Understanding the Music Theory

E X E R C I S E S

1. Define octave. Define register designation.

2. On the keyboard diagram provided, label octave designations.

Figure 2.21

Octave Designations

© Thinkstock

3. On the example provided:

a. Re-write 8va and 8vb segments at pitch.

b. Re-write segments employing

8va

and

8vb

.

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

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

75

Figure 2.22

8va, 8vb

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

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

76

2.5 Pitch Notation: Nomenclature and Solfége

L E A R N I N G   O B J E C T I V E S

1. Understanding how pitches may be labeled.
2. Understanding

solfége

syllables as pitch labels and aural reference.

3. Understand scale degree number notation.

In our system we label pitches using letter names. In other countries pitches are
labeled using

solfége

12

syllables. This tradition originated as a pedagogical device

invented by Guido. The syllables, originally

Ut

,

Re

,

Mi

,

Fa

,

Sol

,

La

, come from the

initial syllable of each line of

Ut queant laxis

, an Ambrosian hymn to St. John the

Baptist. Each line of music starts on a successively higher pitch. Guido employed
this as a pedagogical tool for training singers.

Figure 2.23

Ut queant laxis

© David J. Gonzol. Used by permission.

12. Syllables adapted to denote

pitches. Originally used as a
pedagogical mnemonic.

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

77

Since

Ut

is the only syllable in the collection ending on a hard consonance, it was

eventually replaced by the syllable

Do

(from

Domine

-Latin-“Lord”) to facilitate

singing. In the 15th-century a seventh tone and syllable was added,

Si

, an acronym

for

Sancte Ioannes

, the last two words from

Ut queant laxis

,. This became the syllable

Ti

in 19th-century English sol-fa.The inclusion of the syllable

Ti

is attributed to

Sarah Glover.

Ti

was substituted for

Si

so that each solfége syllable would begin on a

differing consonant. Thus we have

solfége

labels for pitches.

Figure 2.24

Ut queant laxis: Pitches and Syllables

Originally these syllables were fixed: each syllable referred to one specific pitch. “C”
was always

Do

, regardless of context or chromatic alteration, “D” was always

Re

and

so on. This fixed system is prevalent in those European countries, as well as among
musicians trained in that tradition. A modified, moveable system of

solfége

has

become prevalent in American music theory pedagogy. This will come into focus in

Chapter 3 "The Foundations Scale-Steps and Scales"

.

One other notational convention has become commonplace in recent years. A caret
is placed above a number, the caret denoting the words “scale degree.” This is
adapted from the analytical symbolization of the reductive analysis techniques of
the German-Austrian theorist Heinrich Schenker.

Figure 2.25

Scale Degree Numbers

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

2.5 Pitch Notation: Nomenclature and Solfége

78

K E Y   T A K E A W A Y S

•

Solfége

as pitch labels.

• Scale degree numbers.

E X E R C I S E S

1. Define

solfége

and list the syllables in order. Include original syllables as

well as replacements and additions.

2. As an Aural Skills drill:

a. Sing the

solfége

syllables ascending and descending.

b. Concentrate upon and sing

Mi-Fa

and

Ti-Do

(diatonic half

steps).

c. Concentrate upon and sing

Do-Re

,

Re-Mi

;

Sol-La

,

La-Ti

(whole

steps).

(Sing in a comfortable register for now. Do not pronounce the
“L” when singing

Sol

).

3. Explain the use of the caret placed above a number.

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

2.5 Pitch Notation: Nomenclature and Solfége

79

2.6 Moveable C-Clef; Other Clefs

L E A R N I N G   O B J E C T I V E S

1. Understanding Moveable C-Clef.
2. Understanding Alto Clef and Tenor Clef.
3. Other Clefs.

In discussing the evolution and formation of the staff, we saw that the eleven-line
Guidonian staff separated into two five-line staves. The remaining line was not
discarded as such, but rather served as a connective or “shared” line between the
two staves.

This invisible middle line locates the pitch C4 (“Middle C”). On the grand staff this
appears as a note one ledger line below the staff in Treble Clef, or a note one ledger
line above the staff in Bass Clef.

