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8/10/2019 Bach Volume 5 Issue 3 1974 [Doi 10.2307%2F41639924] Randolph N. Currie -- A Neglected Guide to Bach's Use o
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A Neglected Guide to Bach's Use of Number Symbolism Part IIIAuthor(s): Randolph N. CurrieSource: Bach, Vol. 5, No. 3 (JULY, 1974), pp. 3-12Published by: Riemenschneider Bach InstituteStable URL: http://www.jstor.org/stable/41639924.
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8/10/2019 Bach Volume 5 Issue 3 1974 [Doi 10.2307%2F41639924] Randolph N. Currie -- A Neglected Guide to Bach's Use o
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A
Neglected
Guide to
Bach's Use
of Number
Symbolism - Part III
By Randolph
N. Currie
Ohio State
University,
Newark
"84"
in
Other ach
Works
Although
ach chose o revealhis
nterest
n
the
number 84" at the
end
of
the
Patrem
ection f
his
great
Mass,
his
use of the
number
s cer-
tainly
ot
imited o
that
work lone.
In
fact,
he
composer
eems o have
delighted
n
working
ut various
ways
to introduce his same number-
symbolt keypoints n quitea few of hismasterpieces.f course,he
elaborate
ystem
f
interlocking
4s
found
n
the
Mass
movement
see
Part I of this
rticle,
ACH,
Vol.
V,
No.
2,
pp.
36-49)
is not
necessarily
evident
n
such
works;however,
he
41/43
composition
f the total
s
manifestlyresent
n a
highpercentage
f the
examples
ocated
by
this
writer.
he
followingurvey,
hich or
purpose
f
comparison
s limited
to
keyboard
orks,
ill show
Bach's
use of
the
number
n
representative
compositions
panning
is entire
roductive
areer.
Scores
will be
needed
for he
nsuing
iscussion,
articularly
WV
641,
801,
869,
and
668.)
Thespecial ignificancef"84" is apparentn the tructuref several
works
by
the
young
organist-composer;
he 84 measures f the
great
C
Major
Toccata
BWV
564)
present
n
obvious
xample.
Much
earlier,
though,
s the
evidence
ffered
y
the
youthful
Minor Prelude nd
Fugue,
BWV
549,
one of
Bach's
earliest nown
ompositions
1709,
or
earlier). Here,
t
will be
noted,
he
younggenius igned
his virtuosic
show-piece
ith
he
B-A-C-H
motive
n
the
84thmeasure
meas.
55
of
the
fugue;
ee
L.H.,
beats
1
and
2
.50 This
procedureppears
nce
again
on
a much
higher
rtistic
lane
with
the
three-foldllusion to the
B-A-C-Hmotive
n measure
52
(84x3)
of the
mighty assacaglia
BWV
582
(meas.
84 ofthe
fugue).51
Also
dating
rom
heWeimar
period,52
he
organ
horale
Wenn
wir
in
hchsten
then
eyn
BWV
641)
attests o Bach's nterest
n
con-
structingymbolic
assages
nvolving
heuse of
84 notes.Friedrichmend
has
already
alled
ttention
o
the
otal f
158
notes
n
thecantus
ir
mus,
3
signifying
OHANN
SEBASTIAN
BACH
in
gematria.
his
referenceo
the
omposer's
ame
s echoed
y
the
1
(J.
S.
BACH)
notes f
the
cantus
firmus
n the
reworking
f
the
composition
s Vor
deinem
hron,
WV
668
(see
below).
Nevertheless,
mend
did
not mention
hat
the
first
measuref BWV 641 contains 4 notes n thecantus-bearingart with
15
notes
n
the
3
lower
oices
or
total f
29
=
JSB
or
SDG), and,
fur-
3
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8/10/2019 Bach Volume 5 Issue 3 1974 [Doi 10.2307%2F41639924] Randolph N. Currie -- A Neglected Guide to Bach's Use o
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thermore,
hat
he
completion
f
41
notes
n
the
top part
coincides
with
a total f
43
in
the
accompanyingarts
or total f 84
(see
meas.
3).
The dispositionf theparts s as follows:
R.H.
(
Cantus
irmus
:
41
(
J.
.
BACH
(L.H.
=
30)
+
(ped.
