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Books > Performing Arts > Carnatic > Pitch Analysis in South Indian Music (With a Critical Examination of The Theory of 22 Sruti-s)
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Pitch Analysis in  South Indian Music (With a Critical Examination of The Theory of 22  Sruti-s)
Pitch Analysis in South Indian Music (With a Critical Examination of The Theory of 22 Sruti-s)
Description
About The Book

This book embodies the pioneering doctoral research work of Mdhu Mohan konaragiri. This is the first time a comprehensive pitch analysis is presented in South India music holisitically combining ancient Sanskrit musical treatises, medieval and modern musicological interpretations, neurophysiological hearing process and psycholacoustical pitch perception corroborated with computer pitch analysis of actual audio samples specifically recorded for the purpose of this research. This contribution is significant and original.

In his bold and critical analysis, the author shows why the theories of 22 sruti-s are inapplicable to the system of raga music . He explains why surti is not quanitifiable. The modern theories based on Western tuning concepts and mathematics, that place the 22 sruti-s among the various raga-s have been completely debunked. The fluidity of svara has been clearly demonstrated with multiple characteristic Pitch Profiles of svara-s that are context-department. The author talks about intonation guided by the psycho-physiologically driven tonotpic organization in the primary auditory cortex in the brain. He highlights t he non-acoustcal dynamic variability in intonation, influenced by perception. In line with this analysis, concepts such as the octave, intervals, scales, modal shift of tonic, and consonance have been freshly re-examined.

The author explains the fundamental concepts lucidly while clearing some widespread myth. This is book is indispensable for research scholars and valuable for students. The general reader will find informative book quite stimulating.

 

About The Author

Madhu Mohan Komaragiri is a senior consulting electrical design engineer with the nuclear power industry in Canada and is a licensed professional engineer [PEng] in Ontario, Canada he. Secured BEng from Osmanina University and Meng from Concordia University in Montreal, Canada. He worked in several engineering positions in Canada, including an overseas teaching assignment with the University of Guyana. Even while operating at such a high level of engineering proficiency, he managed to pursue Indian classical music passionately and adeptly. He learnt both Carnatic and Hindustani classical vocal music from leading teachers in India. Currently , he trains full-time with the legendary musician, Dr. M. Balamurali Krishan on a one-on-one basis. He is an experienced performing artiste in Carnatic vocal music. He has released music albums in different genres. He picked up a Diploma and gold medal in MMus and obtained PhD from the Madras University for his fundamental research on Pitch Analysis . He is empaneled with the Gandharava Mahavidyalaya, a premier pan Indian music institute for Carnatic music curriculum and doctoral dissertations. To his credit, he has several seminal research articles published in musicological journals and lecture-demonstrations presented in international conferences.

 

Foreword

This book embodies pitch analysis of Carnatic raga music as performed today. The author has carried out extensive research and analysis in the intonation of raga-s in Carnatic music. His comprehensive research proves that the theory of 22 sruti-s is not applicable to the current raga system; he says, "this dearly shows that the widespread belief in the sanctity of the quantification of the twenty-two sruti-s is inadmissible."

The author has based his empirical research on the performance of the various raga-s and not merely on scales. His experimental research on the present-day raga music as performed by great performers shows that "the theory of 22 sruti-s is not valid in today's raga music." This excellent work demonstrates lucidly that sruti-s in practice are innumerable and not limited to finite number such as 22. The approach in the author's analysis is scientific; it is not based on opinions. This pioneering research work is indeed bold and honest in showing as untenable the currently prevailing theories of intonation in Carnatic raga music.

This book contains five chapters induding the Introduction and the Conclusions. In Chapter 2, the author gives a brief background on the term sruti gleaned from themusical treatises. He then examines the famous 2- vina experiment of Bharata as given in the Natyasastra and explores the various intervallic arrangements to show that Bharata's concept of sruti could not be extended to the current raga system where the intervals are variable. He then scrutinizes the interpretations given by Sarngadeva, Ahobala, Venakatamakhi, Govinda, and Subbarama Dixitar. Theories of 22 sruti-s propounded by the modern scholars have been evaluated and the theories placing these 22 sruti-s among the various raga-s have been shown to be flawed. Certain relevant issues such as the ocatve, intervals, scales, modal shift of tonic and consonance have been freshly looked at. This chapter ends with a note on the tambura.

