music in theory and practice

27

C H A P T E R 2Scales, Tonality, Key, Modes

Scale Natural Minor Scale Pentatonic ScalePitch Class Harmonic Minor Scale Nondiatonic ScalesDiatonic Scales Melodic Minor Scale Chromatic ScaleTonic Relative Minor Whole-Tone ScaleScale Degree Names Relative Major Blues ScaleMajor Scale Circle of Fifths Octatonic or Diminished ScaleTetrachord Parallel Relationship ModeTransposition Tonality SolfeggioKey Signature Key Pitch Inventory

Performers often practice scales to develop their technique. The collections of pitches and recurring patterns performers use to focus attention on technical aspects are the same building blocks of musical composition.

A scale is a collection of pitches in ascending and descending order. Musicians use a scale as a convenient way of displaying the notes used in a melody or harmony. In Figure 2.1, the melody consists of 24 notes but only seven different letter names.

A pitch class contains all notes of the same name regardless of octave. The pitch classes for the melody in the second part of Figure 2.1 on page 28 are arranged in ascending order to form a scale. The caret () above each number indicates that the number represents a scale degree.

Figure 2.1

Haydn: Symphony no. 94 in G Major (Surprise), III: Menuetto, mm. 18.

43 1

G

2

A

3

B

4

G

5

D

6

B

7

G

8

G

9F#

10

D

11

C

12

A

13

D

14

E

15

F#

16

D

17

A

18

F#

19

D

20

C

21

B

22

G

23

G

24G

TOPICSTOPICS

IMPORTANT CONCEPTSIMPORTANT CONCEPTS

ScaleScale

Pitch ClassPitch Class

3711_ben01877_Ch02pp27-54.indd 273711_ben01877_Ch02pp27-54.indd 27 4/10/08 3:56:14 PM4/10/08 3:56:14 PM

28 PART A The Fundamentals of Music

w1

G

w2A

w3B

w4C

w5D

w6E

w7F

#wG

8 = 1

Notes of the melody arranged as a scale:

Tonic orKeynote

Octave of Tonic(duplicate offirst letter)

Although an infi nite variety of pitch combinations is available, the following scales represent those in most common use during the past 200 years.

Diatonic (literally across the tones) defi nes a scale of mixed half and whole steps (and an occasional step and a half) in which each individual tone plays a role. The fi rst tone of a scale, the tonic, is a point of rest and is considered to be the most stable. Other tones lead toward or away from it, creating varying degrees of tension or relaxation. Since the tonic is the focal point of the scale, the most stable note, and the point of greatest relaxation, diatonic melodies frequently end on the tonic note. At times the word diatonic is used to indicate a tone that is part of a particular scale patternas distin-guished from a nondiatonic tone that does not belong to the scale pattern.

Each degree of the seven-tone diatonic scale has a name that relates to its function.

Scale Degree Name Meaning1st Tonic Tonal centerthe fi nal resolution tone.2nd Supertonic One step above the tonic.3rd Mediant Midway between tonic and dominant.4th Subdominant The lower dominantthe fi fth tone down from

the tonic (also the fourth tone up from the tonic).5th Dominant So called because its function is next in

importance to the tonic.6th Submediant The lower medianthalfway between tonic

and lower dominant (subdominant). The third tone down from the tonic (also the sixth tone up from the tonic).

7th Leading Tone Strong affi nity for and leads melodically to the tonic. Used when the seventh tone appears a half step below the tonic.

7th Subtonic Used only to designate the seventh degree of the natural minor scale (a whole step below the tonic).

Diatonic ScalesDiatonic Scales

Scale Degree NamesScale Degree Names


29CHAPTER 2 Scales, Tonality, Key, Modes

Two different scales are shown in Figure 2.2 to illustrate the application of scale degree names to diatonic tones.

Figure 2.2

& w

Tonic

1

w

Supertonic

2

w

Mediant

3 w

Subdominant

4 wDominant

5 wSubmediant

6 w7Leading Tone

w8 = 1Tonic

& w1

Tonic

w2

Supertonic

wb3

Mediant

w4Subdominant

w5Dominant

wb 6Submediant

wb 7Subtonic

w8 = 1Tonic

(half stepbelow tonic)

(whole stepbelow tonic)

The major scale is a scale of seven different pitch classes with whole steps separating adjacent tones, except for half steps between the third and fourth degrees and between the seventh and eighth (or fi rst) degrees. The eighth pitch has the same letter name as the fi rst and thus is treated as a duplication. All adjacent keys on the piano are a half step apart. Figure 2.3 shows that by beginning on C and playing in order only the white keys to the next C, you build a C major scale.

