Dissonant Views on Consonance
The Cultural Dependency of Consonance and its Reinterpretation as Euphony
June 2015 MA Thesis in Arts & Culture: Musicology
First supervisor: Dr. Barbara Titus Second reader: Dr. Rutger Helmers
Author: Tim Ruijgrok Student number: 10633014 Date: 18-06-2015 Contents
Preface ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ 2
Chapter 1 - Consonant views on consonance? ∙ ∙ ∙ ∙ ∙ 4
The cultural approach ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ 5
Chapter 2 - Consonance in the Western discourse ∙ ∙ ∙ ∙ 11
Introduction to the case studies ∙ ∙ ∙ ∙ ∙ ∙ 17
Chapter 3 - European common-practice and tonal consonance ∙ ∙ ∙ 20
The contrapuntal concept ∙ ∙ ∙ ∙ ∙ ∙ ∙ 21
The triadic/tonal concept ∙ ∙ ∙ ∙ ∙ ∙ ∙ 22
The sensory concept ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ 24
Chapter 4 - North-Indian classical music and the (absence of) harmony ∙ ∙ 29
Hindustani music ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ 31
Vādī & samvādī ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ 33
The tritone ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ 37
Chapter 5 - Javanese gamelan and inharmonic sounds ∙ ∙ ∙ ∙ 40
Spectrum and timbre ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ 42
Conclusion ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ 45
Bibliography ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ 47
1 Preface
During the two years of enrolment at the University of Amsterdam, my view towards diverse expressions of music has broadened significantly. Attending the UvA with the intention to potentially increase my knowledge or interest in Asian music, I followed the "cultural trajectory" of Musicology. I was fortunate to study Russian popular music and North-Indian (classical) music, both of which – I can conclude – have enriched my knowledge. I could not come closer to my objective in terms of education, hence I attempted to steer my thesis in that direction… however, to no avail.
Being unable to put my knowledge into practice in my main field of interest, i.e. Asian music, I had to make the ultimate sacrifice and leave this out of my scope. This thesis is the result of a long struggle between my own expectations of it and the actual possibilities I felt I had. However, in its present form, this thesis is heavily influenced by experiences during the classes on North-Indian music and the gamelan class I was invited to by my supervisor. The attempts to emulate the singing of the North-Indian vocal tradition, led by dr. Wim van der Meer, and the efforts to play the gamelan instruments under guidance of dr. Citra Aryandari made me realize – mentally and physically – how different music-making can be. A single impetus in the form of a blog post about a "study on consonance", then, was enough to make me wonder about a variety of implications for the particular music I had experienced up to now.
Thanks
Even though I managed to put all my amazement, enthusiasm and criticism towards the subject together in this research, I did not achieve this solely on my own. I want to express my sincere gratitude to all who helped me with the realization of this master's thesis. My expression of thanks goes to my supervisor Barbara Titus, for all the help and encouragements she has given me during our meetings – and for inviting me to the gamelan class! Also, I am especially grateful to my distant but close friend Adrienne Prudenciado for proofreading my thesis and offering countless corrections on my writings. Last but not least, I want to thank my parents and brother for all the emotional support they have given me over the past year.
2 Thesis outline
This thesis is a literary study on the concept of consonance, and will focus particularly the alleged universal application of the concept. As I will show, consonance is a term with apparent semantic problems, and not many satisfying solutions or explanations have been formulated up to now. In spite of this, consonance is often treated as a monolithic concept, and its usage outside the context of Western tonal music is, consequently, often faulty or neglected. By approaching consonance as a form of "euphony", I hope to (re)address the issue of the cultural dependency of consonance, and show that consonance employs many different dimensions that cannot be viewed similarly between musical cultures. This will be exemplified with three case studies in which I will zoom in on the operation of euphony within specific musical cultures.
The aforementioned ideas and problems will be dealt with in five chapters. Chapter 1 will introduce the reader with the term consonance, and the cultural approach that has been advocated decades ago. This cultural approach is taken up by introducing the more neutral term euphony, of which its benefits will be outlined, as well as applied in later chapters. Chapter 2 will provide the reader with an introduction on consonance within the Western discourse, including a brief literary review of important studies on the subject. It will concluded that most views regarding consonance are primarily functional and based on the European tonal music theory. This limitation will be the starting point of the three case studies, in which a particular musical culture will be examined to make clear how diverging notions of euphony actually are. Chapter 3 addresses euphony in the European common-practice, with the goal to trace this generic and limited view on consonance. This formulation will be identified as a conflation of 18th-century ideas of euphony. Chapter 4 will challenge the mutual relationship of consonance and harmony. Additionally, I will turn the discussion to North-Indian classical music to investigate how euphony is seen in a musical practice with a static harmonic background. In this case, the melodic handling of consonance, and the flexible nature of a rāga move away from the fixed and functional approach to euphony. Chapter 5 will offer a totally different view on euphony in Javanese gamelan music by emphasizing the relation between spectrum and scale. It will be highlighted how the scales employed in Java are logical and have a high euphonious value as a result of the spectra of the instruments used. This will all point to the conclusion that consonance is not universal and is dependent on the musical culture in which it operates, and that euphony proves to be a broader and more appropriate concept to address the issue outside the Western discourse.
3 Chapter 1
Consonant views on consonance?
In daily conversations, consonance is often treated as a monolithic concept of which people tacitly assume others know what they are talking about.1 A simplification of the term is evident especially in musical education, where it is taken for granted that particular chords or intervals are consonant and others are not. While it seems that consonance is generally understood in the same way, the contrary is true. Consonance is like culture; a term that immediately confronts one with inevitable semantic problems. Shifting meanings and uses of consonance in the course of history, the result of different cultural and discursive environments, have troubled many scholars in defining the concept in a satisfactory way. So many thoughts, meanings and theories about consonance have been formulated, that a clear-cut definition has not yet been coined – which is, astonishingly, practically impossible. Therefore, before delving into deeper discussions of the subject, we first have to address some fundamental aspects regarding consonance.
The most crucial aspect of consonance is its varied usage, which is determined by its meaning and the context in which it operates. Is it a quality of a tone? Is it purely a music-theoretical term? Is it part of a practice? A social construct? An experience or value judgment? In fact, all of these attributes can apply, which is the reason why consonance cannot be viewed as a monolithic concept. Some encyclopedic sources like Grove Music Online acknowledge this multiplicity of usages and distinguish an acoustical, psychological, musical and perceptual meaning. In Western tonal music, however, consonance is mostly treated as a music-theoretical term. Within this contracted view, different meanings can be derived by closer examination. Take the interval of a fourth, for example. Regarded as a consonant outside musical context, it may be seen as a dissonant in certain chord inversions within the contrapuntal practice. The same is true for the tritone, but indicating the exact opposite (Gauldin 2004: 17). In acoustical science, however, the intervals would be either consonant or dissonant depending on the frequency relations of their sound waves. Thus, in this case, one may observe a difference between consonance used as a term, as a musical practice, or as tonal quality, related to two discursive environments.
One can extend this idea further than most theoreticians do. The ambiguous state of the term consonance makes it very likely that its change in meaning is not limited historically, but likewise culturally. This step is seldom addressed in academic writings about the subject of
1 When discussing consonance as a concept, I also mean its antonym dissonance, unless explicitly stated.
4 consonance. Surprisingly Robert Gauldin, in his Harmonic Practice in Tonal Music, hits the nail on the head regarding this issue. He says:
There must be more to the question of consonance and dissonance than mere physics, however, or people of all cultures and historical periods would define the terms in the same way. (Gauldin 2004: 17)
Even though it was just mentioned in passing, I would contend that Gauldin is right to say that neither historically nor culturally, consonance has ever had the same meaning. The first claim, that meanings of consonance changed historically, is acknowledged by many academic writers such as Norman Cazden (1945; 1980), William Sethares (2005), Richard Parncutt & Graham Hair (2011), to name a few. Additionally, it is the core assumption of James Tenney's book A History of "Consonance" and "Dissonance", which is one of the key works on the subject. The latter claim, that meanings of consonance differ culturally, is mostly not addressed. Fortunately, there are exceptions to the rule.
The cultural approach In the Western discourse of consonance, there are at least two calls for a "cultural approach" towards consonance, both of which seemed to be voices calling in the wilderness as no one extended on these topics (see Lundin 1947; Cazden 1945). Note that both sources are considerably dated, and their content is not taken into account by later writers. If they are cited, it is often with the remark that "familiarity and learning are an important aspect" to the perception of consonance (Parncutt & Hair 2011: 146). Familiarity and learning are not only important to these writers, but altogether crucial. Both Lundin and Cazden agree that judgments about consonance can be learned, and conclude that it is "merely psychological behaviour" (Lundin) or "cultural familiarity" (Cazden) which determines – for a great part – how an individual approaches the phenomenon. In addition, in an even older article, Joseph Peterson (1925) argues that "habituation" is one of the important factors to the perception of consonance. I want to stress these viewpoints once more, especially because they got neglected for no apparent reason. I assume the "problem" is that the flourishing cognitive studies from the second half of the 20th-century and onwards shifted the focus to a biologically based explanation of consonance. Hence, recent studies show a multitude of researches on neural mechanisms (Blood e.a. 1999; Bidelman & Krishnan 2011; Lots & Stone 2008; and countless others), but also on differences between musicians and non-musicians (Roberts 1986; Minati e.a. 2009; Kung e.a. 2014), people with abnormal hearing (Cousineau e.a. 2012), perception of infants (Schellenberg & Trehub 1996; Zentner & Kagan 1998; Trainor e.a. 2002; Masataka 2006) and animal studies on
5 monkeys (Izumi 2000; Fishman e.a. 2001) and even sparrows (Watanabe e.a. 2005). While these studies are valuable in their own right, they do not engage any discussion on a cultural level, and often take a standard formulation of consonance for granted. For example, Shapira Lots & Stone summarize their findings with: "the analysis shows that the mode-locked states ordering give precisely the standard ordering of consonance as often listed in Western music theory. Our results thus indicate the importance of neural synchrony in musical perception" (Shapira Lots & Stone 2008: 1429 – my emphases). Because their results conform to the ideas about consonance within Western music theory,2 they claim to succeed in their experiment. This conclusion is absolutely logical, but I am crestfallen by its short-sighted simplicity. How can such an abstract formulation of consonance acts as standard for a scientific research? Especially this generic and uncritical usage of the word consonance is used in many other researches, and it is painful to see how it limits the scope – and how it ultimately limits the understanding of the whole phenomenon. In addition, the idea that conclusions only have to fit for Western art music should be completely obsolete by now. Unfortunately, consonance is often treated as being a universal value, which it is clearly not.
The lack of recent research on consonance in the cultural segment is noticed by Parncutt & Hair, to which they add a possible cause: "Little recent literature addresses C/D in non-Western music, perhaps because any such discussion runs the risk of ethnocentricity" (Parncutt & Hair 2011: 121). In relation to what I have presently outlined, I sense that the lack of engagement with the cultural aspects implies an ethnocentric view more than any exploration of consonance on a cultural level would possibly do. The mere formulation of Parncutt and Hair – despite their best intentions – speaks volumes. By critically handling the concept of consonance, and eventually breaking it down to an alternative, I ascertain that ethnocentricity is not a huge risk. As I will propose later, the replacement of consonance with euphony will soften the ethnocentric features of consonance.
For these reasons I want to continue in the spirit of those who considered the importance of the cultural context to the whole discussion about consonance. I will pay attention to the problematic theorization of consonance within musicology, since the term is often uncritically used, but the ultimate aim is to deny its alleged universality by showing that the perception of consonance is culturally dependent. Two underlying assumptions make up the core of this hypothesis. The first is that, despite not having any (if any) comparable concept to consonance, notions of euphoniousness in music can be sought within a given musical culture. Secondly, I argue that aesthetic as well as rationalized judgments regarding consonance are dependent on the musical culture they stem from, and subject to cultural conditions and conventions. These understandings will hopefully pave the way
2 As I already have argued, there is no single explanation of consonance within Western classical music. I shall turn to this in more detail later.
6 for a "cultural approach" on the concept of consonance. I want to put this into practice by presenting several case studies on distinct musical cultures: the common-practice European tonal music, North- Indian classical music and Javanese and Balinese gamelan.
