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Compositions for Guitar - W. A. Mathieu

Listen to 'Lattice Work (Lattice-Işi), Movement 1'
from Compositions for Guitar

Compositions for Guitar (2016)

Six Ellipses for Four Guitars
Mobius Trio, with Justin Houchin

Lattice Work (Lattice-Işi)
Tolgahan Çoğulu, microtonal guitar

Composer’s Notes

Six Ellipses for Four Guitars

The “ellipses” of the title is the plural for both ellipse, a kind of oval shape, and ellipsis, which means something left out usually because it is meant to be understood or inferred. So the word leans toward two divergent meanings: on one hand a closed shape, on the other hand an open interpretation. I like such ambiguity in titles, condensed phrases that give a reader room to breathe, in the same way I like musical phrases to have meanings that are various and open for each listener. (By the way, in the previous sentence, the omission, of “that are” would be an ellipsis used in the interest of clarity, and might have improved the sentence.) So, since the title won’t give anything away, here are some further notes.

Movement I was inspired directly by certain phrases from Water Wheel by the Nubian oudist and singer Hamza El Din; the entire suite is dedicated with much devotion to his memory. Movement II takes an introspective turn and has, for me, the quality of aloneness without loneliness — is this the oval aspect? Movement III is a perpetuum mobile giving the feeling of being driven by an internal engine.

Movement IV can be heard as a kind of lullaby sung inside a “turning night of stars,” to use Rumi’s phrase; its rhythmic source is the ritual mbira music of Zimbabwe. The harmonics of Movement V could give the impression of overlapping bells heard from far away. Movement VI is a pattern piece of woven repetitions overlaid with swirling solos.

Six Ellipses for Four Guitars was written a quarter-century ago, during the post-Nam, pre-9/11, good-old-’90s in America. It seems from today’s perspective to have so much more light than dark, the complexion of less troubled times. It was commissioned in 1991 by Don King, founder of Australia’s Waiata Music Publications, had its United States premiere by Mobius Trio with Justin Houchin at the San Francisco Conservatory in 2012.

Lattice Work (Lattice-Işi)

Lattice Work (Lattice-Işi in Turkish) came about through the suggestion of Michael Ellison, a brilliant student of mine who has become, over the decades, a close colleague (they have a way of doing that), and who at the time was heading the Department of Contemporary Music in Istanbul. A brilliant student of his, Tolgahan Cogulu, had built an eight-string guitar with tunable frets on each string thus enabling it to be played in any tuning including, with some finesse involved, music in modulating just intonation.

Just intonation is the way music sounded before fretboards and keyboards got hold of it, and the way it still sounds in cultures not bulldozed over by the West (are there any left?) or wherever a capella singers, or variable-pitch instrumentalists make music with an ear toward maximal harmonic resonance. Just intonation is our original and natural musical condition.

But the more harmonic complexity music has, the more notes it requires. We moderns who use the “twelve-tone equal-tempered” scale allow those very picket-fence twelve tones to stand for the umpteen tones-per-octave our music actually points to, thus gaining a very practical kind of complexity while losing precious harmonic purity. We know how to produce those umpteen tones with electronic keyboards and synthesizers, but that’s electronically. Many contemporary composers want the best of both worlds: an acoustic, under-the-hand instrument capable of both tonal complexity and harmonic purity. Many have tried: multiple keyboards, multiple keys on one keyboard, interchangeable fretboards, and tunable fretboards.

Tolgahan Çoğulu’s innovative idea is to have each of the frets on each, of eight strings able to be reliably tuned according to the needs of each piece. All the frets on the fretboard are movable in the channels under each string. Besides, any number of frets can be inserted into or removed from the fretboard. This means that the spacing of the frets on each string can be irregular and different from the other strings. For the guitarist this can feel like running full speed over rocky ground, and requires a special sort of mastery.

