bach volume 5 issue 1 1974 [doi 10.2307%2f41639913] randolph n. currie -- a neglected guide to...

8/10/2019 Bach Volume 5 Issue 1 1974 [Doi 10.2307%2F41639913] Randolph N. Currie -- A Neglected Guide to Bach's Use o

1/11

A Neglected Guide to Bach's Use of Number Symbolism Part IAuthor(s): Randolph N. CurrieSource: Bach, Vol. 5, No. 1 (JANUARY, 1974), pp. 23-32Published by: Riemenschneider Bach InstituteStable URL: http://www.jstor.org/stable/41639913.

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2/11

Notizbuch

fr Studenten

BACH'S "Notebookor tudents" illpublishelectedtudentrticles

on

Baroque

music s well as

short

apers

of

particular

nterest

o music

students.

ACH

welcomes

ueries oncerning

ublication

f

uchmaterials.

A

Neglected

Guide to Bach's Use of

Number

Symbolism

-

Part I

By Randolph

N. Currie

Ohio

State

University,

Newark

The Controversy

One of

the most

ntriguing,et

ontroversial,

evelopments

n Bach

research

ver

the

past

few

years

has

been

the revelation

f Bach's

use of

number

ymbolism

n

some of

his

compositions.

eaction

o advance

reports

f

this

henomenon

as

ranged

rom

utrightkepticism

o

enthu-

siastic

cceptance.

he

attitude f

most

cholars,

owever,

as

been

a sort

of

polite

eserve.

"Now

isn't

hat

nteresting;

ut

et'swait

nd see

Admittedly,

he

published

tudies

evoted o

Bach's use

of number

symbolism

ave

been

somewhat

aphazard,

nd some

of the

arguments

tenuous,

o

say

the east. On theotherhand, he

difficulty

f

detecting

and

interpreting

umber

ymbolism

s notorious

nd

by

no

means imited

to theworks f

J.

S. Bach.

In thewords

f

Alister

owler,

leading igure

in

the

field

of

English

iterature,

numerical

omposition

as

an

essen-

tially

rcane

ractice

..

;

the

ast

thing

we should

xpect

o

find s an

unveiled uthorial

xposition."1

herefore,

t

should

ome

as no

surprise

that he

usually

eticent

antor

f

Leipzig

maintainedbsolute

ilence n

the

subject.

We

do have

a

kind of

"hearsay"

vidence,

y way

of a

debunking

remarkyMatthesono theeffecthatC. L. Mizler perhaps n private

conversation)

ad claimed

o

have learned

ome

"mathematical

ases

of

composition"

irectly

rom

ach.2

Even

Mizler,

whosemathematical

nter-

est

is

well

known,

eems

never

o have written

wordabout

numerical

composition.

or

did he

publish

rebuttal

o

Mattheson's

nide

remarks,

thus

ontributing

o our

mpression

f

secrecy

nd esotericism

urrounding

the

subject.

Perhaps

his s to

be

expected,

ince,

s

Christopher

utler

points

out,

"From

Pythagoras

nwards,

nowledge

f

the

properties

f

number

ad been

regarded

s a secret

mystery."3

utler

oes

on to

quote

Copernicuso showthat uchmysteriesererevealed only o initiates

and

friends,

nd

then

not

in

writing

ut

by

word

of mouth."4

hus,

t

stands o

reason

thatmost

attempts

t numerical

nalysis

re

open

to

23

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3/11

charges

hat

hecritic

s

trying

o find

ymbolic

eaning

where one

was

intended.Even when the same

patterns

ccur

repeatedly,keptics

an

claimthat uchrecurrences simply coincidence.

Bach's Overt Gesture

In

view

of these

ircumstances,

ven

the

lighest

ndicationhatBach

consciously ngaged

n

numerical

omposition

hould

be

regarded

s

highly

ignificant.

t is the

opinion

of

this

writer

hat

Bach made

just

such n overt

esture

when

he

wrote he number 84" at the

end of the

Patrem

movement f the B-MinorMass

(see

Plate at

the end of this

article).

Friedrichmend,who discoveredhenumbernthe utographcore,

assures s

that he

figures

re

in

Bach's

handwriting.5

lsewhere,

mend

has

observed

hat 84"

represents

he

number

f

measures

n

the

move-

ment nd that t

s

the

product

f the

mportantholy

umbers" and 12.

