Description
This collection would be great for anyone who is trying to learn the music theory, and it's important for any musician.
This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/ 3.0/) license. This book was accessible as of December 29, 2012, and it was downloaded then by Andy Schmitz (http://lardbucket.org) in an effort to preserve the availability of this book.
Study Set Content:
Figure 3.8
Other Examples of Minor Scales
Audio 5
Other Minor Scales
The previous examples demonstrate particular relationships between Major and
Minor scales:
1. Major and Minor scales that have the same pitch content but different
starting pitches are said to be
relative
to one another, for example C
major and a minor.
2. Major and Minor scales that have differing pitch content but the same
starting pitch are said to be
parallel
to one another, for example C
major and c minor.
In order to discover the
Relative Major/Minor
9
relationship, follow this procedure:
1. To find the
Relative Minor
scale of any Major scale:
a. Go to the sixth degree (
Submediant
) of the Major scale.
b. Re-order the scale content from that pitch.
c. Think “
Major to Minor: up to 6
.”
2. To find the
Relative Major
scale from any Minor scale:
a. Go to the third degree (
Mediant
) of the Minor scale.
b. Re-order the scale content from that pitch.
c. Think “
Minor to Major: up to 3
.”
We do not recommend the “three up or three down” method that is sometimes
employed. This leads to confusion on the part of the student. Inevitably, the student
will go down the wrong specific pitch distance, or will confuse which relationship is
which direction.
9. The relationship between
Major and Minor scales
wherein they share the same
pitch content but have a
different order.
Chapter 3 The Foundations Scale-Steps and Scales
3.2 Heptatonic Scales: The Major Scale, The Three Forms of the Minor Scale
95
In order to discover the
Parallel Major/Minor
10
relationship, simply construct
major or minor from the same starting pitch.
Relative and Parallel Major/Minor
Relative
and
Parallel Major/Minor
will extend to our discussion of keys in
"Key Sense, Key Signatures, and The Cycle of Fifths"
.When labeling scales it is
customary to use upper case letter names for major and lower case letter names for
minor. When hand-drawn, a dash is placed above the letter c only. This should not
be used for other lower case letters. These relations commute from each form to the
other: one speaks of Major and its
relative
Minor, or Minor and its
relative
Major. The
same is true for the
parallel
relationship.
Figure 3.9
Relative and Parallel Scales: Major to Minor and Minor to Major
Audio 6
Relative and Parallel Scales
Just as the Major scale has labels for its constituent scale-steps, these labels are also
used for Minor scales. There is one notable exception: since the distance between
scale degree seven and the octave is a whole step, it does not possess the same
sensation of required resolution as its major counterpart (the
Leading Tone
).
Therefore it is labeled
Subtonic
.
Scale-Step Labels for Minor
Figure 3.10
Minor Scale-Step Labels
10. The relationship between
Major and Minor scales
wherein they share the same
starting pitch but different
pitch content.
Chapter 3 The Foundations Scale-Steps and Scales
3.2 Heptatonic Scales: The Major Scale, The Three Forms of the Minor Scale
96
Earlier, the
Leading Tone
was described as the most powerful melodic step that we
respond to in terms of demanding resolution. This half step between scale degrees
seven and eight is not present in the naturally occurring Minor scale. Beginning
with its antecedents in early music, the minor sonority was routinely altered to
address this perceived flaw.
Harmonic Minor
Composers chromatically raised the seventh scale degree in minor as a matter of
routine in order to provide a more powerful melodic resolution. Additionally, this
alteration affected the accompanying harmonies, engendering a more powerful
harmonic resolution as well.
This led to an additional, altered form of the minor scale. The original diatonic form
of the minor scale is called
Natural (or Pure) Minor
11
. Because of its implied
harmonic consequence, the altered version (raised 7, or +7) is called the Harmonic
Form of the Minor scale, or simply
Harmonic Minor
12
.
Figure 3.11
Natural and Harmonic Minor
Audio 7
Natural and Harmonic Minor Scales
The component scale steps for Harmonic minor are:
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
1
2
3
4
5
6
7
8
W
H
W
W
H
(1 + 1/2)
H
Observe several properties:
11. The naturally occurring
diatonic “parent” version of
the Minor scale.
