“Leonardo” premiered at Concordia College

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The Big Band at Concordia College conducted by artist extraordinaire Russell Peterson, premiered my recent work Leonardo on April 11. Super exciting news!

Program notes about the work:

The piece is about Leonardo’s Pizzeria located on the corner of 13th St. and University Avenue in Gainesville, Florida. It is also about the composer Leonardo Balada. It is not about Leonardo Da Vinci.

There is a video of the live performance here.

          Leonardo (version by the UT Big Band, Keith Brown conductor, Alex Reyes, tenor sax)

“Nunca tan lejos” in the Discordia album release

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Album release concert featuring electroacoustic music from the southeast! Nearly all the works appearing on this 2nd release from the EMPiRES label are beign performed at the Dancz Center for New Music in Athens!

Check out this line-up…

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“Nunca tan lejos” – Jorge Variego
Justin Iadonisi, percussion

“Pyromancer” – Peter Van Zandt Lane
Peter Van Zandt Lane, bassoon

“Over $100,000 Worth” – Jason R. Butcher and Don Hassler
Jason R. Butcher and Don Hassler, synthesizers

“From Afar, Drawing Near” – Cody Brookshire
Victoria Bethel, Bb trumpet

~ ~ ~ intermission ~ ~ ~

“Malleis” – Aaron Anderson
Matheus Rocha, piano

“A Cave” – Adam Scott Neal
Hanna Lisa Steffanson, piano

“Tunnel of Quantum Love” – Hanna Lisa Steffanson
fixed media

“fragments/frames” – Rob Seaback
Addison Mason, tenor saxophone

“In Fields Forgotten by the Sun” – John Hennecken
Lucas Scalamogna, violin

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Snacks and beverages will be on hand before the concert and during the intermission. An open post-concert talk/panel/Q&A will immeditaly follow the concert.

Also,the whole thing is FREE! Come out and support these regional composers and performers creating great electronic music!

Generous support from UGA’s Willson Center has made this event possible. See you there!

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Album Description: After the 2014 release of the metallic-tinged electroacoustic compilation “Sonic Flux,” EMPiRES sought to organize a compilation of music by composers and performers from the southeastern United States. Here in this second compilation volume, there is an overarching evocation of discord present across the 10 tracks, musically depicted not only in harmony and timbre, but also in rhythm, space, form, and contrasting characters of sound source elements. With this theme fortuitously arising out of the contributed recordings, it was fitting to use the title “Discordia,” taken directly from the title of the album’s cover art by Frances Jemini.

Nicole Chamberlain premieres “Minute flute” for solo bass flute

To close out the SoundNOW festival, Terminus Ensemble invites you to join us for a unique program of 1-minute solo miniatures by 20 composers from the southeastern US. We are joined by Boston-based duo Transient Canvas (bass clarinet + marimba), who will be performing new works by Georgia-based composers, including Sarah Hersh, Peter Van Zandt Lane, and Brent Milam.

Transient Canvas set:
Rationalize (2016) — Cody Brookshire
ripples (2015) — Adam Scott Neal
[Title tbd] (2016) — Brent Milam
Your Mind is a Maze of Mystery (2015) — Sarah Hersh
Exergy Bubblebath (2015) — Peter Van Zandt Lane

Terminus set (order TBD) — solo miniatures by
John Allemeier, David Brighton, Russell Brown, Nicole Randall Chamberlain, Tom Dempster, Drew Dolan, John Hennecken, Olivia Kieffer, Brent Milam, James Paul Sain, Andrew Sigler, Nolan Stolz, Mitch Turner, Jorge Variego, Rachel Whelan, Natalie Williams, Ryan Williams

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Claude Debussy – Color, Shapes and Proportions in La Mer and Other Works

Claude Debussy – Color, Shapes and Proportions in La Mer (1909) and Other Works

Theories that assert Debussy’s intentional use of mathematical proportions in his works remain as mere speculations for many reasons. Works like La Mer and Estampes show distinctive structural attributes that suggest Debussy’s unequivocal use of mathematical ratios such as the Golden Section and the Fibonacci series. However, those compositions are not outright regarding the intentional or intuitive approach by the composer. These two systems of balance and proportion are pillars of the French Symbolist movement with which Debussy was very much associated towards the end of his student days. At this time, the composer spent more time among writers and painters than with fellow musicians.[1]

As a reaction against naturalism and realism, symbolism was among the anti-idealistic movements, which attempted to capture reality in its rough distinctiveness, and to elevate the humble and the ordinary over the ideal. Symbolism began with that reaction, favoring spirituality, the imagination and dreams.

