https://etudes.pointlinesurface.com Études Sun, 19 May 2019 20:49:50 +0000 https://etudes.pointlinesurface.com en https://etudes.pointlinesurface.com/January-Rhythm-Necklaces-Euclidean-Distribution Fri, 11 Jan 2019 04:26:50 +0000 Études https://etudes.pointlinesurface.com/January-Rhythm-Necklaces-Euclidean-Distribution Rhythm Necklaces &amp; Euclidean Distribution <img width="1152" height="1536" width_o="1152" height_o="1536" data-src="https://freight.cargo.site/t/original/i/a303233324838dddceba9ab0a1b804a2eec9ddabf0fd8e387264b94469502316/IMG_0823.jpg" data-mid="33185664" border="0" src="https://freight.cargo.site/w/1000/i/a303233324838dddceba9ab0a1b804a2eec9ddabf0fd8e387264b94469502316/IMG_0823.jpg" /> Gilbert Rouget Music &amp; Trance University of Chicago Press, 1985 <img width="1152" height="1536" width_o="1152" height_o="1536" data-src="https://freight.cargo.site/t/original/i/d7c05c0d0c1d2419404c857d1ac0d268b674b7050ed450002b2e1f1f213057fe/IMG_0824.jpg" data-mid="33185666" border="0" src="https://freight.cargo.site/w/1000/i/d7c05c0d0c1d2419404c857d1ac0d268b674b7050ed450002b2e1f1f213057fe/IMG_0824.jpg" /> Bruno Latour We Have Never Been Modern Harvard Press, 1993 <img width="1152" height="1536" width_o="1152" height_o="1536" data-src="https://freight.cargo.site/t/original/i/30b59bbc0b57dfb74de81f25bd0412f5c9f06d259348cbcad342c87251cf5404/IMG_0825.jpg" data-mid="33185667" border="0" src="https://freight.cargo.site/w/1000/i/30b59bbc0b57dfb74de81f25bd0412f5c9f06d259348cbcad342c87251cf5404/IMG_0825.jpg" /> Simha Arom African Polyrhythm &amp; Polyphony Cambridge Press, 1991 “What do African bell rhythms, spallation neutron source (SNS) accelerators in nuclear physics, Sturmian words and string theory (stringology) in computer science, Markov numbers and two-distance sequences in number theory, drawing digital straight lines in computer graphics, calculating leap years in calendar design, and an ancient algorithm (the Euclidean Algorithm in computer science) for computing the greatest common divisor of two numbers, originally described by Euclid have incommon? The short answer is: patterns distributed as evenly as possible.” One of the oldest well known algorithms described in Euclid’s Elements (circa 300 B.C.) computes the greatest common divisor of two given integers. It is the oldest nontrivial algorithm that has survived to the present day. The idea is rather simple: repeatedly replace the larger of the two numbers by their difference until both are equal. This final number is then the greatest common divisor. EUCLID ( m; k&nbsp;)&nbsp; &nbsp;&nbsp; &nbsp; 1.&nbsp; if&nbsp; k = 0&nbsp; &nbsp;&nbsp; &nbsp; 2.&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; then return m&nbsp; &nbsp;&nbsp; &nbsp; 3.&nbsp; &nbsp; &nbsp;&nbsp; &nbsp; else return EUCLID ( k, m % k ) What does this have to do with music? Mathematics and music have been formally intertwined since the day Pythagoras discovered that the pleasing experience of musical harmony is the result of ratios of small integers 2500 years ago . However, most of this interaction has been in the domains of pitch, scales, and tuning systems. Until relatively recently rhythm’s correlation to mathematics has been mostly ignored. Over the last few years I've spent a fair amount of time researching alternative notational systems for generative music and have found myself constantly impressed by the complexity possible within the minimal notation of ‘rhythm necklaces’ common in west African music. I read Godfried Toussaint's Geometry of Musical Rhythm and Simha Arom’s African Polyphony &amp; Polyrhythm to help understand how these musical forms were developed. Having formally studied linear western notation I was fascinated to learn that much of the poly qualities generated in west African music came from a technique called rhythm necklaces. Underlying the technique of distributing beat emphasis in the rhythm necklace is the Euclidean algorithm.