Chromatic Scale Construction in Ancient China

Guangming Li

Music theory is an essential part of Chinese music and culture. Its centrality to understandings of cosmology and social order may seem familiar to music theorists trained in the European tradition. Yet because the distinct characteristics of Chinese music theory have only rarely been incorporated into discussions within the history of Western music theory, exploring corresponding approaches to questions such as tuning and scale generation remains a meaningful point of departure. This was demonstrated in the Global Perspectives in Histories of Music Theory conference at Columbia University in February, which showcased the impressive scale and potential of engaging across cultural contexts.

In addition to learning from a range of excellent scholars, I had the opportunity to present my own research on the construction of the chromatic gamut as first recorded in an exchange between the King Jing (d. 520 BCE) of the Eastern Zhou period (770 BCE – 256 BCE) and the court music official Ling Zhoujiu. In this exchange, Zhoujiu mentions the creator of the chromatic scale, describes the purpose for creating pitch reference, the name of the tuning apparatus, and the twelve disyllabic names, among other things. Yet, Zhoujiu offers no direct explanation for how the pitch reference was created and how the twelve disyllabic names were selected.

At present, Chinese music theorists rely on a method called the “a-third-removing-extending” (or ATRE) technique to explain the process of generating a chromatic gamut. Akin to the cycle of fifths, the ATRE method was first recorded in Guanzi, an encyclopedic treatise that dates from the seventh century BCE.  While the ATRE can generate a complete chromatic scale, it cannot account for the scale introduced in Zhoujiu’s exchange with the King.  For instance, it fails to address the two major-third-chains in the pitch name pattern of the chromatic gamut in the process of generating fourths and fifths.

For the purpose of this post, I will explain the basics of the ATRE method and briefly discuss the motivation for my own research on a new understanding of the ancient method for generating the twelve standard pitches.

“A-Third-Removing-Extending” Method

The details of this classical method for generating the pentatonic scale are found in Guanzi, which is named after the philosopher Guan Zhong (719-645 BCE).  Famed for his achievements as the Prime Minister of the Qi State, Guang Zhong came to be called the “Pioneer of the Legalists,” “The Teacher of the Saints,” “First Prime Minister of the Land,” and worshipped as a divine figure by Daoists.  The mathematical process of constructing a pentatonic scale, known as “三分损益,” which I translate as the “a-third-removing-extending” (ATRE) method, is found in a chapter entitled “Diyuan” of Guanzi. The five monosyllabic names for each of the scale degrees in the pentatonic scale are gong, zhi, shang, yu, and jiao.

This process can be illustrated as the following: begin by stopping on a horizontal string at any point no less than 1/4 of the original string length from the left, and pluck the string on the right. Take the tone from the vibrating portion of the string as the initial length, gong (arbitrarily assigned to C4). To obtain the next pitch, zhi (G3), extend ⅓ of the string length of gong (C4) leftward; to obtain the next pitch shang (D4), stop at ⅓ of the string length of the zhi (G4) from the left; to obtain the next pitch yu (A3), extend ⅓ of the string length of the shang (D4) leftward; to obtain the last pitch jiao (E4), stop at the point ⅓ of the length of the yu (A3) from the left.

Arranging these sequences of ratios in an ascending order based on the ratio results in an ascending pentatonic scale: zhi(G3)-yu(A3)-gong(C4)-shang(D4)-jiao(E4).

Figure 1. “A-Third-Removing-Extending” Method (designed by G. Li)

Limitations of “A-Third-Removing-Extending” Method

Meanwhile, in his reply to King Jing, Zhoujiu introduces the names of twelve standard disyllabic pitch names in a complete chromatic scale.  They are: huangzhong, dalü, taicu, jiazhong, guxian, zhonglü, ruibin, linzhong, yize, nanlü, quyi, yingzhong. The relationship among these pitch names in the Western chromatic scale are C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, A#/Bb, and B. The process of applying the ATRE method to construct a complete chromatic scale commonly found in Chinese classics (e.g. in Lüshi Chunqiu, 241BCE) is as follows:

huangzhong (C ) – linzhong (G) – taicu (D) – nanlü (A) – guxian (E) – yingzhong (B) – ruibin (F#/Gb) – dalü (C#/Db) – yize (G#/Ab) – jiazhong (D#/Eb) – wuyi (A#/Bb) – zhonglü (F).

Figure 2. Chromatic scale based on the ATRE method and the issue of major third chains (designed by G. Li)

However, this method cannot account for the appearance of major third chains in the pitch-naming pattern of the gamut. Two major third chains are found among pitches at even number positions in the gamut, and assigned a common suffix-like morpheme in their names. The pitches jiazhong (4), lingzhong (8), and yingzhong (12) share a common morpheme zhong and they form a chain of major thirds Eb4-G4-B4; the pitches dalü (2), zhonglü (6), and nanlü (10) share a common morpheme lü and they form a chain of major third Db4-F4-A4.