Unfortunately,

e did not

choose o

pursue

he matter

ny

further. ad

he

subjected

he movement

o the

kind

of

detailed

umerical

nalysis

e

used n

his

study

f Bach's

Triplex

anon"

BWV

1076),

he

would,

no

doubt,

ave

discovered

hat

he otal

number f

measuress

just

one

aspect

of

a

numerical

abyrinth

f

monumental

roportions.

t

is

the author

sincere

ope

that

hepresent tudywill chart fewof the arger assage-

ways

ontained

ithin his

difice.

Symbolic

Associations of

"84"

Before

roceeding

ith n

analysis

f the

movement

tself,

t

seems

advisable o take

nto ccount he

numerical

roperties

f

84,

a

number

particularly

ich

n

symbolic

ssociations. s a

point

of

departure,

et

us

consider he

relationship

etween he

generating

and 12

mentioned

above.

To the

medieval

mind

these wo

numbers

were

closely

elated,

since

both re theresult

f

combining

and 4:

3 + 4 = 7 (Three ymbolizedhe hingsfheaven;

3

X

4

=

12 four

epresented

he

hings

f

the

arth.)

Thus,

s

Vincent oster

Hopper

tated,

from he

triune

rinciple

f

God and the

quadruple

rinciple

f man

are

produced

he

universal

ym-

bols,

7

and

12.

The

addition f

3

and

4,

spiritual

nd

temporal,

roduces

7,

which

s,

therefore,

he first

umber

which

mplies

otality.'7

rom

Hugh

of St.

Victor,

we learn that

"12

signifies

he

universe,

eing

a

multiple

f

the

corporeal

of the

elements

nd

the

spiritual

."8

It

is

noteworthy

n

this

egard

hat

he

text

ncludes

he

phrase

factorem

oeli

et terrae" (See discussion f textbelow.)

To

Bach,

t

was

perhaps

qually ignificant

hat

4 was

the

product

24



4/11

of

14

X

6.

It

is

surely

ell known

y

now that

14

stands orBACH

by

means fgematria.9he number6" is alsointerestingince trepresents

the number f

days

of

Creation

another

eference

o

God

as "maker f

heaven and

earth"?)

nd is also a

perfect

umber.

A

perfect

umbers

any

number

qual

to the

um

of ts

liquot

parts.

Thus

6=1

+

2

+

3;

the next hree

erfect

umbersre

28,

496,

and

8,128.

Interest

n

perfect

numbers

ates

back to Old Testament

imes;

he

concept

s

usually

n-

cluded

n

any thorough-going

iscussion f Christian

umber

ymbolism.

While

84

is

an

"abundant" ather han

perfect

umber,

he umof

its

aliquot

parts

s

particularly

nteresting:

1+2+3+4+6+7+12+14+21+28+42 = 140 (10 X 14)

It will

be noticed

hat

he series f

divisors

ncludes he

most

m-

portant

sacred"numbers

1, 3, 7,

and

12),

along

with the

first wo

perfect

umbers

6

and

28),

and,

of

course,

he

number

4. The

sumof

the

parts,

n

addition o

being

he

product

f

14

and 10

(the

number

f

law and

completion),

s also the sum of

the first

even

perfect

quares.10

An even

more

striking

roperty

f

84

is

the fact hat

ts

prime

factors

total

14

(2X2X3X7

=

84;

2

+

2

+

3

+

7=

14

-

there

re

only

en such

numbers).

As a final onsideration,tmight e instructiveoexamine hedigits

which

omprise

hisnumber. t

can be seen

that

oth8 and

4

are

powers

of

two,

s is their

roduct

8X4

=

32),

a

fact

which

Bach

seems o

acknowledge

uring

he course f the movement

see below).

Even

the

quotient

nd the difference etween

he numbers

re

powers

of two

(8

--4

=

2;

8

-

4

=

4).

And

finally,

he

umof the

digits

8

+

4

=

12)

brings

s back to one of the "universal"

umberswith

which

thisdiscussion

egan.

The

Central

Position of the

Word factorem

From he

preceding

iscussion,

e can deduce

hat,

rom ach's

point

of

view,

84

might ery

well be

a

dynamic ymbol

with

many

mportant

associations.

f that s

the

case,

he could

hardly

ave

picked

morerele-

vanttext

hanone which

efers o

God

as the

omnipotent

reator f all

things.

