Understanding the Music Theory

2.1 Pitch and Pitch-Class

L E A R N I N G   O B J E C T I V E S

1. Defining and understanding pitch versus pitch class.
2. Understanding the staff (staves) and the Grand Staff.
3. Understanding the use of clefs.
4. Understanding the use of ledger lines.

Pitch

1

is defined as the relative highness or lowness of sound. This is a general

definition: in music we speak of pitch as a specific tone that is specifically placed
and notated.

Pitch-class

2

, a relatively recent term, describes a generalized or

generic relationship of pitches that sound essentially identical but are separated by
a sense of highness or lowness. Pitch-class also refers to tones that share the same
“pitch-space,” that is, they sound identical, but are “spelled” differently.

The Staff

Since early notation was not specific as to exact placement of pitch, a system of
parallel horizontal lines came into use in order to show exact
placement.Interestingly, earlier systems of notation employing parallel lines had
been in use. Many used

only

the lines themselves to locate pitch, not the spaces

between. This

staff

3

originated as a system of eleven parallel lines that

encompassed the theoretical span of available pitches, which was the range of the
male voice from Bass to male Soprano.In St. Paul’s Epistle to the Corinthians he
delivers an injunction to “Let your women keep silence in the Church…” This
became the rationale for the exclusion of women from participation in the early
church. In practice, this complete system was limited to four or five parallel lines
encompassing the range of a given chant melody or voice part.

1. Pitch is relative highess or

lowness of sound. Individual
pitches are specifically located
and notated on the staff.

2. Pitch-classes are all those

pitches which share the same
letter name, or share the same
“pitch-space” but have
different spellings.

3. The Staff (or staves) is a system

of parallel lines used to locate
and notate specific pitches.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

55

Figure 2.1

The Guidonian Staff

Pitches were assigned specific names. The lowest pitch, called

gamma

, extended to

the highest pitch,

ut

: the contraction of these two terms,

gamut

, has entered the

language to mean “a complete range or scope.”

The eleven-line system is visually cumbersome. In early music specific lines were
colored with different dyes, each line locating a specific pitch. All other pitches
were held in relation to these. In time, the eleven-line staff was separated into two
five-line staves. The remaining line between the two staves was not drawn, but was
understood as being “shared” by each staff.

Specific symbols came into use, replacing the colored lines. Clefs (French-“

key

”)

served the same purpose as colored lines, locating exact pitches around which all
other pitches were calculated. These clefs represented general voice ranges and
their names reflect this.

We label pitch-classes by the use of letter-names. Other labels are discussed in

Section 2.2 "Chromatic Alteration: Accidentals"

. The Treble Clef (or “G-clef”),

nominally indicating a high voice, locates the pitch “G” on the second line up on the
staff.

The Bass Clef (or “F-clef”) locates the pitch “F” on the fourth line up on the staff.
From these two fixed points, all other pitches were calculated and placed on the
five-line staff.

Figure 2.2 "Treble Clef and Staff; Bass Clef and Staff"

shows the Treble

and Bass Clefs and pitch placement on lines and spaces.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.1 Pitch and Pitch-Class

56

Treble and Bass Clefs, The Grand Staff

Figure 2.2

Treble Clef and Staff; Bass Clef and Staff

These two staves are combined into a

system

4

called

The Grand Staff

5

.In notation

we call complete lines of music a

system

. This reflects its origins from the Guidonian

staff: two five-line staves, slightly separated, the remaining invisible middle line
shared by both. The Grand Staff now yields the potential for locating and notating
all pitches, from lowest to highest.

Figure 2.3

The Grand Staff

In

Figure 2.3 "The Grand Staff"

pitches are listed just outside the boundaries of each

clef on the Grand Staff. Since the two staves (Treble and Bass) are separated from
one another in the Grand Staff, it is necessary to use symbols to extend each beyond
its five-line boundaries.

Ledger Lines

Short horizontal dashes are used to extend the range of either staff, above or below.
These dashes, called

ledger lines

6

, serve as truncated staff lines. They may occur

above or below a notehead, or they may bisect a notehead.

4. A staff or collection of staves

grouped together. It may also
refer to one complete line of
music.

5. A system of two five-line staves

used to locate and notate pitch.
This evolved from the early
eleven-line staff.