Given that the series of pitch names appeared in an official record that captured dialogue between the King and his music director, the particular sequence of major thirds is not likely to be the music director’s spontaneous creation, but rather a reflection of a well-established convention.  Further, the fact that the music director did not refer to the ATRE method suggests the possibility that a different method of directly building on major thirds and the chromatic gamut could have been applied.

By drawing together a linguistic analysis of ancient texts with acoustic principles and string performance techniques, I offer a different method for constructing the chromatic gamut called the “harmonic-and-stopped-tone-mutual-converting” (or HSTMC) method. Based on ancient Chinese zither design and existing performance techniques, the HSTMC method could have easily been obtained on a monochord. This is based on the fact that a single-stringed zither or yixianqin (akin to the monochord) was commonly known in antiquity.  And given that the historical text describes the creator of the chromatic pitch system as a “divinely blind” music master, the HSTMC method requires only understanding the physical behavior of the string through haptic touch, without the aid of mathematical calculation or the ATRE method.  When applied, HSTMC better corresponds with Zhoujiu’s numerological description of pitch system construction and better aligns with the tenets of Chinese natural philosophy.

Details of the HSTMC method for generating the chromatic gamut remain forthcoming in a paper titled, “New Findings on Non-mathematical Methods of Constructing the 12-tone Chromatic Scale with the Monochord in Ancient China.” This study not only enriches understandings of music theory and music culture in ancient China, but also affords a new perspective on understanding Western music theory beyond exercises in abstract mathematical contemplation.

 Special thanks to Leon Chisholm, Carmel Raz, Nori Jacoby, and Lan Li for their assistance and feedback in writing this post. Special thanks also to the Heyman Center for the Humanities at Columbia University and the Global Perspectives in Histories of Music Theory Conference.

Guangming Li, PhD (UCLA), is a scholar, performing artist, and educator.  His areas of research include issues in music archaeology and history, music theory, music cognition, and music aesthetics.

Some Reflections about Thoroughbass Pedagogy Today

by Peter van Tour

In recent times, quite a few European conservatories have been reintroducing thoroughbass methods in their music theory curricula.[1] The surge of interest in these methods, commonly known as “partimento,” has led to a reevaluation of theory pedagogy more broadly. While this development testifies to a generally healthy trend towards integrating the various subdisciplines in music theory, it also raises questions.

Thoroughbass methods may have a lot to offer in terms of stimulating fluency in playing and of integrating practical playing and singing with theoretical reflection. However, the modern student may ask whether it is really necessary to learn yet another “harmonic” system, not to speak of the practical thresholds of reading C-clefs, which appear unavoidable in the teaching of partimento.

Since I, from time to time, am invited to talk about such issues at conservatories and since I regularly experience both the benefits of the method and the hesitations of students and teachers, I would like to take this opportunity to describe some of my practical experiences. How might some aspects of partimento practice be successfully integrated into modern music theory curricula?

A first and obvious benefit of partimento pedagogy is that its exercises enable the student to work practically with simple textures. Most Neapolitan partimenti are optimally realized in three voices, especially in partimenti with a rather contrapuntal texture. Today it seems that we have limited our attention to four-part harmony to such extent that we have forgotten quite a lot about the appeal of three-part style.

Secondly, the Neapolitans were very much aware of the necessity of practical singing and playing in their education in music theory: they talk about “contrappunto prattico,” and written two-part contrapuntal exercises are termed “solfeggi.” In other words: anything you write should be sung and played.

Thirdly, the Neapolitans were never afraid of clichés. Harmonic and contrapuntal clichés were, in fact, the cornerstones of their teaching in composition.[2] But—and this is essential—these clichés were always varied in numerous ways, in both performance and written exercises.

In my own teaching in aural training at the Royal College of Music in Stockholm, I developed in the past years a common practice at the start of my lessons, of having students play back short three-voice phrases that I then modified in various ways. In my classroom, I had two pianos placed with their backs against each other and played phrases that my students could play back directly afterwards. I offered these exercises to students who studied Western classical music in a Master’s program in choral conducting and / or orchestral conducting. As part of their curriculum they received individual lessons in aural training of ca. 45 minutes a week.

Such a lesson could start something like this:

• I inform the student that the exercise will be in the key of A minor.
• I play a bass line of just a few bars and ask the student to play it back as accurately as possible.[3]

[bass line]

• As soon as the student has managed to imitate the bass line, I add a second voice over this bass and ask the student to imitate the two voices, playing the bass line in the left hand and the upper voice in the right hand.

[bass line + voice 1]

• I repeat this procedure, now with a different upper voice. Like this:

[bass line + voice 2]

• As soon as the student has managed to play this second voice over the bass line, I play them once again together and ask the student to play all three voices. Like this:

[bass line + voice 1 + 2, variant 1]

• After the student has managed to put this together, I play a new and modified version and ask the student to play it back.

