Now that you are familiar with basic pitches and rhythm, we will learn about accidentals, beat divisions, and other clefs.

2.1   Half Steps and Whole Steps

The smallest distance between keys on a keyboard is called a half step (also known as a semitone). Because of the asymmetrical pattern of white keys and black keys on a keyboard (there are 52 white keys and only 36 black keys), half steps can occur between a white and black key or between two white keys. We use a caret (^) to show half steps.

Example  2.1.1. Half steps on the keyboard

• Example 2.1.1A: Half steps can occur between a white key and a black key.
• Example 2.1.1B: Half steps can occur between two white keys only when there is no black key in between. This happens only between two pairs of notes:
  • E and F
  • B and C
  • It is extremely helpful to remember that these are the two white-key half steps.
• Example 2.1.1C: Half steps can occur between a black key and a white key.

Two half steps make a whole step or whole tone. Whole steps can occur between different combinations of white keys and black keys. We use a square bracket to show whole steps.

Example 2.1.2. Whole steps on the keyboard

• Example 2.1.2A: Whole steps can occur between a white key and a black key when there is a white key in between.
• Example 2.1.2B: Whole steps can occur between a black key and a white key when there is a white key in between.
• Example 2.1.2C: Whole steps can occur between two black keys when there is only one white key in between.
• Example 2.1.2D: Whole steps can occur between two white keys when there is a black key in between.

Directions:

• Label the given steps on the keyboard below.
  • For answers on white keys, write your answer on the key itself.
  • For answers on black keys, write your answer above the key.

2.2   Accidentals

At this point, we have only learned the note names of the white keys on the piano keyboard. The black keys share the same note names, but require an additional musical symbol called an accidental.  Accidentals must be used to name black keys on the keyboard, but may also be used to name white keys. There are five different types of accidentals.

Example 2.2.1. Accidentals

• A double flat (𝄫 double flat ) indicates that the note is a whole step lower than the white key.
• A flat (♭ flat ) indicates that the note is a half step lower than the white key.
• A natural sign (♮ natural ) indicates that the previous accidental no longer applies and the note returns to the white key.
• A sharp (♯ sharp ) indicates that the note is a half step higher than the white key.
• A double sharp (𝄪 double sharp ) indicates that the note is a whole step higher than the white key.

We will begin by applying all these accidentals (except the natural sign) to the note D. We will address the natural sign later.

Example 2.2.2. Accidentals on D

• D𝄫D double flat is a whole step below D.
• D♭D flat is a half step below D.
• D♯D sharp is a half step above D.
• D𝄪D double sharp is a whole step above D.

We defined a sharp as an accidental that raises a note a half step from its white key. Many students mistakenly assume that the sharp simply raises a note a half step. However, what if we want to raise D𝄫D double flat a half step? We could not write D♯D sharp—that would raise the note three half steps. Raising D𝄫D double flat a half step would actually result in D♭D flat, while D♯D sharp is a half step above the white key, D.

Just as dot placement is important, so is the correct placement of accidentals. In Example 2.2.2, notice how the third line of the staff passes through the middle of each accidental. There are several common mistakes students make when writing accidentals, marked by the red Xs in Example 2.2.3.

Example 2.2.3. Placement of accidentals

• Example 2.2.3A. When speaking or writing with words, the accidental goes after the note name (e.g., “D-flat”). However, when writing music on a staff, the accidental appears before the notehead.
• Example 2.2.3B. Students often draw the accidental after the notehead, but that is incorrect.
• Example 2.2.3C. Be sure the accidental is large enough. Many students write tiny accidentals.
• Example 2.2.3D. Be sure the accidental is not too large. For example, if the center of the accidental covers a space and a line, we cannot be sure which note should have the accidental.
• Example 2.2.3E. Be sure to position the accidental correctly before the notehead. Placing the accidental above or below the notehead (too high or too low) is incorrect.

Let’s apply all five accidentals to the note E, which is a little trickier due to its placement on the keyboard (Example 2.2.4)

Example 2.2.4. Accidentals on E

Notice that unlike D♯D sharp, which was on a black key, E♯E sharp is on a white key. This is because of the asymmetrical pattern of white keys and black keys on the keyboard: a half step above E is another white key. Many students assume sharps and flats can only be black keys, but that is not the case.

Composers use accidentals all the time. Example 2.2.5 illustrates several accidentals in practice.

Example 2.2.5. Accidentals: Candeille,^[1] “L’Enfant Fidèle,” Theme de Tarare

Example 2.2.5 includes both flats and sharps. Later in this chapter, you will learn when to use flats, when to use sharps, and when to rewrite accidentals.

Directions:

• Write the following pitches on the staff using half notes. Be aware that the clef changes.

Directions:

• Fill in the blank with an accidental to raise or lower the given note by a half step or whole step.
• Then label the pitch on the keyboard below.
  • For answers on white keys, write your answer on the key itself.
  • For answers on black keys, write your answer above the key.

