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Arthur Edward Heacox.

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COMBINING THE MODULATIONS IN LESSONS XXXIV AND

XXXV.

In this lesson a modulation is made to a key a major
third higher or lower and back again to the original key.
Fig. 115.

a.

I



115.




T i r *f
J^. -J-J.



^ - f-f
I e V, i



^J



CV, I




e i CV 2 I 6 V| I e V 7 I
Write and play these modulations.
EXERCISES.



116










90



b.









tK



d.




^






Lesson XXXVII.

EEVIEW.

Be prepared to play or write any of the modulations of
the preceding lessons, as directed. It is desired that the
student become thoroughly familiar with these modulations,
so that in playing or writing them he manifests no hesi-
tancy.

Instead of review, a test may be given on the preceding
lessona



91
DIVISION II. SECONDARY SEVENTH CHORDS.



Lesson XXXVIII.

THE SUPERTONIC SEVENTH IN FUNDAMENTAL POSITION.

Probably the most interesting of the chords of the
seventh is that of the supertonic.

As will be seen in later lessons it allows of many chro-
matic changes of its different members, while still retaining
its identity as the supertonic seventh of the key.

It comprises, in major, a minor triad and minor seventh,
(Fig. 117 a); and in minor, a diminished triad and minor
seventh. Fig. 117 6.




C n 7



c n



In its introduction, the seventh of the supertonic seventh
chord must be prepared either directly (a), or by substitu-
tion (b); or may be used as passing seventh (c); or may be
approached in an upward direction from some other tone
of the same chord (d) Fig. 118. A tone to be prepared
must be in the same voice in the previous chord. Fig.
118 a. To be prepared by substitution it needs only to be
a part of the previous chord, not necessarily in the same
voice. Fig. 118 6.

In resolving, the seventh may descend a degree (); or
remain stationary (f)\ or may ascend a degree if the bass
takes the note of resolution, or its octave (g). Fig. 118.



92



The passing seventh cannot resolve by ascending. Fig.
118 (h).



118.




Good.



J J-fT-J J-n-






ii, V 7 n 7



II- VII-



^ h '4-


| h '|. 1


V 3 ~






^


* H




a


^x 1


2: ^


KB- ^5








-^ H


Good.


Bad.






<3O


'"


& \\


i^ ^




^


~ :H



While these chords may resolve to any chord that per-
mits a proper treatment of the seventh, the following reso-
lutions, however, are preferred, in the order given ; to
chords a fourth higher, a third lower, a second higher, and
a fifth higher.

The most common resolutions of the supertonic seventh
are to V, V 7 , V|, If, in 6 , i 6 , and vi|.



93

Of these the resolutions to V, V 7 , and if are the most
frequently used.

The above resolutions may be divided into three groups:
First, V, V 7 , and Vf (a); second, I| and in 6 (b); third,
I 6 and vi| (c). Fig. 119.



119.



a.




v v % *



-<g-

7 <5^



C n 7 V V 7



c ii? V 3 VI



b.



:===:=




b.



=fc=Zfc



-<s>-



i



ii T



11

II 7



III 6




-<5<-



3d doubled 5th dobbled,

S -J J-^-*



-<s>-



"^^




n




n? VI| Hj



In the resolutions of the first group, those to V and V r
ar^ identical with the resolutions of the dominant seventh
to its tonic, except that in resolving to V 7 the third of the
supertonic seventh remains stationary, becoming the
seventh of V 7 (119 a), and in the resolution to Vf the root
and third of the supertonic seventh are stationary, the
other voices progressing as usual. 119 a.

In the resolution to the dominant triad, when the third
of the supertonic seventh is in the soprano, it is well to
have this third skip down a third to the fifth of the domi-
nant chord. This is done to avoid a bad covered octave,
and also to make the dominant triad complete in all its
parts.

In all resolutions of the supertonic seventh, it is always
better for the root to skip up a fourth instead of down a
fifth. When resolving to 1| or in 6 this is necessary.

In the resolution of the second group to If and in 6
the root skips up a fourth while the upper voices move in
contrary motion to the bass to the nearest chord tones, or
remain stationary.

The ni 6 chord can, in all cases, be used interchangeably
with the I| chord.

