The repertoire of American composer James Tenney (1934-2006) is among the most diverse and stimulating in experimental music. Tenney wrote several works using algorithmic procedure, yet always producing music of striking clarity and unassuming elegance. Most of his pieces explore aspects of sonority and resonance—the gradual change of musical parameters over time (e.g. textural or temporal density), the cognitive resultants of acoustical phenomena (like the infinite glissando of For Ann (rising)), and so forth. Several of his most successful pieces were written in alternative tunings, transferring the acoustical properties of the overtone series into a more immediate musical domain.
The Septet (for six electric guitars and electric bass) is one of such pieces. The entirety of its musical materials is derived directly from the ratios of the harmonics of the overtone series, in this case built upon a low A fundamental. The first section of the piece consists of a unison canon, whose rhythmic figures present a harmonic progression of attacks as the various voices enter in staggered fashion—as marked in the excerpt below.
At the apex of the canon, the seven instrument sound a complex polyrhithm that reflects the ratios of the overtone series up to the 12th harmonic. In the second section, Tenney introduces harmonic pitches for each rhythmic value; for example, Guitar 1, who is playing in sextuplets, switches its As to Es, the latter pitches being the 3rd, 6th, and 12th harmonics of the series. The concept of having harmonic pitches sounding in rhythmic ratios dates back to ancient Pythagorean theories (both musical and spiritual in nature), and was revisited in the 20th century by composers such as Henry Cowell and Conlon Nancarrow.
Some of the harmonics on the series would be quite out-of-tune if played on a regularly tuned, equal-tempered guitar. If the 5th harmonic (major third) is only a little sharp in ET (14 cents, to be precise, with 100 cents equalling one half-step), the harmonic 7th and 11th are more problematic, being 33 and 49 cents sharp in ET, respectively.
Tenney obviates this problem by retuning a couple strings on the guitars responsible for each harmonic—and restricting the musical material for that guitar only to those notes that can be sounded accurately in tune. Guitar 2, for example, tunes its top two strings flat by 14 cents, and sounds a pure major third against the ensemble’s equal-tempered A by fretting a C# on the detuned strings. Similarly, Guitar 3 detunes by 49 cents to play the 11th harmonic in tune, and Guitar 6 deals with the 7th harmonics by retuning its top string by 33 cents. These deviations are marked by the odd looking accidentals in the example below. Tenney’s brilliant solution allows complex harmonic relations to be sounded by the ensemble without the need for custom or otherwise adapted instruments (which can be expensive as well as problematic to get).
Two-thirds of the way through the piece, the series “modulates” up a fifth to E, with a new chord built progressively out of a unison. I put “modulates” in quotes because, strictly speaking, each new pitch is simply a higher harmonic of the original fundamental (A), multiplied by a factor of 3—for example, the 3rd harmonic of E (B), is at the same time the 9th harmonic of A. The modulation is highlighted by two solos: first the Bass plays harmonics of A up to the 12th, then Guitar 3 descends down a series based on E, playing harmonics 8-1. The beginning of the bass solo is also shown in Example 2.
The resulting sonority must be heard to be fully appreciated. There is an unmistakable serenity and a “groundedness” in this music, deriving from the pure, simple-number relationship that governs the rhythmic, harmonic, and melodic ratio between every single pitch.
Tenney’s Septet counted a number of performances at the time of its premiere, which was given by Larry Polansky and the Mills Contemporary Music Ensemble in 1985. A couple of recordings can be found online here and here. More recently ensembles have picked up the piece again—here is a video by the NYC electric quartet DITHER, augmented for the occasion by guest players Nick Didkovsky, Devin Maxwell, and Dan Josephson. There is also a commercial recording by Seth Josel—hard to find, but here’s a link. Josel also recorded Tenney’s other guitar ensemble piece, the monumental Water on the mountain…Fire in heaven, whose workings will have to be described in another post.
The Septet offers incredible musical rewards to any small group of players with the courage to step outside the comfort zone of equal temperament—all that is needed is an electronic tuner, a keen ear, and the ability to count to eleven. Here’s to hoping more and more players people will get a chance to hear Tenney’s mesmerizing exploration of the overtone series.