Symbolist poets believed that art should aim to capture more absolute truths, which could only be accessed by indirect methods. Thus, they wrote in a highly metaphorical and suggestive manner, endowing particular images or objects with symbolic meaning. In the symbolists’ Manifesto, Jean Moréas, who published the document in 1886, proclaimed that symbolism was adverse to “plain meanings, declamations, false sentimentality and matter-of-fact description”, and that its goal instead was to “clothe [sic] the ideal in a perceptible form whose goal was not in itself, but whose sole purpose was to express the ideal”. [2]

They conceived the physical world as a collection of symbols, a language that needed to be deciphered by the spectator, where nothing has a plain meaning, everything evokes an deeper image, a metaphor. The Symbolist influence on Debussy is palpable, and of course Prélude à l’après-midi d’un faune was inspired by Mallarmé’s poem L’après-midi d’un faune.

Those principles also influenced Debussy’s musical perception, where the architectural design of a work and its expressivity were inseparably bound. Every note had a meaning with an enormous expressive potential. In his review on Paul Dukas’ Piano Concerto from 1901, Debussy writes: “[…] you could say that the emotions themselves are a structural force, for the piece evokes a beauty comparable to the most perfect lines found in architecture.”[3]

“Music is a series of perceptible surfaces created to represent esoteric affinities, which Symbolists used to evoke their primordial ideals.” [4] In Debussy, sounds and their succession in time are indirect methods that conceal deeper meanings.

Spirals are present La Mer as a formal device that the composer utilizes in order to revisit certain material from the past that, and at the same time, transform it into new musical ideas that continue to develop in the same fashion. In this work, Debussy reveals his natural tendency towards repeated visits to the same musical territory, a characteristic fixation upon specific sounds, patterns, textures, harmonic structures, sonorities, even absolute pitches and melodic fragments, resulting in what we may call aural images. “One comes to feel that Debussy’s aural images are psychological links between certain works of his; they are signs of his unremitting perfectionism, in that, always doubting his own accomplishment, he may have attempted to pursue some forever-elusive musical idea by resurrecting it in another work turning his whole compositional output into a spiral.”[5]

Musical proportions and numerical experiences could have also come to Debussy through his Baudelaire readings, especially his essay Du vin et du hachish in which the poet describes a particularly vivid experience of music as numbers, intimately related to La Mer’s spiraled construction.


Figure 1. Spiraled form of La Mer according to Howat.

The first edition of La Mer appeared with a reproduction on the cover, at Debussy’s request, from Katsushika Hokusaki’s print The hollow of the wave off Kanagawa, a copy of which also hung on Debussy’s study wall. The dominating motive of the print is the wave, whose lower outline curves in logarithmic spiral, admittedly broader than Debussy’s variety. In addition, the golden section divisions indicated around the picture shows how close the composition comes to overall GS, especially if we consider the upper extremity of the wave, the side of its lower curve, and the top of Mount Fuji.[6] Those curves and extreme points of the waves are actual mathematical functions (if x and y axis are added, for example) that Debussy transplanted into form and the development of his musical ideas. A similar concept of translations of functions into music will be seen later on in this chapter, in the section about Xennakis.


Figure 2. Katsushika Hokusaki’s The hollow of the wave off Kanagawa.