=
13)
:
43
(CREDO)
Total: 84
It
seems
worth
oting
hat
his
pattern
s
completed
t
theend
of
9
beats
n a
work
onsisting
f
9
measures;
t
also stands
n
parallel
o the
final
phrase
f the
cantus
irmus
which
occupies
he last
9
beats,
with
thefollowing atternfnotes:
R.H.
(
cantus
irmus
:
33
(
Christ
(L.H.
=
36)
+
(ped.
=
12):
48
(BxAxCxH)
Total: 81
=
9x9
Finally,
t
should
be mentioned hat
this
prelude
s the
forty-third
completed
horale
n the
Orgelbchlein
ut of a
projected
otal
of
164
(41x4),
which
f
completed
ould
have
made
Wenn wir in
hchsten
Nthen eynNo. 100 in thecollection.54
From
he Cthen
years,
wo
well-known
eyboard
orks
ffer
re-
vealing xample
f
a
parallel
se of the ame
mportant
umber.
Not
only
are thetwo
pieces
n
the
ame
key
B-minor),
ut also
they
re
the
final
pieces
n
two of Bach'smost
mportant
ollectionsf
clavier
works
the
Well-Tempered
lavier,
ook I
(1722)
and
the
Two-
and
Three-Part
Inventions
1723).
The
Well-Tempered
lavier,
ugue
XXIV
(BWV
869,
2)
contains
xactly
4
notes
n
its
oncluding
our
measures
73-7 ).
Once
again,
he
number f notes
n
each
part
eems
o
suggest
hidden
symbolicmeaning:
NOTES
VOICE
NOTES
VOICE
NOTES
VOICE
S
23
T
23
B
14
A
18
Quinta ars55
6
-
41
(J.
S.
BACH)
29
(SDG
or
JSB)
14
(BACH)
(29
+
14)
=
43
+
41
=
84
N.B.
The voices an
also be
grouped
s
follows:
Inner
parts
18
+
23)
=41
Outer
arts
23
+
6
+
14)
=
43
4
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A similar
assage
occurs
n
the last
six
measures f
Sinfonia
5,
BWV
801.
Here,
hethree oices re
deployed
his
way:
S
-
41
A
-
10 A
+
B
=
43
+
41
=
84
B
-
33
S
+
A
=
51
(17 X 3)
+
33
(11
X
3)
=
84
The
symbolism
s
quite
interesting,
uggesting
hat
J.
S. Bach"
is
supported
y
his
faith,
which onsists
f
33
=
Jesus
Christ nd
10
=
God
the Father
nd
Law-Giver.There s
yet
another eferenceo the
Savior,
ince
his
passagebegins
n
measure
3
(after
he fermata
n
the
precedingmeasure).Also, he
41
notes
n
the opvoiceprovide
n
inter-
esting
eversal f the
14
bass
notes t
theend of
theB-Minor
ugue.56
This
survey
oncludes
ith wo
examples
f
significant
4-note
ass-
ages
both
of which
occuron what seemsto
be
the ast
page
of
music
Bach committed
o
paper.57
he
final
threemeasures f the
autograph
version
f the
CanonicVariations
n "Vom Himmel
hoch,
a
komm ich
her"
BWV
769)
present particularly
ngenious
rrangement
f the 84
notes,
o
that he
41
+
43
construction
s
plainly
rticulated
n
two
dif-
ferent
ays
(see
Example
7
at the end of this
rticle). Moreover,
his
patternmmediatelyollows n exceptionallylearpresentationf the
B-A-C-H
motive
tenor,
meas.
39),
which
s
"answered"
y
the
same
pitches
n
retrograde
meas.
41
plus
the
ast
note
n
meas.
40).
58
Directly
eneath
he conclusion
f
the Canon
per augment
tionem
(in
the
manuscript)
here
re the first
5V
measures f
Vor
deinem
Thron re
ch,
BWV
668,
scribed
n
Bach'sown
hand.
(The
remainder
of
the
composition
s
known
nly
hrough
he famous
dictated"
ersion,
BWV
668a,
whichwas
printed
n thefirst dition f
Die Kunstder
Fuge
and is
also known
hrough
arious tudent
opies.)
The 84-note
assage
which ccurs n connection ith hesecondphrase f thecantus irmus
is
part
of
an elaborate
umerical
cheme,
he dimensions
f
which
ie
beyond
he
cope
of
this
rticle.