Natural Sign

As you recall, a natural sign indicates that a previous accidental no longer applies and the note returns to the white key. If there was no accidental initially, there is no need for a natural sign. Accidentals continue throughout the measure, so a natural sign is required when you want to return to the white key (Example 2.2.6).

Example 2.2.6. Natural Sign

• The first pitch is E.
  • It does not require an accidental. Without an accidental, it is assumed to be E, the white key on the keyboard.
• The second pitch is E♭E flat.
  • The accidental is required.
• The third pitch is also E♭E flat, not E.
  • Do not rewrite the flat because the previous accidental continues to this note.
• The last pitch is E♮E natural (or E).
  • On the staff, the natural sign is required. If the natural sign were not there, the note would be another E♭E flat.

Accidentals have specific requirements and do not last long.

• Accidentals are localized: an accidental only applies to a note in that exact octave designation.
• An accidental does not continue after a bar line.

Example 2.2.7 demonstrates how accidentals work.

Example 2.2.7. Application of accidentals

• Example 2.2.7A: This pitch is E and not E♭E flat because the Es are in different octaves.
  • Although the previous note was E♭E flat, the flat only applied to E♭E flat₄. Since the third note belongs to a different octave designation (E₅), the flat does not apply.
• Example 2.2.7B: The pitch is E and not E♭E flat, due to the bar line.
  • Although this E is also E₄, the bar line cancels all accidentals from the previous measure.
• Example 2.2.7C: The pitch is E♯E sharp.
  • The sharp raises a note a half step from its white key on the keyboard. Here, the sharp is actually lowering E𝄪E double sharp because E♯E sharp is a half step below E𝄪E double sharp. However, it is still a half step above E so it is called E♯E sharp.
  • Sometimes students will try to lower a note by adding a flat, but as you can see, this is not always the case.
• Example 2.2.7D: The pitch is E♯E sharp.
  • Because of the bar line, the sharp must be rewritten. If not, the note would be E.
• Example 2.2.7E: Rests do not affect accidentals.
  • The note after the rest is still E♯E sharp since the rest makes no difference.
• Example 2.2.7F: The parentheses around the accidental make the natural a courtesy accidental (or cautionary accidental). Courtesy accidentals are used when the accidental is not necessary, but may be helpful to the musician.
  • Since there were so many accidentals before this point, the performer may get confused. The courtesy accidental confirms that the note is natural.
  • Parentheses are not required for courtesy accidentals.
  • A courtesy natural could have also been used at Example 2.2.7B.
• Example 2.2.7G: The pitch is E.
  • Here, the natural sign is required and should not have parentheses around it.

Example 2.2.8 shows the opening four bars of “Hawaiian Rainbows,” which includes numerous accidentals. The pitches are labeled above the music.

Example 2.2.8. “Hawaiian Rainbows”

Notice a few points regarding the accidentals:

• At the end of the first measure, the pitch is still E♭E flat, even though the flat is not rewritten, and there is a note in between.
• The first note in the second measure needs a flat because it is in a different octave and follows a bar line.
• The only natural sign appears on B♮B natural in measure 5, because the previous note is the same letter name, in the same octave, and in the same measure.

Example 2.2.9 includes both a required natural sign and a courtesy natural sign.

Example 2.2.9.  More accidentals: Candeille, “Romance de L’Orpheline de Berlin”

• First, be aware that although the music is written for grand staff, the bottom staff has a treble clef. The lowest note in measures 2 through 4 is C₄ and is not included in the given note names.
• Number 1: Both D and F have a sharp, so the pitches are D♯D sharp and F♯F sharp.
• Number 2: Although D and F do not have a sharp directly in front of them, the accidentals continue. These notes are still D♯D sharp and F♯F sharp.
• Number 3: Because of the bar line, both D and F require sharps to be rewritten. Otherwise, the pitches would be D♮D natural and F♮F natural.
• Number 4: This time, Candeille wants an F♮F natural. The natural sign is required.
• Number 5: The courtesy natural signs show that both D and F are natural.
  • There are no parentheses around these courtesy accidentals.
  • Although courtesy accidentals are not required because of the bar line, it confirms that the pitches are indeed D and F, and not D♯D sharp and F♯F sharp.

Directions:

• Identify the pitches on the staff.
• Circle the note(s) that should have a courtesy accidental.

Directions:

• Write the pitches on the staff using quarter notes. Be sure to use accidentals when necessary and to avoid them when unnecessary.

2.3   Enharmonic Equivalents

In Example 2.2.3, what appeared to be an F on the keyboard was called E. This is because F and E are enharmonically equivalent. Two notes are enharmonic equivalents when they sound the same and are played on the same key on the keyboard, but have different note names (i.e., are spelled differently) (Example 2.3.1).

