Unedited Review of Konrad Sprenger's Stack Music (2017 PAN) by Nick James Scavo Archaic history declares that Pythagoras invented harmony. Amongst teachings that ranged from the transmigration of the soul, the veneration of the fava bean, and the existence of a “counter-earth,” his philosophies pioneered the various material harmonic relations of the octave and their connection with weight as the measure of tension. It is here where we find Pythagoras’ attempt at an essential sonorous order, or harmony of relation — Pythagoras’ ontologically regulating principle. The myth describes that Pythagoras began his musical thinking after wandering by a forge and hearing the resounding sounds within. “He found five men hammering with five hammers [and] To his astonishment, he discovered that four of the five hammers stood in a marvelous set of proportions, which, when combined, allowed him to reconstruct the laws of music.” Author Daniel Heller-Roazen describes: “Yet, there was also a fifth hammer. Pythagoras saw and heard it, but he could not measure it; nor could he reason its discordant sound. He therefore discarded it.” Much of experimental music in the post-Cagean lineage, especially music adopting minimalist postures, and even more especially music within the first and second generations of New York minimal composers, attempts to explore the excitable tension, microtonality, and reasonable irreconcilability of the fifth hammer. Their art is to integrate this discord into the milieu of general “hammering” — an impossible project for Pythagoras — but one heard in the resounding sonority found in the late Tony Conrad’s droning performance idiom, where hammer tones were blurred in a spectral sound achieved from the droning of precise pitch within special tunings. It is also seen in the work of Arnold Dreyblatt’s “Orchestra of Excited Strings,” Ellen Fullman’s “Long String Instrument,” or Henry Flynt’s exploration of the objective sound elements of blues and country music being, as Flynt himself has noted, “demonstrably incommensurate with the categorization of sound in European musicology.” In a manner similar to and often in-association with many of these artists, Berlin composer Konrad Sprenger “felt restrained by the limits of traditional instruments and the techniques tied to them, [and has] spent years developing various algorithms and custom instruments to realize his work.” For Sprenger too, the resonating string is the tableau and concept-delivery mechanism to precisely integrate the wild sonic excitation discarded by Pythagoras. To do this, Sprenger has developed rhythmic patterns based on the Euclidean algorithm. If any of us needed reminding (me), the Euclidean algorithm “optimizes difference” through a step-by-step procedure based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number. He applies this with a computer-controlled multi-channel electric guitar that, in his own words, can “create complex rhythmical patterns whilst tuning the strings during performance – sounding at once like an electronic instrument, a drum computer, a guitar, a harpsichord, even at times as a full orchestra.” He supplements these sounds with software like Melodyne and progresses them as insistent rhythms in the style of “Minimalism, Krautrock and Techno,” honing their focus as a “propulsive, full-spectrum sound.” Sprenger’s “Stack Music” ——it’s cleanliness, it’s rigorous astringency — evokes the sudoku-like simplicity of stacking pythagorean triangles. It also references Benjamin Bratton’s Stack — a “multilayered structure of software protocol stacks in which network technologies operate within a modular and interdependent order” (from energy/mineral sourcing, subterranean cloud infrastructure, urban software, massive universal addressing systems). Despite the historicity and academic leanings of Sprenger’s project, there’s also sonic allegiance and beautiful overlap with D’eon’s Music For Keyboards suite, as well as some of the pointillistic practices of Lorenzo Senni. “Opening” invokes the core of album’s erudite mood, calling to mind Pyathagoras again with a “hammered” string duclimer tonality — never wavering, just exhibiting the tone, raising it an octave, then blooming it into subtle arpeggiations. Apparently, the piece is based on an early live performance recorded in New York and composed at Phill Niblock’s Intermedia Foundation Loft. “Finale” is immediately more compositionally spacious, conjuring a droning totalism in the style of Rhys Chatham (both his guitar and flute work) as well as primitivist scenery — as train whistles go by in immediate homage to John Fahey’s “Days Have Gone By.” These references could easily come across as overwrought; yet, Sprenger clearly isn’t interested in their mere aesthetic quality or manipulation, as are many within the revivalist practices of contemporary guitarists. Clearly displayed on the Kosmische “Rondo,” there’s an exclusively compositional restraint here that allows reference to smear into further abstraction. This is furthered through computational mediation, pushing the sound toward the substance of minimalist music, a fetishized substance threaded through the wide guitar tableau and explored relentlessly in Pythagorean temples and New York Lofts alike. Asymmetrically, about two minutes minutes into “Largo” (the final piece), the album’s jubilant potential is wondrously unveiled. As ascending melodies skyrocket Sprenger’s conceptual asceticism into visceral emotion — shining, dynamic plucks and cymbals roil in a marimba-like cadence, transforming the album’s bookish tone into an almost raw celebration. It’s a striking revelation, as bass tones stack into a cathartic, flourishing crescendo. Elegant and never tiring, Sprenger’s historical project beautifully expands an experimental archeology many reference but don’t often feel. On Stack Music, this history appears as contemporary as ever — displaying the relentless task for the human to press thumb to wire, sharing sonority with that “counter-earth,” confronting the fifth hammer, optimizing it’s resounding infinitude — however impossibly — for our brief study, our brief celebration.