Figure 2.3

& w1

wholestep

w2

wholestep

w3

halfstep

w4

wholestep

w5wholestep

w6wholestep

w7halfstep

w8 = 1

C D E F G A B C

The major scale includes two tetrachords (groups of four pitches) constructed with the same arrangement of intervalstwo whole steps followed by a half step. The two tetra-chords of the major scale are separated by a single whole step.

Major ScaleMajor Scale

TetrachordTetrachord



Figure 2.4

& w1

wholestep

w2

wholestep

w3

halfstep

w4wholestep

w5wholestep

w6wholestep

w7halfstep

w8

Tetrachord Tetrachord

The melody in Figure 2.5 utilizes the notes of the C major scale.

Figure 2.5

Hatton: Duke Street.

&44 1 3 4 5 6 7 8 7 6 w5 5 5 5 6 5

4 3

w2

& 3 3 2

1 3 5 8

6 5 4 3

w2 5 6 7 .

8 4

3 2

w1

This same major scale pattern of half and whole steps can be duplicated at any pitch. Such rewriting is called transposition. In Figure 2.6, the major scale is transposed so that its fi rst tone is G. This is the G major scale.

Figure 2.6

& w1

wholestep

w2wholestep

w3halfstep

w4wholestep

w5wholestep

w6wholestep

w# 7halfstep

w8 = 1G A B C D E

FFFF#G

From Figure 2.6, it can be seen that a sharp is necessary if the major scale pattern of whole and half steps is to be carried out in the transposition. Figure 2.7 provides a convenient way to memorize the sharps or the fl ats needed when the scale begins on various pitches. The

TranspositionTransposition

Key SignatureKey Signature



arrangement of the necessary sharps or fl ats is called a key signature and appears at the beginning of each staff in a composition after the clef. Notice that each successive tonic, or beginning note, is fi ve scale degrees (called a perfect fi fth) above or four scale degrees be-low the previous tonic. A new sharp is added to the key signature for each ascending perfect fi fth (P5); in the fl at signatures, a fl at is dropped for each ascending P5 (see Figure 2.19).

Figure 2.7

&?

w w w w w w w w

w w w w w w w wC major

&?

bbw w w w w w w w

w w w w w w w wF major

&?

##w w w w w w w w

w w w w w w w wG major

&?

bb

bbw w w w w w w ww w w w w w w w

Bb major

&?

####

w w w w w w w ww w w w w w w w

D major

&?

bbbbbb

w w w w w w w w

w w w w w w w wEb major

&?

###

###w w w w w w w w

w w w w w w w wA major

&?

bbbb

bbbbw w w w w w w w

w w w w w w w wAb major

&?

########

w w w w w w w w

w w w w w w w wE major

Major Key Signatures



&?

bbbbbbbbbb


Db major

&?

##########


B major

&?

bbbbbb

bbbbbbw w w w w w w w

w w w w w w w wGb major

&?

############

w w w w w w w w

w w w w w w w wF# major

&?

bbbbbbbbbbbbbb

w w w w w w w w

w w w w w w w wCb major

&?

##############

w w w w w w w w

w w w w w w w wC# major

The minor scale is another common diatonic scale. It is more varied in pitch material because there are two different versions of both the sixth and seventh scale degrees. Tradi-tionally, the minor scales have been described as having three distinct forms, but in prac-tice, composers use all the scale resources of the minor scale within a single composition. The three traditional forms of the minor scale are called natural, harmonic, and melodic.

The natural minor scale contains seven different pitches with whole steps separating ad-jacent tones, except for half steps between the second and third degrees and between the fi fth and sixth degrees. Its pitches are those of the white keys of the piano from A to A:

Figure 2.8

& w1

wholestep

w2

halfstep

w3

wholestep

w4

wholestep

w5

halfstep

w6

wholestep

w7wholestep

w8 = 1F G A B C D E F G A B

Minor ScaleMinor Scale

Natural Minor ScaleNatural Minor Scale



The natural minor scale can be thought of as a major scale from the sixth to the sixth degree.

