To understand music, we start with the basics: rhythm and pitch.

1.1   Introduction

The first step in learning music is understanding the basics: rhythm and pitch.

Rhythm describes how musical sounds are perceived in time. Notes represent sounds, while rests indicate silence. Both notes and rests can have varying durations, meaning they can be longer or shorter.

Pitches refer to how musical sounds are heard in terms of how high or low they sound. Because of their close connection, the terms “pitch” and “note” are often used interchangeably. Pitches are represented by note names using the musical alphabet:

• A B C D E F G

After G, we return to A:

• A B C D E F G A B C…

The first and second A are an octave apart because they are eight notes away. B and B are also an octave apart, and this pattern continues.

This chapter will alternate between note values and note names, reinforcing each as we move forward.

1.2   Note Values

To determine the duration of pitches, we need to notate the rhythm using different note values. First, we will describe the parts of a note.

Example 1.2.1. Parts of a note

• Notehead: Each note has an oval-shaped notehead that can be unfilled or filled.
• Stem: Most noteheads (but not all) have a stem.
  • When the stem points up, it is placed on the right side of the notehead.
  • When the stem points down, it is placed on the left side of the notehead.
• Flag: Many stems (but not all) have a flag.
  • Regardless of whether the stem points up or down, flags are always on the right side of the stem.
  • Stems can have multiple flags. When there are three or more flags, the stem is lengthened.

Now that we understand the basic parts of a note, we will explore the most common types of notes.

Example 1.2.2. Note types

• Whole note: An unfilled notehead without a stem.
• Half note: An unfilled notehead with a stem.
  • Stems can point either up or down. This applies to all note values with stems.
• Quarter note: A filled notehead with a stem.
• Eighth note: A filled notehead with a stem and a flag.
• Sixteenth note: A filled notehead with a stem and two flags.

In Example 1.2.2, the whole note has the longest duration, while the sixteenth note has the shortest. Each note value is proportionally related to the others. Knowing basic math and fractions helps you understand how note values are connected.

Example 1.2.3. Note values

• A whole note divides equally into two half notes.
  • Since two half notes equal one whole note, one half note is half the value of a whole note.
• A half note divides equally into two quarter notes.
  • Since two quarter notes equal one half note, a quarter note is worth half a half note.
• A quarter note divides equally into two eighth notes.
  • Since two eighth notes equal one quarter note, an eighth note is half the duration of a quarter note.
• An eighth note divides equally into two sixteenth notes.
  • Since two sixteenth notes equal one eighth note, one sixteenth note is half the value of an eighth note.

There are less-common note values that are longer or shorter than the ones listed in Example 1.2.3. Adding more flags creates notes of shorter duration, such as the thirty-second note, sixty-fourth note, and others. The notes in this section are the most common ones.

Any note can be assigned a value of one. Depending on which note is set to one, the other notes will have different values. Refer to Example 1.2.4 to see note values when a whole note is equal to one.

Example 1.2.4. Whole note = 1

If a whole note equals one, the following statements are true:

• A whole note divides into two half notes, making each half note worth half.
• A half note divides into two quarter notes and since there are two half notes in a whole note, a whole note can be divided into four quarter notes. This means that a quarter note is worth one-fourth (or one-quarter).
• Each quarter note divides into two eighth notes, resulting in eight (8) eighth notes. Therefore, a whole note can be divided into eight (8) eighth notes, where each eighth note is worth one-eighth.

Any note can equal one, which changes the values of the other notes. For some students, creating a table helps them understand note values (Example 1.2.5).

Example 1.2.5. Note value table

In Example 1.2.5, notes are listed in order of increasing duration. You can read the table from left to right (smallest to largest note values) or from right to left (largest to smallest note values).

• Notes that are equal to one are shown in blue boxes.
• To determine the value of longer notes, multiply each number by two.
  • For example, if a sixteenth note equals one, then an eighth note equals two because 1 times 2 equals 2.
• To find the value of notes with shorter durations, divide each number by two.
  • For example, if a half note equals eight, then a quarter note equals four because 8 divided by 2 equals 4.

You can also visualize note values as serving sizes of pie.

