September 2019 Print

The Sound of Science

by Dr. Andrew Childs

Art is very pretty science. Good art, certainly. Artists can of course choose to abuse the transcendental absolutes and create works of ugliness, evil, and deceit, but this constitutes bad art, and thankfully few readers of this journal possess the intellectual flexibility—a wizardly ability, obtained at great expense from only the finest institutions of highest learning, to reconcile the irreconcilable, square conceptual circles, simultaneously embrace contradicting points as having equal validity—to appreciate it. Even before considering the mastery of various techniques and media, the artist, just as the scientist does, must submit to natural laws: if you have a lousy tempera recipe, oil paint which turns transparent, misfired clay, or a figure that cracks into pieces before you can successfully free it from the marble, you have not a masterpiece but a mess. If a composer chooses to ignore the laws of mathematics and acoustics, he creates not music, but merely noise.

Artistic technique necessarily evolves with changing schools and developing forms over the course of time. Sufficient to the age is the art thereof, and we view the artist who insists on scrupulous adherence to bygone styles and techniques as an anachronistic oddity rather than a champion for tradition. Though an artist through his technique commands a legion of processes, actions, materials, and contingencies, technique remains a functional element of the art, though highly individual: no two artists, given the same blank canvas and materials—or empty page and pen—have ever produced exactly the same masterpiece. Technical expression—formal, if you will—makes art “artistic.” The science in art exists in the material elements and accompanying natural laws—chemistry and physics of visual art, mathematics and acoustics in music. We tend understandably to focus on the artist, seeing art as the inspired utterance of an individual, taking the material forces of the art for granted. Pity, for wonder lies beneath. Science, as it turns out, is pretty artistic.

No Words Can Reach...

Words inspire thought, emotions follow. Music also inspires thought, but often as a consideration of an emotion stimulated directly and purposefully: a good composer has your heart in his hands. The Greeks knew this and attributed a metaphysical character to music and its effects. “Music,” remarked Plato, “is a moral law. It gives soul to the universe, wings to the mind, flight to the imagination, and charm and gaiety to life and to everything.” He believed that music could discipline the mind, just as gymnastics disciplined the body, warning in his Republic that too much gymnastics made one uncivilized, violent, and ignorant (while also cautioning that too much music made one weak and irritable). Aristotle proposed that music had influence over the character and the soul. Both Plato and Aristotle treat music as an extension of philosophy; for the scientific exploration of music by the ancients, we look to Pythagoras and Aristoxenus.

Music historians credit Pythagoras (570-495 BC) with the “discovery” of intervals, and the development of a tuning system based on mathematical ratios. According to legend, Pythagoras noticed the relationship of various tones hammered out on multiple anvils. Some of the pitches sounded good together, others sounded bad. Intrigued both by the consonances and dissonances, he set out to reproduce and systematize the relationships he heard, and the tuning system he developed remained largely in force for almost 2000 years. A vibrating string held at a constant tension makes a recognizable tone; half of the same string, a ratio of 2:1, will produce a tone exactly one octave higher. A ratio of 3:2 produces a Perfect fifth (C-G on a piano keyboard), the ratio of 4:3 a Perfect fourth (C-F), 5:4 a Major third, and so on. The simpler the mathematical ratio between two tones, the more pleasing the sound. By continuing to add a given interval (Pythagoras limited himself to the Perfect fifth, though different theorists allowed others as well), the composer “discovers” more distinct pitches. Given the finite ranges both of lengths of string and of human hearing, it made sense to contain these various pitches within a single octave; played in order, we recognize these series as scales or modes, three or more notes with a recognizable pattern of intervals, usually of varying size, either tones or semitones (now called whole and half-steps). The various Greek modes were said to have specific character, useful for inciting different emotions.

Aristoxenus (375-335 BC) set out to write a comprehensive treatise on music, the Elements of Harmony. He did not so much contradict Pythagoras and his scrupulous insistence on mathematical concerns, but rather focused on the application of fundamental elemental relationships—between melody and harmony, for example—based on observation rather than pure theory. Though concerned largely with an extinct modal system, many of his observations and definitions remain useful, and medieval music theory owes much to his work.

Roman theorist Ptolemy (ca. 100-170) criticized both Pythagoras and Aristoxenus, yet practically reconciled their two approaches in his writings. Most Greek thinkers believed that the movement of heavenly bodies involved both mathematical and musical “harmony,” to the extent that each planet emitted its own specific pitch as it moved. As an astronomer, Ptolemy’s theories of the universe made numerous references to musical elements; based on his work, later scientists would continue to explore the relationship between music and astronomy, most notably Johannes Kepler (1571-1630).

Martianus Capella (fl. 5th century), in his allegorical work On the Marriage of Philology and Mercury, depicted the seven liberal arts as bridesmaids, highlighting the importance of music—one of the Quadrivium, along with mathematics, geometry, and astronomy—as part of a complete education. Boethius (ca. 480-524) proposed a tripartite division of music in his De institutione musica: musica mundana, the “understood rather than perceived” music of the universe; musica humana, a metaphysical consideration of physical and spiritual harmony; and finally, a section concerning the perception of music produced either by instrument or voice.

Preservation and Permanence

Ancient and medieval theorists had in effect established a periodic table of musical elements. Pitches, intervals, modes, harmonic progression, rhythm, and rules of composition all had a place on the chart. Once released into the air, however, compositions—the practical end and application of all this material—lasted only as long as a listener could remember them, or someone could recall how to perform them. Without notation, entire stylistic schools and genres that existed as part of the oral tradition came and went. Someone had to devise a dependable way to write out the formulas.