Nevertheless,
he
pattern
nvolved
t
the
passage
ndicated
meas.
19b-22a)
follows he now
familiar
recedent
described
bove.
This
time,
he
point
of subdivision
43
+
41)
occurs
at the enter
f the
41 notes f
the ntire
antus
irmus
that
s,
midway
between
he
20th
nd 21st
notes f
the
oppart
meas.
21;
see
Example
below).
A
fascinating
etail
s the
nternal
rouping
f the
43-note
eg-
ment
nto
units
f
14 and
29
notes,
he end of
the
smaller
roupbeing
indicated
y
the
sounding
f
the 84th
note
of
the
pedal part.59
he
fol-
lowing
abulationhows hedistributionfthe
parts long
with he umu-
lative
otal f
all
parts
rom
he
beginning
f the
composition:
5
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8/10/2019 Bach Volume 5 Issue 3 1974 [Doi 10.2307%2F41639924] Randolph N. Currie -- A Neglected Guide to Bach's Use o
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Cumulative
Meas.:
19b
21a
21a
22a Totals
Totals
S: (2 + 4) = 6 + 2 = 8 (2x2x2) 22
A:
(6
+
6)
=
12
+
15
=
27
(3x3x3)
141
T:
(2
+
11)
=
13
+
12
=
25
(5x5)
133
B:
(4
+
8)
=
12
+
12
=
24
(3x2x2x2)
104
Totals:
(14+29)
=
43
+
41
=
84
(3x4x7)
400
Cumulative
Totals:
330]
+
29
=
[359]*
+
41
=
[400]
*
100
notes
rom
ere
o theend of
the
holographopy.
In
order o
place
this
passage
n
context,
comparison
f the num-
ber
of notes
nvolved
n
each
of the four
antus-jirmus
ections
might
e
instructive:
Phrase
Notes
n
C.F.
Notes n Other arts Totals
(A) (T)
(B)(sum)
I
(meas. 8-11)
14
25
21
22
68 82 =41x2
II
(meas.
19-22)
8
27
25
24
76
84
=
42x2,
tc.
III
(meas.29-32)
10 12
19
25
56
66
=
33x2;
11x6
IV (meas.40-45) 9 27 31(+18)* 33 109 118= 59x2
Totals:
41[*or28(+9)
39
33]
309 350=
14x25
N.B.
-
The numbers
or
phrase
V of thecantus
irmus
ollow
NBA
which
ives
tie
n
the
tenor,
meas.41.
0
With
reference
o this
abulation,
t
can
be seenthat
he84 notes
f
phrase
I
participate
n
a
large-scalerganization
hich
ncorporates
any
of the
mportant
umber
ymbols
iscussed
n
this
rticle. articular
tten-
tion shouldbe givento thereferenceo thenumber59" in phraseV,
which
tands
orthe word
GLORIA
by
means
of the
number
lphabet.
The
concept
f
offeringlory
o the creator eems
o have
oomed
arge
in
Bach's
thinking
n
his
final
days.
It
is
interesting
o
note
that
where
the
holograph
reaks
ff
n
measure
5,
there s
a
total
f
459
(
17
x
33)
notes,
nd thus
59
notes
past
the
end
of
phrase
I.61 It
is
tempting
o
interpret
he
totals f each
successive
hrase
s a
kind f
spiritual
dyssey
progressingway
from
elf-absorption
y
means
of faith
41+43)
to
the
glorification
f
a
greater
ower. And
yet,
ach
seems o
suggest
hat
in
the
very
ct of
subjugating
is own will to divine
uthority,
e finds
himselfeflectinghe nfinitelyreater loryfGod.62 here s,ofcourse,
a
scriptural
asis
forthis
paradoxical
oncept
o
be found
n
the often-
6
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quoted
aying
f Christ
bout
osing
one's ife
(see
Matt.
10:39;
16:25;
Mark
8:35;
Luke
9:24,
and
John
2:25-28).
Meanings uggested
y
the Number
-
8/10/2019 Bach Volume 5 Issue 3 1974 [Doi 10.2307%2F41639924] Randolph N. Currie -- A Neglected Guide to Bach's Use o
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A
comparativeeading
f
the two
psalms ertainly
ends o
suggest
a
strong
hematic
elationship,
ince
both
xtol
he
beauty
f
the
City
f
God andthetemplen itsmidst.The famous peninginesof Psalm84
("How
lovely
s
Thy dwelling
. .