Example 2.3.1. Enharmonic equivalents

• Example 2.3.1A: D♯D sharp, E♭E flat, and F𝄫F double flat are enharmonically equivalent because they are the same key on the keyboard, but they have different note names and are spelled differently on the staff.
• Example 2.3.1B: D𝄪D double sharp, E, and F♭F flat are enharmonically equivalent.
• Example 2.3.1C: E♯E sharp, F, and G𝄫G double flat are enharmonically equivalent.
• Example 2.3.1D: E𝄪E double sharp, F♯F sharp, and G♭G flat are enharmonically equivalent.

You may wonder why anyone would choose G𝄫G double flat over F, as shown in Example 2.3.1C. However, as you will learn later, context can determine whether G𝄫G double flat or F is the correct note. For instance, compare the words “I” and “eye.” They sound the same, and “I” is much easier to spell. But if you write “He poked his I,” that would be incorrect. Just like in grammar, context is the deciding factor.

There are two enharmonic equivalents next to each other in Example 2.3.2.

Example 2.3.2. Enharmonic equivalents: Le Beau,^[2] Piano Sonata, Op. 8, i –Allegro ma non troppo

• Notice that measure 62 is full of flats, while measure 63 has only sharps and natural signs.
• Across the bar line in the treble clef, D♭D flat moves to its enharmonic equivalent, C♯C sharp. Since the music is transitioning from flats to sharps, writing the note as C♯C sharp is more appropriate.
• In the bass clef, what was previously G♭G flat now becomes F♯F sharp. This occurs because the music shifts from flats to sharps.

Le Beau takes enharmonic equivalents even further in Example 2.3.3, which comes from a piano quartet. A piano quartet consists of four instruments: violin, viola, cello, and piano. The viola often reads in another clef called the alto clef, which we will learn about in Section 2.8. For now, know that the top note in the viola is a B♭B flat.

Example 2.3.3. Simultaneous enharmonic equivalents: Le Beau, Piano Quartet, Op. 28, iv – Finale. Allegro.

Le Beau writes several enharmonically equivalent notes that occur simultaneously.

• As the viola holds out B♭B flat (remember that the viola usually reads in alto clef), the piano has multiple A♯A sharps.
• The cello plays C♯C sharp at the same time as the piano plays D♭D flat.

Although it may be confusing why a composer would want to use enharmonic equivalents, there is usually a reason (which you will learn about much later). Generally, composers do not randomly switch from one note to its enharmonic equivalent or use two enharmonic equivalents at the same time. In both Examples 2.3.2 and 2.3.3, Le Beau has reasons for spelling pitches enharmonically.

Directions:

• Write two different enharmonic equivalents for the given pitches.

2.4  Chromatic versus Diatonic Half Steps

We learned that D♯D sharp and E♭E flat are enharmonically equivalent. This means that both D♯D sharp and E♭E flat are a half step below E. To determine which one to use, we distinguish between chromatic half steps or diatonic half steps.

Example 2.4.1. Chromatic vs. diatonic half steps

• Example 2.4.1A: Chromatic half steps have the same note name.
  • E♭E flat is a chromatic half step below E because they both share the note name, E.
• Example 2.4.1B: Diatonic half steps have a different note name.
  • D♯D sharp is a diatonic half step below E because they have different note names (E and D).

Referring back to “Hawaiian Rainbows,” we observe both types of half steps. Square brackets indicate diatonic half steps, while carets represent chromatic half steps (Example 2.4.2).

Example 2.4.2. Half steps in “Hawaiian Rainbows”

• Example 2.4.2A: There is a descending diatonic half step between A♭A flat and G.
• Example 2.4.2B: There is a descending chromatic half step between G and G♭G flat.
• Example 2.4.2C: There is a descending diatonic half step between G♭G flat and F.
• Example 2.4.2D: There is an ascending chromatic half step between B♭B flat and B♮B natural.
• Example 2.4.2E: There is an ascending diatonic half step between B♮B natural and C.
  • Although B♮B natural and C are both white keys, remember that this is still a half step.

You can find chromatic and diatonic half steps everywhere, as in Example 2.4.3. Like Example 2.4.2, carets indicate chromatic half steps while square brackets represent diatonic half steps.

Example 2.4.3. Half steps: Szymanowska,^[3] Dance No. 2, Trio

It would be impossible to write the half steps in measure 9 as only chromatic half steps or diatonic half steps without the need to use double sharps or double flats. It is important that you know how to identify and write both types of half steps.

Directions:

• Fill in the table with the correct pitch names.
• You may use the keyboard below to help you.

Directions:

• Identify all diatonic half steps with a square bracket.

Szymanowska, Sérénade for Cello and Piano

2.5   Chromatic Scale

A scale is a collection of pitches that ascends or descends in alphabetical order. The first and last notes of the scale are an octave apart.  Since accidentals are localized, if the first note of the scale has an accidental, the last note of the scale must also have an accidental.

The chromatic scale is made entirely of half steps, using all twelve different keys on the piano. It is written differently depending on whether it ascends or descends. Generally, we use sharps for black keys when ascending, and when descending, we use flats (Example 2.5.1).