[bass line + voice 1 + 2, variant 2]

• I repeat this procedure once again, now with a few other changes.

[bass line + voice 1 + 2, variant 3]

Now, this is of course just a very short example of how playful attitudes in historic milieus can be reused to make music theory lessons more attractive. Such exercises can, of course, be varied in many different ways, both musically and pedagogically. An exercise like the one above allows the student not only to get acquainted with a typical harmonic formula (or cliché), it also teaches how such formulas can be modified and elaborated on. In other words, it teaches not only the standard clichés in eighteenth-century music, but also the playful attitudes through which such music was improvised or composed.

Especially when I use fragments that are taken from larger exercises, I find it useful not only to show the exercise in its entirety, but also to give the student examples from famous classical works in which these models appear. After having worked practically with this kind of models, the student will inevitably recognize the models in real music.

Finally, I would like to emphasize that in many cases it is not really necessary to put too much emphasis on thoroughbass figures. They can be used as an aid in the student’s aural orientation and I thus use figures for memorizing fragments that are later varied in many ways. What at first may appear to be a burden of yet another system may in fact become a playful way of engaging in musical clichés, enabling students to recognize commonly used patterns in the music that they play and listen to.

Together with other authors who have started to develop new teaching materials in this vein, I believe in the pedagogical value of these trends, of integrating aural skills training into the training of counterpoint and harmony.[4]

[1] See, for example, David Lodewckx and Pieter Bergé, ”Partimento, Waer Bestu Bleven? Partimento in the European Classroom: Pedagogical Considerations and Perspectives.” Music Theory and Analysis 1/1-2 (2014): 146–69.

[2] See: Robert Gjerdingen, Music in the Galant Style (Oxford: Oxford University Press, 2007), Giorgio Sanguinetti, The Art of Partimento: History, Theory and Practice (New York: Oxford University Press, 2012).

[3] This particular example is adapted from Carlo Cotumacci’s first disposition and was taken from: [24] Disposizioni a tre, e quattro parti, ossiano Partimenti Del Sig.^r Carlo Cotumacci.” MS: I Mc Noseda E 66-16, olim 7759. Cotumacci was teacher of counterpoint and composition at the Conservatorio di Santa Maria di Onofrio in Naples between 1755 and 1785.

[4] A few examples that may be mentioned here are Lieven Strobbe’s Tonal Tools for Keyboard Players (Garant Publication, 2014) and Job Ijzerman’s forthcoming book on harmony (Oxford University Press) in the field of harmony, and Peter Schubert’s Modal Counterpoint: Renaissance Style (Oxford: Oxford University Press, 2008) and Barnabé Janin’s Chanter sur le livre: Manuel pratique d’improvisation polyphonique de la Renaissance (Lyon: Symétrie, 2014) in the field of counterpoint.

Peter van Tour is visiting professor at the University of Leuven in Belgium. His PhD dissertation Counterpoint and Partimento: Methods in Teaching Composition in Late Eighteenth-Century Naples was recently awarded the 2016 Hilding Rosenberg scholarship in musicology by the Royal Swedish Academy of Music. In his current research, Peter is investigating fugal improvisation in Italy and Germany between 1680 and 1720.

Global Histories of Music Theory

Global Histories of Music Theory is a conference that will be held at Columbia University in New York on February 20, 2017. In the days leading up to the conference, we interviewed the two organizers, Carmel Raz and Lan Li, about their ideas and the experience of interdisciplinary collaboration.

HoT Blog: What inspired Global Histories in Music Theory?

Carmel Raz: I was really inspired by the past SMT History of Theory Interest Group panel with Thomas Christensen and Roger Grant around the genesis, production, and future of The Cambridge History of Western Music Theory (2002). A lot of the discussion focused on strategies for expanding the purview of our field beyond the Western context, and this connected with some of the conversations I’d already been having with my friend and colleague Lan Li, a historian of science and highly accomplished guzheng player, as well as with my colleagues Nathan Martin and Drew Hicks, both of whom contributed expertise and ideas at different stages of planning this event.

HoTB: How did your collaboration come about?

Lan Li: One of our first conversations was about the Otamatone, and Carmel’s ears perked up when I suggested potential parallels with the erhu in Chinese music. Much of our collaboration has been extremely serendipitous ever since. Both of us are coming to this conference with different goals in mind specific to our disciplines, but we also share this genuine interest in thinking beyond disciplinary boundaries as we both were trained in interdisciplinary programs.

CR: Basically since the moment I met Lan I was hoping we’d get a chance to collaborate. Lan has a really original and interesting perspective as both a musician and a historian of science, so it was really exciting to discover our interests converging around global histories of music theory.

HoTB: Lan, as a science historian, how does your work intersect with music theory?

