Mapping Music
“The heavenly motions are nothing
but a continuous song for several voices,
perceived not by the ear but by the intellect,
a figured music that sets landmarks
in the immeasurable flow of time.”
— Galileo Galilei
When we gaze at stars and planets, they appear as stationary points of light, fixed in place in what seems a random pattern across the entire night sky visible to our hemisphere. Time stands still.
Throughout human time, humans have imagined that stars make picture patterns we name as constellations: fish, warriors, goddesses, animals. Only the persistent observers, such as astronomers, identify their nightly march across the sky, rising in the east and disappearing below the western horizon.
Metaphor
Musical sounds mark points in time, like stars. They form immediately into recognizable patterns we call chords, melodies, rhythms, memorable themes. They convey a sense of motion, time surging forward or slackening in our perception of their well choreographed parade.
Astronomers observing and mapping (recording) the myriad points discovered that some of the stars are actually whole galaxies, with exotic forms of spirals and clouds. They observed through the color of the light that all these objects are racing away from us and each other in an expanding universe.
Mapping music means cataloging many possible patterns, distinguishing their contrasts and communalities. We will explore how to measure and compare the periodic rhythmic streams of musical events and their changing momentums. We will define and employ a simple but powerful math tool for cataloging and then creatively sculpting with all natures of harmony and melodic line in our 88-key chromatic universe. We will explore how master composers weave colorful fabrics and grand structures from skillfully crafted materials.
“Mapping” has double meaning. A road atlas measures and records all the routes through a given territory. But we also call “mapping” the creative act of planning out a journey using that information to discriminate the many possible choices. This book is written very much with a composer’s mentality, revealing creative processes to compose a variety of musical journeys.
Pursuing periodicity
My music-mapping Periodicity Project began in 2021 as a comprehensive catalog of musical patterns and processes, meant to provide simple tools for understanding the complexities of modern music. It grew into this book, Mapping the Music Universe, written for anyone who is curious about how music works, especially in the 20th-21st-century modern and “post-modern” eras. For me as a composer, it is also an exploration of how some less traveled conceptual paths lead to interesting creative possibilities.
In 1989 I co-authored a conceptually ground-breaking composition textbook with Larry Austin, Learning to Compose: Modes, Materials, and Models of Musical Invention. My next book, ARRAYS, was an aural skills workbook covering basic modal, tonal, and “post-tonal” music of the Renaissance through the Twentieth Century. Mapping the Music Universe draws in part on the ideas and approaches of both these now out-of-print publications.
The three parts progress logically from fundamental — time and periodicity — to pitch space, then to larger structures, texture and form. They can be read in this sequence or separately in any order. Likewise, within each part, the various topic chapters are presented in a progressive order, but jumping in at any point is not to be discouraged. Terms are defined, sometimes freshly coined, and graphic figures include musical examples, sample etude compositions, tables, and graphic illustrations of patterns and their relationships. The Big Ideas explored include periodicity, complexity, symmetry, relativity, using precise mathematical arrays as well as broad metaphors.
Part IV offers seven creative labs, presented as step-by-step recipes to compose simple pieces based on models of different compositional genres. Each Lab includes an original sample piece following the lab guidelines, illustrating one possible creative outcome. A final collected list of special terms created for Mapping provides a glossary for further thinking and study.
A common assumption within Western culture is that Science is all about observation, measurement, precision, and mathematical rigor . . . and Art is all about the “i” words: imagination, inspiration, intuition, improvisation. Science is Deductive, art is Creative. Our culture has begun to recognize the commonality of all these intellectual strengths, that the best Science can be creatively intuitive and great Art can be rigorous
Pioneer map makers
As an educated musician and professional composer, I also have long been deeply interested in science, especially astronomy. Having read a great deal of general science writing, I am inspired particularly by ground-breaking pioneers who methodically and comprehensively mapped the possibilities of their particular field.
The work and insights of the two on the list representing rigorous study of music, Fux and Forte, were part of my formal education in music and later an integral part of my teaching of composition and music theory.
Pioneer map makers
- Johann Joseph Fux wrote Gradus ad Parnassum in 1725, codifying basic contrapuntal principals of Renaissance music.
- William Smith, a rural surveyor, in 1799 drew a colorful map of the subterranean rock strata of his county in English coal country, launching the modern science of geology.
- Meriwether Lewis kept extensive journals of the 1804-1806 Lewis and Clark Expedition, documenting and illustrating the discovered new world of the Northwest.
- Dmitri Mendeleev devised a “periodic table of the chemical elements,” published in 1869, providing a solid basis for modern chemistry through its graphic and organizational genius.
- Amédée Mouchez launched an ambitious international star-mapping project (Carte du Ciel) in 1887 at the Paris Observatory.
- Henrietta Swan Leavitt, working at the Harvard College Observatory as a “computer,” examining thousands of photographic plates from telescopes to measure and catalog the brightness of stars, identified 1777 variable stars.
- Lawrence Herbert invented the Pantone system in 1956 to analyze and systematize color for printing ink and fabrics.
- Allen Forte published an article in 1964 that launched musical set theory, defining, classifying and comparing all possible collections of “pitch classes” drawn from the equal-tempered 12-tone chromatic galaxy.
Inspired by these ground breaking pioneers, my music-mapping Periodicity Project began as a comprehensive catalog of patterns and processes, meant to provide simple tools for understanding modern music. It grew into this book, Mapping the Music Universe, written for the literate musician, including college music students, especially composers, music scholars, and anyone who is intellectually curious about how music works, especially in the 20th-21st-century modern and “post-modern” eras.
Maps
Carte du Ciel was an ambitious second phase of an international star-mapping project initiated in 1887 by Paris Observatory director Amédée Mouchez. A new photographic process revolutionizing the gathering of telescope images inspired the first phase, the Astrographic Catalogue of a dense, whole-sky array of star positions. Carte du Ciel, never completed after 70 years, used the Catalogue as a reference system for a complex survey of the vast field of even fainter images.
Celebrating the grand metaphor relating astronomy to art music, here is my 8-minute computer-music sound sculpture. In the music, ghostly wisps of sound are punctuated by brighter bursts, clustered in a natural, not-quite randomly dispersed texture.
MAPPING MUSIC 