Figure 2.9

& w w w w w w w w w wC Major Scale

A Natural Minor Scale

The excerpt from a familiar carol in Figure 2.10 employs the natural minor scale.

Figure 2.10

Carol: God Rest Ye Merry, Gentlemen (Refrain).

& 44 3 4

5 6 5

5 4 3 2

1 3 2 1

& 4 3 4

5 6 7 8

5 4 3 2

.1

The harmonic minor scale has a raised seventh degree. The added impetus of a raised seventh degree gives more melodic thrust toward the tonic. Raising the seventh degree creates a step and a half between the sixth and seventh degrees, and a half step between the seventh and eighth degrees. Accidentals used to raise the seventh degree do not appear in the key signature. The pattern of half steps (23, 56, 78) is shown in Figure 2.11.

Figure 2.11

& w1

wholestep

w2

halfstep

w3

wholestep

w4

wholestep

w5

halfstep

w6step

and a half

w# 7halfstep

w8 = 1A B C D E

GGGG#F A

Harmonic Minor ScaleHarmonic Minor Scale



The Mozart excerpt in Figure 2.12 utilizes the harmonic minor scale. Notice the pres-ence of G-sharps in every measure except 5 and 6.

Figure 2.12

Mozart: Sonata in A Minor, K. 310, III, mm. 18.

&?

42

42

1 .p

j. J# .

2 . j# .

3 . j #

4 j #

5 . j

6 . j

7 . j.# J

8 j #

Presto

The melodic minor scale appears in both ascending and descending form. Besides the half step between the second and third degrees, the ascending form includes raised sixth and seventh scale degrees, producing a half step between the seventh and eighth degrees. The descending form is the same as the natural minor. The melodic minor scale developed because composers liked the urgency of the raised seventh, but found the step-and-a-half interval between the sixth and seventh degrees of the harmonic minor scale too harsh, especially for smooth vocal writing. In descending melodic passages, no need exists for the raised seventh, so composers most often used the natural minor with the lowered seventh and sixth degrees.

Figure 2.13

& w1

wholestep

w2

halfstep

w3

wholestep

w4

wholestep

w5

wholestep

w# 6

wholestep

w# 7halfstep

w8 =1

& w8 =1wholestep

wn 7wholestep

wn 6

halfstep

w5

wholestep

w4

wholestep

w3

halfstep

w2

wholestep

w1

A B C D E

FFFF GGGG# #A

Melodic Minor ScaleMelodic Minor Scale



The excerpt in Figure 2.14 includes the ascending and descending forms of the melodic minor scale.

Figure 2.14

Chorale Melody: Schwing dich auf zu deinem Gott, (Soar Upward to Thy God), mm. 512 (transposed).

& 1 5 1 2

U3 1 2

7 7 7 6 5

U4 5

3 3 2 2

#U1 2 7

# # 5 6 7 1

# U1 7 1

An examination of music literature, especially vocal and choral, reveals that composers consider the natural, harmonic, and melodic minors as arrangements of the same scale, with each form to be used according to need. This excerpt by Bach utilizes the various forms of the A minor scale in a single phrase of music:

Figure 2.15

Bach: Herr Jesu Christ, du hchstes Gut (Lord Jesus Christ, Thou Highest Good), BWV 113, mm. 12 (transposed).

&?

cc

# # #

AscendingMelodic Minor

Natural orDescendingMelodic Minor

# U

. j Harmonic Minor

& w w w w w w w wA Natural Minor orA Melodic Minor (descending)

w w w w w w w# wA Harmonic Minor

w w w w w w# w# wA Melodic Minor (ascending)

It is important to associate and compare the patterns present in major and minor scales. Two signifi cant associations are byproducts of the overall organizational scheme: the rela-tive and parallel relationships.

A major and a minor scale that have the same key signature are said to be in a relative relationship. To fi nd the relative minor of any major scale, proceed to the sixth degree of that scale. This tone is the tonic of the relative minor.

Scale RelationshipsScale Relationships

Relative RelationshipRelative Relationship



Figure 2.16

& w6

1

w7

2

w1

3

w2

4

w3

5

w46

w57

w61

w72

w13

C Major Scale

A Natural Minor Scale = half steps

To fi nd the relative major of a minor key, proceed to the third degree of the minor scale. This tone is the tonic of the relative major key.

