circle of fourths - university of new south...

Circle of Fourths

Joe Wolfe

Circle of Fourths Joe Wolfe

Three flutes, one doubling piccolo

One oboe and one cor anglais

Two clarinets and one bass clarinet

Two bassoons

Four horns

Two trumpets

Two trombones and one bass trombone

Tuba

Timpani (ideally four, but playable with two)

Bass drum, cymbals, tam tam, congas, timbales. At least three players

String orchestra

The brief for composing a celebratory piece for the UNSW Orchestra's 100th concert was simple: 4 or 5 minutes of fun,

using everybody and not to compete too much for rehearsal time. The orchestra's archivist (cellist Eric Sowey) was keen

that the piece incorporate the number 100. The Old Hundredth is a chorale, so named because its words are from psalm

100: 'All people that on Earth do dwell'. I took the first five, four or three notes, added syncopation, and used them as seeds

for the three tunes in this piece.

There was another idea that I've wanted to use in a short orchestral work. Nearly every musician spends some time, first in

wonder then in worry, on discovering the circle of fourths (or fifths1). Play four ascending notes in a major scale, say C-F.

Then another: F-Bb. Continuing thus, and setting Gb = F#, we have C-F-Bb-Eb-Ab-Db-Gb(=F#)-B-E-A-D-G-C. On a

piano, Gb = F# so, after 12 fourths, we have covered five octaves and come back 'home' to C - hence the circle.

The worry arises because a perfect fourth has a frequency ratio of 4/3 and an octave 2/1. So 5 octaves = 25 = 32, while

(4/3) 12

= 31.6. Out by 1.3% or a quarter of a semitone, called the Pythagorean comma – it's not a new problem!

Minimising the potential mistuning thus caused is called temperament. There are many temperaments, all with

disadvantages: Lakes of ink have been poured into the problem of temperament over more than two millennia.

But quite apart from the historical, physical and philosophical interest in the circle, I was attracted by the melodic and

harmonic possibilities of successive fourths. Stacked up over five octaves, the circle is an interesting chord and building it

from the bass creates musical tension. By keeping the pedal notes loud and distributing it through the orchestra, I expect

that we shan't have serious temperamental problems. There is, however, the interesting question of where to go after a

chord that contains 12 different notes: this work has a few answers.

The piece is mainly in 8:8 time (3+3+2 quavers) with, for contrast, some interjections of 3+3+3+2+2, a 3:4 slow section in

the middle and some syncopated four at the end.

While I was writing this piece, Larrikin Records surprisingly won a court action against a band that had wittily quoted 11

notes from 'Kookaburra sits in an old gum tree'. So I wondered about the propriety of borrowing up to 5 notes from Lloys

Bourgeois, who wrote the Old Hundredth in the sixteenth century. Or from the unknown inventor of the descending major

scale, because Bourgeois, in turn, had already borrowed the phrase! However, if Larrikin were to buy up the old chorales I

expect that they would start suing Bach first, so I'm probably safe. If not, I'm pleading syncopation. But if Pythagoras sues

me for the circle of fourths, I'm in trouble.

About the composer

Joe Wolfe is a physicist by day, but has written several orchestral works. The first of these, his most notorious, is the

Stairway Suite: a set of seven orchestral variations on the pop song Stairway to Heaven, each in the style of a different

composer (currently being rehearsed by community orchestras in Korea and the UK). Sydney Sketches is music about the

city, Conjunction is an interactive introduction to the orchestra. He also wrote a celebratory overture for the UNSW

orchestra's tenth anniversary, and a jazz-flavoured concerto for SSO trumpeter Anthony Henrichs.

1 A few people have asked: Why a circle of fourths, rather than fifths? First, a circle of fifths is seven octaves, which

stretches the orchestral range and would make it difficult to balance chords. Second, when musicians depart from perfect tuning, they usually stretch intervals. Stretching a circle of fourths reduces the temperament problem, stretching fifths increases it. Third, and most importantly, I preferred melodic and harmonic possibilities of the fourths.

Steady (about 84)

Steady (about 84)

Circle of Fourths Joe Wolfe , 2010revised 2011

Flute 1

Flute 2

Flute 3/Piccolo

Oboe

Cor Anglais

Cor Anglaistransposed

for clarinet 3

2 Clarinets in Bb

Bass Clarinetin Bb

Bassoon 1

Bassoon 2

4 Horns in F

2 Trumpets in Bb

2 Trombones

Bass Trombone

Tuba

Timpani

Bass Drum

Congas

Timbales

Cymbals

Tam-tam

Violin I

Violin II

Viola

Violoncello

Double Bass

mf

mf

mf

mf

mf

mf

ff

mf

mf

ff

f

a 2

a 2

f

mf

p

mf

mf

mf

mf

ff

mf

mf

ff

p

tune E, A

and B,D if there are four

p

f

mf

mf

mf

mp

mp

p

damp

p

damp

p

f

div.

mf

div.

mf

div.

f

div.

mf

div.

pizz

arco

mf

div.

pizz.

arco

f

div.

