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3

keys; also write the resolutions when the bass note (with-
out key) is given.



a 6+



160.



EXERCISES.









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Lesson L.

CHORD OF THE AUGMENTED SIXTH WITH MAJOR THIRD, AND
PERFECT FIFTH.

This chord is also identical with that of the augmented
sixth, except that the perfect fifth above the bass replaces
one of the doubled thirds. Fig. 161 a.

Reading from the bass note, it comprises a major third,
perfect fifth, and augmented sixth. Fig. 161 6.

Beading from the root, it comprises a diminished third,
diminished fifth, and diminished seventh. Fig. 161 c.



161.



133




While the resolutions of this chord are the same as that
of the augmented sixth, it is considered best to resolve it
to If only (Fig. 162), omitting the resolution to V on ac-
count of the resulting consecutive fifths. Fig, 162 b.



162. <




134

The resolution of this chord when the bass note is found
on other degrees than a major third below the key note,
is the same as the augmented sixth chord except that it
cannot resolve to a triad in fundamental position because
of the fifths above mentioned.

It also takes the resolution when the bass skips down
a perfect fourth, to the root of a major triad. The fifth
above the bass note goes to the nearest chord tone. Fig.
162 c.

To find the bass note when the soprano is given.

If the soprano moves upward a diatonic half step it is
the augmented sixth above the bass note. If it moves up-
ward a chromatic half step it is the fifth above. If it is
stationary it is either the third or fifth above the bass.
If it moves down a whole step it is the third.

Write and play the resolutions as directed in Lesion
XLIX.

EXERCISES.



163.




135



\J.




Lesson LI.

CHORD OP THE AUGMENTED SIXTH WITH DOUBLY AUGMEN-
TED FOURTH AND MAJOR THIRD.

In sound this chord is identical with the augmented
six-five chord, and it is also built the same, except that
instead of the perfect fifth above the bass, its enharmonic
equivalent, the doubly augmented fourth, is used. Fig.
164 a.

The chord of the augmented sixth with doubly augmen-
ted fourth is not recognized by many writers as such, but
is considered a misnotated chord of the augmented six-
fifth. Its use, however, is so frequent and logical that it
has been thought best to give it a place in this text.

Reading from the bass note it comprises a major third,
doubly augmented fourth, and augmented sixth. Fig.
1646.



136

Beading from the root it comprises a minor third, doub
ly diminished fifth, and diminished seventh. Fig. 164 c.



c.




164.



ti+ 6+ 6+

5 4++ 4-H-

3 3

The bass note is almost always found a major third bo-
low the key note, in major keys only, and resolves to I.
Fig 165 a. The resolution to in 6 may sometimes be sub-
stituted, as at Fig. 165 b.

When found on other degrees than a major third below
the key note, it resolves to a major six-four chord only.

The leading of the voices is the same as in the resolution
of the augmented six-five chord, the doubly augmented
fourth rising a diatonic half step. Fig. 165 a, 6.



165.




It can not take the resolution in which the bass skips
down a perfect fourth.



137

To find the bass note when the soprano is given.

If the soprano moves upward a diatonic half step it is
the doubly augmented fourth, or augmented sixth. If it
is stationary it is the third.

Write and play the resolutions of this chord in all major
keys.

EXEECISES.

6+
4+
a. 3



166.




p-f pik,







fc




138



If- / * \ ' {?


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T^S IL- E




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1 [








6


6*
4 4*




6

4 ^


6 6 6

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4 5


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6 6

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4



Lesson LII.

CHORDS OF THE AUGMENTED SIXTH IN OTHER THAN THEIR
CONVENTIONAL FORM.

Occasionally the foregoing chords are found in other
than their conventional form. In these cases their resolu-
tions are to the same chords as already mentioned, but not
necessarily to the same form. The leading of the voices
is also tha same. Fig. 167 gives a few of these resolutions.

By this changing of the bass note it sometimes happens
that the augmented sixth is inverted, becoming a dimin-
ished third, in which case the resolution is also inverted,
resolving inwardly instead of outwardly. Fig. 167 6.