Figure 2.17

& b 3

D Minor Scale

& b 1

Its Relative Major (F)

Figure 2.18 summarizes the relative relationships between all of the major and mi-nor scales. The organizational pattern perpetuating the major scale key signatures is also present in minor scales. Each minor key tonic is fi ve scale degrees above (or four scale degrees below) the previous tonic.

Figure 2.18

& w w& # w w& ## w w

Relative Major and Minor Relationships

Major RelativeMinor

Number ofSharps orFlats

LetterNames

Key Signatures andKey Notes

C a None

G

D

e

b

1 Sharp

2 Sharps

F#

F#, C#



&

Relative Major and Minor Relationships

Major RelativeMinor

Number ofSharps orFlats

LetterNames

Key Signatures andKey Notes

& ### w waA f # 3 Sharps F#, C#, G#

& #### w waE c# 4 Sharps F#, C#, G#, D#

& ##### w wa & bbbbbbb wA wAB = Cb g# = ab 5 Sharps7 Flats F#, C#, G#, D#, A#Bb, Eb, Ab, Db, Gb, Cb, Fb =

& ###### wa wa & bbbbbb wA wAF# = Gb d# = eb 6 Sharps6 Flats F#, C#, G#, D#, A#, E#Bb, Eb, Ab, Db, Gb, Cb =& ####### wa wa & b

bbbb wA wAC# = Db a# = bb 7 Sharps5 Flats F#, C#, G#, D#, A#, E#, B#Bb, Eb, Ab, Db, Gb =& bbbb wA wAb f 4 Flats Bb, Eb, Ab, Db

& bbb wA wEb c 3 Flats Bb, Eb, Ab

& bb wA wBb g 2 Flats Bb, Eb

& b w wF d 1 Flat Bb

Another way to visualize the relationship between the major scales and their relative mi-nors is with the circle of fi fths (Figure 2.19). All of the key signatures are given within the circle. The major scale tonics are listed outside the perimeter of the circle. The relative minors appear within the inner circle.

Circle of FifthsCircle of Fifths



Figure 2.19

& bbbbb & bbbbbbb& bbbbbb

&& b & #

& bb & ##

& bbb & ###

& bbbb & ####

& #####& ######

& #######

C

G

D

A

E

F

B

E

A

D

GBC

F

C

Circle of Fifths

ae

b

f

c

d

g

c

f ba e

d

ag# # #

##

##

b bb

b

b

b

bb

b

A major and a minor scale that begin on the same tonic note are said to be in parallel rela-tionship. Figure 2.20 shows the major scales and their parallel minors.

Figure 2.20

& wC major

w w w w w w w & bbb wC minor

w w w w wN wN w

& # wG major

w w w w w w w & bb wG minor

w w w w wN wa w

& ## wD major

w w w w w w w & b wD minor

w w w w wN wa w

Parallel RelationshipParallel Relationship



& ### wA major w w w w w w w & w

A minor w w w w wa wa w

& #### wE major

w w w w w w w & # wE minor

w w w w wa wa w

& ##### wB major

w w w w w w w & ## wB minor

w w w w wa wa w

& ###### wF# major

w w w w w w w & ### wF# minor

w w w w wa wa w

& ####### wC# major

w w w w w w w & #### wC# minor

w w w w wa wa w

& b wF major

w w w w w w w & bbbb wF minor

w w w w wN wN w

& bb wBb major

w w w w w w w & bbbbb wBb minor

w w w w wN wN w

& bbb wEb major

w w w w w w w & bbbbbb wEb minor

w w w w wN wN w

& bbbb wAb major w w w w w w w & bbbbbbb w

Ab minor w w w w wN wN w

Tonality refers to an organized system of tones (e.g., the tones of a major or minor scale) in which one tone (the tonic) becomes the central point to which the remaining tones are related. In tonality, the tonic (tonal center) is the tone of complete relaxation, the target toward which other tones lead.

TonalityTonality



The term key refers to the tonal system based on the major and minor scales. This system is by far the most common tonal system, but tonality can be present in music not based on the major and minor scales (see the later chapters of volume 2).

Although the great majority of western European music written from the seventeenth through the nineteenth centuries is based on the major and minor scales, a number of other scales are found occasionally. The following descriptions are some of these scales.

As its name suggests, the pentatonic scale is a fi ve-tone scale. It is an example of a gapped scale, one that contains intervals of more than a step between adjacent pitches. It is con-venient to think of the common pentatonic scale as an incomplete major scale.