&nbsp; Godfried Toussaint’s published the&nbsp;paper entitled&nbsp;Mathematical Notation, Representation, and Visualization of Musical Rhythm: A Comparative Perspective making the mathematical connections between musical rhythm and other areas of knowledge such as nuclear physics, calendar design, number theory, geometry, and computer science, as well as the work of the Greek mathematician, Euclid of Alexandria. The algorithm exposed here is a mathematical model of rhythm generation that applies to music from all over the world. Toussaint emphasizes that this is not a model of the conscious process by which musicians in any culture arrive at their preferred timelines, but rather of the inherent properties (both mathematical and musicological) of the resulting timelines obtained. I find this even more compelling because musicians’ intuition was able to lead them to a sophisticated spatio-temporal heuristic inside nature. Benin (7,16) F Major 7 Necklace in Four Parts <img width="1697" height="210" width_o="1697" height_o="210" data-src="https://freight.cargo.site/t/original/i/fcd0674faecd809708a208ef24c32626b37b3cdddd0d498aa70484f013cb164b/Samba_dance_pattern.png" data-mid="33187860" border="0" src="https://freight.cargo.site/w/1000/i/fcd0674faecd809708a208ef24c32626b37b3cdddd0d498aa70484f013cb164b/Samba_dance_pattern.png" /> The ostinato figure pictured above is a Ghanan bell pattern visualized in Euclidean space below in the blue diagram. Each figure is identical only rotated creating the polyrhythmic necklace structure when braided together in time. <img width="750" height="750" width_o="750" height_o="750" data-src="https://freight.cargo.site/t/original/i/c434e417eaebb80fa785086997acbc2b1b7e32e10887d8e634a67bcbfbb9f7c4/1.png" data-mid="33186894" border="0" src="https://freight.cargo.site/w/750/i/c434e417eaebb80fa785086997acbc2b1b7e32e10887d8e634a67bcbfbb9f7c4/1.png" /> figure a.1 <img width="750" height="750" width_o="750" height_o="750" data-src="https://freight.cargo.site/t/original/i/bbf9ffdf2a9c7d9e9a958b8ae011f72bf77cff284625c307f1cc9c4222cf006b/2.png" data-mid="33186896" border="0" src="https://freight.cargo.site/w/750/i/bbf9ffdf2a9c7d9e9a958b8ae011f72bf77cff284625c307f1cc9c4222cf006b/2.png" /> figure a.2 <img width="750" height="750" width_o="750" height_o="750" data-src="https://freight.cargo.site/t/original/i/b0c12b3dbccd6a7e10f6c026e30b126860329b698a03b74dd9c0eb6bed5f5b08/3.png" data-mid="33186898" border="0" src="https://freight.cargo.site/w/750/i/b0c12b3dbccd6a7e10f6c026e30b126860329b698a03b74dd9c0eb6bed5f5b08/3.png" /> figure a.3 <img width="750" height="750" width_o="750" height_o="750" data-src="https://freight.cargo.site/t/original/i/c413c8c9df20f7c54bb3b41828f3f19144d3fb262ee62370ca0f93d2a3bd9769/4.png" data-mid="33186899" border="0" src="https://freight.cargo.site/w/750/i/c413c8c9df20f7c54bb3b41828f3f19144d3fb262ee62370ca0f93d2a3bd9769/4.png" /> figure a.4 Ngbaka-Maibo (9,16) Bb 9 Necklace in Four Parts <img width="750" height="750" width_o="750" height_o="750" data-src="https://freight.cargo.site/t/original/i/ab2df4cd1052d920abcd2aefaf52729f3d58973c95892c4e21e5acb0d2e48e65/nm-1.png" data-mid="34645717" border="0" src="https://freight.cargo.site/w/750/i/ab2df4cd1052d920abcd2aefaf52729f3d58973c95892c4e21e5acb0d2e48e65/nm-1.png" /> figure b.1 <img width="750" height="750" width_o="750" height_o="750" data-src="https://freight.cargo.site/t/original/i/5ef23df908abbc8ce169d918ba3b6d62e538d52f5e89386fc975a29c1ce71d8f/nm-2.png" data-mid="34645718" border="0" src="https://freight.cargo.site/w/750/i/5ef23df908abbc8ce169d918ba3b6d62e538d52f5e89386fc975a29c1ce71d8f/nm-2.png" /> figure b.2 <img width="750" height="750" width_o="750" height_o="750" data-src="https://freight.cargo.site/t/original/i/7b6e687cb30b8dbe57cff2c776723b7a4e2154885202dbeb7349fc2b0f7838e3/nm-3.png" data-mid="35582314" border="0" src="https://freight.cargo.site/w/750/i/7b6e687cb30b8dbe57cff2c776723b7a4e2154885202dbeb7349fc2b0f7838e3/nm-3.png" /> figure b.3 <img width="750" height="750" width_o="750" height_o="750" data-src="https://freight.cargo.site/t/original/i/8d8dce9f1621c1675a29d9e034e9a82a7be8266051947a85b5b22386e33dfc63/nm-4.png" data-mid="35582315" border="0" src="https://freight.cargo.site/w/750/i/8d8dce9f1621c1675a29d9e034e9a82a7be8266051947a85b5b22386e33dfc63/nm-4.png" /> figure b.4 When the 9,16 figure is started on the penultimate onset it is the bell pattern of the Ngbaka-Maibo rhythm of the Central African Republic. Bembé (7,12) F Major 7 Necklace in Four Parts <img width="750" height="750" width_o="750" height_o="750" data-src="https://freight.cargo.site/t/original/i/4b1e68c6d485e900927437ffe4ceac74c2f56535ab2e911e79f1b957904210ce/bembe-1.png" data-mid="35107865" border="0" src="https://freight.cargo.site/w/750/i/4b1e68c6d485e900927437ffe4ceac74c2f56535ab2e911e79f1b957904210ce/bembe-1.png" /> figure c.1 <img width="750" height="750" width_o="750" height_o="750" data-src="https://freight.cargo.site/t/original/i/0b5490eeb7335d20bbf079973fb0bfd6d6130e16b9dc05a30db5924264b61315/bembe-2.png" data-mid="35107867" border="0" src="https://freight.cargo.site/w/750/i/0b5490eeb7335d20bbf079973fb0bfd6d6130e16b9dc05a30db5924264b61315/bembe-2.png" /> figure c.2 <img