9.9A, scale degree 7^ in the C natural minor scale was B♭B flat. When raising scale degree 7^, B♭B flat becomes B (Ex. 6.9.9A). A natural sign is not necessary because there is no key signature.
• In Example 6.9.9B, scale degree 7^ in the C♯C sharp natural minor scale was B. When raising scale degree 7^, B becomes B♯B sharp (Ex. 6.9.9B).

Directions:

• Using half notes, construct the following harmonic minor scales on the staff with accidentals. Do not add a key signature. Be aware of stem direction.

Steps to Writing a Harmonic Minor Scale with a Key Signature

The steps are very similar when writing harmonic minor scales with key signatures.

Step one (Example 6.9.10): Write in the minor key signature.

Example 6.9.10. Step one

Step two (Example 6.9.11): Write all the notes diatonically once, either in ascending or descending order, alternating lines and spaces. Doing this will produce natural minor scales.

Example 6.9.11. Step two

Step three (Example 6.9.12): Raise the leading tone: With a key signature, you will always add an accidental.

Example 6.9.12. Step three

In Example 6.9.8A, the raised leading tone (B) did not need a natural sign because there was no key signature. However, in Example 6.9.12A, the natural sign is now necessary because there is a B♭B flat in the key signature.

Writing the harmonic minor scale, whether with or without a key signature, always starts from the minor key signature. Then, raise the leading tone.

Directions:

• Add a key signature but no time signature.
• Using whole notes, write the given harmonic minor scales (ascending only).

6.10   Melodic Minor Scale

When we first wrote the major scale and the natural minor scale, we used whole steps (w) and half steps (h) (Example 6.10.1).

Example 6.10.1. Whole steps and half steps

When we wrote the harmonic minor scale, we started with a natural minor scale (based on the minor key signature) and raised the leading tone. However, notice the special distance between the submediant and the leading tone that occurs (Example 6.10.2).

Example 6.10.2. Harmonic minor scale

The distance between F and G♯G sharp is more than a whole step. In fact, it consists of three half steps. Listen again to the harmonic minor scale: do you notice the large gap of three half steps?

To prevent this large gap, we also raise scale degree 6^, forming the melodic minor scale (Example 6.10.3).

Example 6.10.3. Raising scale degree 6^: The melodic minor scale

Compare scale degree 6^ from Example 6.10.2 to Example 6.10.3. Notice that the F has been raised to F♯F sharp. Now, the large gap of three half steps disappears, leaving a familiar whole step.

Listen to Example 6.10.4: Do you notice that the last half of the scale sounds like the major scale? Compare the first half of Example 6.10.4 to the natural minor scale in Example 6.10.1B and the second half of Example 6.10.4 to the major scale in Example 6.10.1A.

Example 6.10.4. Ascending melodic minor scale

Remember that the harmonic minor scale was created to raise the subtonic (scale degree 7^) to become the leading tone (raised scale degree ↑7^) so that it leads up to the tonic by a half step. However, when descending from the tonic, there is no need to raise the leading tone since scale degree 7^ no longer leads up to the tonic. And since scale degree 7^ is not raised, scale degree 6^ also does not need to be raised. Because of this, the melodic minor scale is different when it ascends and when it descends (Example 6.10.5).

Example 6.10.5. Melodic minor scale

• When ascending, scale degree 6^ and scale degree 7^ are raised so they appear as they do in the major scale (la and ti).
• When descending, scale degree 7^ and scale degree 6^ return to their original forms in the natural minor scale (te and le). Note that the natural sign must be used in Example 6.10.5.

Look at the following melodic minor scales and note which accidentals are used (Example 6.10.6).

Example 6.10.6. Melodic minor scales

• Example 6.10.6A:
  • In G minor, the submediant is B♭B flat and the subtonic is F.
  • For the ascending melodic minor scale, the submediant is raised to E, and the subtonic is raised to the leading tone, F♯F sharp.
  • When descending, the leading tone returns to the subtonic (F), and the submediant returns to B♭B flat. This time, a natural sign is required for F since it was previously F♯F sharp.
• Example 6.10.6B:
  • In G♯G sharp minor, scale degree 6^ and scale degree 7^ are raised to E♯E sharp and F𝄪F double sharp when ascending.
  • When descending, F♯F sharp and D♮D natural (from the natural minor scale) return.