In mathematics, the Euclidean algorithm[a], or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two numbers, the largest number that divides both of them without leaving a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in Euclid's Elements (c. 300 BC). It is an example of an algorithm, a step-by-step procedure for performing a calculation according to well-defined rules, and is one of the oldest algorithms in common use. It can be used to reduce fractions to their simplest form, and is a part of many other number-theoretic and cryptographic calculations. The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference with the smaller number. For example, 21 is the GCD of 252 and 105 (as 252 = 21 × 12 and 105 = 21 × 5), and the same number 21 is also the GCD of 105 and 252 − 105 = 147. Since this replacement reduces the larger of the two numbers, repeating this process gives successively smaller pairs of numbers until the two numbers become equal. When that occurs, they are the GCD of the original two numbers. By reversing the steps, the GCD can be expressed as a sum of the two original numbers each multiplied by a positive or negative integer, e.g., 21 = 5 × 105 + (−2) × 252. The fact that the GCD can always be expressed in this way is known as Bézout's identity. The version of the Euclidean algorithm described above (and by Euclid) can take many subtraction steps to find the GCD when one of the given numbers is much bigger than the other. A more efficient version of the algorithm shortcuts these steps, instead replacing the larger of the two numbers by its remainder when divided by the smaller of the two (with this version, the algorithm stops when reaching a zero remainder). With this improvement, the algorithm never requires more steps than five times the number of digits (base 10) of the smaller integer. This was proven by Gabriel Lamé in 1844, and marks the beginning of computational complexity theory. Additional methods for improving the algorithm's efficiency were developed in the 20th century. The Euclidean algorithm has many theoretical and practical applications. It is used for reducing fractions to their simplest form and for performing division in modular arithmetic. Computations using this algorithm form part of the cryptographic protocols that are used to secure internet communications, and in methods for breaking these cryptosystems by factoring large composite numbers. The Euclidean algorithm may be used to solve Diophantine equations, such as finding numbers that satisfy multiple congruences according to the Chinese remainder theorem, to construct continued fractions, and to find accurate rational approximations to real numbers. Finally, it can be used as a basic tool for proving theorems in number theory such as Lagrange's four-square theorem and the uniqueness of prime factorizations. The original algorithm was described only for natural numbers and geometric lengths (real numbers), but the algorithm was generalized in the 19th century to other types of numbers, such as Gaussian integers and polynomials of one variable. This led to modern abstract algebraic notions such as Euclidean domains.

In 1981 Ellen Fullman began developing the “Long String Instrument,” an installation of dozens of wires fifty feet or more in length, tuned in Just Intonation and ‘bowed’ with rosin coated fingers. Fullman has developed a unique notation system to choreograph the performer’s movements, exploring sonic events that occur at specific nodal point locations along the string-length of the instrument. She has recorded extensively with this unusual instrument and has collaborated with such luminary figures as composer Pauline Oliveros, Berlin-based composer and performer Konrad Sprenger, choreographer Deborah Hay, the Kronos Quartet, and Keiji Haino. She has been the recipient of numerous awards, commissions and residencies including: DAAD Artists-in-Berlin Program residency, Japan/U.S. Friendship Commission/NEA Fellowship for Japan, Meet the Composer, Reader's Digest Consortium Commission, Artist Trust/Washington State Arts Commission Fellowship, and artist-in-residence at Headlands Center for the Arts. Her music was represented in The American Century; Art and Culture, 1950-2000 at The Whitney Museum, and she has performed in venues and festivals in Europe, Japan, and the Americas including: Instal, Lincoln Center Out-of-Doors, Other Minds, the Walker Art Center and Donaueschinger Musiktage. Her release “Ort”, with collaborator Konrad Sprenger, was selected in the top 50 recordings of 2004 by The Wire (London) and “Fluctuations” with trombonist Monique Buzzarté on Deep Listening was included in the Wire top 50 of 2008.

Konrad Sprenger has been collaborating with Composer, Performer and instrument builder Ellen Fullman since 2001. He was introduced to her through composer Arnold Dreyblatt. Sprenger produced and performed on their collaboration LP/CD "Ort" which was released by his Choose label in 2004 and which received international acclaim. He continues to perform and produce with Ellen Fullman, both in Europe and in the United States.