In resolving the third group, the seventh remains sta-
tionary, the other voices go to nearest chord tones. In
the resolution to I 6 , either the third or the fifth may be
doubled. If the third is doubled, both thirds must be



95

treated as passing tones (See Part II, page 11). In the
resolution to vi.f, the bass note of vi| must also be ap-
proached and left degreewisa in the same direction.

The treatment of these chords being the same in minor,
nothing will be said of their treatment, since the illustra-
tioms are deemed sufficient.

The supertonic seventh is often used with raised third
(in minor with raised third and fifth) 120 a, in which case
it resolves to V or V 7 . In the resolution to V it is the
same as that of the regular supertonic seventh. The reso-
lution to V 7 is also the same, except that the raised third
moves down a half step to the seventh of the dominant
seventh chord. 120 b.



120. <




C ii




While this chord may be used in both major and minor,
it is better to confine its use to the major.



96



Fig. 121 contains the resolution of the supertonic seventh
with raised third.

c.

i

I



121.




V 7 fl



This and the following lessons will each contain a frag-
ment of a Bach choral to be harmonized. It is presup
posed that the student has some knowledge in harmoniz-
ing figured basses containing secondary seventh chords,
and for this reason the selection of these fragments in-
cludes those that contain such chords.

EXERCISES.




97



c.






d.



S 6 6 787 8 7 33 7 87 $

3 * - 58 3

35






e.



=t=



6 7 867

6 *
4






777777



E^=l



44
23



7 4 57

3 *



Lesson XXXIX.

INVERSIONS OP THE SUPERTONIC SEVENTH CHORD.

Of the inversions of the Supertonic seventh, the first is
the most useful and interesting. Fig. 123 a. In this form
it is called, by some authorities, "Chord of the added
sixth," also "Chord of the Sub-dominant sixth," it being
the sub-dominant chord with the sixth above the root
added. Fig. 123 b.



a.



123.




The resolutions of this inversion are to V, V 2 , I|, m 6 ,
I 6 and vi I . Fig. 124.



b. c. d. e.



f.






124.



or or or or



C n



V



V



m 6



a. b. c. d. e. f.




Vl



The resolution to V is the same as that of the dominant
six-five chord to its tonic triad. Fig. 124 a The resolu-
tion to V 2 is also the same, except that the third (bass
note) remains stationary, becoming the seventh of V 2 .
Fig. 124 ft.

In the resolution to \\ or in 6 the bass moves upward a
whole step while the other voices move in contrary motion
to the bass to the nearest chord tones, or remain stationary.
Fig. 124 c and d.

In the resolution to I 6 and vi| the leading of the voices
is the same as when resolving the supertonic seventh chord
to I 6 or vi \. Fig. 124 e and/.

The n chord resolves to V, V 7 , If or in 6 . The leading
of the voices is the same as in the resolution of the Super-
tonic six five chord to the above chords. Fig. 125.

a. b. c. d.

Ejf:

125.



C n* V V 7 I in 6



100



a. b. c. d.



rz:,_z '




ll


Xrh k <v


Hr**J /^~




fin


Jjf' "^


,-j fe ll




5* ^^


^ 1 1


tT


or or

/s> <?


or


/W^\ L_ ^*^




& ~ & 11


L^L^"t ?




II


%^^/L* i^




1 \


/




\l



cut V 3 fl



The n| chord resolves only to V 6 or V|, in which
resolutions the voices are also led the same as when re-
solving the Supertonic six five chord to V, or V 7 . Fig. 126.



126.



a. b.



a. b.




C H 2 V e



The inversions of the Supertonic seventh chord may also
be used with raised third. Their resolutions are the same
as those of the inversions of the regular Supertonic seventh
chord, except that the resolutions to I 6 and vi| are ex-
cluded. Figs. 125, 126.

Like the dominant seventh, so this chord may move
freely to its different positions or inversions. Fig. 127.



101



127.



.^



- &:



&



4.



JL J A A.



EXERCISES.



a.









1



b.









102












a.



3 6
5



6 64 58
53






66 74
5 3



6

5fl



J\ f > ^


F


9




!




F\ '\ m ^


i t











VM/ T~


1 I


J








6

5
326


6
4 6-
2


5


6
5


8 7

$-




/iV '> 1








1




I~J->S








^





*fc^ 2HS J














Lesson XL.