LL: I’ve increasingly found music theory as a source of inspiration. My own research involves a comparative history of medical theory, which might be a sort of counterpoint to music theory. There are a number of overlapping concepts in theories about the nature of the body and the nature of music that emerged from the same cosmology. For instance, it’s fascinating to me how theories of Yin and Yang were used to organize 12 pitches in the chromatic scale, in the same way that theories of Yin and Yang were used to classify the 12 meridians in the body (which are still used today). The divergence, perhaps, emerges in questions about historical ontology, which I’d like explore further in this conference.

HoTB: You’ve brought together scholars from an array of disciplines, including musicology, music theory, ethnomusicology, history, history of science, and area studies. Do you think that a global history relies on such collaboration? In what ways do you see it enriching the history of music theory?

CR: The history of music theory is already a very interdisciplinary corner of the field, drawing on music history and theory as well the histories of science, mathematics, philosophy, religion, ideas, and many more. Of course, we have much to learn from other methodological approaches, particularly with respect to global history. But I also believe that our training as historians of theory can help us contribute to broader debates around questions of global flows of ideas, sounds, and instruments.

LL: Right, the same goes for history as a field. Global history, or comparative frameworks, demands new approaches to sources that are in different languages and from different sociopolitical circumstances. For instance, I found literature in transnational feminism to be extremely useful in writing an article about films featuring amateur physicians in China. So, many assumptions don’t hold when we shift into a different context. I’ve also found literature in cultural anthropology, STS (science technology and society studies) literature, architecture, and media studies to be particularly helpful in reframing my own assumptions to approach sources with a new perspective.

HoTB: Carmel, do you see the comparative project underlying this conference as signaling a larger trend in historical studies of music theory?

CR: I certainly hope so! We added an “emerging scholars” component to this conference precisely to encourage early career researchers working in various disciplines to identify their work as history of music theory.

HoTB: “An Evening with the Monochord” is a focal point of the conference. How did the monochord become so central to the program?

CR: We decided to structure the evening panel around the monochord, as an instrument which really makes measurement both visible and audible. It is also found in a large number of cultures, so we thought it could serve as a great departure point for a broader discussion around the nature of a global history of music theory.

LL: Right. I also think that for historians of science, the monochord brings together concerns about measurement and mathematics on the one hand, while also stretching across natural philosophy and cosmology on the other.

HoTB: What have you learned about each other’s disciplines through this collaboration? What have you learned about your own discipline?

LL: Being able to peek into another discipline is such a privilege. It’s also reminded me that interdisciplinary work is not intuitive. We really have to learn how to find common ground. It’s fascinating to me that historians of music theory are also practicing music theorists, and to a certain degree historians of medical theory engage with a range of body practices to explore different ways of knowing.

CR: I’ve learned that there is so much curiosity and good will in both music theory and the history of science, as well as a genuine desire to communicate across disciplinary boundaries.

HoTB: Thank you so much for letting us in on some of your visions for this event. We hope it will inspire vivid dialogue, and we are looking forward to hearing more about it!

Schema Theory and Aesthetic Categories in North Indian Classical Dhrupad

Sumitra Ranganathan

bani (lit. word or sound) is an elusive concept in the performance of Dhrupad, a genre of north Indian classical music with medieval origins that circulates in oral tradition. Historical sources refer to four distinct banis: gaurhar, dagur, khandar, and nauhar. A fifth bani, shuddh, combines the characteristic effects of other banis. Today the concept of bani is mired in debate. Some musicians use the word to describe their entire style. Some say it applies only to the domain of composition, while others apply it to improvisatory sections of performance.  Many say that the word has little relevance to current practice. Meanwhile, in scholarship, some musicologists have tried to map it to musico-aesthetic forms in twelfth-century treatises.[1]

However, the expert Dhrupad musicians I work with—who are descendent from multiple lineages associated with the erstwhile Princely court of Bettiah, Bihar—have a clear conception of what bani is. Based on substantial traditional repertoire and a continuous oral tradition, they understand bani as an aesthetic concept that categorizes stereotypical aesthetic experience with specific musical characteristics and distinctive perception effects in Dhrupad performance. It is best distinguished within the well-defined structure of a Dhrupad composition, but can also be invoked in improvisatory sections of performance.

Here is an excerpt from a gaurhar bani Dhrupad composition. Listen for its characteristic perception effect: “a feeling of space.”

Example 1: excerpt, gaurhar bani Dhrupad, composer Maharaja Anand Kishore Singh of Bettiah, raga sampoorna hindol, tala chautal (sung by Indra Kishore Mishra, Chennai, August 2009).[2]

The Dhrupad banis serve as a case study to investigate whether and how aesthetic categories function meaningfully as conceptual models in composition and performance without necessarily constraining performance by a universal set of rules. I had to contend with some limitations while conducting my research—there are very few references to Dhrupad bani in written sources prior to the nineteenth century and even fewer recordings from the early twentieth century. I hence focused on oral tradition and handed down repertoire to investigate them more generally as musical concepts.

durga anand sagar, a 19th-century bhojpatra (birch leaf) manuscript contains the Dhrupads of Maharaja Anand Kishore Singh. Only portions of this manuscript in tattered condition are available with Bettiah’s hereditary musicians.