")
tendto
suggest
mystic apture
(fainting)brought
bout
by
the
very hought
f the courts f
the
Lord,
while Psalm 48
implies
hat here s
great ignificance
o
the
design
f
theentire
ity:
"Make
heround f Zion
in
procession
count he
number
f her
owers,
take
ood
note
f her
ramparts,
pass
her
palaces
n
review,
that oumay ellgenerationset o come:
Such is
God,
our
God
for
ver
nd
ever;
He shallbe
our
guide ternally."
Ps.
48:
12-14
New
English
ible)
The notion f
significant
tructures
strongly
mplied
lsewheren
the
Bible,
particularly
n
theelaborate
escriptions
f sacred
laces
the
tabernacle,
he
temple
f
Solomon,
he
temple
f Ezekiel
never
ctually
built) and theHolyCityas seenbyJohn.Detailedmeasurementsre
given
for
ll of these
tructures,
articularly
he last
two,
n
which
he
importance
f thedimensions
s
emphasized y
the
ppearance
f an
angel
with
goldenmeasuring
tick
gold
=
purity
r
truth;
ee Ex.
40-43
and
Rev.
11:1;
21:15-17).
An
interesting
eature
f the
prophet's
ision s
that s soon
s all
themeasurements
ere
aken,
learly efining
he truc-
ture,
he
glory
f the
Lord
ppeared
nd
filled he
emple
Ex.
43:1-5).
Although
he
meaning
f
these tructures
s
not
xplained
n
the
Bible
itself,
here eems
to have
been
a tradition
n
ancient imes hat
these
sacred
laces,particularly
he
temple,
were
built
ccording
o
a
divinelyrevealed attern hich ontainedhe ecret tructureftheuniverse. he
cosmologica
ignificance
f
both
hetabernacle
nd the
temple
s,
n
fact,
spelled
ut
by
Flavius
Josephus
n
thefamous
istory
f
the
Jews,
copy
of whichBach is known o have had
in
his
possession
t
the time
f his
death.68 ince
t
appears ikely
hat
he
composer
as
awareof this
tra-
dition
f
symbolic
meaning,
t is
certainly
ossible
hat
he nvolved
lay
on "48" and "84" was intended s a meansof
introducing
he
concept
via
thetwo
psalms.
It is worth
oting
hat
he
German ersion
based
on
the
48-letter
verse rom salm48 is used s thefirstmovementf a cantata orNew
Year's
Day.
Is Bach
introducing
he dea
of
cyclic
ime,
s well? In
the
8
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context
f
the other
movements,
hat
eems o
be
the
case;
at
any
rate,
the
phrase,
bis an
der
Welt
Ende,"
cquires
distinct
schatologicaling
as theresult f itspositionn Cantata 71. 9
While
t
may
ake he ffortsf
a host
f
theologians
o
unravel uch
a
complex
web of
associations,
he outlines eem clear
enough
o add
another evel
of
meaning
o
those
uggested
bove.
At the risk
of
dis-
torting
nd/or
imiting
hemarvelous
epth
nd
subtlety
f the
omposer
thought,
he
following xplanation
s offered orBach's use
of
number
"84"
in
the
B-MinorMass:
"I,J. .Bach, elieve: ndbecause fmyfaith
I am
the
willing
ervant
f the
Maker
f
All
Things;
s
such
participate
n
the
ontinuingrocess
f divine
reation;
furthermore,
ith he
Help
of the
Spirit,
I have
ndeavored
n
this
work
o construct
temple
f sound
or he
ternal
lory
f
God."
Thus,
by
means
f
a
carefully
onstructed
etwork
f
references
nd
allusions,
ach
s
able
to
use the
number
o
that
t
contains
1 his
signa-
ture, 2 hispersonalonfessionffaith,nd ( 3 hispurposenwriting
the
music.70
f
the
composer
ccepted
he
tradition
hat the
Almighty
created
ccording
o
a numerical
attern,
hen
his
own use
of
numbers
becomes
n
imitatio
ei
as
he strives
o create
rder
ut
of
chaos. Seen
in
this
ight,
he
composition
ecomes
Microcosmos
hich
reflectshe
secret
rder
f
the
universe.71
Editor'sNote:
The
final
portion
f
Mr.