SECONDARY SEVENTH CHORDS IN MAJOR.
Fundamental position.

The remaining chords of the seventh are I 7 , in 7 ,
and vi 7 . Fig. 129.



IV 7 ,



103

The tonic seventh comprises a major triad and a major
seventh

The mediant seventh comprises a minor triad and a
minor seventh.

The sub-dominant comprises a major triad and a major
seventh.

The sub-mediant comprises a minor triad and a minor
seventh.



129.




C I 7



in- IV,



The introduction of the seventh of these chords requires
special treatment. It may be introduced: 1st, by prepara-
tion, i. e. it must be in the same voice in the previous
chord; 2nd, as passing seventh; 3rd, or when it is a minor
seventh it may be approached by skip in an upward direc-
tion from some other tone of the same chord. Fig. 130,
a, b, c.

In resohing it may: 1st, descend one degree; 2nd, remain
stationary; 3rd, may ascend a degree, when it is a major
seventh, or the bass goes to the note of resolution or its
octave. Fig. 130, d, e,f, g.



130.




III,



104




The chord of resolution may be a triad or a chord of the
seventh. In this lesson these chords of the seventh may
be used in the root position only.

The resolution to a chord a fourth higher or fifth lower
commonly called the natural or cadencmg resolution is
the most frequent. All chords of the seventh may take
this resolution except IV 7 and vnj and these may do so
when used in a sequence. Fig. 131, a, b, c. The IV 7 ,
even when not in sequence, may take this resolution when
the seventh ascends as in Fig 131 d,




vi 7 ii n 7 IV 7 vn? vn {



105



The next most frequent resolution is to a chord a third
lower. In this resolution the seventh in all cases moves
upward one degree the other voices proceeding to the
nearest chord tones. Fig. 132 a, b, c, d.




d.



v


II


yf


& gy a


ifh ' ^ & <%.


f3 & &


iuj %> i


Gf_ ~- ' " |f


or


^- ^ r ^-


/WA ^-,




\PJ* '^ ^ jr.


<5> <S?


\^^^ '-^ *^


II




II



IV, ii



vi 7 IV IV,



To the above resolutions may be added the resolutions to
chords a second higher and a fifth higher. Resolutions to
other chords are better avoided for the present.

In the cadencing resolution of successive chords of the
seventh, in fundamental position, the fifth is omitted in
alternate chords. Fig. 133.

A sequence of successive chords of the seventh may be
written as in Fig. 133.



106



133. t



=A-=3=& =E= EE:

=E^~ -~v& tz



r






i I



^s



i



I 8 7 IV 7 vn2 ni 7 vi 7 n 7 V 7



EXERCISES.



a.



I



-i r






b.









107



d.






35 7 7 65 7 878365

7






63S35 7 7 87 3877 673
4 5fl 3 33U87



666 76 87fl

252525 25



Lesson XLI.

SECONDARY SEVENTH CHORDS IN MAJOR.

Fundamental position (con.)

EXERCISES.



135.






108



b.







- -









d.



:p=



zz



35 78 4 76 6 582

3 2






6 3 7866 3583

87 4 7 787



I



86 8787





P (t^-HE: ? r I* ^- =^ ^-f

, a^=^-y=SE



109
Lesson XLII.

SECONDARY SEVENTH CHORDS IN MINOR.
Fundamental position.

The remaining chords of the seventh in minor are: I 7)
III' 7 , iv 7 , and VI 7 . Fig. 136.

The tonic seventh consists of a minor triad and major
seventh.

The mediant seventh consists of an augmented triad and
major seventh.

The sub-dominant consists of a minor triad and minor
seventh.

The sub-mediant consists of a major triad and major
seventh.

136.

\UJ " ' ^^~ '-*%(- 'ffj G*

VI,

The resolution of these chords ought to present no diffi-
culties. Like the secondary seventh chords in major, so
these may resolve to any chord that permits of a proper
treatment of the seventh. Owing to the augmented step
between the sixth and seventh degrees of the key, care
will have to be exercised in leading the voices to the near-
est chord tones. Here also the cadencing resolution, and
the resolution to a chord a third lower are the most fre-
quently used.

The sub-dominant seventh cannot take the cadencing
resolution, and in resolving the others so, it is necessary
with some to resolve the seventh upward.

