Dissonant Views on Consonance: The Cultural Dependency of Consonance and its Reinterpretation as Euphony

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

Contents

Preface

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Chapter 1 - Consonant views on consonance?

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The cultural approach

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Chapter 2 - Consonance in the Western discourse

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Introduction to the case studies

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Chapter 3 - European common-practice and tonal consonance ∙

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The contrapuntal concept

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21 The triadic/tonal concept

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22 The sensory concept

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Chapter 4 - North-Indian classical music and the (absence of) harmony ∙

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Hindustani music

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Vādī & samvādī

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The tritone

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Chapter 5 - Javanese gamelan and inharmonic sounds

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Spectrum and timbre

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Conclusion

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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.

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.

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

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

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

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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.

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

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,

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.

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.

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.

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

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The Gestalt theory claims that there are wholes which determine their smaller elements, but which are not determined by its smaller elements.

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

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Twelve tone equal temperament.

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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.

"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

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

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.

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

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

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 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.

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

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

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.

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

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,

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

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

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