When changed from its usual form it cannot take the
resolution in which the former bass note skips down a per-
fect fourth, as the character of that resolution is lost if
the note skipping down is not in the bass.




c.



d.



XI 1^3 & .o




ii


lets * S






\M7 JLiS^ ~-* f


ITS .


&^ C^ 1 1


or


or etc.


f V. Ptf? /(.v^ (V 1




5? O II


Po' a \w & 1









a


(ff xa II



EXERCISES.



6+
a. 5



6f
3 +




140



4+4

c. 3




+ i

t=






4+
3






d.






870

3



6j 6fl 75 5fl 6
44 g 4

2 3JJ



6fl 6S 79
445
2 3f



6fl



3}



3jf-



6j 6x

4 4*



6fl 6 87

44



141

Lesson LLII.

THE NEAPOLITAN SIXTH.

This chord is simply a major triad, the root of which is
on the minor second degree of the key. and as its name im-
plies, is usually used in its first inversion. In this position
its third is doubled. Fig. 169 a

It is used in major or minor and resolves to If, V, V 7 , or
V 9 . Fig. 169 a, b, c, d.

In resolving to 1% the bass moves upward a whole step,
and the upper three voices move in contrary motion to the
nearest chord tones. Fig. 169 a. Care must be taken to
keep the fifth of the Neapolitan sixth below the root, to
avoid consecutive fifths.

In resolving to V, V r or V 9 , the bass moves upward a
whole step, the root skips down a diminished third, and
the other voices proceed to the nearest chord tones. Fig,
169 6, c, d. The characteristic feature of this resolution
is this skip of a diminished third. Fig. 169 b.

There is no feeling of cross relation between the root of
the Neapolitan sixth and the fifth of the dominant triad.
Fig. 169 b.

In the resolution of the Neapolitan sixth to V 9 , in major
keys, the ninth must be a minor ninth; i. e., it must agree
with the notation of the fifth of the Neapolitan sixth.
Fig. 169 d.

The ninth is best kept in the soprano,

There is one other resolution of the Neapolitan sixth
that is much used. In it the root, instead of the third is
doubled. It resolves to V 2 as follows: one root skips down
as usual a diminished third, the other moves upward a
chromatic half-step, and the other tones proceed to the
nearest chord tones. Fig. 169 e.



a.



142

b. c. d. e.



169.



j



F ^F=?

^ J



C N 6 I| N 6 V V 7 V 9 N 6 VJI



b. c. d.




In place of the skip of a diminished third, when resolv-
ing to some form of the dominant chord, the passing
seventh may be used in progressing from the root of the
Neapolitan sixth to the third of the dominant chord.
Fig. 170.



170.



S



:&



=fc



J



C N 6 5 V 9 N 6 5 V 7

Write and play the resolutions of this chord in all keys.



143
EXERCISES.



a.



171.






it



i














1



d.






144
Lesson LIT.

THE NEAPOLITAN SIXTH CHORD. (CON).

The Neapolitan chord is often used in fundamental posi-
tion (N 8 ), and occasionally in its second inversion (Nf ).

When in fundamental position it resolves to Vij (172 b)
or, preferably, to Vf (172 a). The root is doubled, and in
resolving, one root skips down a diminished third, the
other moves upward a chromatic half step, the other chord
tones proceed to the nearest chord tones of the chord of
resolution. Fig. 172.



a. b.



a. b.



172.




C N 8 V* V!



c N 8 V|U V

3fl



The Neapolitan six-four chord is very seldom used. It
resolves usually to another form of the Neapolitan chord,
(173 a), and to V or V 7 . Fig. 173 b, c.



173.



C N| N 6 N 8 C N




145
EXERCISES,



6+



N 6






1



b.



6+
5



N 6



N 6 N 8






N 6



N 6 -N 8 -









87
D



6* 6 6135*
5 4fl 3fl
D



8 7 6tf 8

3 4 5$

3






75 6ii 6 7b 61? 8bb 7b 4 6 8 6b
51 4fe 3fe 5b - 3b 4 6b 5

b - 3



146




Lesson LY.

