Microtonality

Between 1971 and 2006, James Tenney created more than fifty significant works of what is now commonly called ‘spectral music’. In their materials and procedures, his compositions frequently paralleled, sometimes anticipated, and in some instances strikingly contrasted with spectralist developments in Europe. This article provides an analytical introduction to the spectralist component of Tenney’s large and varied output, and explores its emergence and place within a North American tradition of spectral music composition. Among the compositional concerns addressed are the duality of timbre and harmony, the harmonic series as a structural resource, the instrumental synthesis of speech, rhythmic analogs of spectral structures, the expansion of traditional harmonic means, and practical performance considerations.

به طور کلی گام مجموعه ای است از اصوات که فواصل موسیقایی آنها در اکثر اوقات بین ۲ عدد ۱ و ۲ قرار می گیرد. عدد ۱ که اولین درجه گام است پایگی نام داشته و عدد ۲ اکتاو آن است که قاعدتا گام با آن بسته می شود. فرکانس اکتاو ۲ برابر پایگی است :

F2 = 2 × F 1

اکتاو را می توان به اشکال متفاوت تقسیم نمود . مثلا ۱۲ قسمت مساوی که همان گام ۱۲ نیم پرده مساوی است ، ۲۴ قسمت مساوی که گامی ۲۴ ربع پرده مساوی است و …

Technology, Aesthetics, Communication AN INTERNATIONAL JOURNAL 2 2005 ESTRATTO I PISA ROMA ISTITUTI EDITORIALI E POLIGRAFICI INTERNAZIONALI MMV e LUCA CONTI ARTEFATTI E TEORIA NEL SISTEMA NATURAL DE LA MÙSICA (1951) DI AUGUSTO NOVARO S ONO scarsi i documenti che aiutano a ricostruire la vicenda di Augusto Carlos Novaro (Tacubaya, Città del Messico, 3 gennaio 1891-ivi, si novembre 1960).

In the 1920s, the Mexican composer Julián Carrillo (1875-1965) developed a microtonal system called El Sonido 13 (The 13th Sound). Although his pioneering role as one of the first proponents of microtonality within the Western art music tradition elevated Carrillo to iconic status among European avant-garde circles in the 1960s and 1970s, his music and legacy have remained largely overlooked by music scholars, critics, and performers.

Confronting this paucity of scholarship on Carrillo and his music, Alejandro L. Madrid goes above and beyond "filling in" the historical record. Combining archival and ethnographic research with musical analysis and cultural theory, Madrid argues that Carrillo and Sonido 13 are best understood as a cultural complex: a network of moments, spaces, and articulations in which Carrillo and his music continuously re-acquire significance and meaning. Thus, Madrid explores Carrillo's music and ideas not only in relation to the historical moments of their inception, but also in relation to the various cultural projects that kept them alive and re-signified them through the beginning of the twenty-first century. Eschewing traditionally linear historical frameworks, In Search of Julián Carrillo and Sonido 13 employs an innovative transhistorical narrative in which past, present, and future are explored dialogically in order to understand the politics of performance and self-representation behind Carrillo and Sonido 13.

In Search of Julián Carrillo and Sonido 13 transforms the traditional genre of the composer study, treating it not as a celebration of "masters" and "masterworks," but as a pointed postcolonial intervention that offers invaluable insight into the politics of cultural exchange, experimentalism, marginality, and cultural capital in twentieth century Mexico.

In the following essay, I review a series of my own works composed for guitar(s). I argue that these works, which were composed discontinuously over a period of fifteen years, expose a process oriented towards the construction —or the discovery— of a personal guitar (and a personal music). The works take as a given certain initial conditions of the guitar, which are the result of 1) The medium is characterized by an endogamy of guitar composer-performers and/or 2) The inertia of historical repertoire within the genre isolates the guitar from experimental processes necessary for further development. To transcend this perceived barrier, I argue there must be a reflexive work leaning towards expanding the musical language of the guitar. In the first part of this paper, I narrate a progression from what could be called a conventional guitar environment to a more personalized relationship with the instrument and the task of composing for it within the scope of contemporary classical music. In the second part, I list a series of technical resources that are associated with the search of a singular compositional language for the guitar, establishing links between certain techniques and the desired expressive result. Finally, I offer some preliminary conclusions about my path composing for this instrument, and I sketch some possible ways to continue developing my creative work for guitar(s).