6. Ledger lines are small

horizontal dashes above,
below, or through a notehead
used to extend the range of the
staff.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.1 Pitch and Pitch-Class

57

Figure 2.4

Ledger Lines

The student should exercise particular care when drawing ledger lines. A common
mistake of nascent music students is placing the ledger line on the wrong side of
the notehead. When drawing notes observe several other properties:

1. Stems extend up or down from the notehead to the next pitch-class of

the same name.This practice for notating stem length has its early
origins as a pitch designation, not as a durational value.

2. Stems are drawn down from noteheads on the middle line of the staff

and above. Below the middle line, stems are drawn up.

3. In extended passages across the middle line of the staff, stems may be

the same direction. There is no rule for this: it is a matter of visual
uniformity.

4. For stems up: the stem is always on the right side of the notehead. For

stems down: the stem is always on the left side of the notehead.Stem
placement has not always been uniform. When studying scores of
earlier music, one will readily observe that stem placement in relation
to the notehead seemed to be a matter of choice, style, or convenience

Pitch Placement on the Staff

Using these notational devices and practices, exact pitch placement can be shown.
Note that the pitch that is one ledger line above Bass Clef is identical to the pitch
that is one ledger line below Treble Clef (both are “Middle C”). This shared,
connective pitch is reminiscent of the middle line from the Guidonian staff and
serves to connect the two staves.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.1 Pitch and Pitch-Class

58

Figure 2.5

Pitch Placement on the Grand Staff

Observe the Grand Staff. Note that pitches of the same letter name occur
throughout the system. Individual tones are specifically recognized as such. Pitches
having the same letter name but separated by range are recognized as pitch-classes.
Therefore the note one ledger line below the Treble Staff is designated as the pitch
“C” (or “Middle C”), but all notes so labeled constitute the pitch-class “C.”

Also, observe that ledger lines extending notes below Treble Clef may be written in
Bass Clef. Similarly, ledger lines extending notes above Bass Clef may be written in
Treble Clef. At times, it is more appropriate to write pitches using ledger lines,
rather than switching to another staff and clef. Exercise caution when writing or
labeling pitches that cross over “between” the staves.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.1 Pitch and Pitch-Class

59

K E Y   T A K E A W A Y S

• Pitch is relative highness or lowness of sound. The term is also used to

describe specific tones. Pitch-class is a generic designation referring to
tones sounding the same but separated by relative highness or lowness.

• The staff is a five-line system used to locate pitches. The Grand Staff is a

system of two five-line staves spanning the complete useable range of
pitches (with the use of ledger lines).

• Clefs are specialized symbols denoting specific pitches on a staff. All

other pitches are located in relation to these.

• Ledger lines are horizontal dashes that are used to extend the range of a

given staff, above or below its five-line boundaries.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.1 Pitch and Pitch-Class

60

E X E R C I S E S

1. Define pitch and pitch-class.

2. On the example provided, practice drawing Treble and Bass Clefs.

Figure 2.6

Clef Samples

3. On the example provided, practice drawing notes above and

below the staves using ledger lines.

Figure 2.7

Ledger Lines Samples

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.1 Pitch and Pitch-Class

61

2.2 Chromatic Alteration: Accidentals

L E A R N I N G   O B J E C T I V E S

1. Defining diatonic pitches and chromatic alteration.
2. Defining

musica ficta

, accidentals, precautionary accidentals.

3. Understanding enharmonic equivalence.

The term

diatonic

denotes pitches that occur naturally in a theoretical system of

music with respect to its components. A simplistic (and incorrect) view describes
diatonic pitches as “the white notes” on the piano. The word

chromatic

comes from

the Greek word for “color,”

kromos

. In early music, this term was employed to

describe those pitches lying outside of the theoretical collection of pitches, pitches
that were altered for various reasons. The term

chromaticism

7

will recur from time

to time to describe altered pitches and their effects in music.

Early music made use of a fixed number of pitches organized into a system of
overlapping six-tone sequences (

hexachords

). As compositional styles evolved and

new resources added, composers routinely altered pitches for a variety of reasons.
Sometimes a pitch was considered to sound too “hard” and was therefore
“softened” (lowered). Sometimes pitches were altered (raised) to provide a more
pronounced resolution to a following pitch. These altered pitches were called

musica ficta

(“contrived” or “feigned” music; “false” music). Originally the

conditional use of these alterations was understood, therefore not notated. In time,
the symbols representing an altered pitch were added above the note, almost as an
editorial marking. Eventually these symbols were incorporated into the music,
preceding the note they modified.