REVIEW.

Be prepared to write and play the resolutions of the dif-
ferent chords of the augmented sixth, and also of the Nea-
politan chord, as outlined in the proceeding lessons.

EXERCISES,
a. 6+




^zi)ijfc=



JESUS

I 9 -'



N 3 N"



dEdZzjT^F 1 ["3= =^^l~f*1 r-



^^.



ir>/ r \ *T u r


^ T*^ ^* A


Xzjp *


^T 1


- >!' | 1 |


1 I


7 5b 6$ 61? 6J
5b 4 5
3


6* 6
45
33










-W.,.^.^ a-^ . ^ ^ * ^ -




6 55 6* 6 6
4 3J 5 4b 5b
3 3

Lesson LYI.

TEST,


611 7
4



147



DIVISION II. MODULATION. (CON).



Lesson LYII.

MODULATING A HALF STEP UPWARD.

If in the augmented six - five chord the augmented
sixth is changed enharmonically to the minor seventh
above the bass note, the result will be the dominant
seventh of a key a diatonic half step higher Fig. 176 a.

In a key a chromatic half step higher, the augmented
sixth remains the same, while the other voices are changed
enharmonically for the above result. Fig. 176 b.

A modulation, therefore, to a key a half step higher by
way of the dominant seventh of the new key, is really a
modulation by enharmonic change of notation of the aug-
mented six-five chord of the old key to the dominant
seventh chord of the new.



1


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V '~^


1


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1




y


S32 ^


RUB


u


176. <

i




r ! , J __


zz?




fe& a -


#d V&

w^


*&%>






\^y


H




C I


6+ = Db V 7
5


I



148




C I



This means of modulating is good in going from major
or minor to major or minor. Its use is best, however, in
modulating to major from either major or minor. Fig.
177, a, b.




C I DbV 7 I



c i DfeV- 1



NOTE. There are certain altered chords in a key, the
use of which destroys all feeling of the mode of the key.

These chords are the augmented six-fifth, Neapolitan
sixth, and the diminished seventh on the raised fourth de-
gree of the key.

When used for modulatory purposes, they neutralize the
influence of the old key on the mode of the new, and it is
for this reason that modulations made by the use of these
chords, may be made to either major or minor.

A final cadence is needed to make this modulation com-
plete.



149



Since the dominant seventh of the new key is equivalent
to the augmented six-fifth chord of the old key, the pro
gression from the old tonic triad to the new dominant
seventh is made the same as that from the old tonic triad
to its augmented six-fifth chord Fig 177.

The new dominant seventh is best used in fundamental
position.

In this and succeeding lessons, the old tonic chord must
always precede the modulating chord, unless otherwise
mentioned.

The illustration in Fig. 178 contains this modulation.



178.







DbV 7



Write and play this modulation as directed in Lesson
XXY.



EXERCISES.



a.






179.



e=^









150



b.



Es3^=^=6



#fe^=afe=tee



& Ti



$




r^



g



w



3-6J-U - J



d.






^






Lesson LVIII.

MODULATING A HALF STEP DOWNWARD.

In modulating a half step downward, it will be seen that
the old tonic triad is the Neapolitan chord of the new key,
and all that is necessary is to proceed to the new dominant
seventh as directed in Lessons LI II and LIV. Fig. 180 a. 6.



151



180. <




The old tonic is best left in fundamental position, and
must be complete. This means of modulation is good in
going from major or minor to major or minor, but is best in
modulating to major or minor, from major. Fig. 181 a, b.
(See note on page 148.)



181.




B N



In the modulation from minor to major or minor, which
is seldom used, the old tonic, being a minor triad, is not
the Neapolitan chord of the new key. This modulation is
good because the third of the new tonic triad is found in
the old key.

This means of modulating requires no final cadence to
make it complete.

The illustration in Fig. 182 contains this modulation.



152



182.