To understand the banis musically and conceptually, I investigate the cognitive processes through which musicians perceive, stabilize, interpret and communicate them. In developing an analytical framework, I found work on schema theory and categorical thinking in music to be particularly useful. My use of the term schema is consistent with Frederick Bartlett’s definition that emphasizes both the experiential and heuristic character of schemata.[3] Within Western art music, Robert Gjerdingen’s analysis of eighteenth-century style is based on some fundamental claims of schema theory first proposed by Leonard Meyer: (i) prototypical features (schemata) are extracted based on repeated exposure to a musical situation; (ii) they lead to the abstraction of stylistically appropriate mental templates that produce meaning and manipulate expectation during listening; and (iii) such interpretive context is historically and stylistically specific.[4] An important implication of schema theory is that templates function top-down, even if the activation of a template in any given situation occurs bottom-up. Schemata produce approximate models of higher-order musical situations that provide interpretive context, which can be activated by the detection of a sub-set of lower order compositional devices and stylistic figures. (I’ll call these sub-schemata). Schemata are hence basic to the organization of conceptual knowledge, and the cognitive processes of expectation and recall.

In the context of Dhrupad performance, heuristic schemata support and stabilize the aesthetic category of bani. Perception effects operating as higher-order schemata distinguish the overall aesthetic of each bani. As a case in point, all the musicians in my project have said at different times that the overwhelming perception of gaurhar bani is a stretching of tonal space, or a “feeling of space.” An attendant category of perception is a slowing down of time. The evidence for this includes verbalization of the experience, gestural and bodily actions, sensory and bodily memory maps, effort metaphors, analogies, pedagogical instruction and misunderstandings with accompanists in finding the pace of the song.

Compositional and interpretive performance strategies manipulate the interaction between melodic phrase, lyrical phrase and metrical structure to produce the characteristic aesthetic of each bani. These strategies often employ sub-schemata. For example, sub-schemata that work together to produce the gaurhar bani’s characteristic perception effects include (a) the sparsity of musical events reflected by a low syllable-to-note ratio, (b) the masking of strong beats in the tala (underlying metric cycle) by the use of glides and vowels, (c) the use of large loops and loops within loops in executing melismatic phrases, and (d) the use of a series of small gliding arcs to traverse ascending or descending melodic phrases. The song excerpt below exhibits several of these features.

Example 2: excerpt, gaurhar bani Dhrupad, composer Maharaja Anand Kishore Singh of Bettiah, raga bahar, tala chautal (sung by Falguni Mitra with long-term accompanist Apurbalal Manna pakhawaj, Biswanath tanpura, Kolkata, March 2015).

The activation of interpretive context and (top-down) schemata is fundamental to the cognitive function of sub-schemata in maintaining the distinction between banis in performance. This has at least two implications. First, for experienced performers of gaurhar bani songs, a piece of notation can immediately invoke the mental schema of gaurhar bani if any of its common sub-schemata are encountered. As an example, the fragment in the example below is a simple ascending line. In most other Dhrupad traditions, it would be sung in a plain, even staccato manner. However, in the Bettiah lineage of Indra Kishore Mishra, the ascending line is executed using a series of small arcs that connect the notes in a stretching of tonal space.

Example 3: excerpt, gaurhar bani Dhrupad, composer Maharaja Anand Kishore Singh of Bettiah, raga bhairavi, tala sadra (student demonstration, Chennai, January 2010).

The second implication concerns the status of particular stylistic ornaments as lone-standing evidence of a bani’s aesthetic. Ornaments do not function as sub-schemata by themselves. Rather, sub-schemata should incorporate these ornaments in ways that invoke the interpretive context of the bani. For example, the mere presence of loops, glides, arcs (all called by the generic term, meend) does not constitute evidence of gaurhar aesthetic. These ornaments must occur within sub-schemata such as ascending lines, descending lines, loop within loops, hidden strong beats, etc. to prompt the perception of schema characteristic of gaurhar bani enough times in the piece to transform the listening experience. The musicians of the Bettiah gharana have repeatedly demonstrated the distinction to me with examples to drive the point home.

This observation counters one of the prevalent misconceptions about banis amongst both musicians and analysts, many of whom conflate the presence of stylistic figures alone with the creation of an aesthetic. Schema theory also helps us understand why the aesthetic category of bani is perceived more readily within the bounded, repetitive structure of a Dhrupad composition. In contrast, the improvisatory sections of a Dhrupad performance (alap) may only engender fleeting experiences of categorizable aesthetics.