Figure 2.26

C4 (“Middle C”) on the Grand Staff

Moveable C-Clef

From the Guidonian staff a separate clef evolved denoting this particular pitch. This
clef is called ‘C-Clef,” or properly, “

Moveable C-clef

13

.”

13. A clef derived from the eleven-

line staff. This clef locates C4
regardless of what line of the
staff it is placed upon.

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

80

Figure 2.27

C4 C-Clef

This clef may occur on any line in the staff. Regardless of which line it occurs on, it
always locates C4, “Middle C.” Originally, the use of this clef was concerned with
particular voice ranges. The moveable C-Clef kept the majority of pitches of a given
voice within the boundaries of the staff conforming to the typical range of that
voice. Hence the common names for this clef as it occurs on each line reflect the
associated voice part.

Figure 2.28

C-Clefs by Voice

Alto and Tenor Clefs

The C-Clef on the lowest line of the staff is called Soprano Clef, the second line
Mezzo-Soprano Clef, the third line

Alto Clef

14

, the fourth line

Tenor Clef

15

and the

top line Baritone Clef. Until the 19th Century (approximately) choral music was
written in open score, each voice part on a separate staff with the appropriate clef.
Gradually this became an arcane procedure.

Two of the Moveable C-Clefs have been retained in common use in instrumental
writing, primarily because of the ranges of certain instruments. Alto Clef is
predominantly used in writing for the Viola. If Treble or Bass Clefs were used, the

14. The C-clef placed on the second

line of the staff. Used primarily
for Viola.

15. The C-clef placed on the fourth

line of the staff. Used for ‘Cello,
Bassoon, and Trombone.

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

2.6 Moveable C-Clef; Other Clefs

81

Viola part would need to be written with a surfeit of ledger lines-it’s general range
occupies the space “between” and “overlapping” Treble and Bass Clefs. The ‘Cello
often employs Tenor Clef (in addition to Bass Clef). In orchestral and more
advanced wind ensemble literature (but curiously, not in Jazz), Tenor Clef may be
used for the upper register of the Trombone. Again, the purpose is to keep the
majority of the pitches within the boundaries of the staff.

Other Clefs

The remaining C-Clefs are not normally encountered except in autograph scores
and facsimile editions of earlier music. There are several other clefs, one of which
has become very common, the others rarely seen. In Choral writing, Tenor Clef is
commonly replaced by a Treble Clef with an “8” (

ottava

) sign appended to the

bottom of the clef.

As open score became less common, and as fewer musicians were trained to read
Tenor Clef efficiently, this “compromise” clef came into general use. It reads exactly
as Treble Clef but “sounds” down an octave, conforming to the range of the Tenor
voice.

Figure 2.29

Octave Tenor Clef

Two clefs are no longer in use, French Violin Clef (locating G4) on the lowest line of
the staff, and a Bass Clef (F-Clef) located on the middle line of the staff. This is called
French Baritone Clef.

Figure 2.30

French Violin and French Baritone Clefs

The Neutral Clef is used for non-pitched percussion instruments.

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

2.6 Moveable C-Clef; Other Clefs

82

Figure 2.31

The Neutral Clef

Since Alto and Tenor Clefs have been retained in common usage, it is necessary to
learn to read these with some facility. When first encountered, this can be a
daunting task. Some say that familiarization and memorization is the only method
for learning these clefs. There are expedient shortcuts however, that may help to
facilitate the process:

1. For Alto Clef:

a. Think of the note name in Treble Clef and “read” this one line or

space

higher

.

b. This is only the pitch-class name. The actual pitch is an octave

lower. See example.

Figure 2.32

Alto Clef Shortcut

2. For Tenor Clef:

a. Think of the note name in Treble Clef and “read” this one line or

space

lower

.

b. Again this is only the pitch-class name. The actual pitch is an

octave lower. See example.