Example 2.5.1. Chromatic Scale

• • Example 2.5.1A: When ascending, sharps are used for all the black keys except for B♭B flat, since the scale is the B♭B flat chromatic scale. Sharps are generally used for ascending motion.
    • Since the first note is B♭B flat₃ and accidentals are localized, the last note (B♭B flat₄) must also have an accidental.
  • Example 2.5.1B: When descending, flats are used for all the black keys. Flats are typically used for descending motion.

Notice how enharmonic equivalents (such as G♯G sharp and A♭A flat) are spelled differently, based on if the chromatic scale is ascending or descending.

Example 2.5.2 shows a common mistake students make when writing an ascending chromatic scale: the scale uses each letter of the musical alphabet followed by a sharp.

Example 2.5.2. Incorrect chromatic scale

Since there is no black key between E and F and between B and C, E♯E sharp is enharmonically equivalent to F and B♯B sharp is enharmonically equivalent to C. E should go directly to F and B should go directly to C; E♯E sharp and B♯B sharp (circled in red) are errors. Listen to Example 2.5.2–can you hear the two repeated notes?

When you write a chromatic scale, use sharps for the ascending scale and flats for the descending scale. However, when you see a chromatic scale within a real piece of music, the composer may choose to use a mixture of sharps and flats. In Bizet’s “Habanera,” there are several inconsistencies. Ignore the unfamiliar rhythms in Example 2.5.3 for now and focus only on the pitches.

Example 2.5.3. Descending with sharps: Bizet,^[4] “L’amour est un oiseau rebelle,” Habanera from Carmen, Act I

• In the first measure, Bizet uses a C♯C sharp instead of D♭D flat when descending from D to C.
• Although the natural sign on the C is not necessary in the second measure, it is a courtesy accidental. This courtesy accidental does not have parentheses around it.
• The G♯G sharp in the middle of the example connects A to G (instead of A♭A flat).
• The natural sign after G♯G sharp is necessary.

Directions:

• For #1, write an ascending chromatic scale beginning on E₂ using quarter notes.
• For #2, write a descending chromatic scale beginning on G₅ using dotted half notes.
• For both scales, choose an appropriate clef and end with a double bar line.

2.6   Beats and Divisions

We learned that any note can equal one. This means that any note can equal the beat. The beat is the continuous and regular pulse you feel when you experience music—it is how you clap your hands or tap your foot while listening to music.

Although any note value can be worth one beat, the ones we usually come across are beats equaling one half note, one quarter note, or one eighth note.

Recall that the half note can be evenly divided into two quarter notes, the quarter note can be evenly divided into two eighth notes, and the eighth note can be evenly divided into two sixteenth notes. When a beat is evenly divided into two, this is called the beat division, or simply, division.

Example 2.6.1. Beats and divisions

If the beat is a note with a flag (for example, an eighth note), we keep the flag. However, when two notes with flags form a beat division, we beam the flags together.

Example 2.6.2. Beaming

Since eighth notes have one flag, two eighth notes forming a beat have one beam. Sixteenth notes have two flags, so two sixteenth notes forming a beat have two beams. Beaming grouped notes is extremely helpful for musicians to quickly read music since beats are read as a unit. You can compare reading music to reading words: imagine reading one letter at a time instead of one word at a time.

Each note of the division can also be divided into two, called the subdivision (beat subdivision).

Example 2.6.3. Subdivision

Notice that bisecting each note of the division results in a subdivision containing four notes. Because these notes all have flags, they are beamed together. Compare this to the eighth note beat: since it is a single note, it is not beamed and retains its flag.

We use rhythm syllables to help us understand and perform rhythms. Rhythm syllables use numbers or syllables for each sounded note. Styles of rhythm syllables vary, but for this book we will be using the rhythm number system.

Example 2.6.4. Rhythm number system

• For now, we say “1” whenever there is a note worth one beat, or when a note falls on the first part of the beat. (Later, we will use other numbers.)
• When a note falls on the division, we say “and” (“&”).
• When a note falls on the second subdivision, we say “e” (pronounced “ee”).
• When a note falls on the fourth subdivision, we say “a” (pronounced “uh”).

Notice how all the 1s ones are aligned, and how the &s ands are aligned in the division and subdivision. When writing music, it is important to show music as it sounds in time: longer notes have more space after them, while shorter notes have less space after them.

Example 2.6.5 illustrates the division and subdivision of the beat.

Example 2.6.5. Division and subdivision: Fučik,^[5] Einzug der Gladiatoren^[6]

• Because a half note receives the beat, the division is two quarter notes, and the subdivision is four eighth notes.
  • There are no beams for the division made of quarter notes because quarter notes do not have flags.
  • Since eighth notes have one flag, a single beam connects the four eighth notes to equal one beat.
• This example includes three articulation marks we studied in the previous chapter: staccato, slur, and accent.
• Fučik uses nearly the entire chromatic scale from B₄ to B₅ at the end of the example. However, A♯A sharp is missing near the top. Notice how Fučik uses sharps as the chromatic scale ascends.