Example 6.10.7 shows the scales from Example 6.10.6 with key signatures.

Example 6.10.7. Melodic minor scales with key signatures

When there is a key signature, the altered notes become obvious. Only scale degree 6^ and scale degree 7^ have accidentals. The raised accidental can be a natural, a sharp, or a double sharp. The lowered accidental can be a sharp, a natural, or a flat.

Some students find it helpful to think of the melodic minor scale in terms of solfège for scale degree 5^–scale degree 6^–scale degree 7^–scale degree 1^.

• While ascending, the four syllables are sol-la-ti-do. In the minor scale, this means le must be raised to la, and te must be raised to ti.
• While descending, the four syllables would be do-te-le-sol, which means they should return to the natural minor.

Many melodies in minor often use the scale degree 5^ – raised scale degree ↑6^ – raised scale degree ↑7^ – scale degree 1^ (sol-la-ti-do) of the ascending melodic minor scale, as in Dukas’s famous The Sorcerer’s Apprentice (Example 6.10.8).

Example 6.10.8. Ascending melodic minor scale: Dukas,^[14] The Sorcerer’s Apprentice

Example 6.10.8 is in F minor. As the melody ascends from scale degree 5^ (C) to scale degree 1^ (F) in measures 74-75, scale degree 6^ (D) and scale degree 7^ (E) are raised, using the melodic minor scale (sol-la-ti-do).

Composers can utilize both the ascending and descending melodic minor scales, as shown in Example 6.10.9.

Example. 6.10.9. Melodic minor scale: Puget,^[15] La Chanson du Charbonnier

A. Opening

B. Vocalist’s opening

Puget’s song is in A minor, and as usual, we see several raised leading tones (circled G♯G sharps).

• Example 6.10.9A: In the piano introduction, Puget raises scale degree 6^ and scale degree 7^ in measure 3 as scale degree 5^ ascends to scale degree 1^ (sol-la-ti-do). These four notes belong to the ascending melodic minor scale (as well as the major scale).
• Example 6.10.9B: The vocalist begins in measure 9 and uses the descending melodic minor scale as scale degree 6^ and scale degree 7^ are no longer raised. These four notes—scale degree 1^ descending to scale degree 5^ (do-te-le-sol)—also belong to the natural minor scale.

Much like the harmonic minor scale, the accidentals used to raise scale degree 6^ and scale degree 7^ do not alter the key signature. In Example 6.10.9A, every F and G that appear are F♯F sharp and G♯G sharp. However, the key signature for A minor has no sharps.

Directions:

• Identify and label the key followed by a colon.
• Identify and label parts of the ascending or descending melodic minor scale.

Wieck Schumann,^[16] Piano Sonata in G Minor, i – Allegro

Steps to Writing a Melodic Minor Scale without a Key Signature

Just like with harmonic minor scales, we will write melodic minor scales starting from the natural minor scale.

Step one (Example 6.10.10): Write all the notes diatonically once, in ascending and descending order (alternating line–space or space–line). Do not omit any notes, and ensure that the first and last notes are the same with the same accidentals.

Example 6.10.10. Step one

Step two (Example 6.10.11): Write in the accidentals that belong to its minor key. In other words, think of the minor key signature and apply every accidental from that key signature. This creates the natural minor scale. B♭B flat minor has five flats.

Example 6.10.11. Step two

Step three (Example 6.10.12): Raise scale degree 6^ and scale degree 7^ on the way up, and return scale degree 7^ and scale degree 6^ to the natural minor on the way down.

Example 6.10.12. Step three

• When ascending, scale degree 6^ (G♭G flat) and scale degree 7^ (A♭A flat) are raised to G♮G natural and A♮A natural. The natural signs are unnecessary because there is no key signature.
• When descending, return to the natural minor scale, restoring the flats to scale degree 7^ (A♭A flat) and scale degree 6^ (G♭G flat).

Directions:

• Construct the following melodic minor scales on the staff using whole notes.
  • For all melodic minor scales, always write the scale both ascending and descending.
  • Use accidentals; do not use a key signature.
  • Do not add a time signature.
  • Do not add bar lines.

Steps to Writing a Melodic Minor Scale with a Key Signature

The process is very similar when writing melodic minor scales with key signatures.

Step one: Write in the minor key signature (Example 6.10.13).