Chapter 3 elucidates the factors affecting the pitch perception with a realistic flow diagram depicting the complex process of pitch cognition. Understanding the physiological and psychoacoustical factors is vitally essential in the study of musical pitches. It has been explained that the pitch maps stored in the brain guide intonation dynamically. This chapter then talks about the role of mathematics in the study of music.

Chapter 4 presents the computer pitch analysis results. The pitch measurements are depicted in the form of graphs called as "Pitch Profiles." This systematic study conclusively shows that the musical pitches in the present-day Carnatic raga music have characteristic profiles as opposed to rigid values. It has been shown that the intonation is dynamically variable and does not follow the modern theories of 22 sruti-s. For the benefit of the readers, in addition to a lot of technical information, the author provides detailed empirical analysis data in the appendices at the end of the book.

An exhaustive interdisciplinary study of musical pitches such as this, is the first of its kind within the formal context of a doctoral research. This original research will certainly pave way for further research. The author's findings and analysis are thought provoking and refreshing. They reflect the actual practice of current raga music. In fact he syas, "as music undergoes changes, the theoretical framework should also change to accommodate the changes." That way, the unhealthy gap between the theory and the practice of music can be bridged.

This book is no doubt a welcome addition to the musicological literature and stands out as an example of serious research. I am confident that this important, seminal work will be received well and valued dearly by the scholars, academicians, researchers, students of music and the music aficionados including the general readers. I congratulate Dr Madhu Mohan Komaragiri on his significant contribution and wish him all the very best.

 

Introduction

Music is one of the most direct and intimate experiences for human beings. In its basic raw form, it is universal in its appeal. The categorization of music into different genres is human-made. The theorization, particularly of classical genres, is the deliberation of human intellect. But musical experience pertains to the realm of human emotion. The intellectual being and the emotive being are two different entities that operate sometimes in tandem and at other times at tangent. It is the nature of the brain to seek order. It has always been a human endeavor to find that order in nature. Disorder is disturbing. Order is fascinating and mystical; and is considered divine.

Musicologists belonging to different music cultures in the past have tried to rationalize and make intellectual sense of music. But, is music merely rational? In their pursuit of that elusive and divine perfection, they have hitherto overlooked the perception of music. This resulted in irreconcilable differences between the practice of music and its theory. As music is dynamic and is continually changing, theory always lagged behind. This is more apparent in Indian classical music.

Many musicians ignore theory completely without realizing the powerful influence it wields on the practice of music. For example, the name of the higher Ri used in Karnataka music is catuli sruti rsabha. This word comes from theorists. The word carries with it, the idea of 22 sruti-s and the fixation of rsabha precisely on the fourth position from sadja, with a mathematical value of 9/8 assigned to it. But the study embodied in this book shows the fallacies in such pitch fixations. In fact, the very idea of defining a raga purely in terms of iiriihana and aoarohana within the framework of janaka mela-s, resulted from such theoretical deliberations without regard to the laksya. This of course affected fundamentally the foundation of idiomatic raga music. Even major composers were taken in by the 72 mela scheme of Venkatamakhi. This happened because theory was allowed to influence the practice of music. Therefore musicological theories should not be ignored; they should be properly understood and carefully developed to reflect and accommodate existing practice of music.

Musicology should be able to explain the phenomena of music and not restrict or dictate how music should be. But, a theory once formed acts as a guide. This study shows that the extant theories of 22 sruts« cannot explain adequately the phenomena of raga music.

In the field of music like in several other fields, practice precedes theorization. But when theory fails to explain the observed phenomena in music it must be revised. Bosanquet held the contrary view (Bosanquet, 1987) citing examples from Astronomy. But the human element, which is a must in the study of music, necessitates validation of theory from current practice.

In the western music tradition governed by instruments and structured on chord progressions and polyphony, there was a need to fix musical pitches. And since key transposition is an essential element, after testing several octave divisions, Equal Temperament (ET) was adopted despite continued opposition. While this temperament is mathematically perfect, it is not based on the natural harmonic series and is considered acoustically mistuned.

Indian raga music requires neither key transposition nor features to facilitate polyphonic music. The pitches of suara-s (musical notes) therefore need not be fixed unitary values, except to serve as reference to manufacture and tune musical instruments such as the vzr.ta where there is a need to fix the fret positions. The accompanying tambura also provides certain basic reference pitches.

