Bach Volume 5 Issue 3 1974 [Doi 10.2307%2F41639924] Randolph N. Currie -- A Neglected Guide to...

8/10/2019 Bach Volume 5 Issue 3 1974 [Doi 10.2307%2F41639924] Randolph N. Currie -- A Neglected Guide to Bach's Use o

1/11

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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2/11

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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3/11

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



4/11

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



5/11

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



6/11

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


7/11

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



8/11

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



9/11

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



10/11

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



11/11

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