The steps taken to evaluate the hypothesis are structured as follows. In chapter 2, thoughts about consonance within the Western discourse are reviewed to give a general overview of the academic research on the subject. It will show the main focuses of various writers, the hesitation in approaching the concept outside Western classical music, and the problematic "universality" consonance is said to have. The next three chapters will each feature one case study to resolve the aforementioned issues. Chapter 3 will examine euphony during the European common-practice, in which the generic idea about consonance will be pinpointed. Chapter 4 discusses the seemingly mutual relationship of harmony and consonance, and consequently, denies this relationship by discussing euphony in North-Indian classical music. Chapter 5 will focus on the phenomenon of inharmonic sounds, highlighting a new way to approach euphony and make a discussion of Javanese gamelan music possible. These three case studies together will prove the universality of consonance to be a myth. But before I continue with the next chapters, I want to clarify my handling of several terms and concepts to avoid uncritical engagement with them later on.
Euphony
Euphony is a term I prefer over consonance when discussing the judgment of sounds. It is an alternative coined by Norman Cazden, who himself called it "incommensurable with consonance" because it "cannot correspond to the real operation of consonant and dissonant moments in the art of music or, accordingly in its perception" (Cazden 1972: 231). With "the art of music", Cazden refers to several contradictory thoughts of consonance in Western musical theory. He views consonance and dissonance as merely functional terms operating in a particular tonal system (Ibid.: 221). However, the terms are not incommensurable in my opinion. To put it simply, euphony is consonance, but consonance is not euphony. Consonance cannot get rid of its implied counterpart dissonance, and also forces thinking in other binary oppositions such as pleasant/unpleasant, stable/unstable, rough/smooth, tension/relaxation, etc. – which are unnecessary by-products. If people experience music this way, it should be taken into account, but to have a concept that already implies such judgments is very inconvenient. The advantage I see in euphony is that it does not assign absolute values to sounds, and also allows a grey area that consonance/dissonance exclude. Eventually, euphony does not have an intrinsic positive or negative connotation, which makes the term more neutral to work with. All these qualities minimize the risk of ethnocentricity, since they do
7 not, by any means, imply a context of Western music. On top of that, it will not single out Western music as "a different case" as it can be used within Western musical traditions, too. Therefore, I will use euphony as much as possible – referring to the judgment of sounds in a broad sense – but I keep using consonance when I need to point specifically to this term.
(Musical) Culture
Another term that requires attention is culture, as one of the most complicated words in English language (Williams 1985: 87). Its multiple meanings and historical development would put it on equal footing with consonance – if only we would disregard its ubiquity. For culture, I would start with a broad definition, such as Jeff Titon's formulation in Worlds of Music: "the way of life of a people, learned and transmitted from one generation to the next [where] learned is stressed to differentiate a people's cultural inheritance from what is passed along biologically in their genes: nurture, rather than nature" (Titon in Titon e.a. 2009: 3 – author's emphasis). The last part is important to me, because ideas about euphony are a part of inheritance, rather than anything naturally evident. This is contrary to the perception of Jean-Philippe Rameau, who was very pleased to find a justification for music – as a product of culture – in nature, with the harmonic series (Parncutt & Hair 2011: 140). While there may be such "evidence" for consonance in nature, it all depends on how people look at the phenomenon. Like my emphases in this (and the previous) sentence show, in the Western culture, "seeing […] is the privileged sense on gnosiological and cognitive grounds"; perceiving and knowing is primarily expressed as something visual (Menezes Bastos 1999: 91). Rafael José de Menezes Bastos, who studied the Kamayurá Indians (or Apùap) observed that these people express their way of being in an auditory sense. "The senses", Menezes Bastos says, "are here seen not only as natural and universal apparatuses [but] are themselves regarded as subject matters of knowledge and training, being considered to be culturally relative"(Ibid.: 92). Thus, even if sound is "universally" perceived by the inner ear – and in spite of all humans having ears – it cannot account for a universal foundation of hearing. This is an important thing to bear in mind regarding the more recent psycho-acoustical formulations of consonance, based on the work of Hermann von Helmholtz, which certainly will be reviewed later on.
After this short intersection, I will turn to Titon again. His view of a musical culture is pretty basic. He writes: "Because music and all the beliefs and activities associated with it are a part of culture, we use the term music-culture to mean a group's total involvement with music: ideas, actions, institutions, material objects – everything that has to do with music" (Ibid.: 3). He also adds that a music-culture can vary in size, from a family or community to a region or transnational group,
8 but also as genre. There is something missing in the rather static descriptions of Titon; that musical cultures are dynamic, interacting and blending with each other. This is something which Richard Middleton does address when outlining various thoughts about culture. He states that "there is a strong strand right across the theories emphasizing culture as the sphere of meaning, of collective symbolic discourse, webs of significance, processes of signification; culture in this view is the dimension in which humans interpret their activities, institutions, and beliefs to themselves" (Middleton 2012: 7). I would like to reconcile the opposing views Richard Middelton presents here: culture is the sphere of collective symbolic discourse, meaning, signification, and the interaction or interpretation of people with this sphere. Combining Middleton and Titon brings me to Georgina Born's formulation of studying "music as culture", which she explains as "the constellation of practices, beliefs, communications, social relations, institutions and technologies through which a particular music is experienced and has meaning" (Born 1990: 211). In the same constellation, euphony is experienced and has meaning. Diversity within the mentioned aspects of this constellation give rise to disparate evaluations of the musical practice, and hence, to euphony.
Western tonal music / Common-practice
With Western (tonal) music I specifically refer to what is termed the common-practice, tonal music composed roughly between the early 18th-century to the early 20th-century in Europe (Gauldin 2004: xxx). This is the most relevant period as many formulations of consonance apply to tonal music, and Western popular music is primarily based on the same tonal foundations. Moreover, Hermann von Helmholtz' theory of beating (published in 1863) is still the most referred to in later psycho-acoustic studies and cognitive studies (Plomp & Levelt 1965; Terhardt 1984). Initially, Helmholtz' theory was formulated when the practice of tonal music was still prevalent. Radically new theories have not yet been proposed, and his theory still proves to be the most fruitful (Terhardt 1984: 277) – despite all innovations by 20th century avant-garde, atonality, serialism, and the like. Some movements, like the "emancipation of the dissonant" of Arnold Schönberg, actually negates a dichotomy of consonance and dissonance (Taruskin, chapter 6). Every note and interval are thought of being equal, so it actually negates its own relevance in a discussion of consonance. Therefore, this counter-movement against the tonal music is extremely difficult to take into account. It does not mean this era of Western classical music cannot be studied. I am convinced notions of euphony can be traced in Western art music of the 20th-century, yet it abounds my objective, taking all these changes into account will cause the thought to digress from the matter in hand.
9 The last important issue I want to address is the comparative nature of this research. This research will insuperably be comparative to some extent, because all academic research on consonance only addresses Western tonal music, on which its theoretical discourse is grounded. The reason why I compare several musical cultures with Western classical music is certainly not because of the pursuit of achieving something parallel to "the West and the rest" story, on the contrary. I want to highlight the context in which consonance normally operates to shed some light on its mismatch with musical cultures in which consonance does not operate. Since no other attempt has been made in this direction, I feel there is no other choice than elevating these terms and thoughts from the Western discourse and apply them, for a great part – comparatively to particular musical traditions.
10 Chapter 2 Consonance in the Western discourse
With the abundance of recent acoustical, neurological or cognitive studies and experiments, it is striking that the subject of consonance does not get much attention from musicologists nowadays. I have already addressed some writings about consonance that advocate a cultural approach, and have mentioned some important scholars who wrote specifically about consonance. Looking at the dates of publication, one can discover two things: conceptual writings and calls for a cultural approach are old, and recent literature in humanities is scarce. So we have a large body of literature in sciences, in contrast to the relatively scant literature from humanities. This difference between writings in humanities and sciences may be the "research vacuum" observed by David Huron, which, he confronts, is caused by diverging foci of ethnomusicologists and psychologists (Huron 2004: 93). Despite this, there exists a considerable discourse on consonance in Western classical music which I want to address with more detail first.
I deduce that the most efficient way to get an overview of the discourse around consonance in Western music is by looking at the categorizations of interpretations and explanations of consonance. Tenney (1988) differentiates five types of consonance/dissonance-concepts (CDCs); Cazden (1980) distinguishes three "fundamental approaches" of the phenomenon; Parncutt & Hair (2011) divide scientific approaches from those that stem from humanities, and Carol Krumhansl (1990) makes a distinction between "musical consonance" and "tonal consonance". Thereby, Krumhansl's distinction between musical and tonal consonance resembles Cazden's proposal of the term "euphony" as opposed to both consonance and dissonance, which he regards as functional terms operating in a tonal system (1980: 124, 155-156). However, I suppose that Krumhansl uses tonal consonance by following Plomp & Levelt (1965). Other scholars reflect less on different interpretations, like Ernst Terhardt (1984), who only mentions an all-encompassing "musical consonance" that is formed by "sensory consonance" and harmony. Sethares (2005) follows Terhardt's use of "sensory consonance", but being specialized in electrical and computer engineering, he explores consonance from a totally different viewpoint, relating tuning, timbre, spectrum and scale with each other. An extraordinary conceptual approach comes from Mieczyslaw Kolinski (1962), who argues that it is possible to approach the term consonance in an objective way. Lastly, Parncutt & Hair (2011) present a research that synergizes approaches from humanities with those from sciences to formulate a new conceptual structure for "Western consonance and dissonance". It is worth it to briefly outline the posed ideas and shortcomings of these writings.
11 I acclaim that the most comprehensive categorization is that of Tenney's. He observed that the terms consonance and dissonance have been used in fundamentally different ways in Western music history, and differentiates five concepts: monophonic or melodic consonance; diaphonic consonance; polyphonic or contrapuntal consonance; triadic, functional or tonal consonance; and timbral consonance (Tenney 1988: 100). Timbral consonance is now the most prominent concept of consonance in academic research, which mainly relates to Helmholtz' theory of roughness and more recent theories built on it. However, apart from Tenney's book, timbral consonance as a term is never used in relation to the theory of roughness, to my knowledge. William Sethares uses "sensory consonance" instead when referring to Tenney's categorizations, following Terhardt (Sethares 2005). The benefit of these categories is that they do not aim to reduce every theory to one fundamental theory of consonance. The downside is the exact opposite – infinite categories can arise simply because this system is based on primary characteristics of theories. As long as these characteristics cannot fit in existing categories, one could continuously go on identifying new ones. It can also be argued that the first four categories of Tenney all involve "functional consonance" in the sense that they are all based on the compositional feature of requiring resolution or not, as opposed to "aesthetic consonance" understood as a subjective evaluation with terms as pleasant or satisfying (Kolinski 1962: 66). However, such judgments have often formed the foundation for "functional" concepts alike, therefore, a diametrical distinction between the two is challenging to accomplish.
The fundamental approaches Cazden differentiates are the Natural Law theory, the Aristoxenian theory, and the Systemic theory. The Natural Law theory is linked to the doctrine of Pythagoras, and explains consonance as the result of simple ratios. The Aristoxenian theory, on the other hand, considers consonance as a "judgment by the musician's ear" (Cazden 1980: 145), but may also be equated to the Gestalt principle.3 The Systemic approach is a dualistic approach, a reconciliation of the Pythagorean and Aristoxenian theories, linked to a formulation offered by Carl Stumpf who claimed that a special psychoacoustic quality can be found in natural phenomena expressible in simple ratios (Ibid.: 150). These approaches are not particularly interesting, as Cazden has made much more thought provoking statements in earlier essays. I already discussed the advantage of his concept "euphony", and his proposal for a cultural approach (Cazden 1945). Cazden is also one of the authors who clearly stresses the functional part consonance has, or as he contends, that consonance is functional in Western music: "consonance and dissonance are moments less dependent on what a harmony is than on what it does" (Ibid. 1972: 221 – author's emphases). This, along with the central role harmony plays for the formulations of consonance in the Western
3 The Gestalt theory claims that there are wholes which determine their smaller elements, but which are not determined by its smaller elements.