In the past, when laksnakdra-« (authors of musical treatises) spoke about the concept of sruti they were evidently talking about pitches of musical notes and not freguencies (see sect. 1.4 for the difference: between pitch and frequency). Sruti-s are those which are "heard." That is, sruti-s are perceptions of musical pitches, heard in mutual relation and in relation to the ddhdra-soara (tonic). Musical pitches in isolation convey no meaning; a musical context comprising intervals does (Lloyd, 1963).

Thinkers have advocated and allowed pitch deviations from the exact (reference) values. But, what gives these theoretical values the status of being a reference? Deviation from what? This research work examines the validity of the reference itself. Do deviations exist in the absence of such a reference? It is not deviation, but the flexibility and the overall balance in intonation that should be studied. References are theoretical constructs and as such have only an academic significance.

Hawking (1988) gives a detailed account of how the fundamentals of physical sciences have undergone changes over time discarding meta- physical beliefs and mystical associations and adopting more realistic models of the universe based on observation and verification. The idea of a perfect and a static universe and absolute time had to give way to the idea of a dynamic universe and a warped time-space continuum. The Greeks thought that planets orbited in perfect circles and mystically associated musical tones with the perfectly circular planetary orbits. This of course was not founded on verifiable observation and it is now well known that the planets move in elliptical orbits. Nature is not as orderly as it was thought to be. Nature strives for the condition of "ideal disorder" (Winckel, 1967). Laplace's dream of determinism, extending even to human behaviour, had to be jettisoned with the advent of the Uncertainty Principle! of Quantum Mechanics which introduced an unavoidable element of unpredictability and randomness even in physical sciences. (See superscripted numbers in the text in the back matter under heading" otes," pp. 188-94 of this book.)

Not only is the idea of determining fixed singular acoustical values for musical notes is untenable but it runs counter to the exigencies of the raga system. The realm of perception cannot be ignored. The ancient tuning of the griima system has no functionality in the present day Indian music (Powers, 1970) and the associated concept of sruti is also likewise non- functional.

It is essential to clarify certain basic concepts before dealing with the main topic of pitch analysis. This is necessary because of the widespread misconceptions even among musicologists. Let us start with the difference between tuning and temperament.

1.1. Tuning And Temperament
Tuning pertains to the exact positioning of the musical notes, mathematically derived as rational numbers. Temperament is the artistic modification of these pitches to suit a musical style, where, not all the pitches are rational numbers (Barbour, 1953). Tuning provides us a set of reference pitches, which may be used for constructing musical instruments. Temperament is the artistic pitching of musical notes as per the requirements of a musical system. In the context of Indian raga music, tuning pertains to the suara sthdna and temperament is relevant to the svara. Whereas tuning may be physical. temperament is idiomatic, as it is culturally conditioned.

That is, the notion of fixed soara sthana-s applies to the domain of tuning, enabling, for example, the fretting of the vZ1Ja. But the idea of fixed sthdna in the context of temperament is clearly untenable as will i." demonstrated in this book. Raga-s began to be defined in terms of the iirohana and auarohana (i.e., in the scale of reference pitches) around the sixteenth century (Powers, 1970). Therefore the notion of fixed soara-sthiina-s acquired special significance as many modern scholars proposed precise quantification for these suara-s regardless of the context of the raga.

Tuning is different from a musical scale and a mix up results in confusion as is evident from the literature. All the precise mathematical calculations pertain to tuning; a scale on the other hand consists of intervals tempered to fit into one octave. Tuning falls within the realm of physical acoustics, as it is concerned with beats, but temperament belongs to the psycho-physiological realm of perception (Lloyd, 1963) and is culturally inured. Therefore, tuning and temperament are different. (See also Glossary).

1.2. Pitch of Musical Sounds
It is quite difficult to give a precise definition of pitch. According to the American Standards Association, 1960, pitch is generally defined as "that attribute of auditory sensation in terms of which sounds may be ordered on a musical scale." But this definition is neither precise nor comprehensive. Pitch may be explained as the subjective perception of periodic sound impulses in mutual relation, particularly of musical tones. The unit of measurement is Hertz (Hz), or cycles per second (cps)-the same unit as applied to frequency. But there is a difference between pitch and frequency. Whereas frequency refers to any sound impulse physically present, pitch mainly refers to the subjective perception of musical tones as high or low (sect. 1.4). Chapter 3 explains the psycho-physiological factors affecting pitch perception through a conceptual diagram (Fig. 3.1).