J=4



fr%-" ^T 13 ^ -. L -^



J



r"TT

l



W



C I 6

B N 6 V 2

The modulations of this Lesson and Lesson LVII may
be combined as in Fig. 183, but from major to major only.




C I Db V 7



I C V 7



Write and play the modulation of this Lesson, also com-
bine it with Lesson LVII.



EXERCISES.




c.



l==Ut=3E=




* 2



5fl
315



6 7



Lesson LIX.

MODULATING TO KEYS AN AUGMENTED FOURTH OR DIMIN-
ISHED FIFTH DISTANT.

It will be seen that the dominant seventh of the new key
is the Neapolitan chord, with minor seventh added, of the
old key. Fig. 185.



154



185.




t_



-b



C N 8 Ib

Gk(F8)V 7

It is best to approach the new dominant seventh as a V 2
chord, as in Fig. 186 a. Here the upper three voices move
up a half step, while the bass moves down a half step.

Progressions such as Fig. 186 6 are, however, good.
Here, as well as in Fig. 186 a, the fifth of the old tonic
triad which progresses to the fifth of the new dominant
seventh must be kept below the root so as to avoid consecu-
tive fifths as at Fig. 186 c.



186.




C I GbV



This means of modulating is good in going from major
or minor to major or minor, but is best used from major to
major. (See note on page 148).

A final cadence is necessary to make this modulation
complete.

Fig. 187 contains this modulation.



155



187.



\n"/ ~S ^ ~" 7y ~ji^ \sfi} * ljf~^^



Write and play this modulation, and return to the old
key by the same means.

EXERCISES.

a.




188.




b.








156










Lesson LX.

MODULATING BY MEANS OF ENHARMONIC CHANGE OF
NOTATION

(a) Of the diminished seventh chord.

If a chromatic progression of diminished seventh chords
in root position be written, it will be found that the fourth
chord is identical in sound with the first, and the notation
can also be made the same by enharmonic change. Fig.
189.



189.







i^



**=&,







157



There are, therefore, only three different sounding dimin-
ished seventh chords, and since the diminished seventh
chord is used as a chord of the seventh on the leading tone
in major as well as in minor, and there are thirty keys,
each chord or its enharmonic equivalent is found in ten
different keys. Fig. 190. To make this chord agree with
the notation of the different keys requires six changes of
enharmonic notation. Fig. 190.



my ^j /^




-/I


uZffi


-B- &




tg

A, or a Yll? ; C, or c vn% ;

fi hh


Ek, or ekvn? ;


V 12ZK32


r^ II


XL /2 h' c '


g


f TV tt X 2_E


83s II


V i / +f*t % ^>


RZ II



dfvn? ; Gbvn? Fl, or fS vn?

This chord, therefore, readily lends itself as a means of
modulation between those keys to which the chord is com-
mon.

In modulating, this chord may be notated as in the old
or the new key, and resolve directly to the new tonic
(191 a) or, which is better, it may be repeated, at the same
time changing the notation to suit the new key, and plac-
ing it in root position. Fig. 191 b.

b.



191.




vn



158

A final cadence is necessary.
Fig. 192 will illustrate its use.



192. <




(b). Of the dominant seventh chord.

If the seventh of a dominant seventh chord be changed
enharmonically to an augmented sixth, the result will be
the augmented six-fifth chord of a key a diatonic half step
lower, which is resolved to 1^ followed by V 7 , I. of the
new key. Fig. 193.

In a key a chromatic half step lower, the seventh of the
old dominant remains the same while the other chord
tones are changed to suit the notation of the augmented
six fifth chord of the new key. Fig. 193 c. This modula-
tion being made by the use Oi an augmented six-five chord,
is good in modulating from major or minor to major or
minor.



193.



C V,= BI+ II V 7 I C I V 7 =C!?i +




159



This is an interesting means in modulating to keys a
half step lower, and differs, also, from that in Lesson
LVJII.

The modulating chord may be notated like the
dominant seventh of the old key (193 a), or the augmented
six-fifth chord of the new. Fig. 193 6.