• If an entire pie (whole note) is the portion size, then eating half the pie (half note) will be worth half.
• If one-fourth of a pie (quarter note) is the portion size, then eating half the pie (half note) will equal two servings.

Composers often combine different note values to add variety to their music. In Example 1.2.6, Hensel uses all the notes covered in this section. There are many more symbols you might not recognize—ignore those for now and focus only on the different note values.

Example 1.2.6. Note values: Hensel,^[1] “Hörst du nicht die Bäume rauschen,” Gartenlieder, Op. 3, No. 1

• Example 1.2.6 begins with half notes in all four voices.
  • The stem in the alto’s half note points up and to the right of the notehead.
  • The stems of the three other voices point down and to the left of the notehead.
  • We will learn why some stems point up while others point down in the next section.
• The stem directions of the sixteenth notes and eighth notes vary, but the flags are always on the right.
• The other two note values we studied in this example are the quarter note and the whole note.

Directions:

• Fill in the boxes with the appropriate note.

Directions:

• Based on the given note that equals one, calculate the value of the other notes. Use fractions instead of decimals.

1.3   Treble Clef

To identify how high or low pitches sound, we notate pitches on a musical staff using a clef.

• A musical staff (or staff) consists of five horizontal lines where notes are placed. You will be writing on staff paper for many of your assignments. Notes can be positioned in the spaces between the lines or directly on the lines themselves.
• A clef is placed at the start to indicate how high or low the notes sound. There are several different types of clefs, but the staff remains consistent.

Example 1.3.1. Musical staff and treble clef

• Staff: Pitches are written on five horizontal lines called a staff.
  • Notes can be written on a line.
    • The musical staff consists of five lines.
    • The line passes through the center of the notehead and does not extend to fill the space above or below.
  • Notes can be written in a space, which is between the lines.
    • The musical staff consists of four space.
    • The whole note in the space fits neatly between the lines, not going beyond the top or bottom line.
  • Notes can also be written above or below the staff, which will be discussed in Example 1.3.3.
• Treble clef: The treble clef is a specific type of clef that is placed at the beginning of the staff and indicates how high or how low a note sounds.
  • The treble clef is the most common clef for higher voices (such as soprano and alto) and higher-sounding instruments (like the flute, clarinet, oboe, trumpet, and violin).
  • The treble clef is also known as the G clef.
    • When drawing a treble clef, the starting point of the symbol (the middle part that resembles a snail shell) falls on where the pitch G lies. (The note on a line in Example 1.3.1 is G.)
    • The treble clef’s shape resembles the letter G.
  • The treble clef can be tricky to draw, so make sure to practice writing it.
• Bar line: At the end of the staff, there is a vertical line called a bar line that separates music into easy-to-understand segments called measures or bars.
  • There is no bar line at the start.

For the treble clef, the pitches are arranged as shown in Example 1.3.2. It is very helpful to memorize the placement of these pitches on the staff as quickly as possible.

Example 1.3.2. Pitches in the treble clef

• Notes in the spaces of a staff with a treble clef spell FACE.
  • The lowest space is the first space, while the highest space is the fourth space.
  • The pitch in the first space is F.
• Notes on the lines of a staff with a treble clef spell EGBDF. You can use a mnemonic device, such as “Elvis’s Guitar Broke Down Friday.”
  • The lowest line is the first line, while the highest line is the fifth line.
  • The pitch on the fifth line is F. The F in the first space and the F on the fifth line are an octave apart.
• The higher notes appear on the staff, the higher they sound. Think of someone with a high-pitched voice, as opposed to someone with a low-pitched voice.

Although mnemonic devices like Elvis’s Guitar Broke Down Friday can assist you initially, it is vital to memorize how to read notes quickly. Many apps and websites can help you improve your fluency.

In addition to the notes in Example 1.3.2, you should be fluent with a few extra notes above and below the staff. We can use a piano keyboard to assist us (Example 1.3.3).

Example 1.3.3. Keyboard and treble clef

1.4   Rest Values

In music, silence is just as important as sound. Similar to how we use note values to indicate how long to sustain sounds, we use rest values to show how long the silence lasts. Now that we understand the basic note values, we will also explore the less common note values in this section. The notes and rests boxed in blue in Example 1.4.1 are the most frequently used ones.