Pitch primarily depends on frequency, but may not be identical with it; on the harmonic content of a complex stimulus, in that it roughly equates to the fundamental if all the harmonics are integer multiples of the fundamental; on the loudness as explained in chap. 3, sect. 3.3 and on the timbre (including forrnants''). Duration can also influence the pitch perception. A detailed examination of these factors is not within the scope of the current study.

This book shows that mathematically fixing musical pitches goes against the requirements of the idiom of Karnataka raga music. But, that does not mean that any pitch is acceptable. Definite pitch contours exist to characterize raga-s in the Karnataka system. The characteristic pitch movement of a svara over a range in a given raga is herein christened as the "pitch profile." That is, when a note in a raga is not a fixed point but has a range and movement to express itself, it may be called as a pitch profile of that note instead of pitch, to distinguish between a single point and a range (see chap. 4 for the pitch profiles). The empirical pitch analysis offered in chap. 4 exhibits this fact succinctly. It must however be expressly pointed out here that although a pitch profile captures the characteristic pitch movement of a svara, it cannot convey the full meaning of the svara. As mentioned above, pitch depends on several physical factors which are not dealt with here.

The ability to distinguish one pitch from another particularly when they are separated by a small interval is fundamental to the appreciation of music. But the magnitude of separation, called as the Just Noticeable Difference (JND), cannot be uniquely determined, as explained below.

l.3. JUST NOTICEABLE DIFFERENCE (JND)
Just Noticeable Difference (JND) is a psychophysical unit used to determine the minimum detectable change in pitch. It is the minimum amount of change in pitch that can be perceived. JND depends on several factors such as the frequency range, intensity, duration of the tone and suddenness of frequency change. More importantly, it varies from person to person. It also depends on the method of measurement (Roederer, 1995). JND increases proportionally with the magnitude of the stimulus (Goldstein, 1996). Since JND increases with frequency, it is not the same across octaves.

Between any two musical tones in a given scale, the ear can detect many intermediate pitches (Roederer, 1995). The number of pitches that may be detected by the ear within the octave far exceed the number of musical notes that make up a scale. That is, all these intermediate pitches are not taken as musical notes in a given scale. JND is not applicable to the selection of pitches in a musical scale and by extension, cannot be the basis for pitch selection whether it is Bharata's two-vinya experiment or Sarngadeva's twenty-two-stringed sruti experiment. As explained in sect. 3.3 (under Discrimination), there can be more than 4 pitches that can be distinguished in a semitone. Burns (1999) reported discernment of intervals separated by 30 cents or about 6 to 7 just noticeable intervals in a whole tone. Of course, this number is not unique and depends on several factors as explained above. Therefore, JND should not be equated to sruti.

It must be noted further that JND does not necessarily relate only to musical pitch, for, it is the ability to detect a change in the pitch of any sound stimulus within the audible range. The range applicable to music lies below 5 kHz and is smaller than the audible range, which can extend up to 20 kHz, in a healthy young adult with hearing mechanism intact.

The average ear can hear up to 1400 discrete frequencies over 16 to 16000 Hz. And sensitivity to frequency changes increases with the frequency (Olson, 1967). Winckel (1967) however says that the ear can distinguish about 850 different pitches. The ear can discriminate between two frequencies that are about 0.3% different and this discrimination ability diminishes with the frequency (Pickles, 1988; Backus, 1969; Mathews, 2001).

In addition to the concept of JND, even for the perception of a single pitch, there is a minimum time duration that is required. This is explained in chap. 4, sect.4.4.2.

 

Contents

 