Currie's
rticle,
A
Neglected
Guide
to
Bach's Use
of
Number
Symbolism,'
ill be
published
n the
October
974
issue
of
BACH.
Footnotes
50
n
all
major
ditions
xcept
hat
repared
y
Dietrich
ilian,
herehenotes
n
question
re H-A-C-H"
see
NBA
V/5,
.
34);
however,
he
D-minorersion
of
this
omposition
BWV
549a)
printed
n
another
olume
f he
ame dition
does
ontain
he
motive
in
transposition:
-H-D-C#);
ee
NBA
V/6,
.
105.
An
nteresting
etail
f
the
assage
n
question
s
the
ymmetrical
lacement
f
the
itches,
s that
hey
re
nclosed
y
wo
roups
f
14
sixteenth-notes
14-8-14;
the
irst
roup
s set
ff
y
he
ntroduction
f
contrary
otion
51
According
o
David
Mulbury,
hework
was
probably
omposed
n Weimart
some
ime
etween
713
nd
1717";
"Bach's
assacaglia
n
C
minor:
otes
e-
garding
ts
Background,
ssence,
nd
Performance,"
ACH
II
[October
972}
:20;
also
II
[April
972]
18-22).
Thenumber
84"
s
evenly
ivisible
y
he
key tructuralumberssed nthePassacaglia12 and21) aswell s bythesignatureumber4. The astmeasureeforehe uguemeas. 68 84x2)
contains
3
(12
+
21) notes,
hile he
4th
ote
f
he
edal
art
ccurs
n the
first
eat
f
measure
3.
9
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8/10/2019 Bach Volume 5 Issue 3 1974 [Doi 10.2307%2F41639924] Randolph N. Currie -- A Neglected Guide to Bach's Use o
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52
hechurch
ear
713/14
s
the
ate
uggested
y
Ernst
rfken;
f.ZurEnste-
hungseschickte
es
Orgelbchleins,
ach
ahrbuch,
2
(1966)
:50.
53 riedrichmend;p. it., . 17. It seemslausiblehat hemany29) ornamentsin this
iece
retheresult fthe
omposer's
esireocontrolhenumberf
writtenotes.
54
he
omposition
s on
p.
115
of he
utograph
core
BB
Mus.
ms.Bach
283).
Bach
imself
idnot
umber
he
horales;
owever,
he wo ersionsiebster
esu
(
BWV
633
and
34)
are reated
eparately
pp.
60 and
1)
and, hus,
hould
e
numbered
5
and
36
of
the
ompleted
reludes,
ot s
35
and
35a,
s
is
often
stated.
he
numerical
atterns
n
BWV
641
play
n
mportant
ole
n
the evision
of
thework s
BWV
668.
55
s t oftens
the
ase,
t s
difficult
o
be
sure
xactly
heren added
oice
e-
longs;
owever,
t would eem
o
constitute
second
enor r
bass
part
n
this
piece.
Unfortunately,
hiswriter
as
nothad ccess o an
autographopy
o
con-
firm
r
refutehis
eading.
ote,
owever,
he
resence
f
14
notes rom
he
entry
f
his
art
o
the nd f
the
ugue.56 notherarallelothe 4 notest the nd f the ast iece anbeseen tthe
beginning
f the irstnvention
BWV
772)
in which
he
pper
oice as
84
notes
efore
he irstest
n
that
art
meas.
). Furthermore,
isecting
he
5
beats
f
his
hrase
12
+
12
Vi,
meas.
),
one
findshat 1
-f-
3
construction
once
gain.
his
ame
ivision,
xtended
nto
he .H.
part,
venly
ivideshe
0
notes fthat oice s well.
The um fthe wo
arts
134)
might
epresent
he
phrase
OLI DEO
GLORIA
n
gematria.
57
Mus.ms.Bach
271,
.
106;
facsimilesn
BG
XLIV
Bl. 142)
andNBA
V/2,
p.
XII. The
manuscript
ontainswo
arge
ections
the
rgan
onatasnd
the
great
eipzig
horales
separated
y
wo
lank
ages
56
and
7).
