circle of fourths - unsw physicsjw/music/circle/circle2011.pdf · stacked up over five octaves, the...
TRANSCRIPT
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
Wolfe: Circle of Fourths (revised)
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.
Wolfe: Circle of Fourths (revised)
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
Wolfe: Circle of Fourths (revised)
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
Wolfe: Circle of Fourths (revised)
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.
Wolfe: Circle of Fourths (revised)
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
Wolfe: Circle of Fourths (revised)
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
Wolfe: Circle of Fourths (revised)
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
Wolfe: Circle of Fourths (revised)
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
Wolfe: Circle of Fourths (revised)
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
Wolfe: Circle of Fourths (revised)
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.
Wolfe: Circle of Fourths (revised)
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
Wolfe: Circle of Fourths (revised)
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
Wolfe: Circle of Fourths (revised)
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.
Wolfe: Circle of Fourths (revised)
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
Wolfe: Circle of Fourths (revised)
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.
Wolfe: Circle of Fourths (revised)
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
Wolfe: Circle of Fourths (revised)
20