"This paper will focus on microtonal scales and modes, known as maqam, used by musicians in the Middle East and Central Asiatic regions. The sources of these scales and modes come from Iran, Turkey and Arabia, initially, an example being the Dastgah of Persia, and have come to Uzbekistan and Tajikistan by way of foreign influence via inter-cultural interactions and religion, particularly Islam. Maqam is also found in regions surrounding central Asia, such as: Turkey, Iran, Afghanistan, Azerbaijan, and Arabic cultures and serves as a modal structure that has remained relatively unchanged for hundreds of years, despite supralocal changes in purpose and format as coalesced by intercultural exchanges. Despite very few sources for the specific research on Central Asian microtonal scales and modes, this paper will utilize analysis from seminal sources which will bridge into both Uzbekistan and Tajikistan and their shared use, such as use within the shash maqam, along with its concomitant scales, historically derived from these aforementioned regions. This research will primarily be a musicological endeavor and will not engage in particular ethnic diversity over and beyond what will provide such information.
The larger issue for this paper relates to the author’s interest in the expansion of the palette of pitch color and the growing staleness of equal temperament as the 21st century gets underway."

How are musical pitches organized before the creational process of "musical works" begins? How are pitches combined to create scales and superordinated structures? How was music previously organized with 12 pitches per octave, and what led the way to what we commonly call "microtones"? How can we learn to understand them by listening? In compiling this book, the editors invited researchers from many countries to report on the subject.

La seguente tesi di ricerca si occupa di illustrare sufficientemente quali possono essere o non essere i limiti topici attraverso cui il compositore di musica elettronica opererebbe all’occorrenza specialmente nel campo dell’armonia, della melodia e del ritmo.

Las teorías musicales actuales incursionan en la utilización de diversas tecnologías y saberes para poder alcanzar nuevos planteamientos en la guitarra. A lo largo del siglo XX se recuperan y desarrollan los conceptos de tratadistas renacentistas y románticos que desembocan en la emancipación del ruido, el cromatismo extremo, la micro-tonalidad y la síntesis electrónica.
Así considero pertinente el desarrollar las ideas actuales al respecto, de la manera más simple y concisa posible, pero con la terminología y propiedades pertenecientes y actuales de la jerga musical microtonal y la acústica.

Study in Spanish of several deblas by different proffesional flamenco singers in order to establish a repertoire of ornaments and to describe the microtonal and melodic behaviour.
An specific concept of modality has been developep for the case. Analysis and notational resources have been provided for analyzing different flamenco "palos", through several levels.
Also they may be found contributions related to general tuning, rhythmic features, duration and key among other aspects.

JULIUSEDIMUS , CATÁLOGO COMPLETO DE LA OBRA MUSICAL, 2024
INCLUYE  NUEVA LISTA DE LAS OBRAS, FRAGMENTOS DE PARTITURAS, FOTOGRAFÍAS, BREVE CV, BIBLIOGRAFÍA SELECTA, ETCÉTERA. CON ADICIÓN DE PORTADA DEL LIBRO "JULIO ESTRADA. MEMORIES AND SHADOWS IN THE IMAGINARY. A BIOGRAPHY," DE JAMES L. MCHARD, ICONIC PRESS, 2015, 369 PAGES. [email protected]

JULIUSEDIMUS, CATALOGUE COMPLET DE L'OEUVRE MUSICALE, 2024
COMPRENDS UNE NOUVELLE LISTE DES OEUVRES, FRAGMENTS DE PARTITIONS, PHOTOGRAHPIES, BREF CV, UNE BIBLIOGRHIE SELECTE, ETCÉTÉRA . AVEC L'ADDITION DE LA COVERTURE DU LIVRE "JULIO ESTRADA. MEMORIES AND SHADOWS IN THE IMAGINARY. A BIOGRAPHY," DE JAMES L. MCHARD, ICONIC PRESS, 2015, 369 PAGES. [email protected]