Figure 2.33

Tenor Clef Shortcut

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

2.6 Moveable C-Clef; Other Clefs

83

K E Y   T A K E A W A Y S

• Understanding Moveable C-Clefs.
• Understanding Alto and Tenor Clefs.
• Understanding Octave Tenor Clef.

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

2.6 Moveable C-Clef; Other Clefs

84

E X E R C I S E S

1. On the example provided, practice drawing Alto and Tenor Clefs.

Figure 2.34

Drawing Alto and Tenor Clefs

2. For each example in Treble or Bass Clef, re-write in Alto or Tenor

Clef as directed. Label pitches by letter name and by register
designation.

Figure 2.35

Re-write to Alto and Tenor Clefs

3. Examples of Octave Tenor Clef are given. Re-write these in Tenor

Clef.

Figure 2.36

Octave Tenor Clef to Tenor Clef

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

2.6 Moveable C-Clef; Other Clefs

85

2.7 Summary

This chapter acquaints the student with those notational devices and practices that
identify and locate pitch precisely. The concept of generic pitch-class is also
introduced as well as labeling conventions and

solfége

syllables.

This information and the subsequent attainment of fluent use by repetitive drill
shall prepare the student to examine pitch and pitch structures in following
chapters.

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

86

Chapter 3

The Foundations Scale-Steps and Scales

Introduction

In this chapter, we shall examine the small incremental distances called

Tones

and

Semi-tones

. More commonly labeled

whole steps

1

and

half steps

2

, these foundation

scale-steps serve as the building materials from which we construct sequential
orderings of pitches called

scales

3

.

The construction of various scales shall also be examined, especially the Major Scale
and the Minor Scale. Additionally, other important scale patterns will be shown.

1. Adjacent scale steps that have

an intervening half step.

2. Adjacent tones, the smallest

distance between tones in the
current system of tuning.

3. A sequential collection of five

or more pitches.

87

3.1 Scales and Scale-Steps

L E A R N I N G   O B J E C T I V E S

1. Define scales and foundation scale-steps.
2. Define scale types.
3. The Chromatic Scale.

In examining the notation of pitch, we observe that notes climbed or “scaled” the
lines and spaces of staves from low to high. Ordered sequential collections of these
pitches are called scales (Italian:

scala

-“ladder”).

Scales

Scales are comprised of five or more pitches arranged in sequential patterns of
whole steps and half steps spanning an

octave species

. We label scales as to the

number of differing elements they contain:

1.

Pentatonic

: a five-tone scale.A true pentatonic scale divides the octave

into five-equal steps. This is true in the music of many cultures.
Because of the adopted tuning system employed by Western Music
(called equal temperament), we must employ elements larger than
whole- and half- steps when constructing pentatonic scales. Play only
the black keys on the piano and you will readily see and hear this
familiar sound.

2.

Hexatonic

: a six-tone scale.

3.

Heptatonic

: a seven-tone scale.

4.

Octatonic

: an eight-tone scale, and so forth.

Four-note sequences are called

tetrachords

(Greek: “four tones”). In this context,

they are regarded as constituent components of larger scale patterns.

Since scales are orderings of whole steps and half steps, these serve as the
foundation “building-blocks” for scale construction. As we learn to construct and
identify scales, we do so by recognizing their content in terms of

tones

(whole steps)

and

semi-tones

(half steps).Although

tone

and

semi-tone

are proper names, whole step

and half step are commonly used terms. In some instances you may encounter the
terms

whole tone

and

half tone

also. For now, avoid calling whole steps and half steps

Chapter 3 The Foundations Scale-Steps and Scales

88

by any other name, for example, “major-seconds” or “minor–seconds.” Proper
interval identification for whole steps and half steps shall be addressed in

Chapter 5

"Intervals"

.

Throughout the history of music, various systems of referential tuning have
evolved, been adopted, been modified, and been discarded in favor of other
systems. It is not within the purview of this discussion to examine these various and
sundry systems of tuning.An exceptionally clear and concise discussion of the
history and theory of tuning systems may be found in Chapters 1 and 2 of

Chromaticism: Theory and Practice

, Howard Boatwright, Walnut Grove Press, 1994.