Example 6.10.13. Step one

Step two (Example 6.10.14): Write all the notes diatonically once, both ascending and descending, interchanging line and space notes. Doing this will create natural minor scales.

Example 6.10.14. Step two

Step three (Example 6.10.15): Raise scale degree 6^ and scale degree 7^ when ascending, and lower scale degree 7^ and scale degree 6^ back to the natural minor scale when descending. There should always be four accidentals if there are no bar lines within the melodic minor scale.

Example 6.10.15. Step three

The most challenging part of writing the melodic minor scale is remembering which accidentals to use when descending. Always refer back to the key signature.

Writing the melodic minor scale, whether with or without a key signature, always starts from the minor key signature. Then, raise scale degree 6^ and scale degree 7^ on the way up, and lower scale degree 7^ and scale degree 6^ back to the natural minor scale on the way down.

Directions:

• Write the key signature for the given keys.
• Construct the following melodic minor scales on the staff using whole notes.
  • For all melodic minor scales, always write the scale both ascending and descending.
  • Do not add a time signature.
  • Do not add bar lines.

Directions:

• Construct the following ascending minor scales on the staff using whole notes.
  • Use accidentals; do not use a key signature.
  • Do not add a time signature.

Directions:

• Write the key signature for the given keys.
• Construct the following ascending minor scales on the staff using whole notes.
  • Do not add a time signature.

6.11   Transposition: Modal

At the start of this chapter, we began with a familiar tune (“Twinkle, Twinkle, Little Star”), but with a few added accidentals, which shifted the overall mood of the song to “Dingy, Dingy, Little Star.” In doing so, we applied modal transposition, which involves changing the mode from major to minor or the other way around.

There is only one scale degree number that is always unique in a minor scale: scale degree 3^. In Section 7 (“Scale Degrees”), we discussed how the solfège me (instead of mi) gave minor keys their sad or angry sound. The other two lowered scale degrees (scale degree 6^ and scale degree 7^) are only lowered when they are not ascending to the tonic (scale degree 1^). Otherwise, they are often raised, like in major scales.

Transposing from Major to Minor

Compare Examples 6.11.1A and B, which show the start of “London Bridge is Falling Down” in major and minor.

Example 6.11.1. Major to minor: “London Bridge is Falling Down”

A. In major

B. In minor

• In minor keys, scale degree 3^ is always lowered, even when ascending. In the key of C major, the lowered scale degree 3^ is E♭E flat.
• In Example 6.11.1B, scale degree 6^ is also lowered because it does not ascend to scale degree 7^. Instead, scale degree 6^ returns to scale degree 5^, which is why it is lowered as in the natural minor scale.

Now compare Examples 6.11.2A and B, which show the beginning of “Joy to the World” in major and minor keys.

Example 6.11.2. Major to minor: “Joy to the World”

A. In major

B. In minor

• Example 6.11.2A: “Joy to the World” is in G major, and there are no added accidentals.
• Example 6.11.2B:
  • In minor keys, scale degree 3^ is always lowered. In the key of G major, lowered scale degree 3^ is B♭B flat.
  • In measure 1, scale degree 7^ and scale degree 6^ are lowered because they are descending. F(♮ natural ) and E♭E flat belong to the natural minor scale (or the descending melodic minor scale).
  • In measure 3, scale degree 6^ and scale degree 7^ are raised because the line ascends toward scale degree 1^. The notes in measure 3 are part of the ascending melodic minor scale.
  • The accidentals are courtesy accidentals: They are not required because the key signature already provides this information. The courtesy accidentals serve as confirmation.

Alternatively, for modal transposition, you can use the key signature of the parallel key. When doing so, you will use different accidentals (Example 6.11.3).

Example 6.11.3. Parallel key: “Joy to the World”

• With the key signature for G minor, no accidentals are needed in the first two bars since the melody is just a descending natural minor scale.
• However, in measure 3, scale degree 6^ and scale degree 7^ are raised as scale degree 5^ ascends to scale degree 1^ (sol-la-ti-do), using the melodic minor scale.

Directions:

• Add accidentals to transpose the following example into minor.
• Begin by writing the key, adding scale degree numbers, and taking note of scale degree 3^, scale degree 6^, and scale degree 7^.