Benedictine monk Guido d’Arezzo (ca. 990-1050) was not the first to develop a notational system, but his organizational method provided lasting solutions. Notation must indicate not only pitch but duration; early systems would give a more or less specific indication of one of these things, but rarely both. Composers relied on the stylistic mastery of the performer to fill in notational gaps; singers and players would follow what amounted to a sort of shorthand indicating melodic shape and rhythmic relationships. Guido developed a four-line staff to indicate pitch location. The system is intuitively simple: the space between lines or spaces is a fixed interval, and by indicating the beginning note in a modal sequence on one of the lines, the performer could immediately determine the distribution of the tones and semitones. This notational staff solved the problem of preservation, but what if a composer wanted to stray outside of a particular mode; and what if good performers were not necessarily advanced theorists? The answer to highly complicated technical problems is often obvious and organic: Guido gave the notes names, based on their place in a sequence in a hymn the text to which everybody knew, “Ut queant laxis,” which is the Vespers hymn from the Feast of St. John the Baptist. The first syllables of the first words of the opening six phrases of the hymn form the pattern Ut-Re-Mi-Fa-Sol-La. Guido had invented solfege (the French still use Ut instead of Do, a 17th-century substitution), in effect liberating compositional practice by reconciling theory and practice with a mnemonic.

Equal Temperament

Humanist development in four steps:

  1. Dismantle God’s truth or something in the natural world;
  2. Reverse-engineer it;
  3. Reassemble a “sanitized” version, imposing artificial symmetry and proportion;
  4. Claim truth and nature as your own discovery or invention, a triumph of progress and scientific inquiry!

When composers left the still, open waters of modal melody, enchanted by the siren song of tonal harmony, two things happened: they wanted to increase melodic range and tonal centers (keys); and the modal system of melody—with its choice of several scales, each with its own character—had to be abandoned to allow for the emergence of harmony as the predominant musical element. Dorian, Phrygian, Lydian, Mixolydian, Locrian—all gone, consigned to the historical dustbin. But this modal purge didn’t satisfy; the humanist composer refused to be contained by nature (tuning starts to fall apart when you stray too far from home…). He disassembled nature and reassembled it on a stringed percussion instrument purposefully but absolutely predictably out-of-tune with itself.

The multi-octave keyboard and equal temperament were born. Composers loved them. They now got credit for composing in all sorts of different keys, even though all the keys—thanks to the artificially equal size of all of the half-steps—replicate the same single mode on a higher or lower pitch: Ionian, the C-C mode, if you feel happy, and Aeolian, the minor variant A-A mode if you’re blue. Human genius paid for by nature.

Wonderful things can happen in this system, of course. Bach counterpoint couldn’t exist without equal temperament, and the entire canon of musical masterworks assumes the tonal conception, yet when science replaces nature, strange things happen. In the case of music, the subordination of melody to harmony allowed for an admittedly magnificent expansion of sonority, but at the expense of ordered forward momentum. Composers luxuriated in epic harmonic exploration, and one glorious, emotionally-bloated masterwork after another—Bruckner, Mahler, Strauss, Verdi, Puccini, Wagner—sounds as if something will burst: emotionally, sometimes it does. After the sumptuous sound and fury of the Liebestod, or the Symphony of a Thousand, what next? In a word, nothing.

The Modernist Square Peg

Arnold Schoenberg (1874-1951) began his compositional life as a tonal composer. Something changed; then something very bad happened. Perhaps because he sensed the end was near—how much further could tonal composition go? —or perhaps because of some existential crisis (increasingly in vogue after the turn of the 20th-century), Schoenberg decided to pull the whole thing down. He had help, but for the sake of survey, he personifies the atonal techniques of the Second Viennese School. In a nutshell: take the 12 tones (equally tempered, of course), then arrange them in a specific order; voila, your “melody” (which may sound awful, but no matter; genius is afoot…). Call this a “12-tone Row.” Take the same melody and turn it upside down; call this an “Inverted Row.” Same series of notes, upside-down and backwards? Sure thing; “Retrograde Inversion.” Now, for the compositional sorcery. Combine all these bits in the most complicated structural scheme possible, along with some highly dramatic—and highly rhythmically complex—bangings, clangings, and tinklings on various objects serving as percussion instruments, and you have a sort of infernal counterpoint, absolutely mathematically precise…and entirely unlistenable.

The Romantic let his heart grow too large, but still had a brain; though disordered, he remained a man. The modernist solved this problem by cutting out the heart, making himself not an angel, but a monster. By removing the artistic skin in order better to explore the mathematical science beneath, he revealed not beauty, but the horror of exposed flesh. Art—external, and science—internal—must maintain a proper balance for coherent beauty to emerge. The Greeks focused on mathematical principles and philosophic implications of music and left no aesthetic legacy; medieval composers lost everything to faded memory before the advent of notation; in presuming to perfect nature, humanists lay traps into which their modernist descendants predictably fell. The successful composer, poet, painter, sculptor—one who respects both the technical and the organic elements in his craft—works in a remarkable laboratory, subject to the scientific laws of God’s nature, and with free access to the artistry of His creative capacity. The artist indeed makes the world a better place. Deo gratias.