Figure 2.21

& w w w w w w( )Gap Gap

Other arrangements of the gaps are also found in music. The pentatonic scale in Fig-ure 2.22 is based on the natural minor scale.

Figure 2.22

& w w w w w w( )Gap Gap

The sequence of black keys on the keyboard coincides with the interval relationships of the pentatonic scale. A brilliant use of the pentatonic scale occurs at the end of Chopins Etude in G-fl at Major, op. 10, no. 5, the popular Black Key Etude.

Figure 2.23

Chopin: Etude in G-fl at Major (Black Key), op. 10, no. 5, mm. 8385.

&?

bbbbbb

bbbbbb

R R

.

. . . . . . . . .

R R. . . . . . . . . .

j. gggg

j. ggggg&

? u

U

- -

Ravel also used pentatonic material in his Ma mre lOye (Mother Goose) suite. The pitches in Figure 2.24 also correlate with the piano black keys.

KeyKey

Other ScalesOther Scales

Pentatonic ScalePentatonic Scale



Figure 2.24

Ravel: Laideronnette, Imperatrice des Pagodes from Ma mre lOye (Mother Goose), mm. 913.

& ###### j The fi rst two phrases of the following familiar tune are based on a pentatonic scale.

Figure 2.25

Foster: Oh, Susanna, mm. 18.

& # 42 . . . . . Although all the preceding examples illustrate gapped scales typical of Western music, nongapped pentatonic scales (all adjacent intervals of the same size) occur in the music of other cultures. One such culture is Java, where a pentatonic scale consisting of fi ve nearly equal intervals (whole plus a quarter step) forms the basis for a large body of music literature.

A scale that does not observe the interval sequence of the diatonic or pentatonic scales is called a nondiatonic scale. Many nondiatonic scales have no identifi able tonic.

Chromatic Scale

A chromatic scale is a nondiatonic scale consisting entirely of half-step intervals. Since each tone of the scale is equidistant from the next, it has no tonic.

Figure 2.26

& w w# w w# w w w# w w# w w# w wAscending Chromatic Scale

& w w wb w wb w wb w w wb w wb wDescending Chromatic Scale

Chromaticism in Diatonic Music

Sometimes, however, a melody based on a regular diatonic scale (major or minor) is laced with many accidentals, and although all 12 tones of the chromatic scale may appear, the tonal characteristics of the diatonic scale are maintained. The following excerpt from

Nondiatonic ScalesNondiatonic Scales



Purcells Dido and Aeneas demonstrates this use of chromatic half steps by including 11 of the 12 tones in its gradual descent.

Figure 2.27

Purcell: Thy Hand, Belinda from Dido and Aeneas, Z. 626, mm. 110.

&?

bb

bb44

44 J J Jn . J

Thy

*

hand, Be

*

lin da;

DIDO

wb

J . .jb Rdark

* * *

ness

wb7n

.b j jb jshades me, On thy

wb- - - - - -

&?

bb

bb

jb j j jbo

*

som let me

bb9 8 7 6

j jrest; More I

b6b3n

j .jnm rwould,

*

but Death in

b6 7 5b3

7n

- -

&?

bb

bb23

23jn j j b j

vades

*

me; Death

*

is

w5n 6b

j j# .now

*

a wel come

*

5# 6 7 6

.wguest.

w #

w# n-

*Note the chromatic descent.

Whole-Tone Scale

A whole-tone scale is a six-tone scale made up entirely of whole steps between adjacent scale degrees.

Figure 2.28

& w w w w# w# w# wWhole-Tone Scale

Examples of whole-tone material are found in music from the late romantic and im-pressionistic periods:



Figure 2.29

Debussy: Voiles (Sails) from Preludes, Book I, no. 2, mm. 12.

&?

42

42 # -

p # b

Modr ( e = 88)

trs doux. .. .b # b#

Blues Scale

The blues scale is a chromatic variant of the major scale with fl at third and fl at seventh. These notes, alternating with the normal third and seventh scale degrees, create the blues infl ection. These blue notes represent the infl uence of African scales on this music. [See Gunther Schullers Early Jazz: Its Roots and Musical Development (New York: Oxford University Press, 1968), pp. 4652, for a complete discussion of the blue notes.]

Figure 2.30

& w w wb( ) wn w w w wb( ) wn wBlues Scale in C

Non-Western Scales

Other cultures have many scales that are not diatonic. Figure 2.31 shows one of the thaats, or seven-note scales, of northern Indian music.