12. The most commonly used and
expected form of the Minor
scale. It is altered from Natural
Minor by raising the seventh
scale degree to artificially
create a
Leading Tone
.
Chapter 3 The Foundations Scale-Steps and Scales
3.2 Heptatonic Scales: The Major Scale, The Three Forms of the Minor Scale
97
1. The seventh scale degree is raised in this form of minor. Depending
upon the starting pitch and the scale, this may use an accidental in the
form of either a sharp sign or a natural sign.
2. There are three instances of half steps in this form: 2–3, 5–6, and now
+7–8.
3. Because of the alteration the distance between 6 and 7 has been
expanded to form a “step and a half.” This was considered to be a
melodic “flaw.” While inherent and necessary to the form, it was
considered to be “un-singable” and in need of correction in
performance practice.
Figure 3.12
Other Examples of Harmonic Minor Scales
Audio 8
Other Harmonic Minor Scales
Melodic Minor
This perceived
melodic
flaw in Harmonic minor, the “step and a half” between scale
degrees 6 and 7, was subject to routine alteration as well. In order to eliminate this
awkward gap, composers routinely raised the sixth scale degree
as well as the
seventh
. Since this was done to correct the perceived melodic flaw, a third form of
the minor scale came to be recognized, called the Melodic Form of the Minor scale,
or simply
Melodic Minor
13
.
Figure 3.13
Natural, Harmonic, and Melodic Minor Scales
13. The second altered version of
the Minor scale. It is altered by
raising both the sixth and
seventh scale degrees.
Chapter 3 The Foundations Scale-Steps and Scales
3.2 Heptatonic Scales: The Major Scale, The Three Forms of the Minor Scale
98
Audio 9
Natural, Harmonic, and Melodic Minor Scales
The component scale steps for Melodic minor are:
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
1
2
3
4
5
6
7
8
W
H
W
W
W
W
H
Observe several properties:
1. Both the sixth and seventh scale degrees have been raised. Depending
upon the starting pitch and the scale, this uses accidentals in the form
of sharp signs, natural signs, or a combination of the two.
2. The second tetrachord of this scale is identical to the second
tetrachord of the Major scale.
3. It is customary to
revert
to the Natural minor form when descending.
This
must
be shown using the appropriate accidentals. In some melodic
minor scales double sharp signs must be used to alter sixth and
seventh scale degrees. When reverting back to Natural minor, a
Natural sign
followed
by a sharp sign is used,
not merely a sharp alone
.
Figure 3.14
Other Examples of Melodic Minor Scales
Audio 10
Other Melodic Minor Scales
Chapter 3 The Foundations Scale-Steps and Scales
3.2 Heptatonic Scales: The Major Scale, The Three Forms of the Minor Scale
99
Before continuing several very important points must be made:
1. Minor is considered to be only one entity. It is not appropriate to speak
of “three separate minor scales,” as if they are inherently different
species.
2. Although one entity, minor has three distinct
forms
, Natural,
Harmonic, and Melodic. These forms evolved to accommodate musical
and compositional needs over the evolutionary history of Western
music.
3. The three forms have distinct properties:
a. Natural (or Pure) Minor has no
Leading Tone
. This was considered to
be an inherent weakness or flaw.
b. Harmonic Minor seeks to correct this weakness by raising the
seventh scale degree, artificially creating a
Leading Tone
. This in
turn generates a
melodic
flaw in the gap between scale degrees 6
and 7.
c. This melodic flaw was corrected by raising the sixth scale degree
(in the presence of the raised seventh scale degree). Since this
yields a second tetrachord equivalent to its Major scale
counterpart, this process is undone in its descending form by
reverting to Natural Minor.
4. Lastly, Harmonic minor is the expected, normal form of Minor used by
composers in practical composition.
Composers seemed to require the motion from the
Leading Tone
to the
Tonic
. Just as
much, they seemed to favor the naturally occurring sixth scale degree, the
Submediant
, “falling” to the
Dominant
. In the study of music theory,
expect
to see,
expect
to hear, and
expect
to use the Harmonic form of Minor. The unique properties
of the other forms are used sparingly and are subject to conditions for their use.
In summary, major and minor scales form the fundamental source sets, and
therefore the basis of the compositional language in Common Practice music. All
the great music of the recognized master composers employed these same
constructs as the basic elements of their compositional language.