As these few examples illustrate, musicians use many different kinds of schematic knowledge to interpret and communicate stereotypical aesthetic experience in Dhrupad performance. Other dimensions that prompt bani schemata include choice of tempo, choice of raga, and lyrical meaning—topics for a more detailed analysis. Far from making the aesthetic category of bani meaningless, such fluid and multi-dimensional decision-making supported by schemata significantly increases the number of expressive possibilities in composing, interpreting and performing Dhrupads.

Acknowledgments: A big thank you to Leon Chisholm, Stephanie Probst and Preeti Rao for giving me the impetus to extend my dissertation work, a dimension of which is discussed here. Without Leon’s help editing, this blog post would not exist.

[1] For a review of the Dhrupad banis in literature and oral tradition, see Ritwik Sanyal and Richard Widdess, Dhrupad: Tradition and Performance in Indian Music (Aldershot: Ashgate, 2004)Their analysis is both preliminary and inconclusive, however, as it does not include the musically significant oral traditions and traditional corpuses that are the source material for my study.

[2] All recordings included here are field recordings done during the course of my research.

[3] Frederick C. Bartlett, Remembering: A Study in Experimental and Social Psychology (London: Cambridge University Press, 1932).

[4] For schema theory in Western art music see Leonard B. Meyer, Explaining Music: Essays and Explorations (Chicago: University of Chicago Press, 1973), Robert O. Gjerdingen, A Classic Turn of Phrase: Music and the Psychology of Convention (Philadelphia: University of Pennsylvania Press, 1988), and Vasili Byros, “Towards an ‘Archaeology’ of Hearing: Schemata and Eighteenth-Century Consciousness,” Musica Humana 1/2 (2009): 235–306.

With aspiring Dhrupad musicians in Bettiah, Bihar, Oct. 2010

Sumitra Ranganathan received her Ph.D. in Music from the University of California, Berkeley (2015). Her interests include theories of tradition, performance and aesthetics. She uses approaches from music cognition, music theory and the anthropology of the senses to investigate senses of tradition, intelligibility and categorical knowledge in Indian classical music.

Reflections on the Sixteenth Annual Congress of the Gesellschaft für Musiktheorie

Compiled from the reports of Britta Giesecke von Bergh, Sören Sönksen, and Katharina Thalmann

The Sixteenth Annual Congress of the Gesellschaft für Musiktheorie (GMTH) was held in Hanover from September 30^th to October 2^nd, 2016. Over 150 members of the society from Germany, Austria and Switzerland attended the meeting, along with guest participants from countries around the world, including Belgium, Canada, Croatia, Hong Kong, Israel, Portugal, Russia, the UK and the US.

The conference was dedicated to the controversial topic of Klang. The conference theme “Klang: Wundertüte oder Stiefkind der Musiktheorie,” (vaguely translated in meaning as “Klang: music theory’s magic horn or neglected child”) itself speaks to the multiple meanings that the category has assumed in music-theoretical discourses. The program reflected the different connotations in bringing together presentations on the relevance of Klang in (post)avant-garde composition with critical reflections on the problems that Klang poses in music theoretical frameworks. In her opening remarks, Gesine Schröder, president of the society, emphasized the opportunity of the conference as a valuable chance to invigorate dialogue among different approaches.

Certainly, the diversity in approaches and thematic clusters of the program—with almost 90 presentations—put to rest any concerns about a limited range of perspectives. The lectures were grouped in various thematic sections, such as “Klang as analytical category (not only) in new music,” “History of music theory,” “Klang as object of composition,” “Sound in pop and rock music and in film,” “Instrumentation, orchestration, registration,” and “Creation of theory.” Throughout, Klang was portrayed as a significant compositional parameter, in contexts ranging from classical orchestration to electronic music. Methodologies included spectral analysis, Helmut Lachenmann’s theories of Klang, and approaches derived from linguistics.

On the first morning of the conference, philosopher Christian Grüny addressed the challenges that Klang poses for music theory. He demonstrated the inadequacy of terminology and analytical strategies in German music theory through the difficulty in describing the individual timbres of the human voice and other sounds. This criticism of Klang as an auxiliary to tonal structures rather than as an independent parameter in its own right reverberated in later talks.

Other presenters dealt with similar challenges in different ways. Mario Schmidt drew on Theodor W. Adorno’s theory of Klang in terms of a color for composition. Through the example of György Ligeti’s Atmosphères, Schmidt illustrated how color can structure a work and override other parameters like rhythm. Benjamin Sprick approached Klang through the theories of French philosopher Gilles Deleuze. Sprick’s imaginative analogies—including thunder storms, lightning, and sugar water—underscored how Klang can also be understood as a sensation.