This chord may be in any form but must have the con-
ventional form of the augmented six-fifth chord before re-
solving to i| of the new key. Fig. 194.



194.




A final cadence is not necessary.

Fig. 195 will illustrate the use of this modulation.




C I



This modulation may be combined with that of Lesson
LVII, as in Fig. 196.



160



196.



itei



rr



*-H^



V 7



n



M*-"
=!



C VI ii| If V, I

6 +



Be prepared to write and play the modulations by the
use of both means given in this lesson.

EXERCISES.



197.



-3:
A:






avii? Gfevn2



b.






D vn%Abvn?



70/lffV 1170



161




p t_J- J~hr : 3



i



u*-








GV 7



Lesson LX1.

MODULATING BY THE USE OF THE DIMINISHED [SEVENTH
CHORD ON THE RAISED FOURTH DEGREE
OF THE NEW KEY. .

One of the most practical means of modulation is enter-
ing the new key through the diminished seventh chord on
the raised fourth degree of the new key. Fig. 198 a.

This chord is best used in fundamental position. Fig.
198 a. Its first inversion is, however, also good. Fig.
198 6. In either case it must resolve to If of the new key
which is succeeded by V 7 , I. Fig. 198 a, 6.



162



198.




NOTE. In the resolution of the modulating chord in
this lesson, to the tonic six-four chord in major keys, the
seventh resolves by rising a chromatic half step. Fig.
199 a. This is good because the real resolution of the
seventh is not to the third of the tonic six-four chord, but
to the fifth of the dominant chord which follows the tonic
six-four chord. Fig. 199 a. The tonic six-four chord must
only be considered interpolated between the modulating
and the V 7 chords.

Many writers notate this chord, when resolving to a
major six-four chord, as a diminished seventh chord on the
raised second, instead of on the raised fourth degree.
Fig. 199 b.

b.




As was stated in the note in Lesson LVII, this is one of
the chords with which it is possible to modulate from
major or minor to major or minor.



163

In approaching this chord go to the nearest chord tones,
A final cadence is not needed to make this modulation
complete.

The following irregular progressions are permitted in
going from the old tonic to the modulating chord in this
and the next four lessons; viz., (a) cross relation when the
tones between which it exists can be found as an interval
of a minor second in either key; (b) cross relation when the
difference in pitch is a whole step; (c) the skip of an aug-
mented second if it is found in either key as a minor third.
Fig. 200 c.



200.




a I B IV Jf



Db I E iv 6 5 *




Gk I D iv JJ If

9



164

Fig. 201 contains this modulation.



201.



Write and play this modulation.

EXERCISES.




j_. * 9 J



IB



FJIVJfl I!




*=*=&



165




Lesson LXII.

MODULATING BY THE USE OE THE AUGMENTED Six-FivE
CHORD OF THE NEW KEY.

In this means, the new key is entered through the aug-
mented six-five chord on the minor sixth degree (a major
third below the key note) of the new key, which resolves
to If and is followed by V 7 , I. Fig. 203.



203.




In approaching the augmented six-five chord go to the
nearest chord tones.



166



The old tonic triad may be in root position (a), or first in-
version (b) before going to the modulating chord. Fig. 204.

The augmented six-five chord may also be used in other
than its conventional form, but before resolving, it must
appear in its conventional form. Fig. 204 e.

When going to keys a perfect or augmented fourth, or
diminished fifth higher, the augmented six-four-three
chord may be taken before the augmented six-five chord,
(204 c), to avoid consecutive fifths as at Fig 204 d.

These fifths may also be avoided by using the augmen-
ted six-five chord in such form that by inversion they be-
come fourths.



b.



204.






=5fi=.



:g=J&



-J J- -J U j=



-^g U 6?- r^ = "




This means of modulating is good in going from major
or minor to major or minor, and requires no final cadence
to make it complete. (See note in Lesson LVII).

Fig. 205 contains this modulation.



167



205. \



ta-t- ft- - & |-^ p* i \* ag



r



E



1



C I A |+

Write and play this modulation.