Chapter 3 The Foundations Scale-Steps and Scales
3.2 Heptatonic Scales: The Major Scale, The Three Forms of the Minor Scale
100
K E Y T A K E A W A Y S
The student should understand:
• Taxonomy and nomenclature for scale steps and scale components.
• The Major Scale and its attributes.
• The Minor Scale, its three forms and their attributes.
• Relative Major/Minor, Parallel Major/Minor
E X E R C I S E S
1. In your
Scale Thesaurus
:
a. Construct Major scales on C, G, F, D, Bb.
b. Use half notes, ascending only. Use appropriate stem
direction.
c. Label each scale step by scale degree number and mark the
half steps.
2. In your
Scale Thesaurus
:
a. Construct Natural Minor scales on a, e, d, b, g.
b. Use half notes, ascending only. Use appropriate stem
direction.
c. Label each scale step by scale degree number and mark the
half steps.
3. In your
Scale Thesaurus
:
a. Construct the Harmonic and Melodic Minor forms for each
Natural Minor scale in Exercise 2.
b. Harmonic Minor, ascending only; Melodic Minor, ascending
and descending.
c. Make sure to use the appropriate accidentals and mark the
half steps.
Chapter 3 The Foundations Scale-Steps and Scales
3.2 Heptatonic Scales: The Major Scale, The Three Forms of the Minor Scale
101
3.3 Solfége Revisited
L E A R N I N G O B J E C T I V E S
1.
Solfége
systems: a comparison.
2. The audio-acoustic “trigger.”
In
Chapter 2 "The Elements of Pitch:Sound, Symbol, and Tone"
solfége
was
explained in its historical and pedagogical context, and as one way of labeling pitch
and as a mnemonic device. The principal use of
solfége
as a pedagogical tool is the
aural reinforcement of written music.
Many differing
solfége
systems have evolved, each for a specific reason, for a specific
context, or to offer an alternate method to a previous system. They can be classified
into two broad categories:
1.
Fixed Do
14
:
Do
is always sung as some form of the pitch name “C.” All
other pitches are labeled accordingly.
2.
Moveable Do
15
:
Do
will shift to whatever pitch serves as the
Tonic
. All
other pitches shift accordingly.
Several subcategories have evolved from
Moveable-Do
and involve the treatment of
the Minor mode. The two most prevalent are called
La-based Minor
16
and
Do-
based Minor
17
.
1.
La-based Minor
: The
Tonic
in Major begins on
Do
. The
Tonic
in Minor
begins on
La
.
General advantages:
a. Ease of use from a melodic orientation in predominantly diatonic
music.
b. Half step placement is retained between Major and Relative Minor
(
Mi-Fa
,
Ti-Do
).
c. Widely used as a part of Orff-Kódaly training.
Minor syllables in
La-based Minor
:
14. A solfége system wherein
Do
is
always C,
Re
is always D, and so
forth.
15. A solfége system wherein
Do
shifts to the starting pitch of
the scale. Other syllables are
sung in relationship to this.
16. A sub-category of Moveable
Do
.
Major is sung beginning on
Do
,
Minor begins on
La
.
17. A sub-category of Moveable
Do
.
Both Major and Minor begin on
Do
.
Chapter 3 The Foundations Scale-Steps and Scales
102
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
1
2
3
4
5
6
7
8
Natural
Minor:
La Ti Do Re Mi Fa Ti Do
Harmonic
Minor:
La Ti Do Re Mi Fa Si La (Raised 7:
Si
)
Melodic
Minor:
La Ti Do Re Mi Fa Si La
(Raised 6 and
7:
Fi-Si
)
2.
Do-based Minor
: The
Tonic
in both Major and Minor begin on
Do
.
General advantages:
a. More adaptable when chromaticism in encountered.
b. Has greater harmonic consequence pedagogically for the average
student.
c. In use to a greater degree in Music Theory curricula.
Minor syllables in
Do-based Minor
:
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
1
2
3
4
5
6
7
8
Natural
Minor:
Do Re Mi Fa Sol Le Te Do
(
Me
,
Le
,
Te
pronounced
“may,” “lay,”
“tay”)
Harmonic
Minor:
Do Re Mi Fa Sol Le Ti Do (Raised 7:
Ti
)
Melodic
Minor:
Do Re Mi Fa Sol La Ti Do
(Raised 6 and
7:
La-Ti
)
Each system has its advocates and its detractors. Each has perceived advantages and
disadvantages. Having used all known systems, the author has had the greatest
student success employing the
Do-based
model. After an initial familiarization
period (because of the use of altered syllables), the vast majority of typical
undergraduate music theory students respond to this system.