12 discourse, will deliberately be disclosed in another case study. Another interesting point he reiterates in most of his writings is how the concept of consonance is confined specifically to Western tonal music:
Outside the effective culture-area of that music system [i.e. Western tonal music], which of course has now achieved fairly world-wide diffusion, and outside of its historical limitations, the operation of consonant and dissonant moments simply does not apply, and its absence in other musics or in certain modern or archaic trends is indeed among the disorienting features for the listener or participant conditioned to that systemic standard. (Cazden 1972: 221)
Here, he also addresses the problem one encounters when conditioned by a particular system, in this case the Western tonal major-minor system. He rightly states that this affects the view towards music of other cultures, including the "past cultures" of one’s own culture. A distorted view of a past culture may lead to anachronistic assumptions. For example, the critiques Tenney describes in relation to the contrapuntal practice that predates Rameau are made from a post-Rameau point of view, for which the musical system slightly differs (Tenney 1988: 74-75).
En passant, Cazden makes an important reference to the ubiquity of the Western major- minor and/or 12-TET4 system over the world nowadays. This is why one cannot simply conduct experimental research on the perception of consonance in other musical cultures, and collaborations between ethnomusicologists and psychologists as proposed by Huron – no matter how ideal they may be – will not reveal much in this aspect (Huron 2004: 93-94). Either people underwent education in Western classical music, or they appropriated the standards of Western popular music by playing in bands or listening to popular music. For example, in relation to the probe tone method,5 Krumhansl (1990) discusses two cross-cultural studies, one carried out with Balinese music and one with North-Indian music, that show almost no difference in perception of pitch hierarchies among Western listeners and North-Indian or Balinese listeners. While these studies were not explicitly aimed to study the perception of consonance, the familiarity of the listeners with Western music turned out to be a problematic criterion. Reminding what Cazden has argued, perceptions of euphony likely became conflated with the musical standards of Western popular music.
More interestingly, the minimal differences between Indian and Western listeners in the study of Mary Castellano et al. (1984) hints towards the adaptability of humans to other music, hence, culturally learned perception and judgment of consonance and dissonance, as they observe
4 Twelve tone equal temperament. 5 Probe tone method, originally developed by Krumhansl & Shepard (1979), is a method in which listeners are presented with a musical passage followed by one probe tone of the 12 possible chromatic pitches.
13 "little evidence that the Western listeners assimilated the musical contexts [of the Indian musical examples] to the Western system of major and minor scales" (Castellano et al.: 411). This adaptability to music has not yet been studied thoroughly. Alex Wand, a composer, hypothetically experimented with this phenomenon by creating a composition with "odd ratios" to which the listener eventually would become familiar by the end of the 6 minute piece, but it has not been tested scientifically (Wand 2012).
Terhardt, who draws upon Helmholtz' theoretic framework, argues that we have to deal with "musical consonance":
We consider the term musical consonance to be subsuming the principles that are regarded as governing tonal music. […] The principle (whose nature to this point must be considered as unknown) that creates those specific [tone] relations is called musical consonance. This definition meets well the ordinary usage of the term. (Terhardt 1984: 278)
Musical consonance is composed of the components "harmony" and "sensory consonance". Harmony in this sense encompasses tonal affinity, compatibility and fundamental-note relations, while sensory consonance includes sensory features of sounds, such as amplitude fluctuations and spectral energy present at high frequencies (Terhardt 1984: 282). Thus, while maintaining "one" consonance, his idea of "musical consonance" is built from what other writers mostly call tonal or functional consonance, versus sensory or aesthetic consonance. Perceived in this method, I can conclude that this is some common ground among diverse interpretations of consonance within Western discourse.
One last deviating interpretation of consonance is offered by Kolinksi (1962). He formulates a radically different categorization in which the major second and seventh are deemed more consonant (i.e. having more "tint affinity") than the major third and minor sixth. His findings give a strange recognition to the widely used pentatonic scales: "The equally universal distribution of the so-called anhemitonic-pentatonic scale can be easily understood if it is realized that this structure embraces all existing direct tint relationships and that all its parts are directly related to each other through tint affinity or tint identity" (Kolinski 1962: 72). The problem with Kolinski's study is that he practically only changes the hierarchy of consonant intervals. Moreover, his justification of the "Laotian love song", among several other cases he discusses, still does not disclose much about its consonance; he merely shows that it uses many "major seconds".6
6 Since he consults a score in staff notation, I doubt the accuracy of it.
14 The main shortcoming of most studies remains the confinement to Western tonal music. While the semantic and historical problems are carefully outlined by Tenney, they do not transcend the realm of Western classical music. This is also true for the various articles of Cazden on consonance, even though he engages with most semantic problems on the subject. Yet more importantly, he mentions the significance of cultural familiarity and outlines the confinement of consonance to Western tonal music. Parncutt & Hair have made a valuable effort on another level by merging psychological and musicological viewpoints, still their research is confined to Western musical culture as well. The same applies to Terhardt's research, which is framed very obviously and is, consequently, very limited. In my view, it would be of much value to expand the theoretic framework and consider the concept of consonance in other musical cultures.
Strikingly, one of the most interesting ideas emanate from someone who is not a musicologist: the electroacoustics engineer William Sethares. In his impressive book called Tuning, Timbre, Spectrum, Scale (2005), he merges views from psychoacoustics with mathematic concepts, which seeks to answer its core question – whether it would be possible to create a device that measures consonance and dissonance. Sethares not only demonstrates that this is possible with a reliable dissonance meter, he also shows how useful it is in examining Indonesian gamelan music, Thai classical music, determining the tuning for Scarlatti sonatas, creating synthesizer instruments with adaptive tuning, and the application to compositional practices. Exemplified with many mathematical models and musical examples, Sethares concludes that given a tuning, an appropriate scale can be derived, and given a scale, an appropriate tuning can be constituted. The foundation of his work lies, in fact, in Helmholtz' theories, but he extends it massively to make it possible to talk about consonance in relation to "inharmonic" music, such as the Indonesian gamelan music. Undeniably, this is extremely advantageous, but it also is enlightening on its own. I value his work highly for two conceptual considerations: he acknowledges consonance/dissonance as a continuum, and his work is applicable to any musical culture, not exclusively to that of the Western classical tradition. I will show how relevant his findings are in the case study about the Javanese gamelan.
Concluding, it is clear to me that research is restrained to finding theoretical solutions for consonance, or stuck in finding biological or neurological explanations for the phenomenon. Stuck in the sense that they limit themselves to theories, or physical properties. Either the discussion shifts entirely to scientific explanations, or to musical explanations focused only on its functionality in music theory. These limitations are partly self-inflicted, mainly because of the uncritical or simplified formulations of consonance. The cultural aspects, be it psychological, social or aesthetic, or any
15 interaction between them, are largely overlooked. In addition, there certainly has been a hesitation to approach this topic outside the discourse of Western classical music - instead an alleged universality of consonance as understood in Western tonal music is taken for granted given the ubiquity of 12-TET Western popular music. I want to depart from this background and address the topic outside Western tonal music to show that the commonly used "functional consonance" is not something universal, and that consonance, i.e. euphony, is a phenomenon that differs within musical cultures. This will be shown and exemplified in the succeeding case studies.
16 Introduction to the case studies
Now that I have explained the Western discourse very briefly and have reviewed several diverging opinions, I want to turn to three distinct musical cultures to investigate how euphony is evaluated, or how it can be approached. As I have noted, a tacit formulation of consonance can be encountered frequently in the Western discourse of consonance, which seems to be based on a generic idea of European tonal music. This generalization is what I want to examine first: how does euphony operate in the common-practice period of European tonal music? Which thoughts, meanings or theories make up this generic idea of consonance? I assume the common-practice to have a central role in this. Secondly, I want to expand the discussion of the reliance of the Western discourse on harmony, a topic that logically demands attention after having examined the first case study. I feel this is necessary, because the Western musics, both classical and popular, are completely dependent on harmony. Seen on a global scale, the Western musical practices are anomalous in this sense. I want to stress this by turning to Hindustani classical music of North-India in this second case study. How can euphony be addressed in this musical tradition in which harmony is static? Because old concepts of consonance have existed in North-Indian classical music, this musical culture is exemplary of how conceptual ideas about consonance can operate outside a harmony-based environment. For the sake of clarity: when I talk about North-Indian classical music, I refer more specifically to the vocal classical genre. This is partly because I am most familiar with it, but also because the vocal tradition is considered the most important, serving as point of reference for instrumental music and music theory (Van der Meer 1980: xi). Lastly, I want to address a musical culture that seems to be remote from both Western and Indian music: Javanese gamelan music. Largely based on the work of Sethares, I want to demonstrate with this third case study that euphony plays a role in this tradition, too. Acknowledging acoustical properties of metallophones, with their inharmonic spectra, will lead to a new understanding of euphony in said musical practice. Moreover, it will show more clearly why consonance cannot be universal, but is entirely dependent on the cultural (and therefore, musical) conditions: the people who play the music, the instruments used, the conventions and ideas formed, the actual performance practice, etc. In the end, all three case studies together will be able to make the outcome more comprehensible.
The musical cultures I decided to examine within the case studies may seem to be arbitrarily chosen, but they have some features that make them particularly relevant. Because this is a literary research, one requirement was that they needed to have existing music theoretical writings. The
17 European common-practice has a large written discourse, to the extent that the musical practice is heavily influenced by these writings. In addition, the importance of notations is one of the causes of a particular view towards consonance; that of functional or contrapuntal consonance. The North- Indian tradition is not written in the sense of having musical notation, but there are many treatises from earlier centuries about arts in general. Of these, the ā a ā ra is the most well-known reference for arts, and for music as well. In this source, many basic concepts of North-Indian music are formulated, along with the concepts of consonance. In contrast to this, the musical practice is entirely oral. Regarding Javanese gamelan music, there does not exist much written material, and the practice has been an oral one too, although musical notation was increasingly accepted from the beginning of the 20th-century and onwards (Ishida 2008).
What the three musical practices have in common, is that they all have their roots in elite or court music. This has several important implications. Firstly, it means that these musical practices were dominant, and might not have been experienced by the majority of people. This must have been true especially for Javanese people, as the gamelans (as complete ensemble) were reserved for the court. Secondly, the elite musics most probably were well-documented because of their "high" status and relative importance. Thirdly, in relation to the high status, they were to some extent preserved traditions, in the sense that they were kept congruent with older manifestations of "the same" tradition. The last point is clearly visible in European classical music, in which the preservation of the "classical tradition" led to an extraordinary authority of musical scores (Taruskin 1992). In North-India, this need for preservation of traditions has manifested itself in lineages of teachers within a closed social group, called ghārāna , which probably emerged around the 19th-century (Van der Meer 1980: 128-129). This preservation of music is less obvious for Javanese gamelan, and I am not in the position to make more claims about this practice due to the lack of English research regarding this.
Additionally, I have chosen to use several authors as guideline for each case study. For the examination of the common-practice period in Western tonal music, I will primarily draw on Tenney's book. For the discussion on the emphasis on harmony in relation to North-Indian classical music, I will use several thoughts of Cazden. Sethares' findings shall be used to demonstrate an entirely new approach to Javanese gamelan music. These three authors are important for several reasons. Tenney, while not being inclined to place euphony in a cultural perspective, outlines the historical development of thoughts about euphony within European music very well. Hence, he also gives a solid overview of thoughts and theories present in the common-practice of European music. Even though he writes about different "consonance concepts", I make efforts to address them as thoughts of euphony, except when I explicitly need to refer to consonance – since it was the term
18 theoreticians referred to. In relation to the next case study, I will use the different articles of Cazden for a discussion on harmony. As I have argued, Cazden poses relevant questions and tends to think beyond many other authors about the subject. Moreover, his statements can be used effectively for a relevant discussion of euphony in North-Indian classical music. The further examination of North- Indian musis shall be led mainly by writings of Nazir Ali Jairazbhoy, as he wrote extensively on music theory in India. Lastly, Sethares devotes a whole chapter on Javanese gamelan in his book, in which he applies his findings on the relationship between spectrum and scale with said dissonance curves. The relevance of this undertaking is immense, and because it delivers an entirely new view towards euphony in a musical practice to which it hitherto was deemed incommensurable, it shows one possible direction of a cultural approach to euphony.