The
Canonic
Variations
erewritten
y
Bach
himselfn
pp.
100-106
i.e.,
p.
43-49
f the
chorale
ection.
See
descriptiony
Hans
Klotz
n
NBA
V/2,
KB,
p.
15.)
For
another
lay
n
"43"
nd
49,"
eenote
8
below.
58 heresa total f14 notes hichegin hilehe etrograde-A-C-Hssound-
ing
see
Ex.
7).
In
the
manuscript,
he
pagebegins
ith he
econd alf
f
meas.
8,
o
that herere
9
(7x7)
notes n the
age
eforehe
4-note
ass-
age,
esulting
n a
total
f
133
7
X
[7
-f
12])
notes
othe nd. From
he
head
of he
age
own
hrough
he
etrograde
-A-C-H,
herere
3
notes
n
the .H.
and6 in
the
edal
or
total f
49, which,
ombined
ith he
9
notes f
the
R.H.
t the
amemoment
the
ttackf
he
-flat),
roducesgrand
otal f
98
(7
X
14)
atthat
oint.
hus,
herere
9
notes
o he
ompletion
f he
riginal
motivend
49
more o
the
ompletion
f
the
retrograde
ersionn
addition
o
the
9
(R.H.)
+
49
(lower
oices)
ertical
rrangement,
herebyeflecting
he
two-foldivisionf
"84"as
given
n
the ast hree
easures.he
numerical
lay
within
he 4-note
roup
may
xtendo note
alues
41
thirty-second-notes,
1
sixteenth-notes,
4
eighth-notes,
nd
8
longer
otes;
ee
Ex.
7).
59
he owest
art
s
not o
designated;
owever,
he se f
pedals
s
necessary
ince
thehandslone annotpan ll the ntervalsseeKlotz,p.cit., . 106). Other
factors
uggesting
subdivisiontthis
oint
nclude
he otal f
100
notes
etween
the uter
arts
84-f
16)
and
230
(120
alto nd
110
tenor)
etween
he
nner
voices or total f
330
(33
X
10)
in all
parts.
urthermore,
he
womiddle
parts
ross
t
this ne
point,
utnowherelse
n
the
omposition.
There
s also
a
transposed
-A-C-H
ere
n "F"
which
s answered
y
nother
neon
"C"
in
meas.
1
with 4
notes
ounding
etween
he wo A similar
rocedure
an
be found
n
the amous
ccompanied
horale knownn
English
s
"Jesu,
oy
f
Man's
esiring"
from antata
47,
which
ontains
wo
-A-C-H
otives
epa-
rated
y
14
notes,
ll
in
one
part,
meas.
7-50).
The
14
f
29
construction
f
"43"
s
also videntt
the nd
f
WTC
(see
discussionf
BWV
869
above).
60
eeNBA
V/2, B,
p.
105,
.
31.
61
he
number
59"
s
the
irst
umberhose
igits
ill dd
o"14."
Furthermore,
the otalsf"41" (cantusirmus)nd"350" 14X25 = notesn all parts)involvednthefour hrasesuggestnew elf-affirmation.henumber25"
presents
bit
fa
problem,
ince here
s no traditional
eaning
nvolved.s
it
possible
hat his
umber,
hichs
also
prominent
n
other
orks
e.g.,
BWV
10
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8/10/2019 Bach Volume 5 Issue 3 1974 [Doi 10.2307%2F41639924] Randolph N. Currie -- A Neglected Guide to Bach's Use o
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680)
is
an
allusiono Christ'seference
o himself
s
A
and
or "A andZ"
=
1
+
24? A
somewhat
ore
ntriguing
ystery
s
posed
y
he
ouble
ow
f
figurest the ottomfthe age,whichre rrangeds follows:
L h
i A'
JL
i h
8-
9-
10-
1.
2.
3.
4
5
In
facsimile
eproduction
see
note
7),
the
igits
ppear
o
be
in
Bach's
and-
writing.
f
so,
what o
the
numbers
ean?
Were
hey
sed
y
Bach
n
working
outhisnumerical
atterns,
r do
they
ontain
ymbolic
eanings
hemselves?t
is
interesting,
owever,
hat he nderlined
igits,
hen
dded
ogether,ield
he
firstwo
erfect
umbers
6
and
8),
and
hat um f ll the
igures
55
+
15)
produces
he
therwise
ignificant
umber
70"
(JOH.