Figure 2.31

& w wb wb w# w wb w wTodi (a northern Indian mode)

Octatonic or Diminished Scale

The octatonic scale is an eight-note scale composed of alternating whole steps and half steps. Jazz musicians refer to this scale as diminished because the chords resulting from this scales pitches are diminished.

Figure 2.32

& w w wb w w# w# w w wOctatonic or Diminished Scale



Nontraditional Scales

A number of nontraditional scales occur occasionally in the music of the late nineteenth and twentieth centuries. Most of these scales are made of a symmetrical pattern of intervals.

Figure 2.33

& w w# w w w# w wAugmented Scale

The scales used in music have developed and changed over the various historical periods. For additional information concerning the historical periods of music, see Appendix D.

A mode is a series of pitches within the octave that make up the basic material of a com-position. On fi rst investigation it would seem that the terms mode and scale are entirely synonymous, but in certain instances, especially in medieval church music, the modes transcend mere scale formations and are regulated by idiomatic melodic expressions.

From roughly 800 to 1500, the church modes formed the basis for nearly all Western mu-sic. Notice in Figure 2.34 that modal scales are divided by range and that the beginning tone is called the fi nal rather than the tonic as in the other diatonic scales. Modes I, III, V, and VII are called authentic because the fi nal is at the bottom of the range. Modes II, IV, VI, and VIII are called plagal and contain the same pattern of half and whole steps as the authentic forms, except that their range surrounds the fi nal. The prefi x hypo- indicates that the plagal modes begin a fourth lower than the authentic forms.

Figure 2.34

& w w& w w& w w& w w

AuthenticName Number Final

Tonal ScaleComparison

Dorian

Phrygian

Lydian

Mixolydian

Natural minor scale with raised sixth degree

Natural minor scale with lowered second degree

Major scale with raised fourth degree

Major scale withlowered seventh degree

Half StepsBetween

23, 67

12, 56

45, 78

34, 67

I

III

V

VII

Range

HistoryHistory

Modal ScalesModal Scales

Church ModesChurch Modes



& w w& w w& w w& w w

Hypodorian

Hypophrygian

II

IV

23, 67

12, 56

Natural minor scale with raised sixth degree

Natural minor scale with lowered second degree

PlagalName Number Range Final

Half StepsBetween


Hypolydian

Hypomixolydian

VI

VIII

45, 78

34, 67

Major scale with raised fourth degree

Major scale withlowered seventh degree

Early in the Renaissance period (14501600), other modes were recognized. The Aeo-lian is the same as the natural minor scale, and the Ionian is the same as the major scale.

Figure 2.35

& w w& w w

& w w& w w

AuthenticName Number Final


Aeolian

Ionian

Same as naturalminor scale

Same as major scale

Half StepsBetween

23, 56

34, 78

Hypoaeolian

Hypoionian

IX

XI

X

XII

Range

23, 56

34, 78

Same as naturalminor scale

Same as major scale

PlagalName Number Range Final

Half StepsBetween


For a more complete explanation of the modal scales, see Chapter 8 of this volume.



Certain systems of solfeggio (vocal exercises sung to a vowel, syllables, or words) use the syllables do, re, mi, fa, sol, la, ti to indicate scale degrees. The present-day movable-do and fi xed-do systems are derived from Guido dArezzo, an eleventh-century monk who sought to teach sight singing through the use of a well-known hymn to Saint John, Ut queant laxis (Figure 2.36). The beginning notes of the fi rst six phrases of Guidos melody form the fi rst six notes of the scale: C, D, E, F, G, A. The syllables beginning these phrases are ut, re, mi, fa, sol, la.

Scale degree: C D E F G ASyllable: ut re mi fa sol la

Figure 2.36

Hymn to Saint John (Ut queant laxis).

? j J J J J j J J Ut que ant la xis re so na re fi bris

J J J J J J Mi ra ge sto rum fa mu li tu o rum,- - - - - - - - - - - - -

? J J J J J J Sol ve pol lu ti La bi i re a tum,

j J San cte Jo an nes.- - - - - - - - - -

The tonal system of major and minor scales developed during the early part of the baroque period. This coincided with the emergence of key consciousness in music. By the end of the baroque period, the church modes had generally ceased to have any infl uence in music. The major and minor keys were the basis of music in the classical period. Chromati-cism was decorative for the most part, and shifts from one key to another (see Chapter 15) were used to create formal divisions (see Chapters 16 and 17). During the romantic period, chromaticism increased to the point that the major-minor key system began to be threatened. By the end of the period, composers often shifted keys so rapidly over the course of a composition that tonality itself began to break down.