All that is necessary in resolving these chords caden-
tially is to have the bass move up a fourth or down a fifth,
treat the seventh as directed, and go to the nearest chord
tones with the other. voices. Fig 137.




110



187.









~ep". u i



fl



i i i

J. A -A



-



H? Jg-



I 7 iv 7 III', VI 7 VI 7 11?

5 B



J J-



1



=E



-^-



-^-



etc.



f







nr vi



VI 7 II



When the seventh of the tonic seventh is used as pass-
in;.' seventh, it is notated as in the original minor scale,
and must then descend in resolving. Fig. 138.



138.




1



C I 8



Sequences of cadencing chords of the seventh in minor are
impossible.



ni

In the resolution to chords a third lower, the seventh in
all cases ascends in resolving, the other voices proceeding
to nearest chord tones. This is probably the most satis-
factory resolution of these chords in minor. Fig. 139.



139.




la. gz a.



i ft i

^i=^



VI VI 7




iv 7 H n? VI 7 iv iv 7



EXERCISES.



140.







112



b.



-h-j- ,5? ,-0 1 ,














d.






3 6- 76678 5 77877777777
5 5 4 3ft 3* 3*









576*6587



ziti



113

Lesson XLI1I.

SECONDARY SEVENTH CHORDS iiv MAJOR AND MINOR.
Fundamental position, (con).

EXERCISES.






141.






c.







zfc



1



d.



7 67387 2C 6 77 '657
35 4 3B



1



874fl87 6 878787
5fi 3 J



114




Lesson XLIV.

INVERSIONS OF THE SECONDARY SEVENTH CHORDS IN MAJOR.

When inverted, the secondary seventh chord must
always be complete.

In their introduction and resolution the leading of the
voices is the same as when in fundamental position, except
in the cadencing resolution, and in going to a chorda third
lower, in these cases the root remains stationary, instead
of skipping. Fig. 142.



142.



XL


J ^^


III


ith A


O'


Z ^


v^ly ey O


-^


? II


1 !

II ii "' I

1 ,- ^Jt \ - -x | -fS>- -&-


fm\*


^^




II


{3 ^




5? II


\-/


~







C vi| n 7



I!



In the upward resolution of the seventh when it is below
the root, it must be at least a ninth distant from it. Fig
143.



115



p




143.



The most frequent resolutions are the cadencing resolu-
lution, and the resolution to a chord a third lower, and
both of these may be used in sequences, but in major keys
only. Fig. 144.



1




i ,




II


1


rm Z - c>


& A A




II


\




Pfv -> &


t




144. <


^


r~rr


o .
' 1


2


i


/V


Dj^


2S


^2 1 1


I


[J- <V


_^^






\


Clx


S '?=>




/p










1 1




ii iv 2

I 1 r


nig in 2 vi i n 2

5

i 1 1 1 r


r~

Vi V 7


i


yp


=j J^J


d~ jj_


^zz^


~r ti


\G) -


* * -


. *- f -^i


< *


3 H




J ^J

* J


^T -T

J


i


9

etc.


(M\*






9i


41


^t^7-








41



I, VI| IV| II? VII? V| Illf I 2 VI 7 IV | II| Vllg



When it is desired to resolve an inversion of a chord of
the seventh to a chord other than those given above, it is
only necessary to follow the directions for this in Lesson
XXXVIII.



116
The chord of resolution may now be any chord. Fig. 145

>=4=t= r=t



146. <






r r

or etc.



&-



^ 1- \~






t| IV 2 IV I| IV 7 IV

EXERCISES.



HO.










b.



m










117



d.



MB



-






876 426
5 35



m



m



54635466 7
34 7 35 4



e.






7 67

65845
II=



:=t=T

7
5
6 h









1
865

$ 4 $



6

45 66
6 23 547



Lesson XLV.

INVERSIONS OP THE SECONDARY SEVENTH CHORDS IN
MINOR.

The treatment of these chords in minor requires no ad-
ditional directions to what has already been said in major.



118
EXERCISES.



a.



b.






-p-











3 2 64 57 78 82 787& 852
5 3 35 3 458

3 35



1



6 7 67 27767

3 3fl a 3fl5



119



e.