The historical purview of the conference presentations was well spread across music and theory from the 16^th to the 21^st centuries. Presenters drew attention to historically differentiated perspectives on the function of Klang in this long compositional history. Friedmann Brennecke discussed the augmented triad as a phenomenon of compositional technique in the 16^th and 17^th centuries. Ojla Janjuš analyzed topoi in Lieder by Alexander Zemlinsky in the context of symbolistic instrumentation practices. And Jonathan Stark proposed an analysis of Gustav Mahler’s orchestration techniques by comparing his Lieder with piano accompaniment to their fully orchestrated versions.

Ariane Jeßulat’s lecture on “Phantom Counterpoints” employed a number of intriguing examples from compositions of the Classical era to highlight how skillful instrumentation can engender the resonance of overtones. This potential, which can introduce an added layer of contrapuntal texture, has practical implications for performers. As an example, Jeßulat pointed to an instance in Beethoven’s Fourth Symphony whose potential for “phantom counterpoints” has been exploited only rarely by conductors.

In the analysis section, music theorist and sound engineer Nora Brandenburg deconstructed Klang into various subordinate parameters and traced them in pieces such as Arnold Schönberg’s op. 16 (especially No. 3, “Chord-Colors”), Ligeti’s Atmosphères and Gérard Grisey’s spectralism of the 1970s.

Composer and musicologist Wolfgang-Andreas Schulz portrayed the appeal of the Aeolian harp in different historical aesthetic contexts—from its popularity in the 18^th century to its negation of Romantic subjectivity, and to its revival by John Cage. David Wallraf shared insights from his doctoral thesis, which takes the genre “Noise” as a starting point for discussions of such fundamental concepts as pitch, sound, quality, and the (possible) borders between them.

Following tradition, a concert took place on the first evening of the conference. Helmut Lachenmann’s Second String Quartet (Reigen seliger Geister, 1989) was exquisitely played by the Daphnis Quartett, a young quartet from Hanover. Under the direction of Stephan Meier, the Neue Ensemble Hannover performed Tristan Murail’s Treize couleurs du soleil couchant (1978) for flute, clarinet, violin, cello, and piano, and Anton Webern’s Symphony Op. 21, two pieces that showcased divergent compositional treatments of the timbral potential of the ensemble. To conclude, the concert featured Frank Märkel’s (Hanover) piano arrangement of Morton Feldman’s Madame Press died last week at ninety (1970), which convincingly combined the repetitive structure of the composition with the isolated presentation of the piano as soloistic generator of sounds.

Volker Helbing and the theory department of the Hochschule für Musik, Theater und Medien Hannover were wonderful hosts, providing a well-organized collegial environment—and great culinary experience!—for all. The next congress will be held in Graz in fall 2017. We’re looking forward to this reunion!

Britta Giesecke von Bergh studied Music Theory and Germanic Studies (with a pedagogical focus) at the Hochschule für Musik, Theater und Medien in Hanover. She teaches music theory and aural skills in Hanover and at the University of Kassel.

Sören Sönksen teaches music theory and aural skills at the Music Academies of Hanover and Dresden. In Hanover, he is also pursuing a doctoral degree with a dissertation on metrical characteristics in piano suites of the 17^th and 18^th centuries.

Katharina Thalmann is an MA student in music theory at the Lucerne School of Music. She spent the past academic year as an exchange student at the University for Music and Performing Arts in Vienna. She holds a bachelor’s degree in piano performance and works as free-lance journalist in Switzerland.

Blog edited by Leon Chisholm and Stephanie Probst

In Dialogue with Rameau: Diderot, Dissonance, and Bemetzrieder’s Leçons de clavecin

Michael Weinstein-Reiman

For this post, I turn to an unlikely protagonist, self-proclaimed bad musician Denis Diderot, polymath of the French Enlightenment.

Illustration de Le Neveu de Rameau, dialogue. Ouvrage posthume et inédit par Diderot (Paris, 1821)

Dissonance takes center stage in Diderot’s Neveu de Rameau, or Rameau’s Nephew, written in 1761, revised substantially in 1773 and 1774, and published posthumously in 1805. Rameau’s Nephew is a dialogue between Diderot and the fictional nephew of Jean-Phillippe Rameau, composer and theorist of the eighteenth century. We learn that the nephew is a rough outcast: he was recently dismissed from his court position on account of his insubordination, a damaging willingness to speak out of turn—to dissonate against the insipid consonance of courtly politesse. Significantly, Rameau’s nephew relishes his dissonance; he insists upon it during moments of musical pantomime. As Diderot scholar Andrew Clark has shown, through the nephew’s body, we are meant to experience dissonance as an integral part of musical and narrative aesthetics.[1]

The depiction of dissonance in Rameau’s Nephew highlights Diderot’s philosophical materialism, informed by his engagement with music over the course of his life. Diderot’s musical materialism was a theory unique among his contemporaries. He imagined the universe to be filled with vibrating, inherently active and reactive matter. Musicians like Rameau’s nephew possessed “readily harmonic” bodies: their natural states, shaped by knowledge and practice, afforded them access to a dynamic and sensual world of bon goût.[2]