Directions:

• Add rhythm syllables below.
  • Hint: If there are two notes, they are the division; if there are four notes, they are the subdivision.
• In the blank to the right, write the note that gets one beat.
  • Hint: The beat is a single note.

Dotted Notes

Dotted notes can also be equal to one, meaning that a dotted note can also be the beat. Because of the dot, which adds half the value of the note, dotted notes cannot be evenly divided into two. Instead, dotted notes are equally divided into three.

Example 2.6.6. Dotted notes

Just as some notes, such as the half note, quarter note, and eighth note, are most commonly used for the beat, there are dotted notes that are also more frequently used for the beat: the dotted half note, dotted quarter note, and dotted eighth note.

Notice that the eighth-note division and sixteenth-note division are beamed together as a group of three. Remember that whenever notes with flags fall within a beat, they are beamed together.

Each note of the division can be subdivided. Since the notes in the division do not have dots, the subdivision will divide notes evenly into two, not three. It is only when there is a dotted note that you must divide equally into three.

Example 2.6.7. Dotted notes subdivision

Look at the subdivision of the dotted eighth note beat. Imagine how difficult it would be for a musician to distinguish six individual thirty-second notes with flags! Since they are beamed together, musicians quickly recognize that this is the subdivision of a dotted note.

We use different rhythm syllables for dotted-note divisions and subdivisions.

Example 2.6.8. Dotted beat rhythm number system

• For now, we say “1” whenever there is a note worth one beat or when a note falls on the first part of the beat. (Later, we will use other numbers.)
• When a note falls on the first division, we say “la” (pronounced “lah”).
• When a note falls on the second division, we say “li” (pronounced “lee”).
• When a note falls on any of the weaker subdivisions (i.e. meaning, those subdivisions that are not also divisions), we say “ta” (pronounced “tah”).

Example 2.6.9 clearly shows the division and subdivision of the beat.

Example 2.6.9. Dotted note beat: Donizetti,^[7] “Una furtiva lagrima,” from L’Elisir d’amore, Act 2, Scene 3

In Example 2.6.9, a dotted quarter note receives the beat, the division is three eighth notes, and the subdivision is six sixteenth notes.

• For the division, there is a single beam connecting three eighth notes because eighth notes have one flag.
• For the subdivision, two beams connect six sixteenth notes together to equal one beat because sixteenth notes have two flags.

Directions:

• Add rhythm syllables below.
  • Hint: If there are three notes, they are the division; if there are six notes, they are the subdivision.
• In the blank to the right, write down the note that gets one beat.
  • Hint: The beat is a single dotted note.

Comparing Beats

As you can see, the divisions and subdivisions vary significantly depending on whether a dotted note or a non-dotted note is the beat (Example 2.6.10).

Example 2.6.10. Divisions and subdivisions

When performing beats, divisions, and subdivisions, not all notes carry the same weight.

• The sound on the beat itself (“1”) is the strongest, meaning it has more emphasis than the notes in the division or subdivision.
• The next strongest notes are those that fall on the division.
• The other notes that only occur on the subdivisions should not be emphasized.

We can demonstrate the weight of each note using articulation marks (Example 2.6.11).

Example 2.6.11. Weights of subdivisions^[8]

• Example 2.6.11A:
  • The note that falls on the first part of the beat (boxed 1) has the strongest accent.
  • The next strongest accent falls on the division (circled &).
  • The two remaining notes of the subdivision have no accent.
• Example 2.6.11B:
  • The note that falls on the first part of the beat (boxed 1) has the strongest accent.
  • The next strongest accents fall on the divisions (circled la and li).
  • The three remaining notes of the subdivision have no accent.

Directions:

• Fill in the table using the correct note(s). Be sure to beam notes that require beaming.

2.7   Beaming

As long as the total of note values equals one beat, we can combine any notes to equal one beat (Example 2.7.1).

Example 2.7.1. Combinations

Notice the clef used in Example 2.7.1. It is called a neutral clef or percussion clef. The neutral clef indicates that there are no pitches. It is often used with a single-line staff, unlike the five-line staff typically used for pitches. Another way to draw the percussion clef is shown in Example 2.7.2.

Beaming can be challenging for students, so we will analyze each example above step by step.