width="750" height="750" width_o="750" height_o="750" data-src="https://freight.cargo.site/t/original/i/542e3b536c51eeea94cb2835b8e0290d4158a7b6a448626ad8987087885e34b4/bembe-3.png" data-mid="35107869" border="0" src="https://freight.cargo.site/w/750/i/542e3b536c51eeea94cb2835b8e0290d4158a7b6a448626ad8987087885e34b4/bembe-3.png" /> figure c.3 <img width="750" height="750" width_o="750" height_o="750" data-src="https://freight.cargo.site/t/original/i/049cbee0e0ff76ce3d19dcb24b545282b316a76c550d1dedeb7a531e01c72dbb/bembe-4.png" data-mid="35107873" border="0" src="https://freight.cargo.site/w/750/i/049cbee0e0ff76ce3d19dcb24b545282b316a76c550d1dedeb7a531e01c72dbb/bembe-4.png" /> figure c.4 <img width="503" height="116" width_o="503" height_o="116" data-src="https://freight.cargo.site/t/original/i/b14a41c1689e4a771385bc012d878984a99fc698d97dcee473e6b3a5db6b263e/The-pattern-of-Clapping-Music-and-the-Yoruba-clave.png" data-mid="35598661" border="0" src="https://freight.cargo.site/w/503/i/b14a41c1689e4a771385bc012d878984a99fc698d97dcee473e6b3a5db6b263e/The-pattern-of-Clapping-Music-and-the-Yoruba-clave.png" /> A few years ago I read Bruno Latour’s We Have Never Been Modern and have found a striking asymmetry in his work and the cultural excavations done by Godfried Toussaint. It is astonishing that Africa's ancestors developed musical systems that were later used for many of the technical applications mentioned above. In&nbsp;We Have Never Been Modern I found a kinship in Latour’s ideas that discuss that there is no way of removing yourself from the experiment as an “observer.” This epistemological crisis of modernity (and thus science) formalized in Heisenberg’s uncertainty principle vindicates the pre-modern methods of Africa’s ancestors for uncovering processes latent within natural systems. The western model of linear time is derived from an ecclesiastical Christian historical account and has a distinct beginning and end. These transcendental accounts of time and history (further entrenched through Hegelian dialectics) are fundamentally anthropogenic. In Schelling’s words: man has history ‘not because he participates in it, but because he produces it.’ The indigenous notion of circular time rejects anthropocentric temporality and conceives of time as unreliant upon the human or dialectical history. This desubjective model of time rests upon interdependent ecologies and doesn’t require human agency as a requisite for its existence. Music cultivates a different set of qualities when it doesn’t follow linear dynamics. Rhythm necklaces take on a geometric recursive traits by fashioning time as a braid, fabric, or a spiral; the interlocking ostinato patterns develop trance-like characteristics when sustained. After spending extended periods internalizing the necklace techniques, the subtle iterative variances of each cycle give a strong sense of disembodiment for the listener. Being obsessed with ritual and rhythm I picked up a copy of Music &amp; Trance: The Relations Between Music &amp; Possession to learn about the different kinds of ritualistic uses of rhythm. Among many subjects, the book highlights the vast amount of social utility of music lost to modernity. It also emphasizes the rich practice of encoding histories and heritage into song as an intergenerational cultural vessel. Some west Africans believe that these rhythms are transmitted from the language of the Orishas (rhythm deities) and hold magic with respect to a corresponding deity. Inside these songs ancient ancestral secrets can be unlocked by trance drumming and dance. It is remarkable that a computer scientist uncovered a Greek algorithm that uses science to denote something that has been known to non-modern tribes for millenia preceding Euclid. The permutations of repetition take listeners down tunnels of memory into focused places of trance where there are ancestral secrets encoded in rhythm. Resources: <img width="1102" height="1920" width_o="1102" height_o="1920" data-src="https://freight.cargo.site/t/original/i/6d4606aa2bb9a8405a89c602b4cddae3d12c84e32d998a43050d5abdf922045a/timespiral.jpg" data-mid="37178371" border="0" src="https://freight.cargo.site/w/1000/i/6d4606aa2bb9a8405a89c602b4cddae3d12c84e32d998a43050d5abdf922045a/timespiral.jpg" /> Albrecht Durer <img width="492" height="806" width_o="492" height_o="806" data-src="https://freight.cargo.site/t/original/i/84b7478a84f850fa1e4ad8a33aed7f41d041bb47875f0c5c0b46931f562a17c3/durer.PNG" data-mid="37180563" border="0" src="https://freight.cargo.site/w/492/i/84b7478a84f850fa1e4ad8a33aed7f41d041bb47875f0c5c0b46931f562a17c3/durer.PNG" /> Albrecht Durer <img