Offenbach,^[17] Geneviève de Brabant, Act II, Couplets des hommes d’armes

Transposing from Minor to Major

You can also transpose music from minor to major. Rather than lowering scale degree 3^, scale degree 6^, and scale degree 7^, raise scale degree 3^, scale degree 6^, and scale degree 7^ (Example 6.11.4).

Example 6.11.4. Minor to major: Beethoven^[18], Symphony No. 5 in C Minor, Op. 67, i – Allegro con brio

A. In minor

B. In major

Listen to Example 6.11.4B, where every scale degree 3^ and scale degree 6^ are raised. Hearing such a well-known tune in another mode might sound amusing, and writing it is very easy to do.

Composers sometimes use modal transpositions to their advantage. Earlier in the chapter (Example 6.5.2), we learned that the opening of Smetana’s Má Vlast was in E minor. Later in the piece, Smetana transposes the melody to E major. Instead of adding multiple accidentals, he simply changes the key signature to the parallel major (Example 6.11.5).

Example 6.11.5. Parallel keys: Smetana, Má Vlast

A. In minor

B. In major

At first glance, the notes appear to be the same. However, because of the key signature, there are important differences.

Directions:

• Add accidentals to the opening of the Mozart symphony below to transpose it into major.
• Begin by writing the key, adding scale degree numbers, and taking note of scale degree 3^, scale degree 6^, and scale degree 7^.

Mozart, Symphony No. 40 in G Minor, K. 550, i – Allegro molto

6.12   Analysis

We have already practiced the steps for determining the key of a given excerpt. As music students, you will typically listen to the example while looking at it to identify the key. However, sometimes you might not be able to listen to the example. You should still be able to find the key by following these steps.

1. Look at the key signature and note the two options you have with it. There will be a major key and a minor key.
2. Check the first lowest note, especially if it occurs at the beginning of the piece. Does it begin on the tonic (i.e. that is, scale degree 1^)?
3. Look at the final lowest note, especially if it’s at the end of the piece. Does it conclude on the tonic (i.e. that is, scale degree 1^)?
4. Look for a raised leading tone. If the example is in minor and has scale degree 7^, it should be raised unless it is descending.

The final step, which involves looking for a raised leading tone, is new for us. Although it’s fairly reliable, it’s not a guarantee. For example, the excerpt may not contain scale degree 7^, or if scale degree 7^ is part of a descending line, the composer may choose to use the subtonic instead.

Let’s follow these steps to find the key for two examples (Examples 6.12A and B). Do not listen to the examples first.

Example 6.12. Determining the key: Blahetka^[19], Variations brillantes sur un thême hongrois, Op. 18

A. Introduction

B. Theme

• Example 6.12A:
  1. The key signature presents two choices: C major or A minor.
  2. The example begins the movement, and the first lowest note is C.
  3. The lowest note is C, so this example might be in C major. However, this is not the end of the movement.
  4. If this example were in A minor, we would notice the raised leading tone, G♯G sharp. G appears many times, but it is never raised.
  5. In conclusion, this example is in C major.
• Example 6.12B:
  1. The key signature presents two choices: C major or A minor.
  2. The lowest note is A, but this is not the first bar of the movement.
  3. The lowest note at the end is E, not C or A. However, when we examine the E, we see it is beamed to a lower note that falls on a strong beat, A. Therefore, we can conclude that the excerpt ends on A.
  4. If this example were in A minor, we would notice the raised leading tone, G♯G sharp. There are two Gs in this example, and both are raised.
  5. In conclusion, this example is in A minor.

None of these steps for determining a key are completely reliable on their own. In addition to not relying solely on the accidental of a raised leading tone, there are other possible inconsistencies.

• The example might be a snippet that does not have scale degree 1^ as the lowest note.
• Later, we will see examples where the key signature does not correspond to the key.
• We will come across many accidentals that are not raised leading tones.

For now, the keys of musical examples will be fairly obvious. As we progress through the chapters, identifying the key will become more challenging.

Directions:

• Identify the keys of the following examples as quickly as possible without listening to them. In a few sentences, explain why you chose the key.

1. Blahetka, Variations brillantes sur un thême hongrois, Op. 18, Variation 3

2. Blahetka, Variations brillantes sur un thême hongrois, Op. 18, Coda

Terms

• harmonic minor scale
• melodic minor scale
• minor key
• minor mode
• modal transposition
• natural minor scale
• parallel keys
• relative keys
• subtonic