With the breakdown of the major-minor key system, impressionist composers began to ex-periment with other scales. They were particularly fond of pentatonic, modal, and whole-tone scales. Twentieth-century composers have continued to expand the scale basis of their music. The chromatic scale has predominated in much of the music of our period, but a number of composers have experimented with nontraditional scales and microtonal scales (scales with intervals smaller than a half step). Twentieth-century popular music has remained the last bastion of the major-minor key system. Until the 1960s, the great majority of popular songs were written in major keys. This preference for the major keys persists today, but songs in minor keys have become somewhat more common. The blues scale is often found in jazz and popular music with blues infl uence, and the modes are an integral part of jazz composition and improvisation.

As a fi rst step in understanding the structure of a composition, determining its scale basis is important. You can do this by forming a pitch inventory.

Solfeggio SyllablesSolfeggio Syllables

Tonal ScalesTonal Scales

Expanded Scale UseExpanded Scale Use

APPLICATIONSAPPLICATIONS



A pitch inventory is a scalewise list of the tones used in a composition or section thereof. For purposes of organization, the pitch inventories in this text always begin with the pitch A. Many students will have no need to prepare a pitch inventory, but for those students who have yet to develop a hearing eye that would allow instantaneous recognition of keys and tonal centers, a pitch inventory may be a necessity. A pitch inventory permits quick assessment of the selected pitches without prejudice to key or tonality. From there you can make a fairly accurate determination of key by observing the location of half and whole steps, accidentals such as raised sevenths, etc., and particular notes of the melody that are emphasized. With practice, the need for a pitch inventory will diminish and the calculations will become automatic. The following illustration provides a melody, its pitch inventory, and fi nally its scale.

Figure 2.37

Dvork: Symphony no. 9 in E Minor, op. 95 (From the New World), I, mm. 149156.

42 .pj j. . .

. . . J .3

3

& # Pitch Inventory

& # Scale

Pitch InventoryPitch Inventory



1. Write the scales requested in the ascending form. 2. When the melodic minor scale is requested, add the fi rst three notes of the descending

form. 3. Write the accidentals to the left of the notes as they occur in the scale, not as a key

signature.

& w1. F major& w2. C minor (natural) & w3. G minor (harmonic)& w4. E minor (melodic)& wb5. B b major& w6. D minor (harmonic)? w7. B major? wb8. E b minor (natural)? w9. A major? w#10. F# minor (melodic)? w#11. C# minor (harmonic)? wb12. A b major

Assignment 2.1Assignment 2.1

ben01877_ch02.indd 49ben01877_ch02.indd 49 2/16/09 10:46:24 AM2/16/09 10:46:24 AM


Write the key signature for each of the following major and minor scales.

&1.

G major

2.

E b major? 3.

F minor

&4.

D major

&5.

F# minor?

?6.G minor

7.

D b major&

8.

C b major? 9.

B b minor&

10.

A major

&

&11.

B major

12.

A b major? 13.

C# major&

14.

E major

&15.

C minor

?

&16.

B minor

17.

A b minor&

18.

G# minor? 19.

A# minor&

20.

E b minor?

Following are groups of four successive notes of major scales. Most of these tetrachords are part of two major scales, but three examples are part of only one major scale. Name the scales of which each example is a part. (See the example for the pattern.)

? w w# w w______ ______

1. (Ex.)

D G

w w w# w w w w# w2 3 4 5

D major scale

w w w w w w w# w w6 7 1 2

G major scale

? w w w w#______ ______

2.

w w wb wb______ ______

3. wb w wb wb______ ______

4.

w# w w# w#______ ______

5.

w w w wb______ ______

6.

? wb wb w w______ ______

7. w# w w w#______ ______

8. w# w# w# w______ ______

9. w# w# w w#______ ______

10.

wb wb w w______ ______

11.





Each of the following groups of four tones is part of a harmonic minor scale. Name the harmonic minor scale of which it is a part.

& w w wb wb______

1.

w w w wb______

2.

w wb w wb______

3.

w w wb w______

4.

w# w# w# w______

5.