19 Chapter 3 European common-practice and tonal consonance
The first case to examine is that of the European tonal music during the so-called common-practice period. Several examples or remarks regarding this period were given previously in earlier chapters, but as I already have noted, the understanding of euphony within this tradition in European music is not something self-evident either. Nevertheless, ideas of euphony during this period, expressed with the terms consonance and dissonance, are now often treated as universal values. This is partly because people tend to speak about consonance without paying attention to the specific function of this concept within Western tonal music, but where does this general idea come from in the first place? Because of its alleged universality, in spite of its nonspecific usage, it is useful to outline the treatment of euphony within this musical culture essentially.
As I have made clear in the introduction, the common-practice refers to European tonal music from at least the early eighteenth to the beginning of the twentieth century, although a larger timeframe from 1600 to 1910 is used as guideline as well (Hyer: Tonality). Because this period encompasses three hundred years, one cannot treat it monolithically as "one practice". The similarity lies in the harmonic organization of the music from said period, i.e. the minor/major dichotomy and tonic/dominant functions, beside the uncountable differences in musical genres, audiences, social functions, technical developments, etc. Its relevance reveals itself up to present day, since most rules of counterpoint from the beginning of the eighteenth century are still taught in music theory classes, and many of its features serve as foundation for most popular music genres. I argue that the general conception of consonance is a heritage from this common-practice period, which will become clear upon closer examination.
If we turn to Tenney's classifications, it is not surprising to see two (or three, depending on the starting point) distinctive concepts of euphony stemming from this period. Beginning with "contrapuntal consonance", it includes both "tonal, triadic or functional consonance" based on Rameau's writings (Traité de l'harmonie, 1722), and "timbral consonance" based on the theory of Helmholtz (On the Sensations of Tone, 1863/1875). Between these different concepts, the measure of euphony – i.e. the conception of consonance in this case – shifted from "melodic/textual clarity of lower voice" to "stability as a triadic component", and ultimately came to express "smoothness" (Tenney 1988: 115 – author's emphases). While this might look like a gradual "evolution" of one conception into another, it must be remembered that Tenney's classifications are based on the
20 prevailing theories of these eras, and their historical progression is not necessarily linear. For example, Carl Stumpf's theory of tonal fusion ("Konsonanz und Dissonanz", 1898) has a lot in common with what Tenney calls "diaphonic consonance" (CDC-2) of the thirteenth century polyphony, which was based on the blending of tones, and most likely on how well two melodies could be perceived as one (Tenney 1988: 30-31). In a similar vein, one can trace all earlier conceptions of consonance in Rameau's writings, not exclusively the most recent one.
The contrapuntal concept
Euphony in the contrapuntal concept was most prominent approximately from the ars nova to the seconda pratica – roughly between the 14th and 17th-century. Euphony was generally seen in a rational and functional way: rational in the sense that "consonances" were defined as having simple integer ratios, and functional because the categories of euphony formed a direct relationship with the rules of counterpoint. The degrees of euphony were based on the dyads formed with the lower voice. Of high euphony were those "in which the melodic and textual clarity of the lower tone was relatively unobscured" (Tenney 1988: 50). A figured note created consonance if it formed a consonant dyad with the lower note, hence it was the upper note that had to resolve if necessary (Ibid.: 58). A frequent misconception of this practice is that there has to be "one" dissonant among the voices – which, in fact, is an anachronistic application of post- Rameau thinking (Ibid.: 74-5). Even in syncopation, when the syncopated note causes the dissonance, it was not called "the" dissonant note (Ibid.: 57). These new criteria for consonances and the developing rules of counterpoint led to the famous controversy of the fourth, which I have mentioned earlier. The problem of this interval was its disturbing quality in two-part writing, while sounding well in three-part writing unless it was placed against the bass. A comforting conclusion of Tenney regarding this issue is that "this otherwise "anomalous" treatment of the perfect fourth as a dissonance in CDC-3 arose in an effort to maintain the melodic and textual clarity of the lower voice – and thereby avoid clerical sanctions – without sacrificing the richness and complexity of a more elaborate kind of polyphony" (Ibid.: 50).
Strikingly, the gradations of euphony in this era were reduced in comparison with the medieval concepts of the 13th century, although the number of consonances had grown. Richard Crocker (supported by Tenney) argues that the medieval theorists seemed to be more susceptible to what they heard by taking into account their own judgment of dyads, contrary to their successors (Ibid.: 26-27). Despite this, the third and sixth, albeit imperfect, were finally considered consonant. The long delay of accepting thirds and sixths as consonances by medieval theorists most probably
21 was because of their difficult Pythagorean ratios,7 even though the simpler "just" intervals were likely being sung – and known (Tenney 1988: 25; Grout e.a. 2009: 159). Thus, the Pythagorean doctrine continued to guide the evaluation of intervals. The usage of major thirds and minor sixths confronted theorists with a problem, because they could not be derived from the same Pythagorean ratios – i.e. the fifth, fourth, and third could not all be pure (Cohen 1984: 4). A satisfying solution to the problem was given during the mid 16th-century, by Gioseffo Zarlino (Institutioni harmoniche, 1558), who redefined the Pythagorean problem by proving that the harmonic ratios consisting of the integers 1 to 6 were the only consonants (Barbieri 2001: 201). Following from this, Zarlino defined the divisione armonica and the divisione aritmetica,8 which justified the major and minor third, respectively (Kolinksi 1962: 71).
During the 17th century, there was another, physical theory regarding consonances which Tenney does not mention. This was the theory of "coincidences", often attributed to Galileo, but already formulated as early as in 1575 by Francesco Maurolico (Barbieri 2001: 228). Patrizio Barbieri explains that "according to the [coincidence] theory, the greater the number of "coincident" (i.e. in- phase) vibrations of the notes making up an interval, the greater its consonance" (Ibid.: 201). Thus, if we take the fifth (3:2) as example, the tone with higher frequency has to vibrate thrice – and the lower twice – to coincide. Following this principle, the two waves coincide every 6 periods, and because of this, are deemed very consonant (Sethares 2005: 81-82). While the ratios used are similar to those of Zarlino's theory, the coincidence theory has deviating implications to the degrees of consonance. So, the fourth (4:3) is more consonant than the major third (5:3), however, in relation to the rules of counterpoint, conflicting situations occur in three-part writing. Doubling the fourth (8:3) would be more dissonant than the doubling of a third, which creates a major tenth (5:2) – a ratio that is more consonant than the (5:4) ratio of the major third (Barbieri 2001: 207). Regardless of these discrepancies, the idea that simple integer ratios constitute the highest euphonious value remains intact.
The triadic/tonal concept With the advent of the writings of Rameau, a different concept can be distinguished. Even though he did not propose a radically new view on euphony, with hindsight his writings formed the start of a new strain of thoughts. The revolutionary aspect of Rameau's theory in general, is his formulation of the major/minor system, as opposed to the modal system of eight modes of his predecessors (Grout
7 For example, the just ratio for the major third is 5/4, instead of the Pythagorean ratio 81/64. 8 The divisione armonica (1:1/2:1/3:1/4:1/5:1/6) forms a ascending major third, while the divisione aritmetica (1:2:3:4:5:6) forms an descending minor third.
22 e.a. 2009: 305). What Rameau did, in essence, was revising existing ideas. Glareanus' expansion of the modes to twelve (Dodecachordon, 1547) acknowledged both the major (Ionian) and minor (Aeolian) modes, while Zarlino justified the major and minor chord only 11 years later (Miller - Glarean, Heinrich). Rameau's primary success lies in his creation of a coherent unity of these existing theories, by taking the fundamental bass (or "root"9) as main principle (Grout e.a. 2009: 430-433). However, Rameau assumed the idea of a fundamental bass was merely "common knowledge" and already explained by other theorists, such as Zarlino (Tenney 1988: 68). Similar to this, Rameau was equally unaware of his diverging usage of consonance. As Tenney explains:
The century-old habit of ascribing consonance or dissonance to an individual tone in a chord – even if it had been nothing more than a convenient shorthand – had become so commonplace by the early 18th century that even Jean-Philippe Rameau – in 1722 – hardly seems to notice that he is articulating a radically new conception of consonance and dissonance, although he is quite clearly aware of the innovative nature of most of his other theoretical ideas. (Ibid.: 58)
This minimal difference has far-reaching consequences, but before I will address these, I want to turn to the functional usage of consonance from which this "dissonant note" concept originates. Just as in the preceding centuries, euphony is addressed in a functional way. Now measured against Rameau's fundamental bass concept, consonant are tones "that have a simple relationship to this fundamental root and dissonant tones are those that do not" (Sethares 2005: 78). Seen this way, triads were deemed consonant (because they only contain consonances), while seventh chords are dissonant (because they contain one dissonant minor third). According to Rameau, harmonic progression could be explained with the root progression, as a chords remained the same in all their inversions. From this, Rameau coined the terms tonic, dominant and subdominant, forming the hierarchical foundation of tonality (Grout e.a. 2009: 430).
In relation to the said seventh chord, Rameau made a distinction between major and minor dissonances – and this is where the "dissonant note" concept stems from. The minor dissonance is the added minor third in the seventh chord, and the major dissonance is the major third within the original triad. Because they both create dissonance, the major dissonance has to move upwards, and the minor dissonance has to move downwards. In actuality, the major third is not even dissonant in itself, but is made dissonant by the minor third. As Rameau clarifies in a later treatise:
When the minor dissonance is joined to the dominant harmony, which always has the leading-tone as its major third, it communicates part of its harshness to this
9 The terms "fundamental bass", "-tone" or "-root" all refer to the same thing.
23 leading-tone, so that, to satisfy the ear, the succession of both becomes obligatory. (Hayes (trans.) as cited in Tenney 1988: 76)
This distinction is nullified by later writers, because of the conditional state of the major dissonance. Nonetheless, the recognition of a dissonant note – that of the minor dissonance – is an idea that permeated during Rameau's time. The new "dissonant note" concept implied a strict dichotomy between consonance and dissonance, even making it an intrinsic property of a tone. Tenney couples this to the idea that follows from the treatment of those dissonances, i.e. the "condition" of being dissonant requires an obligation to be resolved (Tenney 1988: 77). This way, dissonances also involve motion, a phenomenon completely separated from any acoustical or sensory sound property. In Zarlino's time, imperfect consonances had to move towards perfect consonances, while Rameau attributes this obligation to dissonances. In addition, there is a fundamental difference between Zarlino and Rameau regarding the nature of dissonance. As Sethares summarizes:
Rameau's fundamental bass implies not only the static notion of the lowest note of a chord in root position, but also the dynamic notion of a succession of bass notes. Dissonances occur when the music has moved away from its root, and they set up an expectation of return to the root. Thus, functional dissonance is not a result of chordal motion, but rather its cause. (Sethares 2005: 79)
Dissonance, as understood in Rameau's formulations, was the cause of chordal motion, while in Zarlino's case – and within the contrapuntal concept generally – dissonance was the result of motion. Even though Rameau used Zarlino's statements about motion to justify his own thoughts about the subject, he came to imply the exact opposite (Tenney 1988: 78).
Rameau's theories were gradually adopted by others, eventually creating a new paradigm at the end of the 18th century (Grout e.a. 2009: 433). His ideas became so commonplace, that it would not be surprising if the common-practice period mainly refers to his tonal system and its application many decades afterwards. Of course, his findings suffered from several inconsistencies too, which he (and later theorists) have tried to solve. But it was not until Helmholtz that a radically new theory concerning euphony was posed.