The

actualwords

used

in

the Patrem

movement

ose

a

bit of a

problem,

ince

Bach chose

to

include

he

words

Credo n

unum

Deum,

which

had,

of

course,

een

set to

music

n

the

preceding

movement.11

y

incorporating

hese

words, owever,

ach

brings

he

otal

umber f

words

up

to

14. A

closer xamination

f the

Latin

reveals he

rather

stonishing

fact hat he ext ontainsxactly4 letters. he followinghart abulates

the etters

nd

syllables

long

withthe

gematria

and

cumulative

otals)

for

he

egment

f the

Credoused

n

themovement:

25



5/11

Table

I: Numerical

Analysis

of the Text

Used byBach in the Patrem Section ofthe B-MinorMass

#

LETTERS

#

SYLLABLESGEMATRIA

TEXTURAL

WORD

(TOTAL)

(TOTAL)

(TOTAL)

REPETITIONS

1. Credo 5

-

2

43

12

2.

in

2

(7)

1 22

(65)

9

3.

unum

4

(11)

2

65

(130)

9

4.

Deum

4(15)

2

(7)

41(171)

9

5.

Patrem

6JT)

2

69

(240)

I

6.

omnipotentem

2

(33)

5

(14)

150

(390)

10

7. factorem 8 (41) 3 (17) 77 (467) 32

8. coeli

5

(46)

2

42

(59)

33

9.

et

2

(48)

1 24

(533)

34

10.

terrae

6

(54)

2

(22)

64

(597)

34

11.

visibilium

10

(64)

5

119

(716)

22

12. omnium

6

(70)

3

80

(796)

22

13.

et

2

(72)

1 24

(820)

24

14

invisibilium

12

(84)

6

(37)

141

(961)

25

(285)

There re

also

many

lues o be

gleaned

rom achs treatmentf

the

text.A

cursory

ookat thefull core s sufficiento makeus aware f his

special

nterest

n

theword

actorem.

ot

only

oes

Bach

repeat

heword

frequently,

e

also

exhibits

considerable

ariety

n

setting

t

to

music,

ranging

rom

simple

yllabic

reatmento rather

xtensive

melismas.

Referring

o the textural

nalysis

bove

(Table

I),

we find hat

his,

he

seventh

word,

esults

n

a totalof

41

letters rom he

beginning

f the

sentence. ince

41

is

"

J.

S.

BACH"

in

gematria,

he

composer

interest

in the

word

s

quite

understandable.

otice

also that

when

41

is

sub-

tracted rom

4,

the

remainders

43

(gematria

or

Credo).

In

fact,

he

equation 1 + 43 = 84 becomes dominant otive oth nthe tructure

and n

many

ubordinate

etails f themovement. he

symbolic

meaning

is clear: the

composer roclaims

is

faith,

aying

I

(J.

S.

Bach)

believe."

One

other

etail

upports personal nterpretation

f the

word

factorem

by

the

omposer.

Gematria

or he

word s

77,

a

number hose

digits

dd

to

14

(the

third

uch

number,

heother

wo

being

59

and

68).

The central

osition

f

this

word

n

Bach's

hinking

an also

be seen

in

the

structure

f

the

main theme.

See

Example

1

at

the end of

this

article.)

This

perfectlyymmetricalelody

an

be

analyzed

s

follows:

Words Patremmnipotentem factorem coelietterrae

No.

of

Notes

7

3

7

26



6/11

In the courseof its

17

notes,

Bach

manages

o

incorporate

ll 11

diatonic itchesin A major)which allwithin herange f hisunusually

wide-rangingubject.

The three

epeated

otes t theoutset eem o refer

to the triune

od,12

hile

he

hape

of the

final

egment uggests typi-

callyBaroque

visualizationf the text t

that

point.

The

completion

f

the word

meaning

earth" n

the owest

itch

ontrasts

harply

ith he

word for

"creator,"

hich

begins

with the

highest

ote,

reading

own-

ward witha triadicmotivewhich

s,

in

all

probability,

ymbolic.

t is

with ome

difficulty

hatwe recall hat his

melody,

n a

slightly

ifferent

form,

as once ssociated ith hewords

Gott,

wie

dein

Name,

o ist

auch

dein

Ruhm

bis an der

Welt

Ende,

hetext f the

opening

horus f Can-

tata171.13 See Example .)

A

detailed

nalysis

f Bach's

deployment

f this

pivotal

word s of-

fered elow

see

Table

II):

Table II:

Repetitions

of the word FACTOREM

in the Patrem

Section of the B-Minor Mass

MEAS. NO. OF NOTES

MEAS. NO. OF NOTES

1.

3 3

(Total)

17.

30 3

2. 6 3 6 18. 30-32 7

3.