• Example 2.7.1A: Combining an eighth note (one flag) with two sixteenth notes (two flags) creates one long beam connecting all the notes (since they all have flags) and a second beam connecting only the two sixteenth notes (because they have two flags).
  • A dash shows that the rhythmic syllable should be held out.
• Example 2.7.1B: Same concept as Example 2.7.1A, but the sixteenth notes come first.
• Example 2.7.1C: Sixteenth notes are at both ends, with the eighth note in the middle.
  • One beam connects all three notes because each has at least one flag.
  • Because the sixteenth notes are not paired with another sixteenth note, their second flag cannot be beamed. The second sixteenth flag is represented by a shortened beam, which points inward.
• Example 2.7.1D: A dotted eighth note, which equals three sixteenth notes, is paired with a sixteenth note to complete the beat.
  • Both the dotted eighth note and the sixteenth note have at least one flag, so one beam connects the notes.
  • The sixteenth note has two flags but is not paired with another sixteenth note. Its second flag is shown as a shortened beam that points inward.
• Example 2.7.1E: This is the opposite of Example 2.7.1D.
  • Both the dotted eighth note and the sixteenth note have at least one flag, so one beam connects the notes.
  • The sixteenth note has two flags but is not paired with another sixteenth note. Its second flag is shown as a shortened beam that points inward.
  • The dot is placed to the right of the note because dots are always to the right of the note: they cannot be to the left of the note.

Rests can replace notes in any of the examples in Example 2.7.1. As long as the total of the note values adds up to one, you can substitute any note for a rest (Example 2.7.2).

Example 2.7.2. Notes and rests

The clef in Example 2.7.2 is an alternative way to write the neutral clef or percussion clef.

Notice that some of the rhythm syllables are in parentheses. They are in parentheses because you do not speak the rhythm syllable when there is a rest. They are merely written as place holders.

• Example 2.7.2A: Changing the first sixteenth note to a sixteenth rest results in the last sixteenth note without another sixteenth note to pair with it. Instead, the last sixteenth note has a shortened beam.
  • Notice how the beam still extends over the rest because these notes happen within one beat.
• Example 2.7.2B: Changing the eighth note to an eighth rest results in only the two sixteenth notes being beamed together. Be careful not to assume the two sixteenth notes are the division because it is a group of two.
• Example 2.7.2C: Replacing the first sixteenth note with a sixteenth rest creates a rest on the downbeat.
• Example 2.7.2D: Changing the last sixteenth note to a sixteenth rest creates a free-standing dotted eighth note with a flag. There is no beam because the flag has nothing to pair with it.
• Example 2.7.2E: Changing the last dotted eighth note to a dotted eighth rest also results in a free-standing note. This time the sixteenth note has two flags because the flags have nothing to pair with it.
  • Example 2.7.2D and Example 2.7.2E use the same rhythm syllable (“1”), but you would hold out Example 2.7.2D a little longer.

Scott Joplin’s familiar melody from “The Entertainer” uses a variety of subdivision groupings (Example 2.7.3). He combines eighth notes and sixteenth notes in three different ways, and also uses the basic subdivision of four sixteenth notes, the beat of the quarter note, and two beats of the half note. Ignore the ties (small curved lines) in this example.

Example 2.7.3. Beaming: Joplin,^[9] “The Entertainer”

Notice how the notes are spaced in Example 2.7.3. There is more space after an eighth note and even more space after a quarter note. Additionally, sixteenth notes are evenly spaced apart. It is essential to write rhythm visually as it sounds.

Examples 2.7.4A and B are correctly written, while Examples 2.7.4C and 2.7.4D are not.

Example 2.7.4. Writing rhythm

• Example 2.7.4C: Placing the sixteenth note too close to the dotted eighth note creates the illusion that the dotted eighth note is as short as a sixteenth. In reality, the dotted eighth note is three times longer than a sixteenth note, and the sixteenth note should be positioned at the end of the measure, as shown in Example 2.7.4A.
• Example 2.7.4D: Writing the dotted eighth note far from the sixteenth note makes it seem like the sixteenth note is very long. In reality, the sixteenth note is very short, and the dotted eighth note should be written right next to it to accurately reflect how it sounds (as in Example 2.7.4B).

Directions:

• Write the rhythm syllables below the example. See Example 2.7.3 for a sample. Ignore the tie (small curved line) for this example.

Joplin, “Maple Leaf Rag”

Directions:

• Based on the given note that equals one beat, beam the following groups of notes correctly. Each measure equals one beat.
  • Write the stems in the same direction as the given rhythm.
  • Be sure the rhythm is spaced out correctly so that it matches aurally and visually.
• Beneath your answer, write in the rhythm syllables.

Dotted Note Beats

The same rules apply when you write rhythms in which a dotted note equals one beat (Example 2.7.5).

• Beam all flagged notes together when they fall within one beat.
• Arrange notes visually as they occur aurally.

Example 2.7.5. Beaming for a dotted note beat

The rhythm syllable for “1” in Example 2.7.5D is in parentheses. Since this measure begins with a rest, you do not say “one.”

Antonio Vivaldi uses a combination of divisions and subdivisions in the third movement of Spring from his Four Seasons.

Example 2.7.6. Beaming: Vivaldi,^[10] “Spring” from The Four Seasons, iii

The dotted quarter note equals one beat in Example 2.7.6.

• Example 2.7.6A: Vivaldi uses the basic beat (dotted quarter note) once, and different combinations of the division and subdivision.
• Example 2.7.6B: The basic division of three eighth notes occurs twice, along with different combinations of the division and subdivision.