A COMPLETE UPDATED CATALOG OF MUSICAL WORKS, 2024
INCLUDES A NEW LISTE OF THE WORKS, TEXTS, SCORE FRAGMENTS, PHOTOGRAPHIES, SHORT CV, A SELECTED BIBLIOGRAPHY , ETCÉTÉRA.  WITH THE ADDITION OF THE BOOK "JULIO ESTRADA. MEMORIES AND SHADOWS IN THE IMAGINARY. A BIOGRAPHY," DE JAMES L. MCHARD, ICONIC PRESS, 2015, 369 PAGES. [email protected]

In this paper a new model for microtonal music is developed. After an exploration of the historic and modern use of 12TET the features that give rise to successful models for pitch structure are deduced. Existing models for microtonal music, including those of Partch, Balzano, Blackwood and Sethares, Plamondon and Milne are critically analysed for their strength, practicality and thoroughness, along with the quarter-tone music of Hába, Ives and Wyschnegradsky. No model is found to be of the same strength, practicality and thoroughness of the historic and current use of 12TET. After deducting that 22TET is the most appropriate platform for such a model, a model for microtonal music is detailed. The resulting model is seen to be just as strong as use of 12TET, and more varied, with several scales of different consonances available.

This paper introduces polytempic polymicrotonality as a new musical aesthetic. Microtonality is the basis for its inception, from which the discussion proposes music with more than one microtonal tuning system. Examples from the literature are discussed to give an historic framework showing that this tendency has been present throughout human musical history. Polytempo is a tool for which polymicrotonal structures can function in relief from its background. Polytempo acts as a frame, or ground structure, that is multi-dimensional, akin to the advancement of perspective in Renaissance art. Examples of music literature are displayed for musical precedence in this area, focusing on Charles Ives’s Universe Symphony, unfinished since 1925, and realized recently by Johnny Reinhard in 1996.

Philosopher/mathematician/musician Pythagoras of Samos (ca. 570—ca. 490 BCE) is credited with the historic discovery of the relationship between musical harmony and mathematics, and his teachings about the divine nature of music and numbers live through to today in the concept of musica universalis or “the music of the spheres.” Although Pythagoras left no writings behind, his ideas found expression in the works of Plato, Iamblichus, Nicomachus, Boethius, and others. In the 20th century these ideas inspired the works of American microtonal composer/theorist Harry Partch, along with German “harmonicists” such as Hans Kayser and Rudolf Haase. By tracing a line between the Lambdoma of Pythagoras and the Tonality Diamond of Harry Partch, and through comprehensive review of Pythagorean harmonic concepts embedded in various ancient philosophical texts along with modern works on microtonal music theory, we examine the connection between the two disciplines, and ponder whether a study of either one is truly complete without an understanding of the other.

In this paper I have attempted to clarify the different meanings of shruti (≈microtone). By taking a close-up of the ga (minor third) in Darbari Kanada, as performed by Uday Bhawalkar. http://thoughts4ideas.eu/gandhara-in-darbari-kanada-the-mother-of-all-shrutis/

Music theory has been a part of culture ever since music was invented. In 20 th century academic circles, theorists came up with a way to explain the growing trend of atonal music using their own version of set theory, where conventional diatonic and triadic harmony (older Western tradition) was not needed. Unfortunately, this set theory is only maximally useful in the most used tuning system of the last 100 years, 12-tone equal temperament. Microtonal music theory, which nowadays implies music that is not tuned in 12-tone equal, is more intriguing than ever before in the 21 st century, just as atonality was in the 20 th century. This thesis aims to describe a new set theory proposed to combine microtonal music theory and set theory. This theory is a more thorough and universal method of categorizing scales, because it utilizes their intervallic relationships (scalar classes) in addition to their pitch classes.

Easley Blackwood was a pioneer in the use of small equal divisions of the octave other than 12 for musical composition. Such works present an obstacle for musical analysis. This essay presents analyses of the second and third movements of Blackwood’s Suite for Guitar in 15-Equal Tuning. After first considering the relationship between just intonation, 12TET, 15TET and Neo-Riemannian theory, an attempt is made to apply Roman numeral and neo-Riemannian analyses to the movements, in order to deduce which form of analysis is more appropriate. It is found that, whilst a neo-Riemannian analysis is always appropriate to the movements given its use of major and minor triads in common tone progressions, a traditional Roman numeral analysis is impossible. It is found that a Roman numeral analysis may be applied to movement III with respect, rather than to the traditional diatonic scale, to Blackwood’s decatonic scale, but that the neo-Riemannian approach is more useful overall.