width="1152" height="1536" width_o="1152" height_o="1536" data-src="https://freight.cargo.site/t/original/i/503907dd11cdc9b68bc7f975b864735d8c4991c9e7d91d45861354333476cb02/IMG_0819.jpg" data-mid="33185663" border="0" src="https://freight.cargo.site/w/1000/i/503907dd11cdc9b68bc7f975b864735d8c4991c9e7d91d45861354333476cb02/IMG_0819.jpg" /> Godfried Toussaint’s Geometry of Music Rhythm CRC Press, 2013 <img width="598" height="326" width_o="598" height_o="326" data-src="https://freight.cargo.site/t/original/i/a634fdda67c00d5990d7ca1b2116b8035ff8aa673ecae422769946c569a021b4/spiral.PNG" data-mid="37180575" border="0" src="https://freight.cargo.site/w/598/i/a634fdda67c00d5990d7ca1b2116b8035ff8aa673ecae422769946c569a021b4/spiral.PNG" /> Rafael Araujo Rhythm Necklace: Geometric Sequencing for iOS by Sam Tarakajian &amp; Meara O’Reilly https://etudes.pointlinesurface.com/February-Additive-Synthesis-Spectromorphologies Fri, 11 Jan 2019 04:26:51 +0000 Études https://etudes.pointlinesurface.com/February-Additive-Synthesis-Spectromorphologies Additive Synthesis &amp; Function-based Spectromorphologies <img width="1725" height="579" width_o="1725" height_o="579" data-src="https://freight.cargo.site/t/original/i/ddf85061c588ff2dbed248112d50e7a8cc6ca0e008ea3382e4c0b4c4b708d592/TSU.PNG" data-mid="36622604" border="0" src="https://freight.cargo.site/w/1000/i/ddf85061c588ff2dbed248112d50e7a8cc6ca0e008ea3382e4c0b4c4b708d592/TSU.PNG" /> Concert acousmatic music has the powerful ability to conjure abnormal forms, vectors, and trajectories. Developing a graphical lexicon for expressing these types of spectral gestures has always been an interest of mine that I haven’t ever formalized. In Lasse Thoresen’s essay ‘Spectromorphological Analysis of Sound Objects’ he devises the notion of Temporal Semiotic Units (TSU) that is very attractive to me and partially inspired this étude. These units are effectively visual equivalents of vocabulary taken from structural functions to inform the shaping and manipulation of sounds and meta-data within a sound. These spectromorphological words and gestures are realized both aurally and graphically as singular or composite events. In this exercise I will be using additive synthesis as a timbral palette.&nbsp; The first étude examines stacked paraboloid modulations of internal temporality and the inharmonic series. The second étude examines functional modulation in spatial matrices with fixed musical events embedded in the matrices.&nbsp; Inharmonic Partials &amp; Hyperbolic Paraboloids&nbsp; <img width="2513" height="1488" width_o="2513" height_o="1488" data-src="https://freight.cargo.site/t/original/i/cd713eb67d183be3a259f406897b1cd707d0dc8deb626f48c487dc5f3b40f698/candela.gif" data-mid="37025811" border="0" src="https://freight.cargo.site/w/1000/i/cd713eb67d183be3a259f406897b1cd707d0dc8deb626f48c487dc5f3b40f698/candela.gif" /> The intersecting hyperparaboloids of Felix Candela’s building (pictured above) at Xochimilco, Mexico City mesmerized me when I was visiting last year for the Day of the Dead. I kept hearing spectral motion like this étude when I was there. The diagram above illustrates the parabolic formations shape of the ‘hypars.’ The ‘hypar’ structure means the seemingly complex curves can all be constructed using straight lines, as the diagram above to demonstrates. I used parabolic modulations of the inharmonic series to shape the timbres in this piece. Naturally, this scoring technique owes a great deal to Xenakis’ Philips Pavilion, polytopes, and Metastaseis.&nbsp;‘Music is liquid architecture; architecture is frozen music’&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; - GOETHE Spectral Function Drawings <img width="770" height="960" width_o="770" height_o="960" data-src="https://freight.cargo.site/t/original/i/f586b1e25c7e307bdbad145ffb4349b5e1f8b3104ba577a3c99a073d559e317f/53367895_2717297031644285_6132709370175160320_n.jpg" data-mid="37157682" border="0" src="https://freight.cargo.site/w/770/i/f586b1e25c7e307bdbad145ffb4349b5e1f8b3104ba577a3c99a073d559e317f/53367895_2717297031644285_6132709370175160320_n.jpg" /> <img width="768" height="960" width_o="768" height_o="960" data-src="https://freight.cargo.site/t/original/i/e6d86f3772f09d898da03e92b2b86153b520444d1a297615977f89d44a9c25d0/54519304_2717296944977627_4245244833276362752_n.jpg" data-mid="37157683" border="0" src="https://freight.cargo.site/w/768/i/e6d86f3772f09d898da03e92b2b86153b520444d1a297615977f89d44a9c25d0/54519304_2717296944977627_4245244833276362752_n.jpg" /> Pierre Schaeffer’s phenomenological approach to composition led him to articulate a theory both of listening practices and of sound objects. Schaeffer considered the ‘typo-morphologie’ as a multifaceted tool for the description of all the objects of the audible domain. The table depicted below is derived from his tableau.