For our purposes, we shall limit the discussion to the standardized tuning system
known as

equal temperament

4

. Music in the transitional period between the

Renaissance and Baroque employed different tuning systems that limited
compositional resources. A “compromise” tuning system was proposed and
gradually adopted, whereby pitches were slightly altered enabling the division of
the octave into twelve equal portions or

semi-tones

(half steps). This “evenly-tuned,”

or “equal-tempered” system allowed composers to employ the full resources of the
chromatic collection.This will come into focus in

Chapter 4 "Key Sense, Key

Signatures, and The Cycle of Fifths"

and

Chapter 5 "Intervals"

.

Therefore, the source collection for Western music is the

Chromatic Scale

5

.The

Chromatic Scale, so called because it contains all the pitch “colors,” is also known as
the

Duodecuple scale

(Latin:

duo-deca

, “two and ten”). It is also labeled the

Non-

Selective Scale

, so-called because, all pitches being of equal quality, no one pitch

asserts itself over the others.

The Chromatic Scale

Figure 3.1

The Chromatic Scale

Audio 1

The Chromatic Scale

4. The current system of tuning

whereby pitches have been
adjusted to allow division of
the octave into twelve equal
portions.

5. The source set or collection for

pitch materials as defined
within equal temperament.

Chapter 3 The Foundations Scale-Steps and Scales

3.1 Scales and Scale-Steps

89

(click to see video)

The Chromatic Scale is comprised entirely of half steps. When constructing this, it is
customary to use sharps when ascending and to use enharmonically equivalent flats
when descending.

Music of the mid-17th Century through end of the 19th Century saw the
formulation of a more or less unified system of composition and its supportive
theory. A

lingua franca

of music was established, essentially a common language

shared by all musicians. Music of the period (roughly!) from Corelli through Brahms
is called the

Common Practice Period

6

, or the Common Practice style.

One of the fundamental attributes of this Common Practice style was the use of two
scale types. These two types,

Major

and

Minor

were “distilled” from the multiple

scale types employed in early music. Major and Minor scales became the
predominant resource for Common Practice music. These scale types shall become
essential tools for many of the acquired tasks and skill-sets in the study of music.
Understanding and recognizing these constructs is a fundamental and necessary
attribute of the music student.

K E Y   T A K E A W A Y S

The student should understand:

• The definition of scales and scale types.
• The Foundation (“building-block”) scale steps,

tones

and

semi-tones

(whole steps and half steps).

• The Chromatic Scale.
• The definition of the Common Practice Period.

E X E R C I S E S

1. Obtain a three-ring binder and fill with staff paper. If you wish, purchase

a music manuscript notebook, at least 8.5 x 11. This will become your

Scale Thesaurus

.

2. Draw the ascending and descending Chromatic scale. Use half notes. Use

the appropriate accidentals and enharmonic equivalents ascending and
descending.

6. Music from roughly the 17th-

through the 19th Centuries.
Also may be referred to as
Tonal Music.

Chapter 3 The Foundations Scale-Steps and Scales

3.1 Scales and Scale-Steps

90

3.2 Heptatonic Scales: The Major Scale, The Three Forms of the Minor
Scale

L E A R N I N G   O B J E C T I V E S

1. The Major scale and its attributes.
2. The Minor scale and its attributes.
3. Relative and Parallel Major/Minor.
4. Scale degree nomenclature.
5. The evolution of Minor scales: the three forms of the Minor scale

Any initial discussion of scales inevitably centers around these two seven-tone
scales employed in the composition of Common Practice music.

The Major Scale

The most common scale pattern used is the

Major Scale

7

. It is an arrangement of

whole and half steps as follows:

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

1

2

3

4

5

6

7

8

W

W

H

W

W

W

H

Note that half steps occur between scale degrees 3–4 and 7–8. This is shown in
pitches and the keyboard in

Figure 3.2 "Major Scale, Keyboard and Pitches"

.

Figure 3.2

Major Scale, Keyboard and Pitches

7. A heptatonic (“seven-tone”)

scale consisting of the
following arrangement: W-W-
H-W-W-W-H.