“Despite those facts, none of Debussy’s surviving manuscripts contain any signs of numerical calculations concerning structure. This, however, is inconclusive, and also not surprising. Most of these manuscripts are the final copies given to the engraver, an artist as meticulous as Debussy was over the visual presentation of his scores, both manuscript and printed, would hardly have been so unprofessional as to deliver his finished product with scaffolding still attached. In any case, these final copies are mostly third or fourth drafts of the works concerned, by which stage their forms would be well established. Apart from these final copies, only a very small number of sketches have survived. Debussy is known to have destroyed the large majority of his sketches, and, while that proves neither side of the question, it could be conjectured that the few sketches which remain are those that divulge no secrets […] No firm conclusion can be drawn from the above.”[7]

Debussy was deeply aware of the numerical connotations of music composition, but it is still uncertain if he used them intentionally or not. “Music is a mysterious mathematical process whose elements are a part of infinity”.[8]

“In addition to that, it can be said that Debussy was completely unaware of his proportional systems. His subconscious judgment was responsible for organizing them with such precise logic and he would later have had to completely avoid the possibility of such occurrences in his later works.”[9] That awareness is confirmed if we compare the similar use of proportional schemes that appear in La Mer and La Cathédrale Engloutie two works that are considerably distant in Debussy’s career.

Additionally, the use of a center of resonance as a compositional device is another example of Debussy’s reinterpretation of his ideas throughout his production output. His Prélude à l’après-midi d’un faune from 1895 (one of his most remarkable early works) undoubtedly circles around the pitch class C#; L’isle joyeuse, from 1905 (from his middle period), recurrently plays around the initial pitch class C#; Syrinx from 1913 (in his late period) is, for the most part, constructed around the initial pitch class Bb. These three works have a very similar initial harmonic and gestural structure and spanned throughout all Debussy’s compositional periods. This conceptual material seems to be revisited and reinterpreted, exemplifying Debussy’s natural tendency towards self-recycling. This arabesque ornamentation around a given pitch class is one of Debussy’s trademarks.


Figure 3. Measures 1-3 from Prélude à l’après-midi d’un faune.

Similarly, the idea of Debussy using such scientific means of formal regulation (consciously or not) is quite incompatible with his known distaste for musical formulas, which at the same time were conceptual examples of “plain meanings”, quite unwelcome among the Symbolists. Literally, a formula is a prescribed method, convention or recipe, nothing metaphoric – a definition applicable to such construction as fugue, sonata form and so forth.[10] Debussy desired to evoke images and spirituality through his music and these self-explanatory processes were not a suitable tool.


Figure 4. Measures 1- 2 from L’isle joyeuse.




Figure 5. Measures 1- 2 from Syrinx.

Even though Debussy’s search for perfection in his scores is documented in some of his letters where he specifically expresses concern about golden section proportions. In a letter of August 1903 from Debussy to his publisher Jacques Durand, returning the corrected proofs of the Estampes, Debussy writes:

“You’ll see, on page 8 of ‘Jardins sous la pluie’, that there’s a bar missing – my mistake, besides, as it’s not in the manuscript. However, it’s necessary, as regards number; the divine number, as Plato and Mlle Liane de Pougy would say, each admittedly for different reasons”.[11]

The difference in proportion between the final score and the Sibley manuscript of De l’aube a midi sur la mer makes clear that the music was not composed to fit rigid plans impervious to any subsequent modification.

“If Debussy was applying GS consciously, the plans could evidently be remodeled according to other musical demands, many of which may have been primarily instinctive ones, however consciously carried out and perfected eventually. The point again is that Debussy would never have set his intellect on the rampage without simultaneously applying his intuitive judgment. If alternatively, he was completely unconscious of the proportions just seen, we are left with awkward logic. This is because the Sibley manuscript, even in its final state, does not have overall GS coherence and the final score has. This would mean, therefore, that Debussy’s proportional intuition failed him entirely with the large-scale dimensions in the Sibley manuscript, and then suddenly brought the form to virtually maximum accuracy in one fell swoop […] involving a changed tempo relationship that happily provided exactly the necessary dimensional adjustment.”[12]

Ray Howat has traced Debussy’s use of mathematical proportions in detail. Even though, few analyses of Debussy’s music consider dynamic shape at all, and those that do, tend to focus only on isolated aspects such as the principal climatic point of a work.[13] Nevertheless dynamics are a vital structural element of Debussy’s mature music. The tidal flow of swelling intensities of the dynamics – specifically in works like La Mer – reveals a novel programmatic method with an outstanding dramatic outcome. The tides, undulations of the waves, the wind and its shape, are metaphorically symbolized through the dynamic structure of the work which evokes particular states of mind and aural images that invite the listener to decipher them. As a vital component for the completion of Debussy’s music – the listener is constantly challenged to resolve aural puzzles. What is given appears to be incomplete; the symbols need the spectator to become meaningful. “In ‘Reflets dans l’eau’ the composer evokes the concentric propagation of sound waves, not only are many of the sequences […] visibly reflected round some central musical turning point; but also their reflected portions (or images) tend to be compressed in size, giving an effect of refraction – another aspect of reflection (or deflection) in water.”[14]