&nbsp;According to Schaeffer a typological space should meet three criteria. In spectral macroform, it is possible to define three situations: eumorphism: relevance of all the three categories (inchoativity, durativity, terminativity). The sound object has a well-defined temporal shape; amorphism: durativity dominates, inchoativity and terminativity are made irrelevant. Amorphous sounds are sounds that last indefinitely; anamorphism: profile is compressed, inchoativity and terminativity coincide, durativity is irrelevant, rather the process can be described in terms of punctuality. It is the case of sound objects as pure events. I used Schaeffer’s tableau as a map for sound qualities in the two recordings above. I interpolated between values in the matrix to construct the spectromorphological shapes. The&nbsp; drawings pictured above are Zsuzsa Peter’s C24 and were the visual scores for each etude, respectively. <img width="4743" height="2458" width_o="4743" height_o="2458" data-src="https://freight.cargo.site/t/original/i/d30d97341bdf58707250516e9e055cdc09dec85a527fbfca46d17fbb26f8743f/img-6.png" data-mid="36622576" border="0" src="https://freight.cargo.site/w/1000/i/d30d97341bdf58707250516e9e055cdc09dec85a527fbfca46d17fbb26f8743f/img-6.png" /> Lombardo-Valle's 3-dimensional sound criteria typology inspired by Schaeffer Resources: &nbsp; &nbsp; &nbsp; One of the pioneering pieces for additive synthesis is ‘Studie II’ by Karlheinz Stockhausen, written in 1954. This piece used only sine tones and mixtures thereof in non-tempered intervals and was an impetus for the following voice building. This image is a graphic of one voice used in the second etude. <img width="927" height="384" width_o="927" height_o="384" data-src="https://freight.cargo.site/t/original/i/12ec13d6de2d315528fa13fb2d8a9363e05ee760c9e905cf24f483ee4e5bdb13/pd-klang.jpg" data-mid="36623677" border="0" src="https://freight.cargo.site/w/927/i/12ec13d6de2d315528fa13fb2d8a9363e05ee760c9e905cf24f483ee4e5bdb13/pd-klang.jpg" /> Denis Smalley’s Spectromorphology [1997] Department of Music, City University, Northampton Square, London EC1V 0HB, UK https://etudes.pointlinesurface.com/March-Gong-Studies Sun, 19 May 2019 20:49:50 +0000 Études https://etudes.pointlinesurface.com/March-Gong-Studies Gong Studies &nbsp; <img width="736" height="396" width_o="736" height_o="396" data-src="https://freight.cargo.site/t/original/i/16c8e53fea7910f86c91778dd50182f403f18a73f1eee5583bc22531e74b28a2/CymbalsModes2.jpg" data-mid="43190293" border="0" src="https://freight.cargo.site/w/736/i/16c8e53fea7910f86c91778dd50182f403f18a73f1eee5583bc22531e74b28a2/CymbalsModes2.jpg" />Cymatic patterns of a chau gong excited at various frequencies with surface transduction (pictured right&nbsp;︎) &nbsp; <img width="1536" height="1152" width_o="1536" height_o="1152" data-src="https://freight.cargo.site/t/original/i/f4db017c2fef31b8d426230067b127a053fd4f4d8c8194e53d40afc1a0dacf22/transducer-gong.jpg" data-mid="42703144" border="0" src="https://freight.cargo.site/w/1000/i/f4db017c2fef31b8d426230067b127a053fd4f4d8c8194e53d40afc1a0dacf22/transducer-gong.jpg" /> I’d bathed in their unbridled timbres at meditations and noise shows always lusting after their inharmonic blossoming but a few years ago I finally took the plunge into the primorial sound chasm and procured a 36” Chau gong. After using them in studio drone sessions and various rituals, I’m finally getting around to doing a formal set of études. It is considered that tin was the first metal to flow from stones around 10,000 B.C. As the ovens were capable of getting hotter metallurgists began to separate copper from rocks around 6,500 B.C. The Bronze Age began around thousand years later when the ovens were big enough to allow for the melding of the two. Ancient gong makers discovered that meteorites, when thrown into the casting melts, added to the quality of bronze giving it an improved resonant tone, more powerful and spacious, sustaining its vibration for much longer. The early gong alchemists didn’t know that the special ingredient provided by meteorites was nickel, since during that era of metallurgy it was never found naturally on the surface of the Earth. So it turns out that those dreadlocked ‘sound healers’ that claim that gongs are ‘celestial’ are actually indirectly vindicated&nbsp; ― early gongs partially came from outer space.