Bağlama is an Anatolian (Asia Minor)  necked lute, which is plucked with fingers or plectrum. Ancient lutes found in Asia Minor, Middle East, the Caucasus and Asian originated necked lutes are the ancestors of the bağlama. This article is about bağlama techniques in the ciassical guitar literature.

The main purpose of this study is to propose a notation system based on harmonics series that can enable the pitches used in the performances to be expressed as accurately as possible. The ability to express the preferences and harmonic intentions in the melodic structures of various performers and composers, is seen as an essential need for the underlying theory of the Turkish makam music.
This study is made with the intention of contributing to a comprehensive notation system which is assumed to be the crucial need for the cultural transmission and the development of Turkish makam music.The deep musical knowledge and preferences of the living masters should be written out in the best possible way; thus, this information can be reached to a larger audience to provide change and development. This deep-rooted knowledge and accumulation that has been brewed over the centuries can remain as the basic material of changes for the future.

The Bohlen-Pierce (BP) microtonal tuning system developed in the 1970's is enjoying a re-emergence among experimental composers. The current paper is a tutorial for building a simple synthesizer using the BP tuning system, an alternate suggestion for notation using the system, and a set of three etudes composed for the synth (recording available at https://soundcloud.com/skyron/three-bp-etudes-bargsten ).

This paper offers a description and demonstration of the colored representation of the relative music scale as well as computer program for equal 29temperament. The author of this treatise proposes the model of the musical scale, expressing the reciprocal relationship of attraction and repulsion between the degrees of elevation on the musical scale. The model comprises 5, 7 and 12 different notes for every key, identical to the European and a number of Non-European musical systems of pitches; 17 different notes for every key, identical to the Arab-Iranian system; and 22 different notes, identical to the Indian system "sruti." This model, elaborated in all the keys, would give rise to a system of notes that is inordinately complicated. A necessary and sufficient condition for the problem would be a 29-tone temperament. A suitable keyboard is suggested. The nearby sounds are located at intervals of a fifth, a fact that corresponds to the greater proximity of fifth-interval sounds (the slightest interference of sound waves arises in contemporary resonance). As colours near to one another, we mean those that are next to each other in the spectrum. The author represents a spectrum of 12 colours, which should correspond to the chain of 12 fifths. This coloured chain is condensed into chromatic scale. After several years in which children have contact with coloured representations of a musical system (and a special notation board as well), they begin to have relative associations as regards the "coloured" pitch (short video).

This article (book chapter) explores major the most complicated instrument of the maqām tradition with a fixed supply of pitches, the qānūn plays a central role in the definition of the Near-Eastern tuning system. Originally this instrument had to be retuned separately for every scale structure, comparably to the Iranian santur. During the first half of the 20th century, mandal-s, movable levers, were applied to every course of strings with which the intonation can be adjusted during performance. These small metal bridges, however, have also caused confusion between theory and practice because they are tuned, on all common models, upon the tempered twelve-note scale that has little in common with pure Pythagorean and harmonic intervals as they are described in the traditional treatises. The study provides a brief account, containing four existing systems invented during the 20th century.

Setting the stage to address his new philosophy of music, in 1940 Harry Partch (1901–1974) allegorically described the predominant Western musical tradition as a “great Cathedral,” from which a keen thinker—in Partch’s words: a “zealot”—shall depart. He intended to revolutionize the tenets of Western musical culture, from harmonic structures and the prevalent subdivision of the octave to the musical instruments and dramatic music. The scholarly literature has examined Partch’s revolutionary aesthetic mostly in terms of his music-theoretical—and to a smaller extent in term of his dramatic—impact in the United States. However, Partch’s ideas have affected not only American, but also European composers of microtonal music. This dissertation approaches Partch’s rebellion not as an isolated paradigm, but in relation to Manfred Stahnke’s aesthetic and music—a German composer (born 1951) who has also sought to expand the intonational and tuning idioms of Western art music, whom Partch’s microtonal theories have influenced.
The analysis of the interrelationships between aesthetic decisions, microtonal structures, technological aspects, and theatrical innovations in Partch’s and Stahnke’s stage works articulates the link between both composers. These interrelationships go beyond functioning as mere formative elements; they become means to mediate the philosophical, mythical, ritual, and psychological connotations of Partch’s and Stahnke’s music-theatrical works, as well their cultural discourse. Examining Partch’s Oedipus (1950), The Bewitched (1955), and Delusion of the Fury (1966), as well as Stahnke’s Der Untergang des Hauses Usher (1981), Wahnsinn das ist die Seele der Handlung (1982), Heinrich IV (1986), and Orpheus Kristall (2001), demonstrate the scope of their cultural criticism and the link between them.