5.4

  List of Tables xi
  List of Pitch profiles xiii
  Foreword xvii
  Acknowledgments xix
  Transliteration xxiii
  List of Symbols, Abbreviation, and Formulae xxv
1 Introdcution 1
1.1. Tuning and Temperament 3
1.2 Pitch of Musical Sounds 4
1.3 Just Noticeable Difference(JND) 5
1.4 Pitch and Frequency 6
1.5 Pitch and Sruti 7
1.6 Intonation 7
1.7 Impetus and Purpose 9
1.8 Scope of Research 12
1.9 Terminology and Organization 13
2 Sruti 15
2.1 A brief Background in musical Treatises 15
2.2 Bharata's two-vina experiment 16
2.3 Bharta's tw o-vina experiment with various configurations 17
2.3.1. The Sarana Process with Equal intervals 17
2.3.2. The Sarana Process with Unequal Intervals 21
2.3.3. the Sarana Process with Svara-s as Positions 27
2.3.4. Physics of Vibrating Strings 35
2.3.5. Bharata's Two-vina Experiment with Variable intervals 37
2.3.6. Position Analysis 39
2.3.7. Practical Problems with Bharata's two-vina experiment 42
2.4 Sarangadeva's Interpretation 43
2.5 Sruti and Svara 45
2.6 Suddha and Vikrta Svara-s 45
2.7 Ahobala's Approach 46
2.8 Venkatamakhi's View 47
2. 9 Govinda and Subbarama Diksitar 49
2.10 Summing Up 49
2.11 Modern Theroies of 22 Sruti-s 50
2.12 Theories of placement of Sruti-s in Raga-s 60
2.13 Related Issues 62
2.13.1. Octave 62
2.13.1.1. Octave Equivalence 62
2.13.1.2. Octave Stretching 64
2.13.2. Intervals 65
2.13.3 Scales 66
2.13.3.1. Pythagorean Tuning 67
2.13.3.2. Just Tuning 68
2.13.3.3. Equal Temperament 69
2.13.4. Modal Shift of Tonic 71
2.13.4. Consonance and Samvaditva 76
2.13.5. Effect of Tambura 77
3 Factors Affecting Pitch Perception 77
3.1. Physics of Music 78
3.2. Physiology of Hearing 80
3.2.1. Non-linearity in Hearing 81
3.3. Psychoacousitcs of Perception 83
3.4. Holistic Appreciation 84
3.5. The Role of Mathematics 89
4 Empirical Pitch Anlaysis 89
4.1 Overview of Pitch Analysis 92
4.2 Experimental Setup and Methodology 92
4.3 Software and Validation 93
4.4 Parameters-Assumptions and Limitations 93
4.4.1. Maximum Acceptable Pitch Deviation, p+_ 93
4.4.2. Minimum time for pitch perception 94
4.4.3. Establishing Pitch 95
4.4.3.1. The issue of Averaging 96
4.4.4. Plotting Pitch Profiles 97
4.4.5. Typical frequency range in Karnataka music 97
4.4.6 PRAAT parameters 97
4.4.7. Sampling Rate 97
4.5 Pitch Analysis Schedule 98
4.6 Results and Analysis 99
4.6.1. Gaula 99
4.6.2 Saveri 109
4.6.3. Bhairavi 122
4.6.4. Hindolam 129
4.6.5. Hamsanandi 137
4.6.6. Nata 144
4.6.7. Begada 144
4.6.8. Mayamalavagaula 145
4.6.9. Discussion 145 145
4.7 Intonational Imperatives 146
5 Conclusions 148
5.1. Recapitulation 148
5.2 Original Contribution Made 451
5.3 Suggested Further Research 151
Conclusions 152
  Epilogue 154
  Appendices:  
  A: 22 Sruti-s 159
  B: Various Suddha and Vikrta Svara Positions 164
  Empirical Pitch Analysis Results 170
  Noes 188
  Glossary 195
  References 204
  Index 210

Sample Pages




















Pitch Analysis in South Indian Music (With a Critical Examination of The Theory of 22 Sruti-s)

Item Code:
NAF761
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Hardcover
Edition:
2013
ISBN:
9788121512626
Language:
English
Size:
10.0 inch x 7.5 inch
Pages:
238
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Weight of the book: 660 gms
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About The Book

This book embodies the pioneering doctoral research work of Mdhu Mohan konaragiri. This is the first time a comprehensive pitch analysis is presented in South India music holisitically combining ancient Sanskrit musical treatises, medieval and modern musicological interpretations, neurophysiological hearing process and psycholacoustical pitch perception corroborated with computer pitch analysis of actual audio samples specifically recorded for the purpose of this research. This contribution is significant and original.

In his bold and critical analysis, the author shows why the theories of 22 sruti-s are inapplicable to the system of raga music . He explains why surti is not quanitifiable. The modern theories based on Western tuning concepts and mathematics, that place the 22 sruti-s among the various raga-s have been completely debunked. The fluidity of svara has been clearly demonstrated with multiple characteristic Pitch Profiles of svara-s that are context-department. The author talks about intonation guided by the psycho-physiologically driven tonotpic organization in the primary auditory cortex in the brain. He highlights t he non-acoustcal dynamic variability in intonation, influenced by perception. In line with this analysis, concepts such as the octave, intervals, scales, modal shift of tonic, and consonance have been freshly re-examined.

