The Cycle of Fifths
When musicians speak about the cycle of fifths they are most often referencing the tonal version, that is, the diatonic cycle of fifths that forms as you pass through, by successive intervals of a fifth, the seven tones or the seven triads formed with the seven pitches of any 7-tone scale. The diatonic cycle of fifths is comprised of the seven triads formed from each of the seven degrees of the same scale, and each triad is also formed from the notes of that same scale. These triads are most often harmonically connected by means of their dominant triad, and these triads, are often musically linked by what’s called a diatonic sequence. You can find more detailed material on the internet and you can find some exercises with those materials at this link: Diatonic Cycle of Fifths
This exercise concerns the sequence of perfect fifths (or fourths) which, because of its inherent chromaticism, cannot be considered to be in a specific key. It is not an“atonal” exercise, but there is no sensation of key centre, since the exercise moves quickly from one stability to the next. However, familiarity with the cycle is considered de rigueur for understanding chord relationships, root motion, and harmonic progressions.
I often gave this collection of exercises to piano improvisation students for several reasons. It is a way to become cognizant of the location of these most important intervals—perfect fifths and perfect fourths. [For insight into the layout of the keyboard and the ability to quickly locate intervals without analysis, see https://caseysokol.squarespace.com/blog/keyboard-topography. Facile knowledge of those intervals are needed for intelligent chord formation, for playing bass lines, even for forming resonant tone clusters in free improvisation. The exercises also invite pianists into more demanding challenges of musical attention, which is useful for all your other musical work. For some pianists, there will also be some new challenges for piano technique and some new ideas for ensemble collaboration as well as for your compositional invention.
The Cycle of Fifths (PDF file) (This is a PDF of the Sibelius file and will open in a new window.)
Audio file of the Cycle of Fifths PDF file (This is a MIDI rendition of the Sibelius file.)
Live Performance:
Etude for Two Pianos (Cycle of Fifths) (performance with Prof. Glenn Buhr; from duo-piano concert at Wilfrid Laurier University)
This is not an audio file of all the exercises on this post. It’s limited to the 24 ‘phases’ of the 24-note cycle of fifths (that is the 12-note cycle of fifths followed by its retrograde). It’s not at all intended as a performance piece but Glenn thought it would be an interesting addition to our duo-piano improvisation concert. The ‘premier’ performance of my *Etude for Two Pianos was at the opening of the 1994 Winnipeg New Music Concert Festival. It was played by conductor Bramwell Tovey and Glenn Buhr (composer in residence with the Winnipeg Symphony at the time). This recording was made in a 2001 concert at Wilfrid Laurier.
* A request for the score came in a long-distance call from a pianist who attended that concert and was excited to include the etude in her concert repertoire. I had to explain that there was no score; the whole piece was simply a 24-note loop, performed with continuous rhythmic displacement. Unfortunately the two pianos are not recorded with equal presence, so the effect of the pattern displacement is somewhat diminished.
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I thought it might be useful to those who are visiting this post to see how such materials might play out in a more developed creative project. The link here is to a twenty-minute dance piece commissioned for three-pianos based on a 1953 award-winning fantasy novel by Theordore Sturgeon, “More Than Human.” The plot, in brief, is described on Wikipedia. “The novel concerns the coming together of six extraordinary people with strange powers who are able to "blesh" (a portmanteau of "blend" and "mesh") their unusual capabilities. In this way, they are able to function as one organism. They progress toward a mature gestalt consciousness, called the homo gestalt, proposed in the novel as the next step in the human evolution.
The cycle of fifths was one of several interval sequences I employed as the compositional basis for the piece which is linked below (both the score and recordings). You can see how this and the other interval sequences were used in helping to narrate the story, identifying the characters and events, something like a leitmotif.
The commission for this piece came with an interesting requirement which presented difficulties for composing. The choreography and musical composition were not to begin until we were in the same city and working together. In order to produce preliminary musical suggestions and responses to the choreography and the story, some amount of writing had to be completed with sufficient lead time for the pianists to learn it and record the music for the dancers to work with. There was very little time to put this all together and I realized that I needed an approach to the composing that would be very modular—not only modular in form but also in materials. I saw that, rather than try to begin with any notions of a fixed piece at the beginning, it would be best to compose materials that could be reassembled in different ways, perhaps something like changing patches on an early Moog synthesizer. This interval exercise which was formulated years before turned out to be the fulcrum around which the whole process would be connected.
Each character has a slightly different interval sequence by stacking major and minor thirds in various combinations. It was subtle but worked very well, like associating lighting cues with elements of a story. The playfulness of the teleporting twins was best energized by simple alternations of M3s+m3s. Other characters (or events) were represented by sequences such as M3+M3+m3 or m3+m3+M3, and Janie—who is the Conscience of the new multi-organism—is the only character represented by fourths, specifically the Cycle of Fourths (Fifths). Only in mm.240-280 does the rigour of the interval principle give way to a poignant lyric section.
Here is a PDF of the score… Species
and a recording of the premiere (no video) Species live performance
And a MIDI performance … Species (MIDI)