Mikrotonalität in Werken von Manfred Stahnke
für Zupfinstrumente

Publikation:
MS, "Über Hinterhöfe und Vorhöllen: Wiederbesuchte Mikrotonalität", in einer englischen Übersetzung veröf­fentlicht als: "About backyards and limbos - Microtonality revisited", in: Concepts, Experiments, and Fieldwork: Studies in Systematic Musicology and Ethnomusicology, hrsg. von Rolf Bader, Christiane Neuhaus, Ulrich Mor­genstern. Peter Lang, Frankfurt/M 2010, S.297ff

This paper deals with the musical instrument "Octo" invented in 2010 and aspects of instrument invention in our contemporary setting, especially focused on enabling musical instruments to have playable micro-intervallic properties and spatial capacities. The paper discusses design and playability considerations when accommodating such tonal properties and the future perspectives of developing/remodeling such hybrid instruments as musical tools for the expansion and further development of musical genres and esthetics in our contemporary setting. Background In the 20 th century we have seen various developments within harmony and techniques that have not been explored before, some of them which are:-microintervalic music and "spatial" music. These developments have helped expand the overall musical/compositional language and have brought new compositional tools for composers, that help in turn develop new ways of writing music and new esthetic horizons.

Winner of the Alt Pibroch Club and Altpiborch.com “Modern Pibroch Library” Competition, 2018.

Program Notes and Piece Mechanics:

Shrouded in myth and mystery, a tradition that has been passed from master to pupil for unknown centuries, piobaireachd (Scots Gaelic for “piping” and anglicized as “pibroch”) is the “classical music” of the Great Highland Bagpipe, originating sometime during the Middle Ages. Piobaireachd is the oldest and perhaps most austere of all the Scottish bagpiping genres, focusing on simple tone progressions with slight elaborations over a series of variations. Crucial to this style is tone and timbre, and thus highly refined and particular tunings were constructed around these pieces, generally emphasizing tuning by Pythagorean ratios, particularly focusing on the 7th and 11th partials.

This piece returns the modern Scottish bagpipe to these medieval traditions, however in unconventional ways through building a scale of 15 micro-tonal notes based on octave transpositions of the prime partials of an implied fundamental. Along with the 7th and 11th partials, the scale of this piece incorporates all the prime partials from 2 to 31. This resulting piece is both Medieval in aesthetic and form, but modern in its expansion of Pythagorean tuning and extended techniques on the bagpipe, including unconventional droning, alternative fingerings, and multi-phonics.

The scale is based on octave transpositions of all the prime partials (up to 31) of the fundamental note, which is (approximately) 60 Hz. This fundamental was chosen for convenience, since most Great Highland Bagpipes are tuned to about 480Hz on the lowest “A” of the chanter. The three drones form the second, third, and fifth partials above the non-sounding, implied fundamental of 60Hz. The primary chanter notes (melodic notes), given on the first page of the score instructions, form the other octave-transposed prime partials up to the 31st – 7, 11, 13, 17, 19, 23, 29, 31 – barring the low-A, which is simply a multiple of the 60Hz fundamental (Note: the tuning of these partials is as close as possible, +/- 5 Hz or so, pretty much indistinguishable to most human ears). The additional microtonal inflections or embellishments are totally for color and are not based on any mathematical proportion. They are simply created through alternative fingerings. The primary melodic content, however, is solely based on these prime partials.