Chapter 3 The Foundations Scale-Steps and Scales

91

Audio 2

The Major Scale

(click to see video)

This arrangement of whole steps and half steps is maintained for any major scale on
any given starting pitch. Accidentals are used to modify pitches in order to retain
this same arrangement of whole and half steps. Compare the samples below to the
keyboard diagram. Observe the placement of whole and half steps on the keyboard
that maintain the proper ordering.

Figure 3.3

Other Examples of Major Scales

Audio 3

Other Major Scales

(click to see video)

Observe that in each new octave species, some chromatic alteration is required in
order to retain the same arrangement of scale steps.

An alternate view of major scale construction is an examination of its constituent
tetrachords (from the Greek: “four tones”). Observe that the arrangement of whole
and half steps in the first tetrachord are identical to that of the second tetrachord.
Both tetrachords are W-W-H separated by a whole step.

So, two mnemonics are suitable for remembering Major scale construction:

1. W-W-H-W-W-W-H
2. Identical tetrachords (W-W-H) separated by a whole step.

Chapter 3 The Foundations Scale-Steps and Scales

3.2 Heptatonic Scales: The Major Scale, The Three Forms of the Minor Scale

92

The keyboard diagram is another essential tool for familiarization and recognition
of major scales. The visual reinforcement of whole step and half step placement will
hasten the learning process.

The individual scale steps have specific labels. These terms have come into general
use, having their origins in early 18th-century theoryFrench composer and theorist
Jean Phillipe Rameau employs versions of these terms in his seminal work

Traité de

l’harmonie

(1728). Our current usage of these terms is adapted from this work.

Figure 3.4 "Scale-step Labels"

shows the major scale and its accompanying scale

step labels.

Scale-Step Labels

Figure 3.4

Scale-step Labels

1. The first degree of any scale is called the

Tonic

pitch. This is the pitch

that asserts itself over all the others in the collection, the pitch that
our ear naturally seeks as being the strongest.These terms will be
affiliated with chords in keys as well.

2. The next strongest pitch is the fifth scale degree, the

Dominant

. It is

considered to be the “polar opposite” of

Tonic

: whereas

Tonic

represents stability and sense of conclusion,

Dominant

represents

instability and a sense of tension.

3. The third scale degree lies halfway between these and so is labeled the

Mediant

.

4.

Dominant

is five scale-steps up from

Tonic

. Five steps below

Tonic

is the

fourth scale degree, labeled

Subdominant

.

5. Since the

Mediant

lies three steps up from

Tonic

, three steps down is

labeled

Submediant

(the sixth scale degree).

6. The second scale degree is labeled

Supertonic

.

7. Lastly, the most powerful melodic motion we respond to is the

ascending half step, from scale degree seven to the octave. Our ear is
compelled to resolve this

Leading Tone

.

Figure 3.5

Scale-steps in Order of Importance

Chapter 3 The Foundations Scale-Steps and Scales

3.2 Heptatonic Scales: The Major Scale, The Three Forms of the Minor Scale

93

The Minor Scale

The other heptatonic scale used in Common Practice music is called the

Minor

Scale

8

. It is arranged as follows:

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

1

2

3

4

5

6

7

8

W

H

W

W

H

W

W

Figure 3.6

The Minor Scale

Audio 4

The Minor Scale

(click to see video)

For this example, the pitches are identical to the Major scale example above, re-
arranged from scale degree six.

Figure 3.7 "Minor Scales on a; on c; Major Scale on

C"

shows the same Minor scale pattern, but constructed from the same starting

pitch. Both are then compared to the Major scale.

Figure 3.7

Minor Scales on a; on c; Major Scale on C

As with major scales, minor scales use accidentals to retain the same “shape” when
starting on differing pitches.

8. A heptatonic scale having three

distinct forms, Natural,
Harmonic, and Melodic Minor.

Chapter 3 The Foundations Scale-Steps and Scales

3.2 Heptatonic Scales: The Major Scale, The Three Forms of the Minor Scale

94