&nbsp; Chaotic State Transitions &amp; the Non-Linear Physics of Gongs Most tonal musical instruments are often thought of as linear harmonic systems, and a first-order description of their operation can often be given on this basis with a few inharmonic exceptions such as drums and bells. In impulsively excited instruments, such as gongs and cymbals, the nonlinearity is ‘incidental’ including transitions to chaotic behavior. The allure of a gong is in its signature inhamonic blossoming which is derived from its indeterminate resonance. At a critical amplitude, and over a very small frequency range near the admittance peak, the periodic motion of the gong will develop high amplitude subharmonic components. When I sit in front of the gong I can literally feel thermal energy emissions cascading off the bronze surface. This behavior is critically dependent on the frequency, amplitude, and immediate history of the excitation, but subharmonics of orders 2, 3, and 4 are evoked. Associated with these subharmonics are all multiples of their frequencies. Sometimes the number of peaks on the spectrum are so large that unambiguous assignment of fractional frequencies is not possible, and since the unresolved background intensity is also large, the motion may reasonably be described as chaotic. Subjectively, the sound produced by the gong when vibrating in one of these multiple-subharmonic modes is very similar to the fully developed after ring of the gong when excited by a vigorous blow. <img width="1152" height="1536" width_o="1152" height_o="1536" data-src="https://freight.cargo.site/t/original/i/b8a10e56ae5c6e2189aed21da87a169c2c63afb6a62fc0b4c4b6fd99e2fe9ba9/transducer-gong-2.jpg" data-mid="42703145" border="0" src="https://freight.cargo.site/w/1000/i/b8a10e56ae5c6e2189aed21da87a169c2c63afb6a62fc0b4c4b6fd99e2fe9ba9/transducer-gong-2.jpg" /> The normal modes of gongs are inharmonic, but no attempt is made to tune them to a harmonic or quasi-harmonic series. Instead, the shape and material of the gong determines its spectrum and, when gongs are used in combination, and with the addition of tuned-bar instruments their modal frequencies in turn determine the musical scale. The gongs of the gamelan do not exhibit any marked nonlinearity, because they have thick and highly curved walls, and are played at a moderate dynamic level. However, the wind &amp; Chau gongs of the Chinese opera orchestra that you’ll hear in these études are made of bronze no more than 6mm in thickness and, since they represent climaxes in the action, are struck very vigorously with a padded hammer, excited with rubber, and modulated with amplified transduction (SolidDrive SDG1).&nbsp; The nearly flat central section of the gong is the active vibration region, while the stiffer conical surround both supports this disk and acts as a baffle to increase the sound radiation. The difference in geometry and material between Javanese and Chinese gongs makes an immense difference to the sound in loud playing, though if the gongs are stuck softly they produce a simple and nearly sinusoidal tone at the fundamental frequency of the primary mode. This means that the stiffness and tension of restoring forces are very small, so that the quadratic tension generated by mode displacements has a profound physical effect. Another source of mode coupling and nonlinearity arises from the hammered bumps in the surface since abrupt changes in slope are known to generate mode coupling and nonlinear frequency multiplication. Surface Transduction &amp; Bronze Meditations: The vibration patterns of the gong observed are exciting the surface with a sinusoidal signal (via SDG1 transducer) and room feedback. Ketamine Mantis Mother: This take is a from expanded studio percussion performance that included excitation with caxixi, steel springs, plastic vacuum tubing, rattles, various steel rods, aluminum plates, chop sticks, frame drum, rubber mallet, 1/2” chain mesh Mallet Variations: The vibration patterns of the gong were observed by driving the plate at edge with various mallets (rubber, padded hammer). Padded Hammer Rubber Mallet Resources: Microphones: Neumann KM150 Stereo Hypercardioid Condensors Gong: 36” Wuhan Chau Tam Tam Exciters: SDG1 SolidDrive transducer, rubber mallet, steel springs, plastic vacuum tubes, caxixi, steel rods, aluminum plates, bow, 1/2” chain mesh https://etudes.pointlinesurface.com/April-Wavetable-Studies Fri, 11 Jan 2019 04:26:51 +0000 Études https://etudes.pointlinesurface.com/April-Wavetable-Studies Wavetable Studies <img