2 2 2 56 57587587



3Z-8








,. .


i ii


X ft J


j


1




J


N


$> *





4


J





H


1




*

6


8 7
















i?o *


L


J


^


f f







-V-






F EE





Lesson XLVI.

INVERSIONS OF THE SECONDARY SEVENTH CHORDS IN
MAJOR AND MINOR.

EXERCISES.



148.














120



c.







d.



76 4 66 6 3 4*6fiii 4 2 6*
52* 3$ 4 5 3 3 3 4

36 3



8 5 64t! 6426 86 98
5353 53 577

38 *



__)



6 7
4 3
,2 5_







121



F^ax-t IV.

DIVISION I. ALTERED CHORDS.



Lesson XLVII.

CHORDS OF THE AUGMENTED SIXTH.

In addition to the chords already presented, there are
others much used and of considerable importance. These
are:

1. Chord of the augmented sixth with major third, fig-
ured 6+.

2. Chord of the augmented sixth with augmented fourth

fi 4-

and major third, figured <+

3. Chord of, the augmented sixth with perfect fifth, and
major third, figured f+.

4. Chord of the augmented sixth with doubly augmented



149.



a.


b.




-jj/- ^"3 rc\


(5>-AUg. 4tn




l/l\


,


li.




x~l/


Z& Aug. 6th


ttfi? A \\ft. fith






t<g-Maj. 3rd tr^-Maj. 3rd




SBL^


ir^t


1 x '"


n


l^y*


\


H


^ :


\


H




6+ 6+
4+
3





122



\J


- z^-jfer. 5tn


|




XT














i II


to Aug. Gthl


1


to" A lit*, fith II





k$-Maj. 3rd


US-Ma j. 3rd




:


'"" II








1








II








II



5 4-H-

3

The chief characteristic of these chords is the augmented
sixth from the feass wote. Fig 150 a. They occupy as defi-
nite a position in the key as the dominant seventh chord,
and have resolutions quite as regular* but while the domi-
nant seventh is constantly used in all its inversions these
chords are nearly always found in that inversion which
gives them their name. Fig. 150, 6, c, d, e.

In speaking of the Chord of the augmented sixth of a
key we shall have reference to that chord with its bass
note a major third below the key note. Fig. 150.

In the treatment of these chords, this, their character-
istic position in the key and their resolutions will first be
taken up, after which the deviations from this position and
their resolutions will be treated.



b. c. d. e.



150.




6+ 6+
C or, c 3 4+

3



fr. 6*-

*''



123

CHORD OF THE AUGMENTED SIXTH WITH MAJOR THIRD.

As the "thorough bass" notation indicates, this is a
chord that has as its sixth above the bass note, an aug-
mented sixth. This chord has only three tones; it is there-
fore necessary in four part writing, to double one of these.
The third above the bass note, is doubled. Fig. 151 a.
Reading from the bass note, it comprises a major third
(which is doubled) and an augmented sixth. Fig. 151 a.
Reading from the root it comprises a diminished third and
diminished fifth. Fig. 151 6.

a. b.



151.



-* - -gy


u & Dim. stlT






EJS Dim 3rd




SZ'-iH ff<^ Aug. otn


zT^R^t




w




feH -






EEE







This chord is found in both major and minor keys and
its bass note is a major third below the key note. It re-
solves to 1 1 or V. Fig. 152 a, b.

In resolving, the augmented sixth moves outwardly a
diatonic half step, and the other voices proceed to the near-
est chord tones of I| or V. Fig. 132 a, 6.

The resolution of this as well as the other chords of the
augmented sixth to a in 6 chord is good when the in 6 chord
is substituted for the cadencing tonic six-four chord as in
Fig. 152 d.

While the fifths in Fig. 152 c are not objectionable it is
nevertheless better, where a choice is possible, to use Fig
1526.



124



a.



152.




C6+



6+ V 6+ in 6 V,



b.




V 3 II



6 + III'! V-tj



This as well as the other chords of the augmented sixth
are often found with the bass note on degrees other than a
major third below below the key note. In sach cases the
resolutions are identical with those above mentioned, only
the chords to which they resolve are not I| or V, but sim-
ply a six-four chord (major or minor), or a triad in funda-
mental position. Fig. 153. It must be remembered that
when the triad to which the augmented sixth resolves, is
not V, it may be either major or minor. When a choice
is possible, resolve it to a major triad.