APC and Altpibroch.com:

The Alt Pibroch Club and altpibroch.com are sites dedicated to the pursuit of bringing new approaches to bagpipe performance informed by ancient scores. While we support reconstructions of old playing, they are also interested in bringing new musicality to piobaireachd long since forgotten, much to the detriment of audiences and performers alike. AltPibroch.com is the definitive resource for information on pre-1841 pibroch manuscripts, their interpretation and history. These are the original, unexpurgated primary sources of our art, and the different musical perspective, interpretation and insight they bring is a revelation to those accustomed to the modern pibroch scene. They encourage performers to explore the full musical depth and creativity of the folk music of piobaireachd, from as many sources of instrumentation and inspiration as they can find.

Jordan Alexander Key:

Jordan Alexander Key (b. 1990) currently pursues his PhD in composition and musicology at the University of Florida. He earned bachelor’s degrees in music composition, mathematics, and Eastern Asian philosophy from The College of Wooster (2013), as well as a master’s degree in music composition from the University of Arizona (2015). His significant recent projects include his European premier with Vienna’s PHACE Ensemble performing his Octet, “Threnody on the Death of Children;” a performance by Boston String Quartet of his String Quartet No. 1; a concert with Bold City Contemporary Ensemble performing his Quintet, “Discursus Anachronismus;” a collaboration with the Vancouver Queer Arts Festival for his Art Song, "God Ourselves;” and the display of his recent audio-visual projects as part of the Wolfsburg Kunstmuseum’s new exhibit, “Never Ending Stories: The Loop in Art, Film, Architecture, and Music,” in Germany during the Winter and Spring of 2018. Jordan gives regular concerts on his two instruments: the pipe organ and bagpipes. His performance repertoire focuses primary on music from the Middle Ages, Early Renaissance, and Early Baroque. He has been a bagpiper for 15 years as of 2018. For more information on Jordan Alexander Key and for recent recordings of his works, see his website, www.jordanalexanderkey.com, or search for his work on YouTube (channel, “Jordan Alexander Key”)

Comparative Study of the Modal Systems of Greek Orthodox Church Music and Ottoman Court Music. 

(Excerpt including live links in first page to download the full work from own home page)

Alternatively:
To download the PDF file of the full text (164 MB), please visit this link:

http://larigot.avarts.ionio.gr/users/iani/publications/

or click on this link:

http://larigot.avarts.ionio.gr/users/iani/publications/IchosUndMakam.pdf

This paper explores a new and ambitious tuning system for the Middle Eastern qānūn, conceived and practiced by the French virtuoso Julien Jalâl Ed-Dine Weiss (b. 1953). Since the invention of mandal-s, movable bridges that enable microtonal alterations during performance, the qānūn has become a major source for tuning and fixation of the Middle Eastern pitch inventory. Whereas Arab qānūn-s are based on "quarter tones", Turkish instruments divide the octave into 72 notes. All commonly fabricated models, however, have in common that their tuning is based on 12-semitone equal temperament. This does not conform with the Pythagorean tuning on which the heptatonic framework of the qānūn is traditionally based. For that reason, common qānūn models only approximate the interval sizes that have been described throughout the theoretical tradition by means of arithmetic ratios. Equal temperament causes transformations in the tuning of commonly agreed scale degrees and complicates the...

Analyseversuch von Aspekten aus "Vortex temporum" von Gérard Grisey
Publikation:
MS, "Die Schwelle des Hörens: 'Liminales' Denken in Vortex temporum von Gérard Grisey", in: ÖMZ 6/1999, S.21ff
Siehe auch den Grisey-Teil in: "Zwei Blumen der reinen Stimmung im 20. Jahrhundert: Harry Partch und Gérard Grisey", in: Komposition als Kommunikation. Zur Musik des 20. Jahrhunderts, hrsg. von C. Floros etc., Peter Lang, Frankfurt 2001, S.369-389.

This paper discusses non–octave-based microtonal scales which can express a septimal minor triad formed by the 6th, 7th and 9th partials of the harmonic series. Three methods are proposed for modulating or transferring between each scale: by pivoting on common tones, building joint chords with pitches unique to each scale, or dynamically changing the sizes of generator and period to transform one scale into another. Motivation for this project was to shed light on two relatively unexplored possibilities in microtonality: scales without octaves, and multiple scales within a single piece of music. With today's computers and synthesizers these areas can be explored more easily. The author borrows a goodness-of-fit strategy for a 6:7:9 chord and chooses three scales that divide the perfect fifth into 8, 13 and 18 equal steps. In addition to septimal triads other common tones are identified, e.g. a major seventh 1/6th-tone sharp, and the paper touches on less obvious manners of modulation. This project may be of interest to composers wishing to explore new facets of microtonality in their work.