width="1316" height="1080" width_o="1316" height_o="1080" data-src="https://freight.cargo.site/t/original/i/f1463cdd7b92f71a620be539fb6f86a01835c62e5736c93cb002c93ed6b23490/bank_a_tables_350.PNG" data-mid="34638060" border="0" src="https://freight.cargo.site/w/1000/i/f1463cdd7b92f71a620be539fb6f86a01835c62e5736c93cb002c93ed6b23490/bank_a_tables_350.PNG" /> <img width="1301" height="1056" width_o="1301" height_o="1056" data-src="https://freight.cargo.site/t/original/i/0901b6fefeffe49d736e794f58e033c1e81d179c233409ffd43a0dbb289446af/bank_b_tables_350.PNG" data-mid="34638061" border="0" src="https://freight.cargo.site/w/1000/i/0901b6fefeffe49d736e794f58e033c1e81d179c233409ffd43a0dbb289446af/bank_b_tables_350.PNG" /> Iterative Indices (f+n2) Each index of 64 waves was arranged as an 8x8 array. The “rows” are represented on the X axis and the “columns” on the Y axis (pictured above). The third array (Z index) adds depth to the X,Y array. In this étude this lookup table is modulated with various sources including curvilinear shapes and smoothed bipolar Brownian motion. As the modulation source indexes through the positions in the table a smoothing function for “frame interpolation” has been applied to the waves. This smoothing/anti-aliasing algorithm allows the two outputs to be a continuous blending of one wave to another. During these iterations the algorithms’ calculation adds an order of magnitude of “in-between” waveforms, so that the 192 waveforms are expanded to over 24,000 possible timbres. In these studies no filtration was applied to avoid masking the timbral shifting generating the rich partial series. Anti-aliasing function for higher-order integrated wavetable synthesis: 1. Kth order integration with cascaded first-order integrators 2. Table look-up and interpolation 3. Kth order differentiation with cascaded first-order differentiators K = order of integration N = order of polynomial interpolator <img width="1027" height="274" width_o="1027" height_o="274" data-src="https://freight.cargo.site/t/original/i/6229eac4bdc5b1d3213dec50510299c7190e9bc85cbe4afdde3313b29a4accac/wavetable-smoothing-process.PNG" data-mid="43574820" border="0" src="https://freight.cargo.site/w/1000/i/6229eac4bdc5b1d3213dec50510299c7190e9bc85cbe4afdde3313b29a4accac/wavetable-smoothing-process.PNG" /> Franck &amp; Välimäki 2013 In general, scanning on the X axis generated a smooth progression of timbre. In fact, most of waves in the X dimension are functionally derived from the adjacent wave. Each row (Y), however, is unique. Each Y element is comprised of: &nbsp; sine bankspulse width modulationsfiltered noisevocal formants Spherical Vertex Interpolations A spherical wavetable is another way of grouping waveforms. The modulation parameters for traversing the spherical wavetable in this study include latitude, longitude, and depth. The modulation index navigation morphs between waveforms&nbsp; positioned at various vertices on the surface of the geometry. Although the term “sphere” when talking about the wavetables, the structure of each wavetable is actually a 3-torus. “What’s a 3-torus? A three-dimensional structure existing in a four-dimensional space. To understand what a 3-torus is, first think about a circle. A circle is a single dimensional object that wraps around to its beginning point as it reaches its end point. Any point on the circumference of a circle can be specified by a single number (by an angle from 0° to 360°), so a circle is one-dimensional. However, in order to draw a circle you need a two-dimensional space such as a piece of paper. So, a circle is a one-dimensional object existing in a two-dimensional space. Now, think about a doughnut (a torus, see picture below). You can make a donut if you extrude a circle into a cylinder and then bend the cylinder around so the top and bottom faces are touching. You can specify any point on the surface of the doughnut with just two numbers (an angle of the original circle and a position along the extruded cylinder), so the torus surface is two-dimensional and clearly exists in a threedimensional space. The next step is not as easy to visualize — imagine you took a donut and extruded it through a fourth dimension, and then connected the beginning to the end. This is a 3-torus. It’s a three-dimensional object that exists in a four-dimensional space. If you happened to be on the surface of a 3-torus and you looked far enough in any direction you’d see the back of your own head! If you walked far enough in any direction you’d end up exactly where you started, facing the same direction. The same is true for these wavetables: if you navigate far enough in any direction, you end up back to where you started.” <img