Blue Sphere

The Magic of Pi

Sound sculpture . . . 2022 . . . 6:23

Ever since it was viewed and photographed from space (see below) by Apollo 17 in 1972, Planet Earth has become known as the Blue Planet.

The Blue Marble photograph of Earth, taken by the Apollo 17 mission. The Arabian peninsula, Africa and Madagascar lie in the upper half of the disc, whereas Antarctica is at the bottom.
The Blue Marble

Such a distant perspective reveals the pervasive blue water of oceans, brilliant white of cloud layers, and some brown/green shapes of land masses beneath. It also reveals the spherical shape of our globe. (Euclid said a sphere is a hollow 3-dimensional rotation of a circle, and scientists have measured that Earth is not a perfectly round ball but a solid ellipsoid.) Nonetheless, the eternal, perfect rotating sphere is our iconic notion of Earth’s shape. Spheres and the Euclidean circle that generates them in three dimensions are governed by the mathematical constant π, defined in Euclidean geometry as the ratio of a circle’s circumference to its diameter.

Pi is magic, an irrational number that cannot be expressed as a common fraction. Its decimal calculation never ends, never settling into a repeating pattern of digits, which appear to be random . . . and infinite. It starts 3.1415926535897932384626433…

The beginning of its decimal expression was used in composing Blue Sphere as both a rhythmic timing pattern and a corresponding dance of the lowest 9 pitches of a Pythagorean overtone series. This is one way to literally hear π, expressing musically the eternal restlessness of our rotating blue sphere.


sound sculptures . . . 2022 . . . duration: 10 minutes

Pilot Mountain, North Carolina

I read a fascinating book, Entangled Life by Merlin Sheldrake (Random House, 2021) about the bizarre world of fungi. Mycelium is the root-like mass of a fungus branching out in soil, forming a colony too small to see or grown to span thousands of acres as in Armillaria. Lichens are complex fungal communities of different organisms, like the black rocky shoreline stripes of Hydropunctaria.


branching, thread-like hyphae

Branching is a recursive process, with a pitch splitting into two mirroring lines of pitches, then each of those lines mirror splitting again. By powers of 2, the branches eventually build a tone-mass of 8 lines then even massive 16-pitch sonorities.

Hydropunctaria maura

“water speckled midnight”

Pointillistic speckles are set in the dark tonal colors of a Viennese 12-tone pitch series, never random but kaleidoscopically sparkling in a restless texture of overlapping rhythms.

Leelanau Sketches

Sound sculptures . . . 2022 . . . duration: 30 minutes

Michigan, The Great Lake State, is two enormous peninsulas surrounded by Lakes Michigan, Superior, and Huron. Actually, there are many smaller peninsulas extending out into the lakes. The Leelanau Peninsula (north of the venerable Interlochen music camp where I spent many summers) extends about 30 miles from the northwestern corner of the mitten-shaped Lower Peninsula into Lake Michigan. Algonquian-speaking tribes occupied this area prior to European colonization. The land is now home to lighthouses, wineries, ski slopes, inland lakes, and coastal dunes and beaches.

Listen uninterrupted to all four sketches . . .

Leelanau Sketches

Or separately to any of the individual sketches . . .

Shining Water

The changing patterns of sunlight sparkling on water always fascinates me, particularly on Lake Michigan looking west from the Leelanau Peninsula.

Ice Caves

On the Leelanau Peninsula’s western shore, the Lake Michigan surf sometimes whips up and freezes in mid-air, forming weird ice caverns and ice dunes.

Sleeping Bear Dunes

Ojibwe legend tells of a fierce forest fire on the western shore of Lake Michigan, forcing a mother bear and her two cubs into the water to swim to the opposite shore. After many miles of swimming, the exhausted cubs drowned. When the mother bear reached the eastern shore, she waited on top of a high bluff in hopes that her cubs would finally appear. Moved by the mother bear’s determination and faith, the Great Spirit created two islands to commemorate the cubs, and the winds buried the sleeping bear under the sands of the dunes, where she still waits.

The main dune is enormous, a mountain of sand rising dramatically above the shore of Lake Michigan. The bear’s bluff atop this majestic mass of earth is a serene vista of radiant sun, windblown sand and waves.

See more images at TClark digital art galleries
Autumn on M22

A scenic autumn drive around the peninsula on Highway M22 is a glory of light sifting down through a canopy of colored leaves. The 75-mile drive from Empire on M22 winds northeast to Northport then south around the east side of the peninsula along Grand Traverse Bay to Traverse City.

Great Lake

2021 . . . percussion trio . . . duration: 10 minutes

Horizon . . . Thunder . . . Squall . . . Sun sparkles . . . Powerful waves

The music is fashioned out of a small set of sound resources: simple sounds of drums, bright sounds of ringing metal instruments, and deep shining sounds of tam-tams. The piece is about these distinct timbres – only the sparkles employ any pitch constellations, and then just one “chord” that recycles kaleidoscopically. Most of all, the piece is about time and its articulation in free, ametric rhythm. In Thunder and Waves, the time patterns are governed by the digits of the magical numer Pi. In Sparkles, the timed recurrence of each pitch is determined by prime numbers. Both number schemes transcend periodicity, letting time float.

