Da Vinci

As the Sunflower Turns on Her God

Tim Takach

Minnesota-based composer Timothy Takach weaves together contemporary choral music and mathematics in “As the Sunflower Turns on Her God”. The piece is based on the mathematical concept of Phi, also known as the Golden Ratio, which is purported to be one of the most aesthetically pleasing proportions and is found in living things such as flowers and other plants, as well as many places such as art and architecture. The Golden Ratio is an “irrational” number, meaning that its value extends to an infinite number of decimal places without repeating. 

The Fibonacci sequence, which is formed by starting with 1 and adding the previous two numbers in the sequence to determine the next number, can help approximate the Golden Ratio. This is done by dividing a number in the sequence by the number that precedes it. The farther along in the sequence, the closer this number gets to the Golden Ratio; however, being an irrational number, this can never be perfectly reached. 

To compose this piece, Takach assigned chords to the first 8 numbers of the Fibonacci sequence. Excluding the repetition of the number 1, this includes 1, 2, 3, 5, 8, 13, 21, 34. The chorus’s text recites Phi in Greek to the 82nd decimal place. These chant-like numbers are accompanied by a solo with the text of the initial question that led to the discovery of the Fibonacci sequence, which sought to predict how many offspring a pair of rabbits would produce. 

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Time

Jennifer Lucy Cook

American composer Jennifer Lucy Cook moves easily between genres, composing for the stage and screen, choral music, and pop songwriting. In “Time,” Cook delves into the paradoxical, essential and yet ephemeral nature of the meaning of the song’s namesake. “Time,” writes Cook, “is one of those funny human-made concepts that dictate our lives but are fundamentally meaningless if we didn’t all agree to go along with it.” This rhythmic composition leans into contemporary a cappella harmonies and creates texture through repetitive lyrics whose meaning changes as phrases elide together and disappear, evoking humor and poignancy at different turns. Says Cook, “We lose time when we try to keep it, we spend time as we try to save it – and since it insists upon eluding us, we can only notice the fact that time has been winking at us all along…this piece is my way of winking back.” 

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The Notebooks of Leonardo da Vinci

Jocelyn Hagen

Leonardo da Vinci (1452–1519), perhaps the original “Renaissance man,” made his defining mark on the fields of art, science, and engineering during a time of fertile thought-expansion across Europe. His prolific writing on over 13,000 loose pages and in numerous journals and sketchbooks capture inventions, scientific observations, artistic studies, and philosophical reflections. Collectively known as da Vinci’s notebooks, these papers feature the author’s idiosyncratic “mirror-image” handwriting, as well as meticulous drawings ranging from the literal to the wildly imaginative.

In the spirit of da Vinci’s ingenuity, composer Jocelyn Hagen’s 2019 multimedia work incorporates a novel digital syncing software, invented to expand the boundaries of both visual and aural art. Hagen was first inspired to create a work that centered da Vinci’s ideas in 2016, after viewing the Codex Leicester, a privately-held collection of material from his notebooks. On trying to encompass da Vinci’s work in one symphonic piece, she writes, “There was no way … so my goal became serving the spirit of his work and his curious mind.” To build the music, Hagen selected English translations of texts from da Vinci’s notebooks, setting them to nine movements for choir and orchestra. Visual collaborators Isaac Gale, Joseph Midthun, and Justin Schell created corresponding video projections, made to be played using Ion Concert Media’s video software MUSÈIK. The technology allows the projections to be advanced dynamically—following the conductor’s live tempo, as though the video was another member of the musical ensemble. The result is a rare, organic pairing between the audio and visual components.

The Notebooks of Leonardo da Vinci opens with a solitary flute, appearing to represent da Vinci’s own thoughts as a line of his handwriting scribbles across the screen. As more instruments are introduced, the images from the notebooks expand and shift. Finally, as the visuals rest on a human portrait, the choir sings “O Painter!” A reflection on the overlap between poetry and the work of a painter follows, with an array of da Vinci’s human portraits on screen. The buoyant second movement, performed a capella, introduces knowledge as one of the work’s themes. Like a proverb, da Vinci’s text advises the hearer to ground their work in knowledge, sound theory, and principles, saying that “without this nothing can be done well.” 

In the third movement, the pairing of the music and simultaneous video shines, with images and sound mimicking the splashing of water droplets. Hagen describes this movement as a combination of two ideas: da Vinci’s own fascination with water, and the music of one of his Milanese contemporaries and friends, music theorist Franchino Gaffurio. Musical phrases from Gaffurio’s Missa di Carneval are woven into the orchestral music. The choir boldly announces in the a capella fourth movement: “The greatest good of all is knowledge,” and the text considers the importance of facts in dispensing with errors and speculation.

The fifth movement centers around the iconic Vitruvian man, the most famous of da Vinci’s sketches. It owes its name to Vitruvius, an ancient Roman architect who viewed the human body as perfectly proportionate, and whose work profoundly influenced da Vinci. During this movement, you’ll hear the choir singing and reciting some of these “perfect proportions” aloud. At the same time, the Vitruvian man will come to life onscreen as da Vinci’s own sketches of the human body are superimposed atop a live human dancer (Stephen Schroeder).

Entirely instrumental, the sixth movement features another of da Vinci’s most famous sketches: his flying machines. A visionary well ahead of his time, da Vinci invented several of his own gliders while studying what he called “the science of the winds.” Today, we call it aerodynamics. During this movement, da Vinci’s flying machines take center stage, joined by “little musical machines” that Hagen invented “to accompany them.” The seventh movement then turns to the natural world, loved and revered by da Vinci. The movement opens gently, pairing a clarinet solo with da Vinci’s sketches of a bird, flying across a vast landscape. The choir enters gradually, praising the beauty, efficiency, and simplicity of “Nature’s inventions,” far surpassing that of any human invention. Afterward, the eighth movement is performed a cappella, with all voice parts singing just one set of text: “All our knowledge has its origin in our perceptions.” As the choir repeats the text, several of da Vinci’s sketches of the human eye appear onscreen. Together, these words and images remind us to remain open to new perspectives, especially as we seek to discover the truth.

The ninth and final movement of the piece shifts our perspective outward, honing in on the image of the night sky, “scattered” with stars. In the words of da Vinci, though these stars seem “minute” to the human eye, many are in fact much “larger…than the earth with water.” Additionally, the text underscores the all-encompassing power of time, which “destroy[s] and devour[s] all things with the relentless teeth of years.” In a similarly grandiose fashion, Hagen rounds out her composition with exuberant, upbeat scoring that includes sharp dynamic contrast and pizzicato violin (when the instrument’s strings are plucked by finger rather than bow). As the music progresses, you will see da Vinci’s portrait of an old man (rumored to be, in fact, a self-portrait) gradually appear onscreen, filling the night sky. And to conclude, Hagen chooses to leave us with one of the most famous, impactful quotes from da Vinci’s notebooks: “Wisdom is the daughter of experience.

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