EB.BACH
n
gematria;
14
X
5;
and
ts
prime
actors
otal
14").
62
similar
rocess
f
purification
f the
go
has
been
uggested
s
part
f the
symbolism
f notherate
work
y
rich
chwebsch
n
Johann
ebastian
ach nd
DieKunster uge Stuttgart,931),pp.137ff.63
eenote
9
atthe nd
fPart
I of his
tudy.
64
he antata
ovement
acks he irstix
measures
f he
ersionsed
n the
Mass
also,
here
s ess
ndependence
n
the
nstrumental
arts.
See
note
9
below
or
more
n the
elationship
etween
he wo
ersions.)
65
he
mirror-image
elationship
etween
he
numbers
s
obvious;
owever,
he
meaningignified,
f
any,
s not
uite
o
clear. t is
likely
hat
hese ndother
similar
ets
e.g.,
12
and
21,
14
and
41,
23
and
32,
34
and
43, etc.)
are
mystical
ransformation
ymbols,
ith
abalistic
r
even lchemical
rigins.
nce
again,
here
re
craps
f vidence
hich
uggest
long
radition
or his
ind
f
numerical
lay.
ee
Kees
Vellekoop,
usammenhnge
wischen
ext
ndZahl n
der
Kompositions
rt
Jacob brecht,
ydsschrift
ande
Verenging
oorNeder-
landse
Muziekgeschiedenis,
X
(1966),
p.
108.
Another
lay
n "48" is
sug-
gestedy he nusedage f14stavesn theMass, hichurnsut obethe 8thpage ast he nd f f he atrem.
N.B.
This
page
nd
pages
04 and
105
arethe
nly
eaves
with
4
staves,
lthough.
152
and the
ntire
ona
could
ave
een
o
notated.
66
ach's
ahlensymbolik,
n
seinen
assionen
ntersucht,
ach-Jahrbuch
4
(1937):
107ff.
lso ee
Smend,
p.
cit.,
p.
10,
17.
67
Maren-Sofie
ostvig,
Structure
s
prophecy
the nfluence
f
Biblical
xegesis
upon
heories
f
iterary
tructure,"
n Silent
oetry,
d. A. Flowler
London,
1970),
p.
41.
In
the
passage
uoted,
iss
Rostvig
s
speaking
pecifically
f
Cassiodorus.
he
entire
ssay
pp.
32-72)
s
an
important
ontribution
o
the
history
f
Christian
umerical
raditions,
ndone
to
which hiswriters
deeply
indebted.
68
eeAntiquitiesII, vii/7 nd WarsV,v/5.Josephusxtendshe osmologicalinterpretationothe empleurnishingsthe7-branchedandlestickepresentshe
planets,
hile he
2
oaves
ymbolize
he
odiac,tc.)
nd
ven
he
riest's
est-
ments.
uite
imilar
oncepts
ere
evelopeduring
he
Middle
ges
with efer-
ence
o
the
great
hristian
athedrals.
he
Rationale
ininorum
fficiorum
f
Durandus
c.
1290),
s
a
compilation
f
these nd
other
raditions;t,
n
turn,
became
he
uthorative
ocument
or
matters
elated
o
church
esign
ndusefor
the
ext everal
undred
ears.
ormore n
the
peculative
ignificance
f
Medi-
eval
rchitecture,
eeOtto
on
imson,
he
Gothic
athedral,
ev.
d.
New
York,
1962),
Chapters
and 2.
It is of
particular
nterest
hat he musical"atios
(1:2,
2:3,
3:4,
7:8)
seem
o have een
sed n
most
f these difices.
lso,
he
axial
ymmetry
f the
Biblical
tructures
ay
ave nfluenced
ach's
oncept
f
form
see
note
0).
69
or
years
t has
been
ssumed
hat
he
Patrem
s
a
parody
f the antata
ove-
ment;owever,cholarshohave tudiedantata11closelySpitta, hittaker,and thers) ave een issatisfiedith hedea fthe antataersionsanorig-
inal
composition.
he
manuscript
eems
o
be
a "revision
opy"
f
an
earlier
work,
rompting
eumann
NBA
1/4,
KB,
p.
105
f.)
to
suggest
lost nstal-
li
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