8-10

7

19. 31-32

6 120

4.

9

3

16 20.

41

3 123

5.

12-14

7 21.

44-46

7

6.

13 3

26 22.

45

3 133

7.

16

3 29 23.

48-50 7

8. 18-20

7

24.

48-50 7

9.

19 3 39

25.

49

3

150

10. 22-23 7 26. 52-54 6

11.

22-24 11

27.

53 3 159

12.

22-24

7

28.

59-61

8

13.

23 3

67 29. 59-62

10

177

14.

26-28

12

30.

65-66

3

15.

26-28

9

88

31.

65-67

7

16.

30-33

16

32.

66

3

190

Note

simultaneous

r

overlapping

tatements.

Cumulative

otals

re

given

t the ndof each

group.

27



7/11

The

preponderance

f

3

s and

7

s is

arresting,

articularly

n

view of

the

ymbolic

ssociationsf those

numbers.

ven more

triking

s thefact

that here re

exactly

4 statements ith

3

notes

ach,14

hilethe7-note

statements

ccur

10 times

7

X

=

70

==

14

X 5).

15

Bach even

seems

o

"count" he

number f statements

t

times,

s

in

the

case of the

eleventh

nd

sixteenth

tatements,

hichhave

11

and

16 notes

respec-

tively.16

ven the

32

words

endered

n

gematria

32 X

77)

yields

16

as the umof the

digits

2,

4 6

4).

Bach marks he

midpoint

n

the

repetitions

f

factorem

ith

par-

ticularly

ntricate

esign.

Not

only

are there16

notes

n

the sixteenth

statement,

ut

we

also

find

totalof 16

notes

n

the3 accompanying

presentations

17,

18,

and

19

in

Table

II).

The

resulting

2

notes re

bisected

y

the

barlinewhich

begins

the

thirty-second

easure f the

movement.

With

a

sense f

wonder,

e discover

hat

he

16-note

actorem

is the

32nd

word

n

the lto

part

To

cap

it

off,

ach

constructed

bril-

liant

16-note

anopy

n

the

portion

f the

high

trumpet art

which

ies

overthe

ong

alto statement.

As

a final

ouch,

he

composer

ntroducedhe

only

two sixteenth-

notes n

the

ntiremovementt

this

very

moment

trumpet

art,

measure

32; seeExample at theendof this rticle).As noted bove n thedis-

cussion f

the

properties

f

84,

32

is the

product

f

the2

digits,

nd,

ike

16,

t

s a

power

f

2.

Looking

urther,

e

find hat

ach

was as

thorough

in

his use

of

numbers

s

he

was

in

other

spects

f his art.

Counting

he

instrumental

arts

n

the

segment

elineated

y

this

group

of

factorem

statements,

e arrive t a

total f

119

notes.

That

number

would seem

to

imply

hat

heMaker

f

theUniverse

s

visible

verywhere

n

creation.

This

interpretation

s

supported

y

two

facts:

first,

19

is

gematria

or

visibilium;

nd

second,

hat

word

s the

only omplete

ord

n

the

oprano

part

while he

other oices

ing

factorem

see

Ex.

3).

Also

notice hat n

the3 lowerparts, he32 noteson factoremre augmentedy9 notes

(bass

and

tenor,

m.

32-33),

bringing

he otal n

those

arts

o 41

notes.17

If

the

reader

has

begun

to

suspect

multiple

meanings

orthe

word

"Maker,"

e

might

ind

he

vidence

resented

y

the

twentieth

epetition

illuminating.

ere,

n

measure

1,

the

word

actorem

ppears

n

isolation

in

the

soprano art,

ringing

he total

number f

notes n

that

word

up

to

123

(41

X

3).

This

occurs

ust

prior

to the

recapitulation

f

the

Credo n

unum

Deum in

measure 2. In

fact,

he

absence

f

the

other

voice

parts

fter he

first

ote

n

measure

0

serves

o

throw

he

soprano

text nto harp elief: potentemactorem. nceagain, hepatternf

notes n

theother

arts

s

highly

ignificant

see

Ex.

4).

The

following

chart

abulates

henotes n

each

of the

four

ounding

arts:

28



8/11

Table

III: Tabulation of Notes

in

Each Notated Part

Part No. ofNotes Interpretation

Trombai

14-

BACH

Ob

I &

Violin

18

6 (

days

f

creation;

12 21

bach volume 5 issue 1 1974 [doi 10.2307%2f41639913] randolph n. currie -- a neglected guide to...

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