Example 1.4.1. Notes and rests

A. Notes

B. Rests

First, notice a few things about the less-common notes (Example 1.4.1A, in black):

• The only note value larger than a whole note is the breve, also known as the double whole note.
  • A breve is worth twice as much as a whole note. This is not used very often.
• The thirty-second note has three flags.
  • A thirty-second note is half the value of a sixteenth note.
  • Because there are so many flags, the stem length is extended.
• The sixty-fourth note has four flags.
  • A sixty-fourth note is half the duration of a thirty-second note.
  • Because there are even more flags, the length of the stem is extended even more.

1.5   Bass Clef

1.6   Dots

We learned that different notes can have a value of one, which makes other notes worth varying amounts.

Example 1.6.1. Note values

However, is there a note equal to 3? Yes, there is a note if we add a dot after the note (Example 1.6.2).

Example 1.6.2. Note value = 3

When we add a dot (or augmentation dot) after a note, it becomes a dotted note and increases the note’s value by half. Although the dot appears after the note, we say the word “dotted” before the note’s name. For example, a half note with a dot becomes a dotted half note. In Example 1.6.2, the dotted half note equals 3.

Example 1.6.3. Dotted notes

• Example 1.6.3A:
  • Quarter note = 1
  • Dot = Half of 1
  • Half of 1 = ½
  • Quarter note + dot = 1 + ½ = 1½
  • Therefore, the dotted quarter note equals 1½ beats when the quarter note equals one beat.
• Example 1.6.3B:
  • Half note = 2
  • Dot = Half of 2
  • Half of 2 = 1
  • Half note + dot = 2 + 1 = 3
  • Therefore, the dotted half note equals 3 beats when the quarter note equals one beat.
• Example 1.6.3C:
  • Whole note = 4
  • Dot = Half of 4
  • Half of 4 = 2
  • Whole note + dot = 4 + 2 = 6
  • Therefore, the dotted whole note equals 6 beats when the quarter note equals one beat.

Just as with notes without dots, dotted notes vary in value depending on which note is equal to one. In Example 1.6.4, the notes that are equal to one are boxed in blue.

Example 1.6.4. Varying note values

• Example 1.6.4A: Eighth note equals one.
  • Eighth note = 1
  • Eighth note (1) + dot (½) = 1½
  • Quarter note = 2
  • Quarter note (2) + dot (1) = 3
  • Half note = 4
  • Half note (4) + dot (2) = 6
• Example 1.6.4B: Half note equals one.
  • Quarter note = ½
  • Quarter note (½) + dot (¼) = ¾
  • Half note = 1
  • Half note (1) + dot (½) = 1½
  • Whole note = 2
  • Whole note (2) + dot (1) = 3

Students often struggle to understand note values less than one, such as notes that require fractions. Creating a table similar to Example 1.2.5 can be helpful.

Dots must be precisely written on the staff (Example 1.6.5).

Example 1.6.5. Dotted notes

• For notes on a line, the dot is placed in the space above the line where the notehead sits (see dotted whole note, dotted quarter note, and dotted sixteenth note).
• For notes in a space, the dot is placed immediately to the right of the notehead (see dotted half note, dotted eighth note, and dotted thirty-second note).
• For notes with flags, position the dot correctly next to or above the notehead, but after the flags (see dotted eighth note, dotted sixteenth note, and dotted thirty-second note).

Dot placement might seem insignificant, but it is important.

• If you draw a dot on a line, it is likely to be hidden and unseen.
• If you draw a dot in the wrong place, another note might be held out longer than the one you intended.

Example 1.6.6 shows dotted notes in context.

Example 1.6.6.  Dotted notes: Brooman,^[6] “Den emsamna Makan”

• Brooman uses three different types of dotted notes: a dotted eighth, a dotted quarter, and a dotted half note.
• The placement of the dot for the dotted eighth note is above the line because the notehead is on a line. The dots of the other two dotted notes are in the spaces next to the noteheads because the noteheads are in spaces.

Rests can also have dots and are used in the same way (Example 1.6.7). Similarly, the name of the rest includes the word “dotted” before it, while the dot appears after the rest. For example, a quarter rest becomes a dotted quarter rest, but the dot comes after the rest.