width="1375" height="898" width_o="1375" height_o="898" data-src="https://freight.cargo.site/t/original/i/dd02e0d44b2d10ba594be3d329e5b99569d9386a549e786f8dc04599f7e8b0ea/torus.PNG" data-mid="43581047" border="0" src="https://freight.cargo.site/w/1000/i/dd02e0d44b2d10ba594be3d329e5b99569d9386a549e786f8dc04599f7e8b0ea/torus.PNG" /> Stochastic Matrices &amp; Steady State Transitions In this next étude I make use of Markov (stochastic) matrices as a method of using probability to index through the wavetables outlined in the first section. The modulation source steps through the Markov process (pictured below) resampling at 1Hz. Using this sample rate conversion technique, arbitrary musical pitches were generated indexing through the set of wavetables: downsampling was used for raising the pitch and upsampling for lowering it. For posterity, let’s look at the properties of the stochastic matrix: In a stochastic matrix, all entries are nonnegative, and each column sums to 1.The product of stochastic matrices is stochastic.In a Markov chain, elements move from one state to another with the same probabilities at each step in the process.The transition matrix for a Markov chain is a stochastic matrix whose (i, j) entry gives the probability that an element moves from the jth state to the ith state during the next step of the process.The probability vector after n steps of a Markov chain is Mnp, where p is the initial probability vector and M is the transition matrix.A limit vector for a Markov chain is always a fixed point (a vector x such that M x = x, if M is the transition matrix).A stochastic square matrix is regular if some positive power has all entries nonzero.If the transition matrix M for a Markov chain is regular, then the Markov chain has a unique limit vector (known as a steady-state vector), regardless of the values of the initial probability vector.If the transition matrix M for a Markov chain is regular, the positive powers of M approach a limit (matrix) all of whose columns equal the chain's steady-state vector. <img width="1560" height="1247" width_o="1560" height_o="1247" data-src="https://freight.cargo.site/t/original/i/08a3cd397cd920b0b397393e6d6e9d25fefb04e801807a520e08df0dd4d95694/MC-diagram.png" data-mid="43574649" border="0" src="https://freight.cargo.site/w/1000/i/08a3cd397cd920b0b397393e6d6e9d25fefb04e801807a520e08df0dd4d95694/MC-diagram.png" /> https://etudes.pointlinesurface.com/Info Fri, 11 Jan 2019 04:26:53 +0000 Études https://etudes.pointlinesurface.com/Info Extended Techniques — Figurations, Variations, &amp; Classifications “You must be like me; you must suffer in rhythm.”&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ― JEAN-PAUL SARTRE The purpose of this set of études in microcomposition, technique, and mutant instrumentation is to publish unorthodox and incomplete processes from my studio practice. I’m aiming to forego formalism to examine and rehearse rudimentary forms and sonorities without being encumbered by compulsions to situate them into any broader compositional framework. Variations and refigurations of motifs, tunings, systems, timbres, and temporalities will be the primary material examined here. This will also be an exercise in documentating the materials utilized in my compositions, sound design, and recordings. I will be publishing documentation of process software, architectural acoustic experiments,&nbsp; mutant instruments,&nbsp;circuits, physical materials, microphone techniques, mathematical functions, and photos in the field collecting data or sounds. Notation, visual scoring, and graphical representation of the musical, spectral, temporal, and spatial domains will be another region of experimentation that I’m aiming to undertake with the project. Graphical notation will complement the extended techniques as an aesthetic counterpart for the musician, ensemble, or computers. ABSTRACTION AND ANALYSIS “Ideas are distributed in space. An idea isn't only in one part; one part can't express the idea any longer, only the union of parts can completely express the idea. The idea found it necessary to be presented by several parts. After that, there was a rapid flowering of polyphony.” ― Anton Webern (From the Path to New Music, 1975.) <img width="478" height="502" width_o="478" height_o="502" data-src="https://freight.cargo.site/t/original/i/3e9b3ac6b3c9812d872f91ef16f0ad4df4ba148a587b844c197058cc75a0da2a/future-cities-p1-png.png" data-mid="37035084" border="0" data-no-zoom src="https://freight.cargo.site/w/478/i/3e9b3ac6b3c9812d872f91ef16f0ad4df4ba148a587b844c197058cc75a0da2a/future-cities-p1-png.png" />