In Example 2.7.6, observe how longer note values have more space after them, while sixteenth notes are evenly spaced by the smallest distance.

Directions:

• Write the rhythm syllables below the example. See Example 2.7.6 for a sample. Ignore ties (small curved lines) for this example.

Vivaldi, “Spring” from The Four Seasons, iii

Directions:

• Based on the given note that equals one beat, beam the following groups of notes correctly. Each measure equals one beat.
  • Write the stems in the same direction as the given rhythm.
  • Be sure the rhythm is spaced correctly so that it matches aurally and visually.
• Beneath your answer, write in the rhythm syllables.

2.8   C Clefs

We already learned about the two most common clefs for pitches: the treble clef and the bass clef. There are also other types of clefs called movable C clefs. They are so named for the following reasons:

• They are movable because five different types are placed in various parts of the staff.
• They are called C clefs because the center of the clef is positioned where middle C is.

Example 2.8.1 shows one type of C clef.

Example 2.8.1. C clef

The C clef in Example 2.8.1 is the most commonly used C clef, known as the alto clef. We previously saw the alto clef in Example 2.3.3. You should be familiar with it, as it is the third most common clef after the treble and bass clefs. Since you know where middle C is, simply count up or down to find other pitches (Example 2.8.2).

Example 2.8.2. Pitches in the alto clef

Here are some shortcuts to use when initially learning the alto clef:

• If your primary clef is the treble clef, the alto clef is read a whole step higher than the treble clef on the staff.^[11]
  • For example, the first note in Example 2.8.2 would be C in the treble clef, but it is D in the alto clef.
• If your primary clef is the bass clef, the alto clef is read a whole step below bass clef.^[12]
  • For example, the first note in Example 2.8.2 would be E in the bass clef, but it is D in the alto clef.

The viola typically uses the alto clef but also uses the treble clef. Example 2.8.3 shows an excerpt from a common chamber ensemble called a string quartet, which includes two violins, one viola, and a cello. The pitches for the viola are written above its part.

Example 2.8.3. Hensel,^[13] String Quartet in E-flat Major, H277, ii

• The two violins read in the treble clef.
• The viola’s part is in the alto clef.
• The cello’s part is in the bass clef.

As mentioned, the alto clef is one type of movable C clef, and movable C clefs are called so because they can move up and down the staff. There are four other types of moveable C clefs (Example 2.8.4).

Example 2.8.4. Movable C clefs

The notes in Example 2.8.4 are all middle C in the different movable C clefs. The movable C clefs share the names of vocal ranges. The treble clef and bass clef also have movable versions, where G₄ moves in the treble clef and F₃ moves in the bass clef. However, those clefs are infrequently used.

• Example 2.8.4A: The soprano clef is the lowest C clef, used for voices or instruments with the highest range because it enables higher pitches to be written without ledger lines.
• Example 2.8.4B: The mezzo-soprano clef places C₄ on the second line.
• Example 2.8.4C: The alto clef is the most common C clef. The viola most often reads the alto clef.
• Example 2.8.4D: The tenor clef is the second most common movable C clef. It is sometimes used by instruments such as the bassoon and cello.
• Example 2.8.4E: The baritone clef is the highest-placed C clef. It is used for voices or instruments with the lowest range because it allows for the lowest pitches before ledger lines are needed.

Example 2.8.5 shows an excerpt in tenor clef, written for the bassoon. The pitches are notated below the staff.

Example 2.8.5. Ravel,^[14] Bolero

The bassoon reads music in both bass clef and tenor clef. Tenor clef is used when the bassoon plays higher pitches. The first note in Example 2.8.5 is B♭B flat₄. The bass clef would require four ledger lines. Although it may seem inconvenient to learn another clef, once you become fluent in it, reading is much easier than trying to quickly interpret multiple ledger lines.

There are only five different movable C clefs because there are five lines on the staff. The movable C clefs do not extend beyond the staff. Observe what happens if we extend the placement of C₄ outside the staff with ledger lines.

Example 2.8.6. Beyond the C clefs

We do not have a movable C clef above or below the staff because those ranges are already represented by the treble and bass clefs.

Directions:

• Identify the pitches on the staff using octave designations.

Directions:

• Write the pitches on the staff using correct beaming based on the given rhythm. Assume a quarter note equals one beat.

2.9   Dynamics

In Chapter 1, we learned about articulation marks: symbols that tell musicians how to perform specific notes. In this section, we learn about dynamics:  symbols that tell musicians at what volume (how soft or how loud) to perform specific sections. These symbols are abbreviations of Italian words based on piano (soft) and forte (loud).

Example 2.9.1. Dynamics

The spectrum in Example 2.9.1 shows various dynamics from the softest to the loudest. Notice that both piano and forte add -issimo to mean more softly or more loudly; adding -ississimo means even more softly or loudly. There are even softer and louder dynamics (e.g. for example, fortissississimo (ffff)), but they are not as common.