The author explains the fundamental concepts lucidly while clearing some widespread myth. This is book is indispensable for research scholars and valuable for students. The general reader will find informative book quite stimulating.

 

About The Author

Madhu Mohan Komaragiri is a senior consulting electrical design engineer with the nuclear power industry in Canada and is a licensed professional engineer [PEng] in Ontario, Canada he. Secured BEng from Osmanina University and Meng from Concordia University in Montreal, Canada. He worked in several engineering positions in Canada, including an overseas teaching assignment with the University of Guyana. Even while operating at such a high level of engineering proficiency, he managed to pursue Indian classical music passionately and adeptly. He learnt both Carnatic and Hindustani classical vocal music from leading teachers in India. Currently , he trains full-time with the legendary musician, Dr. M. Balamurali Krishan on a one-on-one basis. He is an experienced performing artiste in Carnatic vocal music. He has released music albums in different genres. He picked up a Diploma and gold medal in MMus and obtained PhD from the Madras University for his fundamental research on Pitch Analysis . He is empaneled with the Gandharava Mahavidyalaya, a premier pan Indian music institute for Carnatic music curriculum and doctoral dissertations. To his credit, he has several seminal research articles published in musicological journals and lecture-demonstrations presented in international conferences.

 

Foreword

This book embodies pitch analysis of Carnatic raga music as performed today. The author has carried out extensive research and analysis in the intonation of raga-s in Carnatic music. His comprehensive research proves that the theory of 22 sruti-s is not applicable to the current raga system; he says, "this dearly shows that the widespread belief in the sanctity of the quantification of the twenty-two sruti-s is inadmissible."

The author has based his empirical research on the performance of the various raga-s and not merely on scales. His experimental research on the present-day raga music as performed by great performers shows that "the theory of 22 sruti-s is not valid in today's raga music." This excellent work demonstrates lucidly that sruti-s in practice are innumerable and not limited to finite number such as 22. The approach in the author's analysis is scientific; it is not based on opinions. This pioneering research work is indeed bold and honest in showing as untenable the currently prevailing theories of intonation in Carnatic raga music.

This book contains five chapters induding the Introduction and the Conclusions. In Chapter 2, the author gives a brief background on the term sruti gleaned from themusical treatises. He then examines the famous 2- vina experiment of Bharata as given in the Natyasastra and explores the various intervallic arrangements to show that Bharata's concept of sruti could not be extended to the current raga system where the intervals are variable. He then scrutinizes the interpretations given by Sarngadeva, Ahobala, Venakatamakhi, Govinda, and Subbarama Dixitar. Theories of 22 sruti-s propounded by the modern scholars have been evaluated and the theories placing these 22 sruti-s among the various raga-s have been shown to be flawed. Certain relevant issues such as the ocatve, intervals, scales, modal shift of tonic and consonance have been freshly looked at. This chapter ends with a note on the tambura.

Chapter 3 elucidates the factors affecting the pitch perception with a realistic flow diagram depicting the complex process of pitch cognition. Understanding the physiological and psychoacoustical factors is vitally essential in the study of musical pitches. It has been explained that the pitch maps stored in the brain guide intonation dynamically. This chapter then talks about the role of mathematics in the study of music.

Chapter 4 presents the computer pitch analysis results. The pitch measurements are depicted in the form of graphs called as "Pitch Profiles." This systematic study conclusively shows that the musical pitches in the present-day Carnatic raga music have characteristic profiles as opposed to rigid values. It has been shown that the intonation is dynamically variable and does not follow the modern theories of 22 sruti-s. For the benefit of the readers, in addition to a lot of technical information, the author provides detailed empirical analysis data in the appendices at the end of the book.

An exhaustive interdisciplinary study of musical pitches such as this, is the first of its kind within the formal context of a doctoral research. This original research will certainly pave way for further research. The author's findings and analysis are thought provoking and refreshing. They reflect the actual practice of current raga music. In fact he syas, "as music undergoes changes, the theoretical framework should also change to accommodate the changes." That way, the unhealthy gap between the theory and the practice of music can be bridged.