Chapter 3 The Foundations Scale-Steps and Scales
3.3 Solfége Revisited
103
Figure 3.15
La-based and Do-based compared
Regardless of which
solmization
system is used, the purpose remains the same. After
a period of familiarization and rote drill, the student will begin to recognize
patterns aurally. This is to say that recognition will not merely be aural recognition
when heard, but rather, specific patterns will be “engraved” in the student’s mind.
These patterns will be
solfége
-triggered responses. This
audio-acoustic trigger
response will increase and become more fluent with practice.
K E Y T A K E A W A Y S
The student should understand:
•
Fixed-Do
as opposed to
Moveable Do
.
•
La-based
as opposed to
Do-based
systems.
Chapter 3 The Foundations Scale-Steps and Scales
3.3 Solfége Revisited
104
E X E R C I S E S
1. In a comfortable register, practice singing a Major scale using syllables,
ascending and descending. Gradually increase your tempo.
2. From your
Do
, sing down, “
Do-Ti-La
.” Now sing the Natural Minor scale
in
La-based Minor
, ascending and descending. Increase your tempo.
3. Next, sing the same Natural Minor scale, but use
Do–based Minor
syllables.
4. As an audio-acoustic exercise, think of the patterns,
Ti-Do
,
Do-Re-Do
,
Do-
Mi-Sol
,
Do-Mi-Sol-Mi-Do-Sol-Do
,
Sol-Ti-Re-Ti-Sol-Do
. Sing what you hear.
Confirm at the piano.
Chapter 3 The Foundations Scale-Steps and Scales
3.3 Solfége Revisited
105
3.4 Heptatonic Scales: Introduction to Modes
L E A R N I N G O B J E C T I V E S
1. Defining Modes as heptatonic scales and in historical context.
2. Identifying Modes.
3. Constructing Modes.
Brief Survey
Pre-Tonal (pre-Common Practice) music is generally considered to be music prior to
1587 or16001600 is a convenient benchmark. 1587 is sometimes used as a more
specific date. This coincides with the establishment of the
Florentine Camerata
, (or
Camerata di Bardi
after its patron), a colloquium of Northern Italian Humanists,
Poets, Musicians, and aesthetes. In attempting to “rediscover” and recreate ancient
Greek dramatic forms, they developed a new style of music, the “Second Practice,”
or “New Style.” This was the origin of Opera.. This period is often referred to as the
Modal Era
(as opposed to the
Tonal Era
that is the Common Practice period).
The source materials for Tonal practice consist of the Major/Minor
duality
. Music of
this period essentially relied upon Major and Minor scales and their extrapolated
constructs as the formative resources for composition.
In the Modal Era, the source materials were a collection of scalar constructs called
Modes
18
. Originating as tetrachords in early Greek theory, in early Western music
they consisted of a collection of interlocking hexachords, each with specific
attributes. In time, as compositional resources evolved, supported by accompanying
theoretical principles, Modes became a series of heptatonic scales, each with very
specific attributes.
Although these were the theoretical basis for early music, modes languished during
the Tonal Era. Composers in the 20th-Century, looking for alternative resources to
Major and Minor scales, “re-discovered” modes. Modal “flavors” are found in
abundance throughout examples of music since 1900.
Modes have become an integral resource in the Jazz style as well. Since the mid-to-
late 1950’s, modes are considered to be the initial, or primary source scales for Jazz
improvisation, especially in the pedagogical practice called chord/scale
18. Heptatonic scales used in early
music. Also used in post-Tonal
music.
Chapter 3 The Foundations Scale-Steps and Scales
106
equivalency.Most Jazz scholars identify the seminal recordings of Miles Davis in the
late 1950’s as heralding the advent of modal use in Jazz. There is evidence that
trumpet player Don Cherry may have used modal resources earlier in the decade.