My implementation of Tolgahan’s idea is to use affective tunings in three separate (but overlapping) tonal fields corresponding to each of the three bass strings. The highest of these is the low E of standard guitar tuning, then proceeding stepwise down, the added D string, then the added C string (same pitch as the lowest string on a cello). Each tonal center allows a full panoply of modal coloring, with fluid modulation among the three, giving a wide range of pure harmony — from the many flats of C Phrygian to the many sharps of E Lydian. Add to these a sprinkling of the quarter tones characteristic of Middle Eastern music and a few of the septimal “blue notes” characteristic of jazz, and you have 42 different tones scattered over the range of the instrument, all of them in pure tuning.

The Adjustable Microtonal Guitar was designed by Tolgahan Çoğulu in 2008, and funded as a scientific research project at Istanbul Technical University. The first prototype was made by Ekrem Özkarpat. New versions have been made by Briken Aliu since 2014.

The Lattice of Perfect Fifths and Pure Thirds

A lattice of perfect fifths (3:2) and pure thirds (5:4) appears on the back cover of the CD, with the three tonal fields bounded in color. The four “spines” of perfect fifths stretch northeast-southwest. Each spine is separated from the one above or below it by the distance of a pure third, resulting in five spines of pure thirds stretching roughly north-south. This configuration allows the tones to be represented on staves (forget about octave transpositions for now), and the nearest resulting triads to be indicated. (Not appearing on the lattice are four quarter-tone tunings and two septimal tunings.) The colored outlines represent harmonic fields centering on C (purple), E (orange), and D (green), which are the tonal centers for the first, second, and third movements respectively.

The Tuning as Navigated by the Guitarist

The image on the right panel to the right of the CD is a kind of picture of the guitar itself, with the frets in place. The pitches are extrapolated from the lattice for each of the eight strings from high E to low C (as marked in the left margin). Notice that each note-head has a special shape that corresponds to its position on the lattice. The colored lines above each staff show the harmonic field(s) in which that note appears.

The Tuning as Navigated by the Composer

The last image on the CD shows the available pitches the ear hears, from lowest to highest. The composer needs to keep the information shown on all of these diagrams in mind at once. This might seem rather like a mental knot, but it does all become intuitive with practice. Lattice Work was three years in its conception, strategy, and composition, and three more in its realization. As for the listener, the harmonies derived from these tunings may sound unfamiliar at first, but the pure tones are built into our nature, so let them take you where they may. Tolgahan writes: “I feel so lucky to have met Allaudin through my teacher Michael Ellison. I had already read Allaudin’s great book Harmonic Experience and listened to his wonderful music. When we agreed to collaborate I felt like an historical just intonation guitar piece was so close to me, and after several years of hard work by both of us, I am glad with the result: the first just intonation guitar piece in the world in three keys, each with wide-ranging modality thanks to the eight-string movable fret guitar. Every time I play it, I feel an indescribable peacefulness with the music and just intervals. I’d like to thank Allaudin one more time for providing this emotion.”

Performers' Bios

Mobius Trio, founded in the Bay Area in 2010, “collaborates with composers and other musicians to commission pieces in which the walls between genres cease to exist and old dichotomies start to unravel.” Their website is

Justin Houchin, a rising Bay Area guitarist-songwriter, can be contacted at:

Tolgahan Çoğulu is the first-prize winner at the 2014 Margaret Guthman Musical Instrument Competition. His first CD with microtonal guitar, Atlas, was published in 2012 by Kalan Music. His microtonal and fretless guitar duo and lecture recital, ‘Microtonal Guitar Music,’ has taken him to many festivals and universities in 30 countries. Tolgahan is building a repertoire for microtonal guitar with more than thirty composers involved at this point. In 2013, he became an associate professor in guitar at Istanbul Technical University’s Turkish Music State Conservatory, where he had founded the classical guitar department in 2010. His latest CD, Microtonal Guitar Duo, was published by Kalan Music in June 2015.

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