This book is no doubt a welcome addition to the musicological literature and stands out as an example of serious research. I am confident that this important, seminal work will be received well and valued dearly by the scholars, academicians, researchers, students of music and the music aficionados including the general readers. I congratulate Dr Madhu Mohan Komaragiri on his significant contribution and wish him all the very best.

 

Introduction

Music is one of the most direct and intimate experiences for human beings. In its basic raw form, it is universal in its appeal. The categorization of music into different genres is human-made. The theorization, particularly of classical genres, is the deliberation of human intellect. But musical experience pertains to the realm of human emotion. The intellectual being and the emotive being are two different entities that operate sometimes in tandem and at other times at tangent. It is the nature of the brain to seek order. It has always been a human endeavor to find that order in nature. Disorder is disturbing. Order is fascinating and mystical; and is considered divine.

Musicologists belonging to different music cultures in the past have tried to rationalize and make intellectual sense of music. But, is music merely rational? In their pursuit of that elusive and divine perfection, they have hitherto overlooked the perception of music. This resulted in irreconcilable differences between the practice of music and its theory. As music is dynamic and is continually changing, theory always lagged behind. This is more apparent in Indian classical music.

Many musicians ignore theory completely without realizing the powerful influence it wields on the practice of music. For example, the name of the higher Ri used in Karnataka music is catuli sruti rsabha. This word comes from theorists. The word carries with it, the idea of 22 sruti-s and the fixation of rsabha precisely on the fourth position from sadja, with a mathematical value of 9/8 assigned to it. But the study embodied in this book shows the fallacies in such pitch fixations. In fact, the very idea of defining a raga purely in terms of iiriihana and aoarohana within the framework of janaka mela-s, resulted from such theoretical deliberations without regard to the laksya. This of course affected fundamentally the foundation of idiomatic raga music. Even major composers were taken in by the 72 mela scheme of Venkatamakhi. This happened because theory was allowed to influence the practice of music. Therefore musicological theories should not be ignored; they should be properly understood and carefully developed to reflect and accommodate existing practice of music.

Musicology should be able to explain the phenomena of music and not restrict or dictate how music should be. But, a theory once formed acts as a guide. This study shows that the extant theories of 22 sruts« cannot explain adequately the phenomena of raga music.

In the field of music like in several other fields, practice precedes theorization. But when theory fails to explain the observed phenomena in music it must be revised. Bosanquet held the contrary view (Bosanquet, 1987) citing examples from Astronomy. But the human element, which is a must in the study of music, necessitates validation of theory from current practice.

In the western music tradition governed by instruments and structured on chord progressions and polyphony, there was a need to fix musical pitches. And since key transposition is an essential element, after testing several octave divisions, Equal Temperament (ET) was adopted despite continued opposition. While this temperament is mathematically perfect, it is not based on the natural harmonic series and is considered acoustically mistuned.

Indian raga music requires neither key transposition nor features to facilitate polyphonic music. The pitches of suara-s (musical notes) therefore need not be fixed unitary values, except to serve as reference to manufacture and tune musical instruments such as the vzr.ta where there is a need to fix the fret positions. The accompanying tambura also provides certain basic reference pitches.

In the past, when laksnakdra-« (authors of musical treatises) spoke about the concept of sruti they were evidently talking about pitches of musical notes and not freguencies (see sect. 1.4 for the difference: between pitch and frequency). Sruti-s are those which are "heard." That is, sruti-s are perceptions of musical pitches, heard in mutual relation and in relation to the ddhdra-soara (tonic). Musical pitches in isolation convey no meaning; a musical context comprising intervals does (Lloyd, 1963).

Thinkers have advocated and allowed pitch deviations from the exact (reference) values. But, what gives these theoretical values the status of being a reference? Deviation from what? This research work examines the validity of the reference itself. Do deviations exist in the absence of such a reference? It is not deviation, but the flexibility and the overall balance in intonation that should be studied. References are theoretical constructs and as such have only an academic significance.

Hawking (1988) gives a detailed account of how the fundamentals of physical sciences have undergone changes over time discarding meta- physical beliefs and mystical associations and adopting more realistic models of the universe based on observation and verification. The idea of a perfect and a static universe and absolute time had to give way to the idea of a dynamic universe and a warped time-space continuum. The Greeks thought that planets orbited in perfect circles and mystically associated musical tones with the perfectly circular planetary orbits. This of course was not founded on verifiable observation and it is now well known that the planets move in elliptical orbits. Nature is not as orderly as it was thought to be. Nature strives for the condition of "ideal disorder" (Winckel, 1967). Laplace's dream of determinism, extending even to human behaviour, had to be jettisoned with the advent of the Uncertainty Principle! of Quantum Mechanics which introduced an unavoidable element of unpredictability and randomness even in physical sciences. (See superscripted numbers in the text in the back matter under heading" otes," pp. 188-94 of this book.)