The Ecclesiastical Modes (or “Church” Modes) were seven-tone scales built upon D,
E, F, and G. Each was ordered as an octave species from the modal
final
19
(modal
“tonic”). Each also had a re-ordered version wherein the top tetrachord of each was
placed below the modal
final
(Latin:
finalis
). The original ordering was called the
Authentic
20
form of the mode, the transposed version was called the
Plagal
21
form.
These alternate
Plagal
orderings were not new modes: each pair,
Authentic
and
Plagal
, had the same
final
. A particular form was so labeled based upon the range of
the modal melody as well as upon the perceived modal dominant within each form.
Ecclesiastical (“Church”) Modes
Originally, modes had specific names. These names reflect regional or place names
from the Hellenistic world but were really stylistic indicators. In early church music
modes were numbered sequentially. Eventually, the early names were re-used
reflecting their early origins. We label modes using these names.
Figure 3.16
Ecclesiatical Modes
Audio 11
The “Church” Modes
In and of themselves, the theoretical modes were considered to have certain flaws
in regard to their use in practical composition. These perceived flaws were treated
19. The modal equivalent of
Tonic
or keynote.
20. The original ordering of a
mode as an octave species from
the
final
.
21. A re-ordering of the mode
wherein the top tetrachord is
placed below the
final
.
Chapter 3 The Foundations Scale-Steps and Scales
3.4 Heptatonic Scales: Introduction to Modes
107
by the use of
musia ficta
: composers routinely altered pitches to achieve the desired
result. For example, the “softening” of the fourth scale degree in Lydian, or adding
a
Leading Tone
to Dorian and Mixolydian.Because of its unique character, Phrygian
was resistant to any alteration.
Figure 3.17
Modes and music ficta
Greater Modal System
In practical composition, the altered version of the mode became the version used.
The resulting mixtures of mode and alteration in time yielded new scales,
recognized as such by established practice. This was codified in the Greater Modal
System.
Figure 3.18
The Greater Modal System (Abbreviated)
Audio 12
The Modes
Note that Ionian is the Major scale and Aeolian is the Natural Minor scale. The other
earlier modes (again by established practice) gradually polarized toward one or the
other of these two forms. Due to the perceived flaws of each mode, they eroded
under the weight of their own inefficiency and distilled into either the “Major”
mode, or the “Minor” mode. The Locrian mode, while recognized as a theoretical
mode was not used in practical composition due to its unstable final
resolution.Locrian was not included in the system of modes until 1482 where it was
Chapter 3 The Foundations Scale-Steps and Scales
3.4 Heptatonic Scales: Introduction to Modes
108
described in the treatise
de Musica
of the Spanish composer and theoretician
Bartolomé Ramos de Pareja.
Associative Method
This sense of polarization toward either Major or Minor becomes one useful
technique for learning modes and familiarization with their characteristics. The
Associative Method
22
classifies modes as having the same basic characteristics as
either Major or Minor and then recognizes the variances.
Major Sounding Modes
Minor Sounding Modes
Ionian: Major
Aeolian: Natural Minor
Lydian: Major, raised 4
Dorian: Minor, raised 6
Mixolydian: Major, lowered 7 Phrygian: Minor, lowered 2
Locrian: Minor, lowered 2 & 5
(
or Locrian: Phrygian, lowered 5
)
Figure 3.19
The Associative Method for Modes
Audio 13
Associative Modes
This method is extremely useful in many instances, especially for recognition
purposes and as a tool for learning to hear and sing modes.Some advocate a similar
22. Recognition of modes by
association with either the
Major or the Minor scale and
observing the variances from
these.
Chapter 3 The Foundations Scale-Steps and Scales
3.4 Heptatonic Scales: Introduction to Modes
109
system wherein the student is compelled to memorize modes as variances from the
major scale. We reject this as being unwieldy and narrow. As such, it cannot be
recommended. Modes are labeled by the letter name they begin upon followed by
the mode name.
Figure 3.20
Sample Modes and Labels
Audio 14
Other Modes
Revolving Scale Method
A second method is more complete and serves well for the identification of modes,
as well as the construction and transposition of modes to other pitches. Observe
Figure 3.21 "The Revolving Scale Method for Modes"
abbreviated Greater Modal System is projected as a
revolving major scale
. In other
words, it appears to be a C major scale constructed upon successively higher scale
degrees. In this
Revolving Scale Method
23
, each successive reordering of the scale
corresponds to one of the modes.