The sensory concept The "timbral" concept, which I will refer to as "sensory" to keep it more consistent with its modern usage, is characterized by Helmholtz' theory of beating coined in book On the Sensations of Tone. Like the previous theories, it is not entirely new, or formulated out of the blue. According to Barbieri,
24 this theory, instead of being a product of the scientific revolution, came from Nichomachus of Gerasa, and was taken up by the mathematician Francesco Maurolico in 1575. However, it was Marin Mersenne (Harmonie Universelle, 1636-7), who first formulated the phenomenon more correctly; more or less as a consequence of the coincidence theory. Mersenne observes that "every time the vibrations "se rencontrent" (i.e. are in phase), their amplitudes are added together, thus producing periodic rises in the intensity of the sound" (Barbieri 2001: 216). This reinforcement of two sound wave is called "constructive interference". Mersenne did not expain, however, that out-of-phase vibrations result in periodic "destructive interference" – a decline in intensity (Sethares 2005: 40-41). Despite this, Mersenne's observation can be regarded as Helmholtz' theory of beating in a rudimentary state. He also correctly observed that:"the number of beats is equal to the number of coincidences (rencontres); and it is specified, though with a certain degree of approximation, that the number of beats of the semitone 16:15 is over four times greater than that of the comma 81:80, precisely "because 81 contains 16 more than four times" (parce que 81 contient 16 plus de quatre fois); the higher the octave in which the given interval occurs, the faster such beats will be" (Barbieri 2001: 217). Especially the notion that beats will be faster in higher octaves is stunning, as it is one of the criticisms of Carl Stumpf against the validity of the beat theory (Cazden 1962: 306). The example of Apel, cited in Cazden (1962), show that the number of beats doubles if a sonority is transposed into a higher octave, and for this reason, the major third c-e is equally dissonant as the major second c'-d'. However, it is not my intention to pick on inconsistencies in Helmholtz' theory, as the criteria about what constitutes euphony are primarily of interest. Three important implications can be derived from Helmholtz' theory of beating and roughness caused by it: consonance depends on the spectrum of tones; individuals tones have an inherent "dissonance"; and, consonance is measured in gradations.
The discovery that spectral distribution is as equally important as the fundamental frequencies of sonorities, including Helmholtz' equation of the spectrum of sunlight to the spectrum of complex tones, is entirely different from older theories (Wand 2012: 73). This idea of "sunlight projecting through a prism" is called a Fourier transform, a discovery of Jean Baptiste Fourier at the beginning of the 19th-century. He demonstrated how a periodic signal is composed of sum of partial sine waves; a decomposition of these partials result into a spectrum (Sethares 2005: 333). Within this new understanding of spectrum, interval relations are not the primary factor anymore in constituting consonance. Helmholtz has given spectral distribution practical validation, too. Regarding the special nature the clarinet (which only has oddly numbered partials), he asserted that depending on the interval, it will sound better when the clarinet takes the upper tone. If an oboe and a clarinet play a major third together, the clarinet should take the lower note so that both instruments have more
25 coinciding partials, while negating several "disturbing" coincidences because of their absence in the spectrum of the clarinet (Tenney 1988: 90-91). The second implication is that virtually any sound is inherently dissonant, except a plain sine wave. Because every musical sound differs in spectral distribution and has some irregularities, they cannot be free from roughness. Like how Sethares puts it: "any tone with more than one partial inevitably has some dissonance, because dissonance is caused by interacting partials" (Sethares 2005: 80). Similarly, any combination of tones inevitably results into beating. The third implication is that consonance and dissonance is not a binary, but a graded concept. This, actually, fits well into the concept of euphony, but the words consonance and dissonance unfortunately do not live up to this implication. Consonance as gradation has continually been used in psychoacoustic studies, and reinforced by important experiments such as that of Plomp & Levelt (1965).
Now that the three most prominent concepts are examined, along with their smaller developments and/or inconsistencies, the remaining question would be how they relate to music of the common- practice. As I argued in the introduction of this research, consonance has a manifold of dimensions, which makes is difficult to identify the manner in which it operates. In this chapter, I have shown that it has been seen a quality of a tone, a music-theoretical term, an acoustical phenomenon, and it has been part of a practice. All of these attributes of consonance are formed on different grounds, often at different times and situations. However, somewhere between all these formulations within the period of the common-practice, the generic idea of consonance should be traced. Which ideas have been crystallized to this persistent formulation of consonance?
For the contrapuntal concept, there are several elements that do not correspond to later practice of European classical music. The most important change is the replacement of the modal system by the tonal system after Rameau. Even though contrapuntal rules are still taught in theory classes, their relevance can be questioned because the rules are merely taken for granted for the sake of practice. Consonances are more likely evaluated by the harmonic series, than by the ratios of Zarlino. To recapitulate one example I already have given: no one really questions the consonance of the fourth, third and their octave enlargements, or distinguishes one of them as being more consonant. Rather, the "natural law" of harmonic series is taken as benchmark, which is clearly related to Rameau, who was excited to find this relation between "nature and culture" (Parncutt & Hair 2011: 140). Conversely, the struggle of Rameau with the minor third, which is not to be found in said harmonic series, is no issue anymore. It is looks like the different theories around the 18th- century are conflated, and some generalization of them has remained. The issue, then, is slightly more complex than Parncutt & Hair explain, as they find it suffice to say that "C/D is one of the
26 principal components of MmT [Major-minor Tonality], which now dominates the music of the world" (Ibid.: 131). Indeed, major-minor tonality obviously inclines towards a broad understanding of Rameau's ideas, but there are two other cornerstones of his theory alive: that of the dissonant note, and that of stable/unstable moments caused by motion. These come very close to the general conception of consonance held by most academics (and I think people in general), as Tenney explains:
Thus, the "dissonant" quality which is carried by a dissonant note must also include this "obligation" (which will later be called – rather anthropomorphically – a "tendency" or "need") to resolve – which is to say – to move. And it is here, I think, that we can locate the unique and precise point of origin of two notions which are currently held by many theorists – and which are completely at odds with earlier forms of the CDC: (1) that there ought to be an absolute dichotomy between consonance and dissonance, and (2) that they involve merely "phenomena of motion," "stability/instability," etc., in a way that is entirely divorced from any acoustical or immediate sensory properties of the isolated sound or sound- aggregate. (Tenney 1988: 77)
Some variant of the tonal concept has thus become a common understanding of consonance. I would even extend this by saying that exactly these two notions are so often deemed universal and unconsciously applied to music in which they do not make any sense. The dissonant note is determined by the relation with its referent, the root, and makes this relation absolute. Furthermore, the opposition stable/unstable can be replaced by virtually any opposition associated with it, such as relaxation/tension, agreeable/disagreeable or smooth/rough, something which also reflects judgment within the common-practice period. These two classifications can be mixed, so that a hypothetical reaction may conclude that gamelan music sounds dissonant (because the total experience is disagreeable) or that scale steps of the pelog scale sound dissonant with each other (because of thinking in roots, intervals and ratios). As I will explain in the case study about the Javanese gamelan, thinking in such terms do not do justice to the musical tradition in question, moreover, they do not explain anything substantial.
Can Helmholtz' theory add something to this? Probably not, although I assume it has more ground among scholars and, perhaps, musicians nowadays. There are several shortcomings of this theory, such as its lack of relation with musical practice:
In contrast [to contrapuntal and functional consonance], sensory dissonance and tonalness are static conceptions in which every collection of partials has some
27 dissonance and there is not necessarily any relationship between successive clusters of sound in a musical sequence. (Sethares 2005: 80)
Tenney gives Helmholtz' theory more relevance, while acknowledging the same problem Sethares observed. Tenney writes:
Although the relevance of CDC-5 to musical practice has frequently been questioned (especially by music theorists concerned with more "functional" definitions of 'consonance' and 'dissonance'), it is the form of the CDC implicit in most psychoacoustical studies that have been done since the work of Helmholtz, and is probably the basis for the prevailing colloquial uses of the terms (even by many musicians). (Tenney 1988: 97)
Obviously this work is of high importance in psychoacoustics, but the fact that it remains relevant after 150 years is quite remarkable. However, I am not sure about the "prevailing colloquial uses" Tenney describes. To my experience, terminology such as beating and roughness are not widespread, and I think both authors are correct to say this is because of its detachment from music theory. Most people have gotten familiar with the concept of consonance by music lessons, and not by psychoacoustical studies. It seems to me this theory is quite exclusively an academic one. In studies of acoustics, Helmholtz' theory is, in turn, far more relevant than music theoretical ponderings.
The different "concepts of consonance" reviewed in this chapter could easily be viewed as notions of euphony. Actually, Tenney's categorizations are made with a quite similar thought, that of looking at formulations of consonance without taking one as immediate reference, and search for deviating characteristics. To some readers, the usage of euphony in this chapter might seem a mere reformulation. In one sense, it is. As I have noted, euphony embraces the different dimensions of consonance, but the reverse is not the case. Therefore, to put this case study on equal footing with those about North-Indian classical music and Javanese gamelan music, it has to be made evident that euphony is capable of making discussions in various musical cultures possible. Euphony in the common-practice is evaluated on different grounds, and the generic formulation of consonance is just one way of approaching euphony in this musical tradition. Regarding the phenomenon of euphony itself, Western tonal music is absolutely not a special case.
28 Chapter 4 North-Indian classical music and the (absence of) harmony
In the previous chapter, the generic formulation of consonance is identified within the common- practice, although one persistent attribute of this formulation is not mentioned explicitly: the mutual relationship between consonance and harmony. This will be discussed further in this current chapter, as the assumption of this relation has obstructed research on consonance outside Western tonal music. I will proceed to discuss North-Indian classical music to make clear that a static harmonic background has different implications for euphony, and that this "absence of harmony" does not exclude any thoughts or theories about euphony. The North-Indian classical music is particularly interesting in this sense, as this music tradition lacks harmonic progression, but stands out from other musical cultures because it initially had known terms for consonance and dissonance.
Consonance and harmony
Consonance and dissonance are moments less dependent on what a harmony is than on what it does. (Cazden 1972: 221 – author's emphases)
One assumption often made regarding consonance, is specifically its explanation of harmony in Western tonal music. In the previous examination of major ideas about euphony within European tonal music, only Helmholtz' theory was not directly linked to harmonic progression – but to individual sonorities. Cazden's phrase may not appear as a big revelation, but many Western theoreticians, such as Terhardt – and therefore, Helmholtz (Terhardt 1984: 281-82) and virtually any advocate of Pythagorean or natural overtone ratios (remind Rameau), claim that consonance is a foundation of harmony. Cazden's contention that consonance legitimates harmony rather than it constitutes harmony, is a thought-provoking one. I agree with Cazden that the consonance as concept is entangled in harmonic progressions, ratios, and other constructs. These fixed constructs put the experience of music on a sidetrack, so to speak. My concern, additionally, is that it obstructs any discussion of musical genres or traditions which lack these frameworks. But as both Tenney and Sethares point out, Cazden generally attacks the concept of "sensory consonance" from a "tonal/functional" viewpoint, since Cazden is quite insistent on the motion of dissonances (Tenney 1988: 92-93; Sethares 2005: 85). However, realizing from the statement above, Cazden cannot be seen as a primary advocate of functional consonance – because he would attack his own viewpoint
29 with such an assumption. The main idea here remains that consonance explains harmony, but harmony does not explain consonance. Harmony cannot explain all different dimensions in which consonance can operate, even though many theories from the Western discourse were designed to explain harmony. This relation between consonance and harmony is quite similar to that of consonance and euphony.
Either way, as harmonic practice lies at the core of Western tonal music and consonance is often attributed to harmony, it is no surprise that harmony has taken a central position in these discussions. Cazden calls this functional consonance, based on harmonic relations and/or progressions in the spirit of Rameau, which is intrinsic of the idea of Western tonal music. It explains what alienates this musical tradition from the diverse musical traditions in the world. For the same reason, it makes clear why it is preferred to talk about euphony, since consonance – understood within this functional framework – is deeply rooted in the Western musical system. To transcend this harmonic framework, euphony proves to be an appropriate substitute to consonance.
