Circle of Fourths - Joe Wolfe

An orchestral overture celebrating the Circle of Fourths.

The score is here.


About the piece

The invitation. Commissioned as a celebratory piece for the UNSW Orchestra's 100th concert, the brief 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 to make the three tunes in this piece. Of course, these notes are just a descending scale with the first note repeated, so I'm pretty sure that no-one would have noticed if I didn't point it out here. But I did want Eric to know that I've fulfilled this aspect of the commission!

The circle of fourths. An idea that I've wanted to use in a short orchestral work is the circle of fourths that gives this piece its name. 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 them through the orchestra, I expect that there won't be temperamental problems (see below). 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, rather, 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.

diagram of a circle of fourths

What is a circle of fourths and why?

Nearly every musician spends some time, first in wonder then in worry, on discovering the circle of fourths (or circle of fifths*). 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, which is shown at right.

diagram of a circle of fourths 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.

If one retains perfect fourths and fifths, the fourths make a spiral, as shown in the figure at right, rather than a circle.

About the composer

Joe Wolfe started writing music in the seventies and has since written sporadically for jazz and fusion groups, including incidental music for plays and films. He has written five other orchestral works: The most notorious is "The Stairway Suite", a set of orchestral variations on the pop song "Stairway to Heaven" in the styles of Schubert, Holst, Glen Miller, Mahler, Bizet and Beethoven. "Sydney Sketches" is a set of tone poems, each of which is based in different Sydney location at a different time of day; "Conjunction" is an 'interactive introduction to the orchestra', written for orchestra and primary school choir. "Overture" was written for the UNSWO's 10th anniversary and a trumpet concerto was written for Anthony Henrichs of the Sydney Symphony.

Almost a circle. In the full score, it is closed by the piccolo, but I've only shown the strings here. The complete score shows how the circle is distributed in the orchestra (bars 11, 43 and 152).

part of the score showing a circle of fourths

* 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 like the melodic and harmonic possibilities of the fourths!


Joe Wolfe / J.Wolfe@unsw.edu.au /61-2-9385 4954 (UT+10,+11 Oct-Mar)