Brunelleschi's Dome

Walking through the streets of Florence surrounded by the glowing orange light of sunset and bright green shutters, it is still stunning every time one comes to a cross street where the dome of the Cattedrale di Santa Maria del Fiore suddenly comes into view. For musicians, this structure is of particular importance in relation to one of the major Renaissance works we study, Guillaume Dufay's motet Nuper rosarum flores, because the piece was written for the consecration of the dome in 1436. This particular motet is studied for its intricate use of proportions in the form, proportions that some scholars say were written based on those of the cathedral below.

Studying the work and reading Charles Warren's article, “Brunelleschi’s Dome and Dufay’s Motet,” in graduate school, I was intrigued to visit the cathedral and listen/see for myself how the proportions and the music felt in the space. Although Craig Wright’s “Dufay’s Nuper rosarum flores, King Solomon’s Temple, and the Veneration of the Virgin” outlines other possible explanations for the proportions of the piece—that it is not based on the proportions of the Florence Cathedral at all, and rather is based on the dimensions for the Temple of Solomon and symbolic number representation for the Virgin from a biblical passage—I am personally more intrigued and convinced by the architectural proportions as hypothesized in Warren’s article.

Returning to Florence this week, I was struck by the incredible feat of building the dome itself. The cathedral had been under construction for years, and it was only because there was a model of what the church might look like when completed with a large dome that the problem arose in the first place. Someone had a vision that the church would have an enormous octagonal dome even though it was clear for over fifty years that no one in Italy knew how to actually build it. The mystery of the dome was put forth as a competition, and goldsmith and clockmaker Filippo Brunelleschi rose to the challenge. In the process of building the dome, Brunelleschi solved countless problems and invented various machines over the years, taking risks, having incredible failures, all for the sake of problem solving and following through with a vision (Ross King's Brunelleschi's Dome goes into great detail and is fantastic further reading for those interested). Through these banalities, failures, and innovations, Brunelleschi was able to create a structure that still inspires and creates wonderment today.

Continuum in Music, Architecture, and Academia

Finally sitting down to process an incredible couple of days in Cyprus at the Continuum2016 conference on the Continuum in Music and Architecture hosted by the Centre Iannis Xenakis and the University of Cyprus Department of Architecture. I presented a paper based on material from my dissertation Andrew Norman's The Companion Guide to Rome: Influence of Architecture and Visual Art on Composition, using Xenakis’s ideas about structure-in-time as a framework to analyze Norman’s music that is inspired by architectural forms. It was a wonderful chance to meet scholars from all over the world and gather ideas, inspiration, and various wonderful teaching resources:

Keynote performer Peter Sheppard Skærved's speech set the tone by emphasizing the importance of making space for reflection—in one's craft as an artist, in the depth of one's knowledge and therefore ability to make a difference as a scholar, and finally in being aware of communities—the importance of continuum as self-awareness and global awareness.

Sharon Kanach presented a lecture on Scelsi's compositional process (and his influence on Xenakis's music), full of rich information and history from her experience working with both composers personally. Keynote speaker Athanassios Economou shared several interactive tools such as GRAPE from SWAP Plus, the online research and devel­op­ment depart­ment of SWAP Archi­tects. GRAPE, a parametric shape grammar interpreter, allows the user to visualize various manipulations/transformations of geometric shapes given various restrictions/rules.

Eight variations of one spatial relationship from GRAPE.

Others presented research in progress, including Konstantina Kalfa's presentation on Villa Mache (continuum in the architecture and use of light in Xenakis's designs). Composers presented their own work, including Nicoleta Chatzopoulou, who talked about using silence as a landscape in musical composition.

Architectural drawing of Villa Mache

It was inspiring to be around both young and established scholars who value critical thought, feedback, and making time for both rigorous academic focus and reflection. The arts allow us to perceive nuances in continuum if we have patience: in music, learning to support others' voices; in visual art, to literally be able to create/have perspective; in dance, to learn to support the weight of another human being. Gatherings such as these allow for that optimism and critique to find its place in the ongoing struggle for relevance and reflection in the arts/academia.