Strikingly, Western tonal music is – especially in regard to the common-practice – a musical tradition that is primarily led by harmonic progressions. If it was not the process of cultural imperialism that made it ubiquitous nowadays, it would be a legitimate question to ask why exactly this "anomaly" among many musical traditions is taken as "exemplary" for the concept of consonance. As Parncutt & Hair comment:
C/D is one of the principal components of MmT, which now dominates the music of the world (including so-called World Music; Nettl, 1985). As much as people appear to love music in major and minor keys, we may also regard such domination as a regrettable form of cultural impoverishment that can be explained by a combination of political and psychological considerations. Politically, Westerners have for a long time had more resources and weapons (Diamond, 1997). Psychologically, music based on MmT may have some kind of cognitive advantage over music whose tonal structure is less clear or more complex: a clear tonal structure makes music easier to encode, store and recall musical structures, so they place less load on the cognitive system (Deutsch, 1980; Tillmann et al., 2000). (Parncutt & Hair 2011: 131)
The observation that "MmT" has a cognitive advantage over music with a more complex structure seems right in the sense that the majority of people is drawn to simplicity rather than complexity. However, I am highly suspicious about the argument that the same "MmT" has a cognitive advantage over practically any other musical system in the world, which is what Parncutt & Hair imply as well. Evaluating musical systems on the presupposition of "cognitive advantage" is
30 completely dependent on what the criteria for advantageousness are, and how these are measured. In spite of having a clear tonal structure, music based on MmT varies in complexity, too. "Simpler" forms of music always have existed, and are – for a great part – determined by power relations or social hierarchy, i.e. the distinction of classical music or "art music" versus folk or "vulgar" music. To mind comes the so-called salon music in 19th and 20th-century Europe, mostly referring to piano pieces for private usage by less educated people. In North-Indian music, classical music strictly refers to genres that show the rāga in all sections (such as dhrupada), whereas "semi-classical" genres as humrī stress words in favour of the rāga (Van der Meer 1980: 79). Often, the distinction is caused by the exclusion of education in music, and therefore simplifications of rules, techniques, instruments, language, etc., are logic results. One example of this exclusivist attitude is to be found in the tradition of the qin, a Chinese zither instrument which for a long time was associated with the literati (i.e. the Chinese elite). Many treatises for this instrument deliberately omitted chapters about finger techniques and descriptions of tablature symbols, because the qin masters did not want "unqualified people" to have access to this knowledge (Kaufmann 1967: 273). The literati also experienced "[that] "improper" music is far more attractive than the tones of solemn rites" and tried to preserve their tradition this way (Henochowitz 2010: 375). I, therefore, contend that every musical culture has simpler genres of music, which emerged not necessarily because of any cognitive advantage, but because of technical, educational or financial shortcomings. Additionally, it is entirely dependent on the frame of reference what makes music (cognitively) simple, because no generalization can be made between distinctive musical traditions in the world.
This brings me back to the perception of euphony, something which is dependent on a frame of reference as well. As I have noted multiple times, seeing euphony as "legitimization of harmony" is an inadequate point of view in musical traditions around the world in which harmonic progressions do not exist or are insignificant. The connection Rameau found between the major triad and the harmonic series is not something self-evident, likewise, such a correlation would not arise from the mind of a musician in North-India or Java, merely because their musical reality did not demand such explanations. As argued above, the disconnection of harmony from consonance shows the advantage of the use of euphony. The implications this absence of a "harmonic framework" has for the notions of euphony within the classical music of North-India will be discussed below.
Hindustani music North-Indian (or Hindustani) music as it is known today has taken much of its present form since the 14th and 15th centuries, even though old treatises on arts, like the ā a ā ra or the Dattilam still
31 have influence on the musical practice. There are several points of interest regarding the Hindustani musical culture. It is primarily based on melody and rhythm, with much emphasis on improvisation. In case of vocal music, the singer is accompanied by a constant drone of the ambūrā, a second melodic instrument such as the ārangī or harmonium, and a percussion instrument, mostly the ablā or the pakhavaj. Most of the primary instruments in the North-Indian music tradition indisputably have harmonic spectra (i.e. the voice and the ambūrā). The ablā, probably contrary to one’s expectation, largely has a harmonic spectrum caused by its membrane of nonuniform density (Vautour e.a. 2013). Indian percussion instruments are a distinct group of percussion instruments, as they are characterized by having many harmonic partials in general.
The musical practice is guided by the most important and all-embracing "concept" rāga. In its narrow and technical sense, it embodies the melodic framework of scale, phrases and intonation, but it has an ideational side too.10 The framework of measure or time, called āla, defines rhythmic cycles and stresses. Musical performances develops in melodic and rhythmical ways within distinct sections (Carterette e.a. 1989: 87). Because the emphasis of the music lies more on the melodies of the singer or that of the lead instrument, one can expect a higher importance of euphony between tones, as opposed to simultaneous sounding tones. This is reinforced by the fact that the modern practice of North-Indian classical music is characterized by the drone of the ambūrā, which creates a static harmonic background – and there is no such things as modulation (Ibid.: 86-87). With this in mind, it is time to turn to the early concepts of euphony.
Despite being a musical tradition that is not based on harmony, terms for consonance and dissonance have existed in North Indian classical music. This would suggest that the perception of consonance is not dependent on harmony or harmonic relations, given the fact that these terms come from the ā a ā ra, often ascribed as being from the first two centuries AD (Arnold 1999: 23). The same could be said from the theories of Pythagoras and Boethius, as they predate the polyphonic (and therefore, harmonic) music in Europe. This is reminiscent to the notion that consonance does not necessarily stem from simultaneous sounding tones, which is already discussed in passing in an earlier chapter. It might be tempting to look at old musical sources like the ā a ā ra or the Dattilam, but a little can be gained from them in relation to the current musical practice. Even though music theory in North-India is old, it is a severe misconception to think it remained unchanged over two millennia. Counter-intuitive as it might be, assumptions like these have often been made from a Western point of view regarding traditional music elsewhere in the world, including North-Indian music: "it is often assumed that traditional cultures, as e.g. in India, are
10 Van der Meer argues that rāga actually escapes the category of concept, and rightly so, because it is present in so many levels. One must bear in mind that I only use the technical implications of rāga in this section.
32 rather inert and that the art forms hardly ever change" (Van der Meer 1980: ix). Although such viewpoints are scarce now – 35 years later – there also remains a strand of scholars who are inclined to explain today's musical practice with theories of the past (Jairazbhoy 2008). When this is done too strictly, a continuity is assumed between ancient theories and contemporary musical practice, thereby ignoring changes in meaning and usages. This is quite similar to "natural law" theories, which are, following Cazden, "inadequate as explanation of historical change in music" (Cazden 1945: 3).
For North-Indian classical music, an alleged continuity between the ancient past and contemporary practice seems inadequate, too. As Jairazbhoy points out regarding the conflicting ideas about ru i , many of the old terms appearing in the ā a ā ra are now out of usage. He states that "the only element of continuity that remains is in the names of the seven notes, but the names of the grāmas, jātis, and those of the fourteen (or twenty-one) mūrcchanās as well as the twenty-two śrutis are no longer in use" (Jairazbhoy 2008: 353). A more striking example is that two characteristic concepts of North-Indian music nowadays do not appear in the ā a ā ra, i.e. a Sanskrit term for drone, and the word rāga (Ibid.: 353). One can argue that the drone of the ambūrā and the concept of rāga now are the most idiosyncratic or vital aspects of North-Indian music, while both concepts probably stem from the 14th or 15th-century (Carterette e.a. 1989: 86). This must have changed the musical practice radically, hence the “continuity theory” does not seem to be tenable.
Vādī & samvādī The same can be expected of the old concepts of euphony in North-India. The ancient qualification of tones, as given by the ā a ā ra and many musical treatises afterwards, are vādī (sonant), amvādī (consonant), anuvādī (assonant, i.e. neutral) and vivādī (dissonant). Indeed, for these concepts the same applies as above; the names are consistent, but not their usage and significance (Jairazbhoy 1971: 43). Originally, the important note in a mode was called aṃ a, but the term vādī was treated as a synonym by later writers and more or less replaced the term in the course of time. In a similar vein, amvādī is now treated as "second important note", generally – but not necessarily – a fourth or a fifth apart from the vādī. According to Jairazbhoy, anuvādī and vivādī are still sometimes used by theoreticians, although the meaning of vivādī is vague. Anuvādī can be any note that is not vādī, amvādī or vivādī, but for vivādī is remains unclear if it would be an omitted note in a rāga, or a non- essential note that may be used effectively by experts (Ibid.: 44).
The opinions about these concepts in contemporary practice differ. Since vādī and amvādī are not fixed in a given rāga, there is much deliberation about how to apply the terms, and which notes are the most important. Bhātkhaṇḍe, as cited by Jairazbhoy, formed the theory that the time
33 of performance of a rāga is connected to its scale and vādī, resulting in a cyclic organization of ha s11 (Jairazbhoy 1971: 61-64). In a later article, Jairazbhoy states that this categorization in time of Bhātkhaṇḍe probably influenced the author's choice for certain vādī, but as Bhātkhaṇḍe is a influential scholar, his theory is widely accepted (Jairazbhoy 1972: 67; Ibid. 1971: 45). There does not seem to be a guideline for the designation of a vādī in a particular rāga. According to Van der Meer, the relation vādī- amvādī is not audible too:
Neither students nor listeners can distinguish between rāgas on the basis of the importance of notes and a systematician is baffled by the fact that each note has its own importance, depending on circumstances. Undoubtedly the importance given to the function of individual tones in the ancient treatises has led modern scholars to exaggeration. The musicians mostly attach value to the negative aspect, i.e. wrong usage of tones or overstressing of a particular tone in a rāga (Van der Meer 1980: 4).
It seems that the allowance of irregularities is quite a vital part of a rāga. Firstly, rather than formulating rigorous treatment of consonances as observed in the contrapuntal and tonal period of European music, much depends on the circumstances in Indian classical music, and its improvisational character grants the performer relative freedom. However, this must not lead one to think that Indian classical music is freed from any fixation. It precisely is the most "classical" genre, dhrupada, that has a fixed arrangement of sections, i.e. a proper introduction of the rāga (ālāpa), the full composition (with fixed melodic movements) and concluding with rhythmic variations (Van der Meer: 28). Secondly, it is striking that musicians "attach more value to the negative aspect" of their melodies. Thus, instead of formulating rules to treat melodies properly, they are more concerned with how to do it "not improper" – which seems a subtle difference to me. Reminding the statement of Jairazbhoy about vivādī notes, this difference becomes more apparent. Not designing notes as vivādī and omitting them from the rāga would logically lead to a fixed practice. But allowing them "when [they are] used with sensitivity, it is considered particularly beautiful" (Jairazbhoy 1971: 45). Based on these assumptions, the vivādī notes can enrich the rāga in particular circumstances, if used with great prudence. As will be demonstrated in further examples, the dynamic character of rāgas has more answers relating to melodic problems, too.
I have talked about vivādī often, but is there any consensus about amvādī notes, as understood in the old meaning of "consonance"? This question can be answered affirmative, although not entirely unanimous. Many scholars agree on the importance (and consonance) of the
11 A hā is a group of rāgas based on their scale the placement of accidentals in this scale (Carterette e.a.: 96).
34 fifth and the fourth in Indian music (Van der Meer 1980; Jairazbhoy 1972; Widdess in Arnold 1999). This is reasonable because they are mostly present in the drone (Carterette e.a. 1989), but also because the scalar notes sa and pa have an immovable quality – they cannot be altered (Cooper 1977: 13). Even though there are three different tunings of the ambūrā (pa, ma and ni12), pa is the most commonly used tuning. This relates well to Van der Meer's remark:
We may conclude that the majority of important rāgas are based on scales with strong fifth consonance and that the possibilities of consonant scales are fairly well exhausted by the extant rāgas. (Van der Meer 1980: 15)
Indeed, there may be many rāga with no clear "fifth consonance", but it is a solid manifestation if they are less used in practice. In addition, Van der Meer goes on to say "that the [harmonic major third is important] in particular due to the tānpurā, where the ga is stronger than the tonic itself" (15- 16). This sounds questionable, since the ambūrā is never tuned with the third scalar note ga. In addition, Jairazbhoy does not name ga as consonant, and Narendra Kumar Bose (1960) contends that the minor third is more consonant than the major third. However, if one looks at the graphs of Carterette e.a., the claim that ga is stronger than sa is perfectly demonstrated. In the case of the hā s Kafi, Bāge rī and Bhīmplā ī, ga is dramatically enhanced when applying the juari,13 and for Kafi and Bhīmplā ī, ga is far more present than sa – for Bāge rī they are almost on the same level (Carterette e.a. 1989: 100-101). On the other hand, the pa tuning does not feature an enhancement of ga in neither of the hā s, so it must be noted that it is dependent on the tuning of the ambūrā.