Somehow anticipating Le Corbusier, Debussy was also bound to the intrinsic properties of sound explained by Pythagoras and their numerical implications. Le Corbusier used the Pythagorean theory in order to justify his own set of ideas in which he desires to import the universality of the proportions of the individual components (harmonics) of a given sound into a model for architectural design not based on the properties of sound but on the human figure and its scope. On the other hand, Debussy finds a more poetic interpretation of the ancient theory: “[…] the old Pythagorean theory that music should be reduced to a combination of numbers: it is the ‘arithmetic of sound’ just as optics is the ‘geometry of light’.”[15]

Interestingly, his use of proportions never becomes formulaic, as it is never used in the same way twice. The similarities between Debussy’s pieces are always offset by a sharp contrast. In Debussy, the presence of spirals is always recurrent.


[1] Ray Howat, “Debussy in proportion. A musical analysis”, (1983), 163.

[2] Jean Moreas, “Symbolist Manifiesto”, (1886).

[3] Ray Howat, Ibid. 173.

[4] Jean Moreas, Ibid.

[5] Mark De Voto, “Debussy and the Veil of Tonality”, (2004), 24.

[6] Ray Howat, Ibid. 178.

[7] Ray Howat, Ibid. 6.

[8] Ray Howat, Ibid. 171. Debussy (1977), 199.

[9] Ray Howat, Ibid. 162.

[10] Ray Howat, Ibid. 9.

[11] Ray Howat, Ibid. 7.

[12] Ray Howat, Ibid. 91.

[13] Ray Howat, Ibid. 12.

[14] Ray Howat, Ibid. 28.

[15] Ray Howat, Ibid. 171. Debussy (1977), 255.

Vitruvius – Book V

In Book V, Vitruvius applied Pythagorean principles of harmonic ratios in the design of theatres. He implemented a “room equalization system” based on bronze or earthen vessels – called “echea”placed under the seats of theatres, to assist, by their resonance, the voices of the performers.

This is one of the first examples of an enclosed space conceived as a musical instrument where its design features are intended to enhance specific sounds that take place within it. The Vitruvian theaters interact with the performers, amplifying and “equalizing” the sounds of their on-stage performances. In figure 2-2 we can clearly appreciate that the tuning of the room is not indifferent to its design; small and large theaters were tuned differently.

“The harmonies that human nature can measure out are called symphoniae in Greek, and number six: diastesseron (fourth), diapente (fifth), diapason (octave), and disdiatesseron (octave + fourth), disdiapente  (octave + fifth) and disdiapason (double octave).“In theaters, likewise, the bronze vessels – the ones the Greeks call echea – which are enclosed underneath the seats, are placed according to mathematical principle based on their pitch. The vessels are grouped in sections around the circle of the theater to create intervals of a fourth, a fifth and so on up to a double octave. As a result, the speaker, as it occurs onstage, should be so located in the theater’s overall design that when it strikes the echea it will be amplified on impact, reaching the ears of the spectators as a clearer and more pleasant sound.”

        Picture 3

Tuning system for the vessels.

The vessel tuning suggested by Vitruvius follows the progression of the first four partials after a fundamental tone, which are also separated by a fifth, a fourth and the resulting double octave. By reinforcing the first partials of an implied fundamental he provided the space with a characteristic resonance. Like in brass instruments, that “theoretical fundamental” is the lowest possible resonance that can be obtained from an instrument – in this case an enclosed space – related to its size and length of the sound waves. That resonance is not aurally present but it is the basis for the harmonic series. Vitruvius’ design follows that same principle, using the vessels tuned to the first partials of a harmonic series to provide the space with a particular formant. However that approach depends almost exclusively on the richness of the spectrum of the sound performed on-stage. The pure tone of a lyre would rarely provide enough spectral energy to stimulate the vibration of the vessels and – on the other hand – a strong baritone voice would take true advantage of them.  Following a basic acoustical principle, the Vitruvian vessels can reinforce properties already existing in a sound source but they are unable to generate them as there is no acoustical design capable of filling frequency “holes”. “Indeed, we can observe this from performers who sing to the lyre, who, when they want to sing in a higher key, turn toward the stage doors and thus avail themselves of the harmonic support that these can provide for their voices. When, however, theaters are constructed of more solid material, that is, of masonry, stone, or marble, which can not resonate, then they should be outfitted with echea for just that reason.”