Because dynamics are relative, hearing the difference between mezzo-piano (mezzo meaning “half” or “middle” in Italian) and mezzo-forte can be challenging. However, the distinction between piano and forte should be clear.

Example 2.9.2 is the familiar children’s song “Twinkle, Twinkle, Little Star” with added dynamics.

Example 2.9.2. Applied dynamics, “Twinkle, Twinkle, Little Star”

Example 2.9.2 concludes with a final double bar line because it marks the end of the song. Notice that the second line is thicker than the first, setting it apart from the other double bar lines we have used.

Using the terms we learned, we can write sentences about the dynamics in Example 2.9.2:

• Example 2.9.2 begins pianissimo at measure 9 and becomes mezzo-piano in the middle of measure 10. The melody suddenly switches to forte for two bars (mm. 11-12) until the final note, which is piano.

Based on the given dynamics, each change of dynamics would occur suddenly, or subito. For example, mm. 11-12 would be forte until the final note, which is subito piano (suddenly soft). The effect of subito piano has its own dynamics symbol: fp (abbreviation for forte-piano) or sfp (abbreviation for subito forte-piano).

The Overture (or opening of Mozart’s opera The Magic Flute features a range of contrasting dynamics, including piano, forte, and subito forte-piano (Example 2.9.3).

Example 2.9.3. Contrasting dynamics: Mozart,^[15] The Magic Flute, Overture

• The second violins’ eighth notes begin piano until sixteenth notes marked forte suddenly appear.
• The pattern of piano and forte continues as the first violins join in.
• To emphasize the strong contrast in dynamics, Mozart writes subito forte-piano for the half notes.
  • These half notes should suddenly be forte at the point of attack, then immediately drop to piano. The entire duration of the half note should not be forte.

Although Mozart wanted sudden dynamic changes, they can sometimes sound harsh and less musical (as in Example 2.9.2). To transition smoothly between dynamics, we have terms and symbols that instruct us to gradually become softer or louder (Example 2.9.4).

Example 2.9.4. Gradual dynamics, “Twinkle, Twinkle, Little Star”

• Crescendo means that the music gradually becomes louder. There are two ways to represent crescendo.
  • Hairpins (stretched out “less than” symbol) visually indicate an increase in volume (measures 9-10).
  • The abbreviation “cresc.” can also be used.
• Diminuendo or decrescendo means that the music gets softer. There are three ways to represent the decrease in volume.
  • Hairpins (stretched out “greater than” symbol) visually indicate the softening of sound (measures 11-12).
  • The abbreviation “dim.” can be used.
  • The abbreviation “decresc.” can also be used.

Oftentimes, other words are paired with these gradual dynamics symbols to emphasize how they should be performed:

• • • Molto (“much”) is used when a great change in volume is desired (e.g., molto cresc.).
    • Poco (“little”) is used when a subtle change in volume is desired (e.g., poco decresc.).
    • Poco a poco (“little by little”) is used when a subtle change in volume is desired a little at a time (e.g., poco a poco dim.).

Example 2.9.5. More specific gradual dynamics, “Twinkle, Twinkle, Little Star”

The specific gradual dynamics in Example 2.9.5 provide more insight into how to perform the excerpt.

• The music begins very softly (pianissimo) and gradually gets much louder (molto cresc.) starting at measure  10, ending at a medium-soft (mezzo-piano) level.
• Measure 11 begins loudly (forte) and gets softer little by little (dim. poco a poco), ending softly (piano).

Example 2.9.6. shows a well-known example of a powerful crescendo.

Ex. 2.9.6. Powerful crescendo: Beethoven,^[16] Symphony No. 5 in C Minor, Op. 67, iii to iv

Example 2.9.6 shows the end of the third movement and the start of the fourth movement of Beethoven’s Fifth Symphony. Movements are like chapters in books; usually, there is a clear separation between chapters and movements. However, in Beethoven’s Fifth Symphony, the third movement seamlessly blends into the fourth movement without a pause. Before Example 2.9.6 begins, the music is pianissimo and starts to crescendo at measure 366. The music gradually builds until it reaches an explosive fortissimo at the start of the fourth movement. Be sure to listen to a recording.

Directions:

• Arrange the following dynamics from softest to loudest by writing their abbreviation onto the spectrum arrow below.

Directions:

• Based on the example below, answer the following questions. The flat immediately following the treble clef and bass clef is called a key signature, which we will learn about in Chapter 4. Ignore it for now.

1. Does this example start at the beginning of the piece? If not, where does it begin?
2. Based on the beaming, what note is worth one beat?
3. In measure 7, why is there a natural sign on F₄?
4. In measure 7, why aren’t the dotted quarter note and eighth note beamed together?
5. In measure 8, why is there a flat on E₃?
6. In measure 8, why is there a natural sign on E₄?
7. Are the symbols above the treble clef in measure 9 diminuendo markings? If not, what are they?
8. Is this the end of the piece? If not, why not?
9. In 2-4 complete sentences, describe the dynamics in this example.

Smyth,^[17] The March of the Women