Example 1.6.7. Dotted rests

Observe the placement of the dots. Remember that for dotted notes, their dots change position depending on the notehead’s location. For dotted rests, dots are always placed in the third space.

Sometimes, you might see two rests in a row instead of a dotted rest. For example, instead of a dotted quarter rest, you may see a quarter rest followed by an eighth rest. Example 1.6.8 shows several dotted rests in context.

Example 1.6.8. Dotted rests: Kinkel,^[7] “Das Schloss Boncourt”

• After the dotted half note, the example continues with two dotted half rests and one dotted quarter rest.
• As an alternative to the dotted quarter rest, the example ends with a quarter rest followed by an eighth rest.
  • In the actual score, the quarter rest and eighth rest both appear as a dotted quarter rest. However, they are written this way because you may come across two rests in a row like this instead of a dotted rest.

Directions:

• Based on the given note that equals one, write the note values of the other notes. For a sample, see Example 1.6.4.

1.7   Grand Staff

Review the pitches in Example 1.7.1.

Example 1.7.1. Bass clef example

Although the first five notes may be easy to read, the next four might be more challenging. We can add ledger lines for notes above middle C in the bass clef, but a simpler way to read these notes is to read the first five in the bass clef and the last four in the treble clef. This can be done by using a grand staff, which combines the treble and bass clefs at the same time.

Example 1.7.2. Grand staff

• It is essential that the grand staff begins with a brace and bar line. (Recall that when we wrote for only treble clef or only bass clef, there was no bar line at the beginning.) The brace and bar line are necessary at the start of a grand staff because both staves^[8] must be read simultaneously.
• Without the brace and bar line, the staff with the treble clef would be the first system, and the staff with the bass clef would be the second system. In Example 1.7.2, the grand staff forms one system.
• The grand staff is most often used by keyboard instruments, such as the piano. If you played Example 1.7.2 on the piano, your left hand would play F-G-A-B-C, and your right hand would play C-D-E-F-G. You would only play middle C once, as it appears in both hands at the same time.

Example 1.7.3 is the opening of one of the most famous piano pieces, Beethoven’s “Für Elise.” Ignore the unfamiliar parts for now, and only focus on the grand staff.

Example 1.7.3. Grand staff: Beethoven, “Für Elise,” WoO 59

The grand staff in Example 1.7.3 clearly indicates which parts are played by the right hand and which are played by the left hand. The brace and bar line at the beginning of the grand staff remind us that both staves are to be read simultaneously.

Octave Designation

Octave designations range from A₀ to C₈ because a piano keyboard has 88 keys. However, the octave designations in Example 1.7.4 illustrate the notes most commonly used.

Although the musical alphabet repeats after G (i.e., A-B-C-D-E-F-G-A…), the octave labels change with each new C.

• This means that as the pitches ascend with each C, the octave designation increases by one.
• In Example 1.7.4, observe the two pitches in the box (B₄ and C₅). B₄ did not go to C₄ because C₄ is middle C, which is below B₄. The note above B₄ is C₅.
• After B_x, the next note is C_x+1.

Directions:

• Identify the pitches on the staff with octave designations. Be aware that the clef changes.

Octave Signs

When writing notes below C₂ or above C₆, it is much easier to use octave signs instead of adding multiple ledger lines. Octave signs indicate that the pitches sound an octave (or two) higher or lower than written (Example 1.7.5).

Example 1.7.5. Octave signs above

• Ottava :  8va (ottava alta, or “octave above”) is written above the notes and followed by a dotted line to show which notes sound an octave higher than written.
• Quindicesima : 15ma (“at the fifteenth”) is also written above the notes and is followed by a dotted line. However, the “15” indicates which notes sound two octaves higher than written.

Without octave signs, you would need nine ledger lines to write C₈! Octave signs below can be written the same way (Example 1.7.6).

Example 1.7.6. Octave signs below

• Ottava: 8va is written below the notes and is followed by a dotted line to indicate which notes are to sound an octave lower than written.
• Quindicesima: 15ma is also written below the notes and is followed by a dotted line to indicate which notes sound two octaves lower than written.
• Other ways to indicate an octave below include writing 8vb (ottava bassa or “octave below”) or 8va bassa below the notes.