Picture 2

Theater ceiling and audience area suggested by Vitruvius.

It is clear that the Roman master was foreseeing two core acoustical issues of theater design: reinforcement of sounds events happening on-stage and the frequency response of the space. His solution came from a combination between the steep angle of the audience seats and the design of the ceiling (sound reinforcement) and the resonating vessels system (frequency response). “By this contrivance the voice onstage, poured forth from stage – as it were, from the center of the theater – and circling outward, strikes the hollows of the individual vessels on contact, stirring up an increased clarity and a harmonic complement to its own tone.”

Vitruvius was already considering in his designs the quality of the sound perceived by the audience in a theater. He sought for a “clear and pleasant sound” with the desire to provide every member of the audience with the same aural experience. Those concerns are very much current today when la­rge audiences are the norm. In the design of theaters, aural architects have to simultaneously deal with the general acoustic properties of the space and their perception, reassuring that they propagate evenly throughout the audience area.  Parameters of balance, warmth, brightness and clarity are of standard use by architects in order to measure the desirable qualities of a space designed for performance. The aural pleasure of the audience was Vitruvius’s ultimate desire. Sound was his main concern in theatre design, and he strived to achieve an “ideal sound” that would please the audience members. Vitruvius translated the general harmonic proportions of sound into theater design. In other words, he made a theater a “tuned resonant body”.

Vitruvius, the importance of a good ear in times of war

In Book I of his Ten Book of Architecture, Vitruvius discusses the importance of the integral education of the architect who not only should be a capable draftsman but also well versed in many other disciplines like medicine, music and philosophy. This concept of the architect as a “master builder” derives from the Greek arkhitekton, arkhi– “chief” + tekton “builder, carpenter”; this Roman model of a “chief builder” was much broader than the one we conceive today. A modern architect is exclusively dedicated to the design, plan and construction of buildings; in the 1st c. BCE the architect was also a broad-spectrum technician who was well versed in fields that spanned from urban planning to military engineering.

“For neither native talent without learning nor learning without native talent create the master craftsman. To be educated, he must be an experienced draftsman, well versed in geometry, familiar with history, a diligent student of philosophy, know music, have some acquaintance with medicine, understand the rulings of legal experts, and have a clear grasp of astronomy and the ways of Heaven.”

That general instruction had very specific applications. Vitruvius served as a ballista (artilleryman) where musical instruction became very practical when aiming catapults. The tension of the cords in the catapults was calculated by “ear”, a perfect straight shot could only be achieved if the tension chords were perfectly “in tune”.

“The architect should know music in order to have a grasp of canonical and mathematical relations, and besides that, to calibrate ballistae, catapults and scorpions. In the headpieces of war machines there are hemitone spring holes, right and left, through which the twisted sinew cords are pulled tight by windlass and handspikes; these cords should not be wedged in place or fastened down unless they give off a particular and identical sound to the ears of the catapult maker. For when the arms of the catapult have been cocked to these tensions, upon release they should deliver an identical and equivalent thrust; if they are not tuned identically, they will keep the catapult from launching a straight shot.”

Figure – Tuning of the catapult, from the Ten Books of Architecture.

“Next, the ends of the ropes are threaded in through the spring holes of the capitals, and carried across to the other side, and then they are fastened around the windlasses and wound around them, so that when the ropes are stretched over them by the levers, when struck with the hand, each of them will give off a corresponding tone. […] They are stretched with handspikes on windlasses until they make an identical sound, and in this way catapults are adjusted to tone by propping with wedges according to the musical sense of hearing.”