Accidentals

These symbols became what we call

accidentals

8

. The need for these alterations

came about because of our inherently flawed system of notating pitch: we have
twelve pitches in our system yet only seven letter names. Accidentals accommodate
these alterations. The “sharp” sign (the octothorpe or “pound” sign) raises a pitch,
the “flat” sign (lower-case “b”) lowers a pitch. The natural sign cancels any other
accidental. Double flats and double sharps may occur occasionally, their use
determined by context.

7. Chromaticism refers to those

altered pitches that lie
“outside” the range of a
particular collection.

8. Accidentals are those

specialized symbols used to
show chromatic alterations.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

62

Figure 2.8

Accidentals

Accidentals are always placed before the note that they modify, never behind. As a
notational convenience, an accidental will stay in effect throughout the measure
where it occurs. Any repetitions of that modified note within the measure remain
modified. The note reverts to its diatonic form in subsequent measures.In much
music of the modern era, accidentals only modify those notes that they
immediately precede. If this is the case, it is so indicated in performance notes.
Often however, as a reminder, composers will place a precautionary accidental
before the note that was previously chromatically altered.

Enharmonic Equivalence

All pitches, but chromatic pitches especially, may be “spelled” in different ways.
These differing spellings are context-dependent (or a matter of convenience) as will
be discussed below. Notes that share the same pitch space but employ different
spellings are said to be

enharmonically equivalent

.

Enharmonic equivalence

9

is an

attribute that will come to have greater significance as our argument progresses.

Figure 2.9

Enharmonic Equivalents

9. Enharmonic equivalence

describes pitches that share
the same pitch-space (sound
identical) but are “spelled”
differently.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.2 Chromatic Alteration: Accidentals

63

K E Y   T A K E A W A Y S

• Diatonic versus chromatic pitches.
•

Musica ficta

, accidentals, precautionary accidentals.

• Enharmonic equivalence.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.2 Chromatic Alteration: Accidentals

64

E X E R C I S E S

1. On the example provided, practice drawing notes with

accidentals.

Figure 2.10

Accidental Samples

2. On the example provided, draw the enharmonic equivalent for

each note listed.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.2 Chromatic Alteration: Accidentals

65

Figure 2.11

Enharmonic Equivalents

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.2 Chromatic Alteration: Accidentals

66

2.3 The Keyboard as a Visual Tool

L E A R N I N G   O B J E C T I V E S

1. Familiarization with the layout of the keyboard.
2. Recognition of note placement on the keyboard.
3. Understanding the use of the keyboard as a visual tool.

The keyboard serves as a visual reference for locating and identifying pitches.
Observe

Figure 2.12 "Small Keyboard Diagram"

below. Notice the layout of the

keyboard: there are two black keys grouped together, then three black keys
grouped together. These visual reference points will help the familiarization
process. Also observe the labels for the keys on the keyboard.

Figure 2.12

Small Keyboard Diagram

© Thinkstock

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

67

All musicians, regardless of discipline or instrument, should familiarize themselves
with the keyboard. We are all visual learners to a greater or lesser extent. The
visual layout of the keyboard will foster an understanding of pitch placement,
register designation, scale construction, interval distance, chord construction-
virtually every acquired skill in the study of music. The keyboard is a powerful and
valuable tool.

In

Figure 2.12 "Small Keyboard Diagram"

observe that some white note pairs have

an intervening black note and two pairs do not. Let us focus upon those two.
Adjacent pitches are called

semi-tones

(or ”half steps”). The pitches E-F and B-C (the

two white key pairs) are called

diatonic half steps

. Half steps that are measured from

a white key to a black, or vice-versa, are called

chromatic half steps

.

The distance of a

semi-tone

or half step is the same for any two adjacent pitches

across the keyboard.

Figure 2.13 "Keyboard and Half Steps"

shows this relationship

in pitches.

Figure 2.13

Keyboard and Half Steps

© Thinkstock

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.3 The Keyboard as a Visual Tool

68

Notes that are separated by an intervening note are called

tones

, or whole steps.

Whole steps are formed by spanning the distance of two half steps.

Figure 2.14

"Keyboard and Whole Steps"

shows representative whole steps.