Harmonics, Waveforms, and the Overtone Series

This week in our Extended Techniques for Strings class, the subject of different types of waveforms and timbre as harmonic spectrum came up. Posting these diagrams here for ease of reference (scroll down for a summary of basic terms):

Overtone Series on C, Partials 1–16 (Arrows indicate sixth tone or quarter tone alterations which occur naturally in the harmonic series). Yes, that's an alto clef. Diagram by Lanzilotti

UPDATE: These partials can be notated above the octave node on viola at pitch with a small circle above the notehead, or below the octave node at their locations with a diamond. See these charts:

• Viola harmonics notation chart

• Violin harmonics notation chart

• Cello harmonics notation chart

The Natural Harmonic Series and Fractions of the String. Diagram by Lanzilotti.

Sine waves contain only the fundamental. Square waves (a form of pulse waves) and triangle waves contain only odd harmonics (with distinct amplitudes), giving them their individual sounds. Sawtooth waves have all partials present, but they decrease exponentially in relation to the ratio of the partial to the fundamental.

Harmonic spectra shown using musical notation. Diagram from Holmes's Electronic and Experimental Music

Some other terms that came up were:

• frequency: pitch, measured in hertz (Hz) or cycles per second

• amplitude: volume/loudness

• timbre: tone color, determined by the set of harmonics or overtones in the sound

• duration: how long the sound lasts (is audible)

• envelope: overall shape of the amplitude of the sound over time including the attack, sustain, and decay of the sound

The Art of Orchestral Playing, or How to Find a Tennis Ball in the Woods

In memory of Pierre Boulez (1925–2016). This article was originally published in the September 2009 online version of MUSO Magazine.

"No, no, no, no, no." Pierre Boulez stops us again and asks for the bass section to check the tuning of their harmonics at the beginning of one of the movements of "Notations." In a piece that's so complex and detailed, it's a wonder that each of us is keeping track of our individual parts, but Boulez has been keeping track of all of us. He hears everything.

Although my father is not a musician, he knows who Boulez is, and thinks that the Lucerne Festival Academy is an amazing opportunity for young musicians to work with someone who is already a well respected master in the field. Between listening to recordings of John Adams and Boulez (and various other composer names I throw at him), my dad spends a lot of his free time playing tennis. As a good amateur player, being at a festival like this he said would be like him getting to play a set with Nadal, and then get tips from him on his serve. A fitting metaphor this week, since we just started working on Debussy's Jeux—a piece about three young people in the woods looking for a tennis ball.

Rehearsing with Boulez on these pieces is interesting because he unfolds the layers of the music, making each one pristine and clear so that when the layers are put together again, we are able to play better together and hear more ourselves. I must admit that our first reading of "Jeux" sounded more like the bounces and whimpers emerging from the court of a beginner tennis player trapped defending himself from an out‐of‐control ball machine. However, through the patience of our coaches from the Ensemble Intercontemporain (EIC) and Boulez's insistence for detail and clarity, it's starting to come together.

The amount of detail and precision that we are putting into these pieces is partially about having respect for the composer and what is written, but it is also about personal respect for demanding a high quality product and a higher standard than is usually requested in a educational orchestral setting. My father always said that you have to have pride in everything you do, whether it's sweeping the floor, ironing a shirt, or writing a novel. No matter how small the task, one must have the personal pride and respect to do it well. So why do we sometimes accept less from ourselves when we are rehearsing or performing?

Working with Boulez and the EIC at the Lucerne Festival Academy, it is clear that they always demand the highest standard from themselves. The EIC premieres pieces that other players might refuse to learn because they contain techniques that no one else has figured out how to do, or because they don't make sense at a first glance. Working with mentors that live daily with such a standard for themselves and the music is incredibly inspiring. There is so much more energy that comes from a performance of this quality. When each of us takes the time and has the personal pride to really play our best at all times, the result is astonishing.

In these moments, even if normal ears could not tell you specifically what was happening, they would know that there was a spark and an energy in the orchestra that would move them. And I think Boulez can hear each one of us when this happens.