9

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

f

ff

3 3 3 3 3 3 3

on picc.

ff

ff

3 3 3 3 3 3 3

ff

ff

ff

3 3 3 3 3

3 3

ff

3

3 3 3 3

3

3

3

3

ff

f

3

3

3

3

f

3

3

3

3

3

3

3

3

ff

ffl.v.

f

div.

al niente

div.

al niente

f

div.

al niente

al niente

al nienteWolfe: Circle of Fourths (revised)

2

15

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

mf

mf

pp

mf

p

p

ppp

ppp

ppp

p

mf

damp

damp

p

mf

mf

mf

mf

pizz.

p

Wolfe: Circle of Fourths (revised)

3

23

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

p

p

p

p

p

p

ppp

p

mf

damp

if 4 timpselse tacet

if 4 timps

solo

p


4

32

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

f

f

fp

f

f

f

a 2

f

f

f

f

a 2

mf

mf

a 2

mf

mp

f

mf

f

damp

if 4 timps

if 4 timps

mf

mf

p

f

fp

f

fp

f

f

f

div.

f

f

arco

div.


5

40

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

f

f

sempre picc.

f

al niente muta in flauto

f

f

f

f

3

3

3

3

3

3

f

f

mf

mf

ff

tune E,A (and D,G if 4)

ff

l.v.

p

ff l.v.

f

div.

pp

f

div.

pp

f

div.

pp

ff

f


6

47

poco rit.

poco rit.

Meno mosso

Meno mosso

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

ppp

pp

ppp

mp

solo

mf

pp

solo

mf

pp

solo

mf

3

3

ppp

mp

a 2

solo

mf

pp

ppp

solo

mf

pp

solo

mf

mp

pp

play if no bass clarinet

mp

play

mf

ppp

mpsolo

ppp

ppp

ppp

ppp

ppp

mp

solo

ppp

ppp

ppp

ppp

ppp

l.v.

l.v.

pp

suspended

pp

l.v.

ppp

l.v.

ppp

p

l.v.

al niente

al niente

al niente

ppp

al niente

solo touch 5th on A

ppp

o

p

o

o

ppp

sempre ppp

a 1


7

59

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

pp

p

pp

p

pp

sul flauto

p

f

solo

f

f

solo

mf

p

a 2

mp

p

play

p

a 1

p

a 1

pizz.

mp

div.

pizz.

mp

pizz.

mp

o

o

o

o

ppp

o

tutti pizz.

mp

div.


8

69

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

p

pp

p

pp

pp

pp

pp

mf

solo

arco

mf

div.

arco

p

mf

arco

mf

arco

mf

pizz.

mp


9

79

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

solo

mf

pp

p

muta in picc.

pp

pp

a 2

pp

mf

a 1

mf

a 1

ppp

mf

mf

p

mf

solo

mf

p

a 1

p

pp

pizz.

p

pizz.

p

div.

p


10

89

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

match discord with picc

p

sul picc

p

match discord with fl2

ppp

ppp

pp

a 1

pizz.

p

div.

pp

arco div.

pizz.

p

div.

pp

arco

div.

p

p

pp


11

99poco rit.

poco rit.

Tempo 1

Tempo 1

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

muta in flauto

mf

p

mf

a2

mf

a2p

p

mf

horns

a 1

pp

pp

mp

p

mp

mp

mp

hands, not sticks!

p

mf

suspended

p

damp

mp

l.v. damp

mf

l.v.

arco

mf

p

mf

sempre pizz


12

108

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

mf

mf

fl3

f

mf

f

f

mf

f

f

f

f

f

pp

mp

f

p

p

f

take sticks

p

mp

damp

damp

p

p

mf

arco


13

115

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

pp

solo

f

pp

muta in piccolo

pp

pp

pp

pp

a 2

f

pp

f

pp

pp

f

a 2

f

a 2

f

f

a 2

f

f

con corni

f

f

damp

ppp

l.v

mf

sempre l.v.

f

ppp

mf

mf

f

mf

sticks

damp

f

f

sempre arco

pizz.

ff

pizz.

ff

ff

pizz

ff

sempre pizz.


14

121

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

P

P

f

P

f

P

f

P

P

a 2

p

p

P

P

pp

f

p

f

p

pp

mf


15

128

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

ff

ff

picc

ff

ff

ff

ff

ff

ff

ff

ff

ff

horns

ff

ff

ff

a 2

ff

play

ff

ff

tacet (or pedal?) if only 2

ff

ff

ff

ff

arco

ff

ff

arco

ff

arco

ff

arco


16

134

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

if enough playersthese could be crash

ff

div.


17

140

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

a 1

p

pp

p

2nd

a 1

p

pp

p

4th

play

damp

tune E & A

p

p

mf

mf

fp

fp

fp

div

mp

sempre pizz.

p


18

147

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

ff

ff

on picc.

ff

ff

ff

ff

ff

ff

ff

f

f

mf

ff

ff

f

mf

p

f

div.

f

div.

f

div.

f

div.

arco

f

div.


19

152

Fl.

Fl.

Fl3/picc

Ob.

C. A.

CA->Cl

Cl.

B. Cl.

Bsn.

Bsn.

Hns.

Tpts.

Tbns.

B. Tbn.

Tba.

Timp.

B. D.

Congas

Timb.

Cym.

T.-t.

Vln. I

Vln. II

Vla.

Vc.

Db.

sempre f, non ff

ff

sempre f, non ff

ff

ff

damp

l.v.

ff

ff

p

damp

l.v

ff

fff

mf

ff

ff

mf

ff

solo

fff

damp

fff

damp


20

circle of fourths - university of new south...

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