Konrad Sprenger's relationship with composer and performer Arnold Dreyblatt has represented an intense meeting of musical generations and genres. Since 2000 Sprenger has collaborated with composer Arnold Dreyblatt in many performances and recording projects, including the production of his current Ensemble. He has also been involved in editing and mixing recordings of Dreyblatt's music, and in the production of many of his sound installation and performance projects. His own label "Choose Records" has recently issued a retropective LP of live Dreyblatt recordings entilted "Choice" and an LP recording of the current ensemble (which includes Sprenger) is in development. Dreyblatt has initated contacts which have resulted in many of the recordings on Choose and their dialog has extended into many realms of music making and based on years of discussion and collaboration. Konrad Sprenger has played a pivotal role in the Arnold Dreyblatt Ensemble (now again called "The Orchestra of Excited Strings") which was formed in 2009 for a performance organized by Nymusikk in Oslo , followed by numerous performances in Berlin, Utrecht, Hasselt, Bari, Geneva, Marseille, The Hague and St. Petersburg and Dortmund. In 2014 the Ensemble performed at the MaerzMusik Festival at the Berghain in Berlin. The ensemble performs in two formations, with three or four musicians, including Arnold Dreyblatt on Excited Strings Bass and Laptop; Konrad Sprenger on Percussion and digitally controlled Electric Guitar ; Joachim Schütz, on Dreyblatt's prepared Electric Guitar and often Robin Hayward on microtonal Tuba. A DVD of a live performance has been issued by the Neue Berliner Kunstverein in 2010.

About the computer-controlled multi-channel electric guitar: Konrad Sprenger explores rhythmic patterns based on the Euclidean algorithm, to evoke a kind of cognitive insecurity through metrical dissonance. Sprenger approaches the strings of the guitar as frequency generators, tuned and set into motion by various electronically controlled mechanical actions. The music relates to the insistent rhythms of Minimalism, Krautrock and Techno, and their shared focus on transcendence through propulsive, full-spectrum sound. The custom-built instrument was conceived by Konrad Sprenger, and realized bySukandar Kartadinata and Daniel van den Eijkel.

Konrad Sprenger is the pseudonym of Joerg Hiller, a composer, music producer and artist based in Berlin. He was born in 1977 in Lahr, Germany. Hiller runs the Choose record label, for which he has produced recordings by artists Ellen Fullman, Arnold Dreyblatt, Robert Ashley and Terry Fox among others. Since 2000 Hiller regularly performs and works together with minimal music composer Arnold Dreyblatt and composer/ instrument builder Ellen Fullman, the bands Ethnostress and Ei and collaborates with the art collective Honey-Suckle Company. His recent focus has been on live performance with a computer-controlled multi-channel electric guitar. His music and installation work have been presented at Hamburger Bahnhof, Berghain, Gallery Giti Nourbakhsch, Podewil, Schaubühne, Pavillon der Volksbühne, Berlin; Badischer Kunstverein, Karlsruhe; Kunsthalle, Baden-Baden; Frankfurter Kunstverein; Künstlerhaus Stuttgart; Kunsthalle Basel; MoMA PS1, New York; Cubitt Gallery, London; Sonar, Barcelona among others. About the computer-controlled multi-channel electric guitar: Konrad Sprenger explores rhythmic patterns based on the Euclidean algorithm, to evoke a kind of cognitive insecurity through metrical dissonance. Sprenger approaches the strings of the guitar as frequency generators, tuned and set into motion by various electronically controlled mechanical actions. The music relates to the insistent rhythms of Minimalism, Krautrock and Techno, and their shared focus on transcendence through propulsive, full-spectrum sound. The custom-built instrument was conceived by Konrad Sprenger, and realized by Sukandar Kartadinata and Daniel van den Eijkel.

Informed by early American folk music and its descendants (John Fahey et al), his new album Stack Music presents a selection of recordings over the years from residencies and live performances, such as ’Opening’, an early live performance of the digital guitar system recorded in New York and composed at Phill Niblock’s Intermedia Foundation Loft, whilst ’Rondo’ consists of recordings of the guitar played by a motor with shoelace exciters, horns, and piano harp. In ‘Largo’, he utilises the software Melodyne to generate midi notes from a original guitar system recording.

Early on, Hiller realized that the harmonically complex sound of strings are impossible to reproduce digitally, and therefore became interested in the development of mechanical instruments, visiting European collections of Pianolas, Orchestrions in Belgium and Holland. Within his live performances and on this new recording, his music is influenced by the insistent rhythms from Minimalism, Krautrock and Techno, and their shared focus on transcendence through a propulsive, full-spectrum sound.

The unique system can create complex rhythmical patterns whilst tuning the strings during performance – sounding at once like an electronic instrument, a drum computer, a guitar, a harpsichord, even at times as a full orchestra. Hiller has long collaborated and performed with minimalist Arnold Dreyblatt, and musician/instrument builder Ellen Fullman amongst others, and first built primitive acoustic mechanical instruments, gradually developing a more complex, digitally-controlled system. “My guitar gives me the possibility to discover almost every aspect of the sound produced by the excitation of the string – as if scientifically under a magnifying glass.” He says. “I can control such parameters as the speed and time, length of the attack, the intensity, the pitch (allowing the use of different tuning systems), and the location of each string in space by the use of 6 speakers.”

Having felt restrained by the limits of traditional instruments and the techniques tied to them, composer, music producer and artist, Konrad Sprenger (b. Joerg Hiller), spent years developing various algorithms and custom instruments to realize his work. His recent focus has been on rhythmic patterns based on the Euclidean algorithm, using a computer-controlled multi-channel electric guitar.