Growing up in the Great Lake State, being surrounded by three of the five Great Lakes formed a big part of my Michigander character. Since many summers working at what was then called the National Music Camp in Interlochen, my favorite was the closest, Lake Michigan. Its magnificent coast forms the western edge of the lower peninsula, stretching from New Buffalo all the way up to the Straits of Mackinac. Its waters reach from many Michigan harbor towns across to Chicago and Milwaukee. Its varied environments offer fascinating features such as sand dunes, ice dunes, and remote islands. This piece depicts three phenomena: approaching thunder echoing across the vast lake; sunlight sparkling on the cold surface; and eternal, powerful waves.

STAGING: Antiphonal, three widely separated batteries

LEFT – 4 low tom-toms, bass drum, orchestra bells

CENTER – small and large tam-tams, vibraphone

RIGHT – 4 low tom-toms, bass drum, orchestra bells

Mapping the Cosmos

2021 . . . Etudes for Piano . . . Total duration: 10 minutes . . . COMPLETE SCORE

Mapping the Music Universe produced several small etudes to illustrate the compositional potential of musical patterns explained in the ebook. The inspiration to collect them into a series came from many years of fascination with Bartók’s wonderful Mikrokosmos series of 153 piano pieces in modern styles. Some of the Mapping etudes were originally sketched for piano, others adapted from more complex textures. They range in difficulty for the pianist from the simpler 1. Pisces to the more challenging 6. Scorpius.

The first seven are simpler, with each etude titled with an astronomical entity named for a mythological character.

Though the whole set is 10 minutes in length, the pianist wishing to perform some of them is welcome to select a suite of three or four. Each etude is titled with an astronical entity named for a mythological character:

  1. Pisces – The Fish; 12th constellation of the Zodiac

2. Cygnus – The Swan; a northern constellation

3. Milky Way – Way of the White Cow in Irish myth; the galaxy containing our Solar System

4. Pleiades – Seven Daughters of sea-nymph Pleione; an open star cluster

5. Laniakea – Immense Heaven in Hawaiian; supercluster of galaxies that includes the Milky Way

6. Scorpius – The Scorpion; 8th constellation of the Zodiac

7. Andromeda – Cassiopeia’s daughter, saved from the sea monster Cetus by Perseus; a spiral nebula and nearest large galaxy to the Milky Way

Experience all seven in synthesized-sound color video on YouTube or audio only:


The last five Mapping the Cosmos etudes are each suitable as short stand-alone recital pieces or as a set. Beyond Mikrokosmos, they pay homage to Debussy’s revered books of Preludes. These pieces embrace the Impressionist approach to texture and form, while evolving beyond Debussy’s tonal language. Stonehenge and Lunar Litany both draw material from the 1975 four-movement piano work Geography of the Chronosphere.

8. Moonlight – an arpeggio homage to Beethoven’s famous Sonata

9. Deep Sky – profound mysteries glimpsed by telescopes

10. Stonehenge – ancient site of human worship in the cosmos

11. Lunar Litany – moon cycles governing human activity

12. Star Map – celebrating early star catalog project Carte du Ciel


2021 . . . chamber orchestra (Flute, Oboe, Clarinet, Bassoon, 2 Horns, C Trumpet, Trombone, Timpani, Percussion, Strings)

Duration: 21 minutes in three movements – I. 8 min.; II. 8 min.; III. 5 min.

Mozart’s Jupiter Symphony is one of his greatest masterpieces. His No. 40 in G Minor and No. 38 “Prague” are also magnificent. It makes one wonder if he had lived longer, what other stunning music would have poured forth. Back to No. 41 Jupiter, the first theme is a curving melody of such rhythmic vitality and fascinating turning shape that I used it as an example of both in my ebook, Mapping the Music Universe. Mozart makes the theme into a fugato, and I have adopted it in my obsessive study of canons. You can see the shape of its first six notes in the violin opening of Jupiter Rising, then elsewhere it permeates the contrapuntal material of the rest of the piece. The middle movement takes a break from it, setting the main themes from the opening of the G Minor No. 40 as a languid tango tune, followed by a trio in slow waltz meter that reverts briefly back to the bright Jupiter tune. The final movement actually extends our signature Jupiter theme into a 12-tone row, generating a more expansive tonality in its animated landscape.

I. Jupiter Rising depicts the mysterious splendor of moonrise, large and deeply-hued in the eastern evening sky. This movement creates a sonic metaphor for that visual phenomenon, but portraying instead the rising of Jupiter, the largest object in the solar system other than the sun itself. It only looks much, much smaller to us than the moon because it is so much farther away. My favorite Mozart symphony is Symphony No. 41 in C Major, K.551. His longest and last symphony, it is nicknamed “Jupiter” — fitting that his lengthiest and greatest symphony is named for the largest planet, a great gas giant. A vivid musical motive begins and generates the majestic final movement. I use it as the musical subject of this movement, relentlessly canonic in deployment. At some moments, as many as 8 contrapuntal soundings overlap each other in a gentle, cloud-like texture.

II. Tango is set in an actual key, appropriate for this venerated dance form though uncharacteristic for my writing. The harmonies flow like dancers, the musicians feeling their way through the tonalities while never seeing an actual key signature.

III. Blue Ridge refers to the beautiful hazy curves on the horizon as one gazes out from the top of the Blue Ridge Parkway, an hour west of my former home in the Piedmont in North Carolina. I also remember a similarly mystic vista looking south from Monterrey, Mexico toward the foothills of the Sierra Madre Oriental mountains. The musical fabric is what I have called an “animated landscape,” not a still postcard but a soaring flight over and through the soundscape.