Figure 3.21
The Revolving Scale Method for Modes
23. Recognition of modes by their
consistent order in the context
of the Revolving Major Scale.
Chapter 3 The Foundations Scale-Steps and Scales
3.4 Heptatonic Scales: Introduction to Modes
110
This modal ordering remains constant regardless of the major scale used.
Therefore, it can be used as an “algorithm,” a known value for comparative
problem solving, and used as a tool for identifying, constructing, and transposing
modes. In
Chapter 4 "Key Sense, Key Signatures, and The Cycle of Fifths"
modes will
be revisited and the Revolving Scale model will be used in conjunction with other
tools to perform these tasks.
Figure 3.22
Revolving Model from F
K E Y T A K E A W A Y S
The student should:
• Define modes and understand their historical significance.
• Know mode names.
• Understand the Associative Method and the Revolving Scale Method for
modes.
Chapter 3 The Foundations Scale-Steps and Scales
3.4 Heptatonic Scales: Introduction to Modes
111
E X E R C I S E S
1. In your
Scale Thesaurus
:
a. Construct a revolving Major Scale from C.
b. Label each revolution with its proper mode name.
c. Perform the same task from G and Bb.
2. In your
Scale Thesaurus
, using the Associative Method,
construct the following modes:
a. D Lydian, F Mixolydian, E Lydian, Eb Mixolydian, Gb Ionian
b. D Dorian, A Phrygian, E Locrian, Bb Aeolian, G Dorian
Chapter 3 The Foundations Scale-Steps and Scales
3.4 Heptatonic Scales: Introduction to Modes
112
3.5 Other Commonly Used Scales
L E A R N I N G O B J E C T I V E S
1. Introduction to other commonly used scales.
2. Pentatonic, Whole Tone, “Augmented,” Octatonic, Lydian-Mixolydian
and “Nearly” Whole Tone.
The
fin de siécle
period, the crossover period between the 19th- and 20th Centuries,
witnessed monumental changes as to how music was composed. By this point in the
evolution of Western music, Tonal music had not exhausted itself, but had
developed as fully as it could in terms of compositional resources.
Pentatonic Scale
Composers began to explore alternate scalar resources to Major and Minor. Modes
were employed as was the
Pentatonic scale
24
. The absence of a
Leading Tone
in the
Pentatonic scale, as well as its folk music associations, made it an attractive,
naturalistic alternative to Major and Minor scales.
In Jazz pedagogy, two distinct forms of the Pentatonic scale are recognized, called
Major Pentatonic
and
Minor Pentatonic
. They are so-called due to their inherently
Major or Minor sounding qualities.
Figure 3.23
Pentatonic Scale Rotation
Audio 15
Pentatonic Scale
24. Properly, a scale that divides
the octave into five equal
portions. In equal
temperament, this is most
closely approximated aurally
by playing the black keys at the
piano.
Chapter 3 The Foundations Scale-Steps and Scales
113
Symmetrical Scale Patterns
Composers in this historically transitional period and throughout the 20th Century
seemed fascinated by aspects of symmetry in musical constructs.The symmetrical
nature of the Pentatonic scale is not overtly obvious. The symmetry is there, but its
explanation must be held in abeyance contingent upon other acquired information.
In scale construction, this took the form of division of the octave into symmetrical
portions. This is apparent in the types of scale patterns that came into common use
in the late 19th Century and continued throughout the 20th Century.
Whole Tone Scale
The
Whole Tone Scale
25
, properly considered to be a Hexatonic (six-tone) scale,
displays numerous symmetrical traits.There are numerous “axes of symmetry” in
whole tone scales. Only those pertinent to this discussion are included here. It is
comprised of all whole steps, dividing the octave symmetrically into six portions of
two half steps each.
Figure 3.24
The Whole Tone Scale
Since this symmetrical division accounts for six of the possible twelve pitch-classes
from the chromatic collection, the other six pitch-classes of the chromatic
collection form one other whole tone scale.
Figure 3.25
Whole Tone I (WT I) and Whole Tone II (WT II)
Audio 16
Whole Tone Scales
25. A hexatonic scale comprised of
only whole steps that divides
the octave symmetrically into
six equal portions of two half
steps each.
Chapter 3 The Foundations Scale-Steps and Scales
3.5 Other Commonly Used Scales
114