EXERCISES.



r



206.




a



; -r



b g+



b.






Db 5+




?^5^^^^5^^ffi^i^

~{ _I - t/g) ^ R~ I 51- a/ j



eT"



168



d.










bl? 1+

Lesson LXIII.

MODULATING BY THE USE OF THE NEAPOLITAN CHORD
OF THE NEW KEY.

A modulation by this means is made by entering the
new key through its Neapolitan chord, which resolves in
one of its several ways. Fig. 207 a, b, c.

This chord may be in either root position (Fig. 207 a),
or first inversion. Fig. 207 6.



207.



- '




169



Modulations may be made by its use, from major or minor
to major or minor.

Approach the Neapolitan chord by going to its nearest
chord tones The old tonic triad may be used in root posi-
tion or first inversion, and may have any interval doubled
before progressing to the Neapolitan chord. It is best to
make the notation of this chord agree with its key, but its
enharmonic equivalent may be used if it simplifies the
reading. Fig 208.



208.




A final cadence is not necessary.
Fig. 209 contain this modulation.




C I a AN 6

Write and play this modulation.



170
EXERCISES.



a.



210.



ZC-B / ^




-4


. f


3*






, J /


f T\ * \ i & &>




.




<"i ^




. Pf



s



Db N



b.



bN



E N



a.



^_ / >






C N



171

Lesson LXIV.

MODULATING BY THE USE OF THE DECEPTIVE RESOLUTION
OF THE DOMINAT SEVENTH.

A modulation may be made by resolving the dominant
seventh deceptively to the dominant seventh of the new
key. Fig. 211.




C VJ F* V 7

The progression to fche new dominant seventh is made
by going to the nearest chord tones.

No voice may progress more than a whole step, or its
equivalent.

The progression of a diminished or doubly diminished
third is good, as the movement is equivalent to a whole,
and a half step, respectively. Fig. 212 a, b.

b.



212. \




Either dominant seventh may be used in any inversion,
and when used in fundamental position, the fifth may be
omitted in either or both.



172



The upward resolution of the seventh is permitted in
this and in Lesson LXV, when it progresses a half step, or
its equivalent.

In modulating to keys a half step lower, double the root
in the new dominant seventh (a), and when going up a
half step, double the root in the old dominant seventh;(6).
In both instances, both dominant seventh chords must be
in root position. This is necessary to avoid consecutive
fifths. Fig. 213 c, d.




218.



C V 7 BV 7 B V r CV 7

This modulation is good in modulating from major or
minor to major or minor, except the Homonymic key (C to
c or c to C).

A final cadence is needed.

Fig. 214 contains this modulation.

L I i



214.



C V 7 F* V 3

Write and play this modulation.




173
EXERCISES.






V 7



b.









tftafc:






V 7 V 7



c.



-^i-



V 7 . V,



d.






V 7



174

Lesson LXV.

MODULATING BY THE USE OF THE DECEPTIVE RESOLUTION
OF THE DOMINANT SEVENTH. (CON.)

A modulation may be made by resolving the dominant
seventh deceptively to the tonic triad of the new key.
Fig. 216.



216-




A V 7 Bb 1 Et? V 7 FS If



Approach the new tonic triad by going to the nearest
chord tones.

All progressions permitted in the preceding lesson may
be used here.

A final cadence is needed, except when the deceptive
resolution is made to a I'l chord with fifth doubled, as at
Fig. 217.



217. (




Kb I



Vl a



175

Fig. 218 contains this modulation.



218,





i



fS if V 7



Write and play tlits modulation.

EXERCISES.



219.










B I



b.




?Eg=[SESE

ttESEE



A I



o,

rfe






r






C I



176




F I



Lesson LXVI.

REVIEW OR TEST.

Be prepared to write or play any of the modulations in
the preceding lessons, taking not more than three minutes
for each modulation.



177



Lesson LXVI1.



SUSPENSIONS.

The substitution of a tone which is a degree higher (or
lower) than the regular chord tone to which it later pro-
ceeds, is called a suspension. Fig. 220 b.


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