Jairazbhoy (1972) states that only the fifth and the fourth are considered consonant according to the ā a ā ra, in which the major third is an assonant. On the other hand, only the seventh and second are considered dissonant in the ā a ā ra. This leads to some dubious relationship between vādī and saṃvādī, especially when augmented or diminished intervals are in play:
There are, however, several rāg in North Indian music where the relationship between vādī and saṃvādī is extremely dissonant, for instance, in the rāg Pīlū, Mārvā and Khamāj, where it is an augmented fifth (or diminished fourth), and in rāg such as Śrī and Gaurī, here, according to Bhātkhaṇḍe's system, it is an augmented fourth. (Jairazbhoy 1972: 66)
12 In order of occurrence. Pa is the most common, ni is only used when both pa en ma are absent in the rāga (Carterette 1989: 88). 13 The juari is the "life-giving" thread applied on the ambūrā that strengthens many upper partials.
35 I am puzzled by Jairazbhoy's usage of "extremely dissonant" in this phrase, as he only names the minor second and major seventh as vivādī, drawing on the ā a ā ra. In relation to his tritone hypothesis (which he formulated more than thirty years later), there is some evidence to regard these intervals, the augmented fourth or diminished fifth, as dissonant. However, I am doubtful about this seemingly weird conflation of Indian and Western ideas of consonance. Jairazbhoy also speaks of a augmented fifth or diminished fourth as being dissonant, while he states – regarding a different issue about the usage of both the natural and altered fourth in a particular scale – that "musicians do not appear to distinguish between the Ma♯ as an augmented fourth and the Ma♯ as a diminished fifth" (Jairazbhoy 1971: 50). According to him, this reinforces the argument for the 12-TET system as well (Ibid.). From this point of view, I wonder if the augmented fifth/diminished fourth he mentions in the citation above, then, is not perceived as minor sixth/major third. After all, this interval would at least be classified as anuvādī (assonant), and in 12-TET they are unquestionably equal. To get clarification on this matter, I think one has to turn to actual practice, rather than theory, and pose such questions to musicians.
Examinations of the North-Indian tradition that pursue justification from Western theories – mainly that of Helmholtz, and in effect, Rameau – seem to exist too. Somehow, it is not surprising to see such an undertaking as that of Bose (1960), in spite of the fact that this is exactly what I would claim to be a faulty practice if it would come from a Western scholar. In his book Melodic Types of Hindusthan, Bose calls this an examination "from the scientific point of view" (Bose 1960: 60). Maybe the only comfort is that it is only one chapter in a quite dated book. I was really disconcerted by Bose's elaboration on ratios, triads(!), and the application of the "fundamental bass" to North-Indian music – without mentioning Rameau, as he mostly refers to Helmholtz. Speaking of strange conflations between theories from Western classical music and Indian classical music! However, there is one thing to learn from such a strange chapter in this colossal book that even underpins my contention that the perception of euphony cannot be universal. In Bose's chapter, it is clearly visible how a different handling of numbers (and ratios) leads to a completely different understanding about the relationships between tones and triads. For example, Bose concludes that the minor triad is perfect and the major triad is imperfect, and that their second inversion is more pleasant than the "root" position, followed by the first inversion (Ibid.: 45-46). This is done with the same ratios as those of Zarlino or Rameau. Later in the chapter, he applies the same reasoning for the consonant triads to the dissonant ones, and concludes the chapter by stating that "all perfect melodic phrases are based on these fourteen triads [dissonant triads and consonant triads] in different forms according to their positions in the scale" (Ibid.: 52). It justifies a lot of things, but it stands miles away from the actual practice to sound relevant. To me, it is only a justification how far interpretation of
36 the same information – but in a different frame of thought – can deviate. That being said, I want to proceed to a last discussion of a theory within Indian music that is more carefully formulated than the latter.
The tritone The interesting discussion Jairazbhoy raises is that of the tritone in North-Indian music, of which he contends that it is treated as a “devilish interval” like in Western classical music (Jairazbhoy 2008: 358). In the ā a ā ra, the jā i (the old modes) were described with a feeling or mood called rasa. While all jā i have positive associations, the jā i starting on dha (called Dhaivatī, comparable to the Locrian church mode) is connected to the rasa of bibhatsa (disgust) and bha ānaka (terror). Reasons why these emotions are coupled to this mode is something that probably can never be answered, but the hypothesis is that it is the cause of the tritone interval. However, Jairazbhoy, who calls this the tritone a urān ar (demon’s interval), does find that this interval still affects the classical music of present day. Many rāga feature alterations or omissions of notes within their scale ( hā ) to establish balance and avoid the tritone. For instance, several rāga in Mārvā hā (Mārvā, Sohnī, Pūri ā and Pūri ā Kal āṇ) would include two tritones based on how Mārvā hā is constructed, with a lowered second step (re) and a raised fourth step (ma). However, all these rāga are notable because they all omit pa and, frequently, sa.14 This is because pa cannot constitute a consonant fifth with re komal, and sa cannot constitute a consonant fourth with ma īvr, but both constitute tritones instead (Ibid. 2008: 370). While these instances of tritones are slightly less obvious than in the Dhaivatī scale, in which it occurs between sa and pa, there is ample evidence to say that the interval is omitted on purpose in musical practice. On the other hand, Jairazbhoy initially claims that these alterations of the hā are unconsciously applied. Regarding the tritone in Bilāval hā , he says that the use of both ni komal and ni uddh are subconscious alterations of the performers:
It is obviously this tritone which is in some way responsible for the two mas and nis in these [i.e. Bilāval and Kalyāṇ] rāgs. Since musicians are not consciously aware of the tritone between ma and ni, and there is no conceptual or linguistic term for the interval, the accidentals ma♯ or ni♭ are evidently introduced subconsciously in response to this scalar imperfection, in order to temporarily produce the perfect fourth interval, either m♯ to ni, or ma to ni♭. (Jairazbhoy 2008: 367)
14 This is striking because sa and pa normally are both important scalar notes in Indian music. Sa, however, can never be completely absent because it is always present in the drone (Jairazbhoy 2008: 369).
37 This is an intriguing case. If the interval of a tritone would be seen as dissonant, or "disgusting", it is striking that there is no linguistic term for the phenomenon, or in other words, that this phenomenon is not recognized in a theoretical way. In a same manner, while the jā i of dha, listed in the ā a ā ra, has negative connotations, the tritone is not recognized as vivādī (dissonant) in the same book. On the other hand, these subconscious alterations of the performers do suggest a perceptual disturbance created by this interval, a more subjective approach of the musicians to what they perceive as a less euphonious interval. This view is actually strengthened by Van der Meer's observation regarding "inconsistencies" within scales – the problem that the fifth, fourth and major third cannot be all perfect in the same scale:
N.K. Bose has made an impressive study of these questions and suggests that the dropping of notes, the usage of certain melodic phrases and ornamentation provide the answer to dissonant intervals. Western music has chosen for equal temperament but this is quite unacceptable to the Indian ear. It is my contention that the raga itself is the solution of this dilemma. Various sounds, pure tones as well as inflections, are put together in such a manner that the impression of imperfection in the scale is subdued by the melodic totality. Pitch is not an independent phenomenon but relates to volume, timbre and even ornamentation. (Van der Meer 1980: 10)
Bose, to whom Van der Meer referred, relates the solution of omitting notes to the nature of the scale:
There is, however, a scientific justification for the omission of notes which […] is to be found in the necessity of avoiding false Thirds, which are inherent in the structure of Scales. It has been shewn that the two extreme notes of every Scale Hepted are related to each other as false Thirds. One of these two notes must be omitted in every good melody in pursuance of the melodic rule that every third note must be consonant. Every Scale must, therefore, be used in one of the two possible hexatonic forms… (Bose 1962: 419)
These "false thirds" relate to a common problem of scales, in this case it is the "just intonation", but the Pythagorean scale faces the same problem: the perfect interval relations cannot be put together. Recalling the problem in Zarlino's time: the fifth, fourth and third cannot all be perfect. As Van der Meer points out in the quote above, 12-TET has gradually become the norm in Western musical practice to bypass the intonation problems. However, as both he and Bose claim, such measures were not necessary in Indian music, because the inconsistencies could be solved due to the dynamic character of rāga . While Van der Meer is the only one naming ornamentations and inflexions –
38 which I see as an outstanding feature of the vocal practice in Indian music – I think this also offers the most effective way to conceal these inconsistencies in tuning and scale.
As it gradually became clear, one cannot formulate different concepts of euphony from these different viewpoints in the Indian classical music, like Tenney did for European classical music. I cannot prove this with assurance, because I am not aware of what is known about the handling of euphony in, say, 18th-century India. The backwards looking tradition that emerged in the 19th-century, the practice of "continuity thinking" I explained earlier, could have invalidated the variation that might have existed in the 19th-century, but that is mere speculation. Using the euphony as substitute for consonance made it possible to address North-Indian classical music without struggling with the harmonic framework in which consonance is encapsulated. As I have demonstrated with the conclusions of Bose, a mingling of Western and Indian ideas about consonance can lead to a highly questionable mixture of both.
Another thing that has become evident in this chapter, is that there is no single measure for what constitutes a vādī; the most (and second) important notes are not by any means the most played note – they are not even always a pair of two – they are also not necessarily in a fifth- or fourth-relation to each other, and sometimes the relation between them is dissonant (Jairazbhoy 1971; Carterette e.a. 1989). While many writers agree on the consonance and/or importance of sa and pa, or the "fifth relation" of them, for other scalar notes various theories and statements differ from one author to another, and not even within such a long timeframe. Furthermore, in the North- Indian classical tradition, euphony is not treated harmonically, but melodically. In relation to Jairazbhoy's tritone theory, it has become evident that it is possible for performers to correct certain theoretical inconsistencies by omitting or adding notes, or by using certain vocal inflections, due to the flexible nature of rāga . Euphony, then, is mainly approached with relation to the musical practice, rather than in relation to theory.
39 Chapter 5 Javanese gamelan and inharmonic sounds
The idea that dissonance is a function of the timbre of the sound as well as the musical intervals also has important implications for the understanding of nonwestern musics, modern atonal and experimental compositions, and the design of electronic musical instruments. (Sethares 2005: 5)
The majority of theories on consonance in the Western musical discourse considered the interval relationship of tones to be the cause of dissonance. It is not until Helmholtz that other aspects of tones (i.e. timbre) were deemed important. Like Sethares argues, the notion that dissonance is an interplay of the timbres of sounds leads to a better discussion of music in various cultures and of certain genres, thereby offering more insight in these musics. No theorist I have mentioned in this research considered the possibility that the types of musical instruments used in musical practice are able to influence the perception of euphony. This is exactly what this timbre-based view takes into account. What could be gained from this should become clear when considering Javanese gamelan music.
Gamelan music (whether Javanese or Balinese) has very little in common with Western tonal music outlined in the first case study, or the North-Indian classical music I have discussed in the second. One could guess that a textbook definition of consonance is completely irrelevant here as well. There are at least four distinct features of gamelan music that have an impact on the perception of euphony. Firstly, a gamelan mainly consist of metallophones like the bonang, kenong, gender, saron and gong. This group of instruments, as I shall explain below, have features that do not correlate with the acoustical theory of strings (on which Helmholtz based his theory too). Secondly, gamelan music is oriented on melodies which are played in a heterophonous setting. Thirdly, two idiosyncratic scales are employed, called pelog and slendro, both of which are very different from the Western 12 tone equal temperament (12-TET). Lastly, since there is no fixed tuning, every gamelan is tuned differently. These four briefly addressed aspects all affect the way euphony can be seen in Javanese music. All aspects have their own implications, even though they might not be directly obvious.