Lecons de Clavecin, par M. Bemetzrieder (Paris, 1771)

Interestingly, Diderot’s musical materialism crops up in a contemporaneous document of music theory, Antoine Bemetzrieder’s Leçons de clavecin, or “Keyboard Lessons,” which Diderot edited and saw through to publication in 1771, only two years before he revised Rameau’s Nephew. Like Rameau’s Nephew, the Lessons is a dialogue between a young female keyboardist, her teacher, Bemetzrieder, and Diderot, cast in the role of “Philosophe.” Musicologist Jean Gribenski has illustrated how Bemetzrieder’s unassuming keyboard tutor overlaps remarkably with Diderot’s own philosophical outlook.[3] While provenance and influence are difficult to ascertain, it is likely that Diderot edited the Lessons in order to accentuate these concordances. The most intriguing aspect of the treatise is Bemetzrieder’s theory of the grande dissonance, or “great dissonance,” and the theorist’s principle for the resolution of dissonance, the appel, or “call.” Bemetzrieder formulates his theory as an extension of arguably the best-known music-theoretical principles of his day, the concepts of the fundamental bass and the corps sonore, developed in the first half of the eighteenth century by Jean-Phillippe Rameau.

In his theory of the fundamental bass, Rameau asserted that, within a harmonic progression, every non-tonic harmony contained within it a dissonant seventh, whether or not the seventh was articulated or audible.[4] Rameau’s theories were addled by problems related to musical subjectivity. Even if no dissonance manifested in the non-tonic chords between iterations of the corps sonore, Rameau insisted that the performer or listener imagined a chordal seventh where one ought to have been. Therefore, all non-tonic sonorities were unstable even if there was nothing physically dissonant about them.

Bemetzrieder imagines the “great dissonance”—a chord composed of the pitches B, D, F, and A—as a natural companion to the corps sonore. As the character of the Philosophe, Diderot amplifies Bemetzrieder’s theory thus:

In this great dissonance of the leading tone [sensible], followed by the corps sonore with all its overtones, my ear is offered first all the dissonants [dissonnans] of the scale [game], pure and unmixed, and then the corps sonore and its retinue, with each in their natural position, the scale divided sharply into two portions: on one side that which nature has produced; on the other that which art has conjured to enhance nature and make [nature] desirable. [5]

Given that Diderot edited the Lessons and likely exerted some influence over what his character might say, I underscore here how the Philosophe theorizes musical dissonance. With his insistence on music’s audible and material dynamism, motivated on the one hand by the stability of consonance and on the other by dissonance’s natural expressiveness, Diderot fortifies Bemetzrieder’s pedagogy with his materialist outlook. For Bemetzrieder and Diderot, the scale is an emblem for the vibrant physical interactions among natural phenomena. On their account, every sonority contains the materials for the production of consonance and dissonance. Dissonance does not, as Rameau indicated a generation prior, inhere in sound as an ideational concept; it becomes a productive material state rather than a foreign entity to be purged.

Together, Rameau’s Nephew and the Lessons shed light on a philosophical take on dissonance that is more discursive than empirical. For Diderot, good musical taste was a constant dialogue between consonance and dissonance. And framed as exchanges between people, either real or imagined, Diderot’s texts insist on discourse amid a flurry of eighteenth-century quarrels and polemics.

—
[1] Andrew Herrick Clark, Diderot’s Part (Burlington: Ashgate, 2008), 144.
[2] On the notion of “readily harmonic” bodies, see Matthew Riley, “Straying From Nature: The Labyrinthine Harmonic Theory of Diderot and Bemetzrieder’s Leçons de clavecin (1771),” The Journal of Musicology 19, no. 1 (2002), 23.
[3] Jean Gribenski, “À Propos des Leçons de clavecin (1771): Diderot et Bemetzrieder,” Revue de musicologie 66, no. 2 (1980), 126.
[4] For detailed commentary on Rameau’s fundamental bass theory, see Christensen, Rameau and Musical Thought in the Enlightenment (Cambridge: Cambridge University Press, 1993).
[5] “Dans cette grande dissonance de la sensible, suivie du corps sonore avec tous ses harmoniques, on offre d’abord à mon oreille tous les dissonnans de la game, purs et sans mêlange; puis le corps sonore avec son cortége, et les uns et les autres dans leur position naturelle, la game partagée rigoreusement en deux portions; d’un côté ce que la nature a produit; de l’autre ce que l’art a imaginé pour la faire valoir et désirer.” Bemetzrieder, Leçons de clavecin et principes d’harmonie (Paris: Bluet, 1771), 340.

Photo: Alyssa Tamayo

 

Michael Weinstein-Reiman is a doctoral student in music theory at Columbia University. His research interests include keyboard music, technology, gender, aesthetics, and the history of music theory.

 

 

Blog edited by Leon Chisholm and Stephanie Probst