Example 1.7.7 shows the opening of Grieg’s famous Piano Concerto. Although some items may be unfamiliar to you, there are new concepts we just learned. In particular, notice how Grieg can cover seven octaves on the piano in only three measures!

Example 1.7.7. Grieg,^[9] Piano Concerto No. 1 in A Minor, Op. 16, i

A concerto is a piece composed for a soloist and orchestra. Example 1.7.7 begins with a measure of rest because the orchestra is performing (though not shown), while the pianist waits. When the piano starts, the octave sign shows that the highest note is one octave higher than A₆. The example identifies the different As with octave designations.

Because the piano begins so high, the left hand’s part does not start with a bass clef, but rather, a treble clef. Although the grand staff typically begins with treble and bass clef, it is not uncommon to see two treble clefs (or two bass clefs). The bass clef makes its return halfway through the example, when the pianist’s left hand starts to move below the middle of the keyboard.

Directions:

• In the staves below, write a grand staff and end with a double bar line.
• Using dotted eighth notes, write the given notes on the grand staff. Separate each example with a bar line.
  • Add an octave sign if you exceed two ledger lines.

1.8   Articulation Marks

We learned that any note can be equal to one. For example, a quarter note can be equal to one. However, not all quarter notes will be performed the same way, depending on the articulation mark. An articulation marks is a symbol added to a note that tells the musician how to perform it. Example 1.8.1 illustrates seven of the most common articulation marks.

Example 1.8.1. Articulation marks

• Staccato: Notes performed short.
• Staccatissimo: Notes performed even shorter than a staccato.
• Accent: Notes performed loudly.
• Marcato: Notes performed even louder than an accent.
• Tenuto: Notes held out to their full duration.
• Fermata: Notes held out longer than their full duration.
• Slur: Notes held for their full value with minimal silence between them. Slurs cannot be used for a single note—they must connect at least two notes.

Notice that articulations are positioned directly above or below the notehead, on the opposite side of the stem. The exceptions are the marcato and fermata, which are always placed above the note when there is only one voice, and the slur, which connects multiple notes.

Many words used in music are Italian. When using words from other languages, they are italicized (e.g., tenuto). When using words in English, they are not italicized (e.g., accent).

Several articulation marks are abbreviations, not symbols. For example, sforzando markings, which are similar to accents, are not symbols but abbreviations of the word (Example 1.8.2).

Example 1.8.2. Sforzando

Sforzando is an articulation mark that indicates that the note should be accented (played loudly). The different letter abbreviations include forzato, forzando, and sforzato. The two blue abbreviations in the middle of Example 1.8.2 are the most common ways sforzando markings appear.

Example 1.8.3 illustrates several different articulation marks in a short three-measure except.

Example 1.8.3. Farrenc,^[10] “Souvenir des Huguenots”

• Most of the notes are to be played staccato (short).
• In measure 6, the accents on the quarter notes tell the pianist to play those notes louder.
• In the last measure, there is a staccatissimo symbol (indicating a very short note) and a sforzando symbol, which should be played even louder.

Directions:

• Using quarter notes, write the given notes with articulation marks on the grand staff.

Terms

• articulation mark
  • accent
  • fermata
  • marcato
  • slur
  • staccatissimo
  • staccato
  • tenuto
• bar line
• bass clef
• brace
• clef
• dot (or augmentation dot)
• dotted note/rest
• double bar line
• eighth note/rest
• flag
• grand staff
• keyboard
  • black keys
  • white keys
• ledger line
• measure (or bar)
• measure number (or bar number)
• middle C
• musical alphabet
• notes/rests
  • sixty-fourth note/rest
  • thirty-second note/rest
  • sixteenth note/rest
  • eighth note/rest
  • quarter note/rest
  • half note/rest
  • whole note/rest
  • breve/breve rest (or double whole note/rest)
• note values
• notehead
• octave
• octave designation
• octave sign
  • ottava alta
  • ottava bassa
  • quindicesima
• pitch
• rest values
• rests (see notes/rests)
• rhythm
• sforzando
  • forzando
  • forzato
  • sforzato
• staff (musical staff)
  • lines
  • spaces
• staff paper
• stem
• system
• treble clef