The usage of (mainly) metallophones in gamelans shows a preferences for a specific type of instruments, that is, instruments made of metal. The striking difference here is that the physical
40 properties of metal bars, chimes and bells produce inharmonic spectra, as opposed to the harmonic spectra of mainly string instruments.15 There is only one metal instrument with a long history in Western music, the church bell, musically used in a carillon, that would have similar acoustic properties. However, publications about the acoustic behaviour of idiophones, to which these metallophones belong, are very scarce (Schneider & Beurmann 1993: 201), and their acoustic properties are difficult to explain. The implication of the preference for metal instruments in Java and Bali is that it renders approaches based on "natural overtones" useless. For instance, the partials of a bonang are as natural as those of a violin; in spite of being totally unrelated. Similarly, the much loved Pythagorean ratios explain nothing in this case. This will be demonstrated in more detail later.
The second aspect that is important, is the practice of the music, which, in the case of Javanese and Balinese music, is often described as melodic and heterophonic (Perlman 2004: 123). This means that music is composed of a melody,16 which is reiterated differently by the instruments in a gamelan. The performed music is constructed of cycles of melodies, rather than harmonic progressions. As mentioned in the previous chapters, any theory based on dissonance in harmonies, is something that exclusively explains a phenomenon in Western classical music, and does not reveal anything for Javanese music as well.
Thirdly, Javanese and Balinese music employ two idiosyncratic scales, a seven tone scale called pelog and a five tone scale called slendro. The most remarkable facet of these scales is that they are not fixed, as there is no fixed tuning of gamelans either. Somehow theorist have been extremely fond of calculating the intervals of slendro and pelog scales in cents after Jaap Kunst, who was the first to do so in his work Music in Java (1949). However, after a better examination, it quickly becomes clear that such an undertaking is oversimplified, and almost meaningless for the pelog scale. While slendro equals a 5-TET scale, and approximates intervals of 240 cents (as observed by Kunst), the actual intervals still depends heavily on the gamelan used. Stretched or compressed octaves are not uncommon, intervals differ from octave to octave, and, in addition, most gamelans attune one note so that both scales have one note in common (Sethares 2005: 211). For the pelog scale, the story is even more complicated, because the scale has irregular tone steps. Even the average cent intervals Sethares provides for two gamelans may differ more than 30 cents in comparison to the average intervals measured over 70 gamelans by Surjodiningrat et al.. Generally speaking, the pelog
15 Harmonic spectra are defined as tones having partials with multiple integer frequencies, while inharmonic spectra contain irregular or non-integer multiples of frequencies. 16 According to Ishida (2008: 495), gendhing used to refer to the basic composition or melody in pre-notational period, while balungan took over that position when notation was adopted. The changes that came along with this implementation reversed the meaning of both concepts.
41 scale can best be described in terms of small and large steps (SSLSSSL), which is true for every pelog scale, although the sizes still differ (Ibid.: 213-214).
The last important factor to note is the tuning of a gamelan, which differs per ensemble. The tuning of a gamelan is constituted mostly by the saron and gender, and, apparently, sometimes by the gambang kayu (Gomperts 1995: 181). All other instruments in the ensemble are tuned to these instruments, but there is no fixed guiding tone towards all gamelans should be attuned. This "loose" practice is metaphorically explained by Purwardjito, as quoted by Sethares, who says that "Gamelans are tuned to nature. In the west you tune with your mind. In Indonesia, we tune with the heart" (Sethares 2005: 215).
Bearing these differences in mind, one will not come far with, for example, redefining consonance in a way Kolinski (1962) does and applying that result to gamelan music. It asks for an approach that transcends the general "interval based" concepts of consonance. To my knowledge, people have not used specific terms that denote any degree of euphony between successive notes in Javanese or Balinese music. But the simultaneous or successive sounding notes are not the only factors that constitute consonance. William Sethares perfectly demonstrates that by analyzing two different gamelans in terms of sensory consonance, shifting the attention to the relationship between spectrum and scale as shown by dissonance curves rather than supposed qualities of individual tones or harmonic relations between them. The term sensory consonance is adopted from Terhardt (1984), who reformulated Helmholtz' term Konzonanz as such. According to Terhardt "sensory consonance is defined as the more or less complete lack of annoying features of a sound; it is pertinent to such sensory parameters as roughness and sharpness (i.e., on the physical side, amplitude fluctuations and presence of spectral energy at high frequencies)" (Terhardt 1984: 282). Although somewhat awkwardly formulated as "annoying features", these properties of sounds are essential for the perception of them. It baffles me, then, to think of what would be perceived as more annoying: a plane sine wave or a powerful gong strike.
Spectrum and timbre What draws my interest here, is that the realm of spectrum and timbre offers a new ways to approach euphony. That is, a way that is not solely based on pitch interval relations, and more importantly, a way to take euphony of inharmonic sounds into account. Firstly, pitch relations are not the primary criterion anymore, as the relation between spectrum and scale (one that is derived from that specific spectrum) shows different degrees of euphony for certain frequencies. Secondly, one aspect that keeps permeating discussions about consonance is that of ratios, a theory which is
42 grounded on harmonic frequency relations. These ratios do not apply for inharmonic sounds, which are characterized by irregular (or non-integer) partials. Discussing inharmonic sounds is crucial, because in reality there are more distinct inharmonic sounds than harmonic ones.17 Harmonic sounds contain frequencies of vibration that are integer multiples of its fundamental frequency, in theoretical models often referred to as the vibrations of an "ideal string" (f, 2f, 3f, 4f, 5f, 6f). Half- open air columns also fit in this pattern, but their spectra only include the odd-numbered partials. Inharmonic sounds do not have a particular spectrum they correspond to, because their spectra are mostly irregular. While infinite deviations on a harmonic spectrum are possible, a common approximation of one inharmonic spectrum is that of an "ideal bar". Contrary to the integer multiples of a fundamental frequency, the first six partials of an ideal bar are f, 2.76f, 5.41f, 8.94f, 13.35f, 18.65f (Sethares 2005: 114). The gongs used in a gamelan, on the other hand, have a spectrum totally unrelated to that of metal bars and harmonic spectra, as their six partials are approximated by f, 1.49f, 1.67f, 2f, 2.67f, 2.98f (ibid.: 208). A theoretically "ideal gong" does not exist, as is the case with many other irregularly shaped instruments like bells (Ibid.: 116).
The spectra I had provided as examples may seem irrelevant, but they are crucial to the method Sethares uses for the calculation of a dissonance curve, and how he applies sensory consonance. The basic idea of his theory is that specified partials of a sound (like those above) can be used to calculate a dissonance curve that shows minima at certain points where sensory dissonance is minimal. From these minima, an appropriate scale can be derived that is in tune with its spectrum. This is the only theory that makes much sense for the gamelan music. Like the dissonance curve shows the relation between the diatonic scale and harmonic sounds, it also shows the relation between the Javanese scales and the inharmonic sounds. In fact, it gets slightly more complicated than this simple analogy, because both harmonic and inharmonic instruments are used in a gamelan. This can be overcome by calculating the spectrum of a Javanese instrument together with a harmonic spectrum (Sethares 2005: 216). Sethares demonstrates how the first four partials of a bonang in combination with a harmonic sound create a dissonance curve that fits the slendro scale, and even concludes that it approximates 5-TET even better than the just scale does for 12-TET (Ibid.: 217). Even though pelog is a more complicated scale because of the variety in tuning, the approach is still fruitful albeit specific to one specific gamelan. In this case Sethares combines the spectrum of the saron with a harmonic sound, which fits all but the second and last tone(s) of the pelog scale. While it might seem a mismatch, this result actually is quite reasonable for the last scale steps in pelog show the most differentiation, even from octave to octave within a gamelan (Ibid.: 219). In addition, the
17 Because the distinction between harmonic and inharmonic can be simplified to A and not-A, it becomes obvious that not-A has greater variety than A.
43 calculations of Sethares even provide an explanation for the unique intonation of Balinese music, that of audible beats caused by a slightly different tuning in pairs of instruments (Gomperts 1995: 191). In both cases, Sethares found multiple minima around the octave (e.g. at f and f1.02 in case of the bonang) which may account for the audible beating (Sethares 2005: 217).
Initially, there has not been a single theoretical model that makes sense for Javanese gamelan music. However, Sethares' approach clearly shows how spectrum and scale are interrelated, and how degrees of euphony (or the perceived sensory consonance) differ depending on the situation. As shown in this chapter, this interrelationship and the consequences of spectrum and scale have proven to be extremely useful regarding Javanese gamelan. Contrary to showing how "weird" or "foreign" the pelog scale is – something which studies of tone distances in cents only would achieve – it rather shows how reasonable the scale actually is given the circumstances, i.e. the spectrum of the instruments used. The exploration of inharmonic sounds holds a pivotal position in conclusion, which unfortunately is a subject that has been touched upon by very few scholars.
This discussion of Javanese gamelan could not have taken place if I had started with consonance. The confinement to consonance to either harmony or ratios leads to another overarching problem: it is based on harmonic partials. Euphony, free from being tied to functional harmonic progressions, can still be used within this inharmonic context without becoming obsolete. Sethares' terminology (that of a dissonance meter or dissonance curve) is a bit confusing, although it can easily be seen as "euphony meter" of "euphony curve", because the graphs show how euphonious frequencies relatively are in regard to each other. Concluding, in the case of Javanese gamelan music, a radically distinct dimension of euphony can be demarcated.
44 Conclusion
Do we all perceive consonance the same way? Has consonance been treated the same way at any time, in any culture? Are the aesthetic and rationalized judgments of it trans-cultural?
These questions can all be answered with a firm "no". Contrary to what many scholars and theorists want us to believe, there is no universal formulation of consonance. There is no single answer to all different dimensions in which consonance can operate. There is no all-encompassing theory that has proven to be infallible; there has been no natural law, no physical property of a tone that comes to us objectively as a pure fact – neither do they have equal importance to anyone in the world. Rather than seeking universality for euphony, its operation in a variety of dimensions and its unique features of it should be embraced. As I have examined in the case studies, the three distinct musical cultures – which are on their own vibrant, dynamic and subject to change – have not formulated consonance in the same sense. A generic application of consonance has been formulated within the "petrified" discourse of Western tonal music. While it has been treated as a universal value, it is incommensurable with two other distinct musical traditions, that of North-Indian classical music and Javanese gamelan, because of its implicit emphasis on harmony. This problem could be overcome by taking euphony as guiding principle, instead of consonance. Euphony has shown to be a less loaded term, and is able to adapt to different frames of reference. This is especially true for the discussion on the Javanese gamelan, as it would be impossible by using consonance. This new method to study euphony in musical cultures that are not dependent on harmony started off with the fairly new approach of Sethares. The observance of the relation between spectrum and scale makes it possible to talk reasonably about euphony in the gamelan tradition, and shows great potency for further research. Thus, what these case studies pointed out is clearly not a universal treatment or attitude towards euphony and consonance, but a great variety in the operation of the concept due to cultural and musical differences between the musical traditions.
Surprisingly, all problems around the concept of consonance I have addressed in this research have caught little recognition, and they lack serious engagement of musicologists of the present day. The cultural approach I have taken as guideline stems from ideas back in the 50s of the past century – and has been overlooked perpetually since then. While scientific studies on consonance are increasing, I hope this topic will garner more attention on a cultural, social, or practical level. That being said, this research unfortunately falls out on the latter aspect: is its connection to musical practice. As I have discussed, some matters can only be cleared up by looking
45 at the actual practice, such as in case of the tritone hypothesis of Jairazbhoy. It would be really interesting to hear from musicians how they evaluate euphoniousness in their music, rather than focusing entirely on musical theories. Related to this, an option for further inquiry would definitely include a focus on the social circumstances in which the perception of euphony emerge, because this matter is almost never touched upon. The Western and Indian classical music were, at least for a long time, music of the elite, and gamelan initially was court music. These social structures within music making should also have had an impact on the concept of euphony. Another option for research would be related to the study of Carterette e.a., which can be verified or reworked with the dissonance curve approach. The relation of ambūrā spectra to different hā s is exactly what a dissonance curve shows. Given a specific spectrum of a ambūrā tuning, scales can be matched to it accordingly. The effect of juari ("life-giving threads") can be measured as well. There are many more instances for which the dissonance curve can be used effectively, particularly to sounds or instruments with inharmonic spectra. Transcending the boundaries of Western tonal music in all possible ways listed above will broaden the view towards euphony, eventually dissolving the vague universality consonance has been attributed with. Hopefully, my research provides a small contribution to this objective.
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