& w# w w# w#______

6.

w w w wb______

7.

w# w w# w#______

8. w w w w______

9. w wb wb w______

10.

The scale and scale degree are given, but the letter name of the note is missing. Fill in the letter name. Be sure to consider both ascending and descending forms of the melodic minor scales.

Scale Letter Scale LetterScale Degree Name Scale Degree Name 1. G minor (harmonic) Submediant 6. C# minor (harmonic) Dominant 2. B major Supertonic 7. G# minor (melodic) Submediant 3. Bb minor (natural) Subdominant 8. D major Mediant 4. F# minor (melodic) Submediant 9. F minor (natural) Subtonic 5. Eb major Leading tone 10. D# minor (harmonic) Subdominant

1. Match the column at right with the column at left. The left column refers to key signatures. 2. Number 1 is completed correctly as an example.

Key Signature Key 1. 1 sharp A. Relative major of D minor 2. 4 sharps B. Relative major of B-fl at minor 3. 2 fl ats C. Parallel minor of C-sharp major 4. 5 sharps D. Parallel minor of F major 5. l fl at E. Relative major of E-fl at minor 6. 2 sharps F. Parallel major of A minor 7. 6 fl ats G. Relative minor of B-fl at major 8. 3 sharps H. Relative minor of G major 9. 5 fl ats I. Parallel major of B minor10. 4 fl ats J. Parallel minor of B major




HH



1. Each of the following seven melodies is based on one of the following scales:pentatonic chromatic whole tone minor

2. Determine the scale upon which each melody is based and place the name in the blank provided.

3. For melodies in minor, indicate the form that predominates.

& 86 # b b1. ___________________________

n # # F p # nF Jb .

? bb 169 .J .J .J2. ___________________________ n # .J .J .J .J # .J .j

& bbbbb 42 P 3. ___________________________

. j 3

3

& ### 85 4. ___________________________

. j

& ### 44 >f> >

5. ___________________________

.> n > 3

.# > > >

? #### 23 w 6. ___________________________ .w .w

? b 44 p

7. ___________________________

. J # . J #




On the blank staff under each of the following melodies, write: 1. The pitch inventory beginning on A (or A-fl at or A-sharp). 2. The scale with the tonic as the fi rst note. (Indicate scale degrees with carets.) 3. The key. (For melodies in minor keys, indicate the form that predominates.)Suggested procedure: 1. Sing each melody enough times to be familiar with it. 2. Look carefully at the pitch inventory to determine the number of sharps or fl ats. 3. Reconstruct the key signature if possible. Remember that the raised seventh degree in

the harmonic minor might mislead you. 4. When you think you have the correct key signature, you should then try to determine

whether the melody is major or minor. 5. Go back to the melody itself and sing it again. Your ear can be a great help. Sometimes

the fi rst and last note will be a clue as to the tonic note. If this fails, try to fi nd outlined triads in the melody linesuch outlined triads are often either tonic or dominant.

6. When you have decided the key signature and the tonality (whether major or minor), write the scale on the blank staff.

1. Haydn: Symphony no. 28, IV: Presto assai, mm. 14. CD Track 8

&86 J# # J # J # J

&Inventory

&Scale

Key _________

2. D. Scarlatti: Sonata, K. 53, L. 261, mm. 15. CD Track 9

&44 # # #

# # #

&Inventory

&Scale

Key _________

3. Mozart: Eine kleine Nachtmusik, K. 525, II: Menuetto, mm. 15. CD Track 10

&43 # &

Inventory

&Scale

Key _________




4. Franck: Quintet for Piano and Strings, mm. 710. CD Track 11

&44 b b b b b b b &

Inventory

&Scale

Key _________

5. Bach: Little Prelude, BWV 943, mm. 15. CD Track 12

&43 b b b b J

&Inventory

&Scale

Key _________

6. Kirnberger: Les Carillons (The Bells), mm. 2125. CD Track 13

&C # # #

&Inventory

&Scale

Key _________

7. Couperin: Concerts Royaux, no. 8. CD Track 14 Number 7 is slightly more diffi cult than the fi rst six. Your best clue is the contour of the melody notes and the notes on the accented beats.

&43 # # # .# J .

&Inventory

&Scale

Key _________


music in theory and practice

Documents

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tonic note

nondiatonic tone

individual tone

scale of mixed half

lower dominantthe fi

th dominant

leading tone strong