This essay was originally published in Portuguese as contribution for the book Estudando o Som [Studies on Sound], which was printed as a collection of texts on sound art related to the Brazilian context. The book was published in 2021 by Numa Editora, organized by ChicoDub. Available at: <http://www.numaeditora.com/2021/06/04/estudando-o-som-10-anos-do-festival-novas-frequencias/>. ISBN 978 - 65 - 87249 - 39 – 1.

***

Microtonalities-[limits-locality-points]-discrete interval relations, melodic and harmonic material derived from specific tuning systems, interval subspaces.

Macrotonalities-[of acoustic elements-space-vectors]-continuum, total sound field, latent space of timbre, textures, noises, field recordings.

Metatonalities-[self-reflexive systems-functions-topological spaces]-possible life forms, transculturality, diverse practices, locale.

***

What follows are notes, references and preliminary personal research about microtonality and its unfoldings in sound-music theory and practice. The thoughts presented here emerged from different readings, personal and collective shared observations and experiences. This text is not intended to be a definitive, normative or overly precise theory about mathematical and acoustic matters concerning human cochlear perception, nor a project for any precise tuning system. About all the imperative affirmations, I can only state that they are personal poetic and methodological positions. Several of the more “literary” speculations presented in this text are “mental images”, attempts at creating analogies and means of signification for a too abstract phenomenon, as old as music itself: sound. Some of the speculative propositions operate as “crossing points” between different scales of analysis – as schemas for hypotheses and reflective models of the matter in question.

During the 1980s, Julien Jalâl Ed-Dine Weiss, founder of the Al-Kindi ensemble of Aleppo, invented a qānūn in just intonation with which he attempted to solve a major discrepancy between the theory and practice of maqām-scales. Weiss objected to the introduction of Western standards, observing that they distort the significance of interval ratios and prevent a comparative understanding of the modal system as a transnational phenomenon. In the twentieth century, the implementation of equal-semitone temperament emerged simultaneously with a notable invasion of sociological criteria into musical inquiry. The polarity observed between westernisation and tradition can be seen most visibly in the present search for identity amongst Middle-and Near-Eastern musicians, but this schismogenic process can also be observed in the history of the Western avant-garde, where microtonal explorations have been halted in favour of extra-musical conceptuality. While cross-cultural musicians are faced with a new climate of distrust, it seems most likely that the principles that draw us apart may originate in the very patterns of thought in which our notion of culture operates. Weiss's tuning system may serve as a helpful tool to foster a new and universal epistemology of tone, bridging and transcending the apparent contradictions between the two spheres.

Microtonal music is gradually developing a more important role in contemporary music. Also the mathematical theory of
tuning has developed lately, and it is providing composers with an opportunity to explore tuning beyond simple
speculation or intuition. This thesis is the description of my own experiments with the tuning system of 31 equal divisions
of the octave, using two works I composed for the Fokker organ ? the 31edo pipe organ at the Muziekgebouw aan?t Iij
concert house in Amsterdam, the Netherlands. The target audience of this thesis is not only theorists but also composers
looking to get a starting point in microtonal music and to enlarge their harmonic knowledge. Audio examples, either from
performances or created on a computer, are given, providing hearable evidence of the techniques used.
The core of the thesis is divided into two main parts: first, the theory behind the music is presented, including a short
presentation of Just Intonation, commas, and the meantone temperament. Then, four relevant commas are described
through the way I used them in the two 31edo works I have composed so far. Although most of the text is presenting the
mathematical theory of the commas, I have attempted to describe my subjective experience of each comma in particular.
In other words, I have attempted to give a concrete example of how to convert equations into music.

"The discoveries offered here open the ear and the heart to what was within us all along. I do not mean the mere allure of reaching outside the cage of equal temperament, but rather the truth that this liberative gesture represents: an ancestral, unbounded sound, a free space of play, feeling, and purpose, a vibratory field of possibility spanning humankind’s thousand centuries."

Album link: https://hafezmodirzadeh.bandcamp.com/album/facets