Figure 2.14

Keyboard and Whole Steps

© Thinkstock

Figure 2.15 "Piano Keyboard"

shows the entire piano keyboard. Each occurrence of

the pitch-class “C” is labeled, as is the span from one C to the next. This visual
reference will be helpful in understanding the following section.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.3 The Keyboard as a Visual Tool

69

Figure 2.15

Piano Keyboard

© Wikicommons, Artur Jan Fijalkowski

K E Y   T A K E A W A Y S

• Layout of the piano keyboard and note placement.
• Using the keyboard to visually recognize whole steps and half steps.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.3 The Keyboard as a Visual Tool

70

E X E R C I S E S

1. Define whole steps and half steps in the context of the piano keyboard.

Define

diatonic

and

chromatic

half steps.

2. On the keyboard diagram provided, label all pitches. Give

enharmonic spellings for all black keys.

Figure 2.16

Keyboard

3. As an Aural Skills drill, perform the following:

a. At the piano, play adjacent pitches (half steps) at random.

Match and sing.

b. Play whole steps at random. Match and sing.

c. Repeat both tasks

descending

.

d. Play single notes at random. Sing a half step above and a

whole step above.

e. Repeat this task

descending

.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.3 The Keyboard as a Visual Tool

71

2.4 Register Designation, The Octave, 8va, and 8vb

L E A R N I N G   O B J E C T I V E S

1. Understanding the use of register designations and labeling specific

pitches.

2. Understanding the term octave and its use.
3. Understanding

8va

and

8vb

as notation conventions.

By using the Grand Staff, we can locate specific pitches from low to high. However it
is necessary to assign more precise values to pitches according to their specific
range in this spectrum. For this task we employ

register designations

10

.

The Octave

To do this, we first separate the entire span of pitches into discrete segments
labeled

octaves

(Italian:

ottava

“eight”). In this context, an octave is a segment of

pitches spanning the distance from one pitch to its pitch-class counterpart above or
below. Further, it is customary to speak of pitches as residing in some particular
“octave.”

Figure 2.17

Octave

Using the

octave

11

as a range-specific designator, pitches can be precisely located

and identified by letter name as well as by register. Originally, a register
designation system evolved that employed upper- and lower-case letter names.
Multiple lower case letters (C, CC, CCC) denoted lower octaves while upper-case
letter names followed by one or more apostrophes denoted higher octaves. While
this system may still be encountered occasionally, it is gradually being abandoned
in favor of a more malleable system.

Register Designation

In the 1970’s, the Acoustical Society of America instituted a register designation
system based upon the layout of the piano keyboard. This system uses letter names

10. The labeling system used to

locate pitch based upon the
piano keyboard.

11. In this context, an eight-tone

species

, or sequence of pitches.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

72

to denote pitch. Each letter name is followed by a number denoting the octave
within which that pitch resides. Each octave begins with the note “C” and extends
to the “B” seven steps above.

There are three pitches below the lowest C (C1) on the average piano keyboard.
These notes are labeled in two ways: A0, Bb0, B0, or simply A, Bb, B. So, the entire
piano keyboard spans the range from A0 to C8.

Figure 2.18 "Keyboard with Octave

Designations"

shows this entire keyboard with each octave designation labeled.

Figure 2.18

Keyboard with Octave Designations

© Wikicommons, Artur Jan Fijalkowski

The use of register designations is coupled with, and reinforced by, the visual tool
of the piano keyboard. This becomes an indispensable skill for every musician.

Often the range of a particular segment of music will be written in extremes of
register, high or low. This is notated using multiple ledger lines. Often, as a
notational convenience and to make for ease of reading, composers may employ
symbols denoting that a passage is played an octave higher than written (

8va-

ottava

), or an octave lower than written (

8vb-ottava bassa

). In order to avoid using

ledger lines, the passage is written in a lower octave, then labeled above the staff if

8va

, below the staff if

8vb

. A bracket extends from the

ottava

symbol to the end of

the passage that is raised or lowered.

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.4 Register Designation, The Octave, 8va, and 8vb

73

Figure 2.19

8va, 8vb

At times composers will use the symbols

15ma

and

15mb

to denote that the passage

is to be played two octaves higher or lower. While uncommon, this is occasionally
used, especially as a notational convenience. A composer may indicate that a
passage is to be performed two octaves higher or lower by including this as an
instruction.

Figure 2.20

15ma

K E Y   T A K E A W A Y S

• Understanding and employing register designations for locating pitch.
• Use of the piano keyboard to support recognizing registral designations.
•

8va

and

8vb

,

15ma

and

15mb

Chapter 2 The Elements of Pitch:Sound, Symbol, and Tone

2.4 Register Designation, The Octave, 8va, and 8vb

74