125



b.



153.



3C


i






XL /r, /9


& \






(u) ^






2?




& I




or


9- 7?
>


&

or

^-i


/W"\ -^ i-*^ ^y


u^5 L ^ r


<E^ ^ 2?




s ^2 /*"7


i,




Q*


II




ii


C 6+ IVI


I 6+ V^


II




6+ vi| in 6+ IV 6+ n| vi

It will be seen that- all of the above chords of the aug-
mented sixth are on degrees other than a major third be-
low the key note; as a consequence they resolve, not to If
or V, but simply to a six-four chord (major or minor), or a
triad (major or minor) in fundamental position.

One other resolution, when the bass note is found on
degrees other than a major third below the key note, calls
for especial attention The bass note sometimes skips
down a perfect fourth to the root of a major triad. The
augmented sixth above the bass resolves, as usual, up a
half step, and the other voices proceed to the nearest chord
tones. Fig. 154.



126



154.




In approaching the chords of the augmented sixth all
voices may move in similar motion, providing no faults
occur (Fig. 155, a), but contrary motion of some voice or
voices, especially in approaching the augmented sixth, is
preferable. Fig. 155, &.



a.



a.



155.



*_ o. a


J a




m & *^


1 ft?




tj " $9- jf' 5 "


fex


" - "


II






^^%^ n


6*


6f
5


6+
4+
3




Lfry '^ j^^ ^-^




^


f^




-


1 i

6+


6+


6+


4 5


3



127

To find the bass note when the soprano is given.

When the soprano of the augmented sixth chord rises a
diatonic half step in its resolution, it is the augmented
sixth above the bass. When it progresses anywhere else
it is the third above the bass.



156.



EXERCISES.













+ + +






d.



128



\-s U .H>V i g)


- M- '




r F UP -i


S






J


5


6 6,
3


66* 6
3
3


1 1 1

3
3


! /W^*^ if


1 -mm




i; ||


1 ^y **T Li "tf


n


i 1 1 1 i


. ,


\^^ "C "rfij. nfl


J




ta






3 h/-J L^


~r r & II


6 6
4 3
3


6 6*-
4 3 -
3 -


- 6 6 6
-43 4
3


ST

87



Lesson XLYIII.

CHORD OF THE AUGMENTED SIXTH WITH AUGMENTED
FOURTH AND MAJOR THIRD.

This chord is identical with that of the augmented
sixth chord except that instead of having the third above
the bass note doubled, as is the case in the augmented
sixth chord, one of the thirds is replaced by the augmented
fourth above the bass. Fig. 157 a.

Reading from the bass this chord comprises a major
third, augmented fourth and augmented sixth. Fig. 157 b.

Reading from the root it comprises a major third, dimin-
ished fifth, and minor seventh. Fig. 157 c.

b. c.



zz^ A J?S-? th - itun^ rMin 7lh

XnftH&A.C5



157.




129

Its location and resolutions are the same as those of the
augmented sixth, the resolution of the augmented fourth
being to the nearest chord tone. . The treatment of this
chord when it is on any other degree than the major third
below the key note is also the same, the augmented fourth
in all cases resolving to the nearest chord tone. Fig. 158,
a, l>, c, d.



158.




6+
4+



*
3fl



To find the bass note when the soprano is given.

When the voice progresses upward a diatonic half step,
it may be the augmented fourth, or the augmented sixth
above the bass note. When it moves upward a whole step
it is the augmented fourth. When it remains stationary
it may be the third or the augmented fourth. When it
descends it is the third.



130
EXERCISES.



159.



b.






Put 6+ chord wherever marked.
C.



1 /k ft ( *


a -r




-&-


4-


-jS> 1



6+



d.



3 6 2 6fi 65 6 6fi 65 6

4 44 3 44

33 3



131



m



6 6fi 6 61 59 62 6 6fl 6| 6 6 8 7
5 4 4 41 B 4j 5 4 4 3fl 3D
332 3



Lesson XLIX.

CHORDS OF THE AUGMENTED SIXTH AND THE AUGMENTED

SlX-FoUR-THBEE. (CON).

Play and write the resolutions of the 6+ and Jj; in all


1 2 3 5 7 8

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