Not only is the idea of determining fixed singular acoustical values for musical notes is untenable but it runs counter to the exigencies of the raga system. The realm of perception cannot be ignored. The ancient tuning of the griima system has no functionality in the present day Indian music (Powers, 1970) and the associated concept of sruti is also likewise non- functional.

It is essential to clarify certain basic concepts before dealing with the main topic of pitch analysis. This is necessary because of the widespread misconceptions even among musicologists. Let us start with the difference between tuning and temperament.

1.1. Tuning And Temperament
Tuning pertains to the exact positioning of the musical notes, mathematically derived as rational numbers. Temperament is the artistic modification of these pitches to suit a musical style, where, not all the pitches are rational numbers (Barbour, 1953). Tuning provides us a set of reference pitches, which may be used for constructing musical instruments. Temperament is the artistic pitching of musical notes as per the requirements of a musical system. In the context of Indian raga music, tuning pertains to the suara sthdna and temperament is relevant to the svara. Whereas tuning may be physical. temperament is idiomatic, as it is culturally conditioned.

That is, the notion of fixed soara sthana-s applies to the domain of tuning, enabling, for example, the fretting of the vZ1Ja. But the idea of fixed sthdna in the context of temperament is clearly untenable as will i." demonstrated in this book. Raga-s began to be defined in terms of the iirohana and auarohana (i.e., in the scale of reference pitches) around the sixteenth century (Powers, 1970). Therefore the notion of fixed soara-sthiina-s acquired special significance as many modern scholars proposed precise quantification for these suara-s regardless of the context of the raga.

Tuning is different from a musical scale and a mix up results in confusion as is evident from the literature. All the precise mathematical calculations pertain to tuning; a scale on the other hand consists of intervals tempered to fit into one octave. Tuning falls within the realm of physical acoustics, as it is concerned with beats, but temperament belongs to the psycho-physiological realm of perception (Lloyd, 1963) and is culturally inured. Therefore, tuning and temperament are different. (See also Glossary).

1.2. Pitch of Musical Sounds
It is quite difficult to give a precise definition of pitch. According to the American Standards Association, 1960, pitch is generally defined as "that attribute of auditory sensation in terms of which sounds may be ordered on a musical scale." But this definition is neither precise nor comprehensive. Pitch may be explained as the subjective perception of periodic sound impulses in mutual relation, particularly of musical tones. The unit of measurement is Hertz (Hz), or cycles per second (cps)-the same unit as applied to frequency. But there is a difference between pitch and frequency. Whereas frequency refers to any sound impulse physically present, pitch mainly refers to the subjective perception of musical tones as high or low (sect. 1.4). Chapter 3 explains the psycho-physiological factors affecting pitch perception through a conceptual diagram (Fig. 3.1).

Pitch primarily depends on frequency, but may not be identical with it; on the harmonic content of a complex stimulus, in that it roughly equates to the fundamental if all the harmonics are integer multiples of the fundamental; on the loudness as explained in chap. 3, sect. 3.3 and on the timbre (including forrnants''). Duration can also influence the pitch perception. A detailed examination of these factors is not within the scope of the current study.

This book shows that mathematically fixing musical pitches goes against the requirements of the idiom of Karnataka raga music. But, that does not mean that any pitch is acceptable. Definite pitch contours exist to characterize raga-s in the Karnataka system. The characteristic pitch movement of a svara over a range in a given raga is herein christened as the "pitch profile." That is, when a note in a raga is not a fixed point but has a range and movement to express itself, it may be called as a pitch profile of that note instead of pitch, to distinguish between a single point and a range (see chap. 4 for the pitch profiles). The empirical pitch analysis offered in chap. 4 exhibits this fact succinctly. It must however be expressly pointed out here that although a pitch profile captures the characteristic pitch movement of a svara, it cannot convey the full meaning of the svara. As mentioned above, pitch depends on several physical factors which are not dealt with here.

The ability to distinguish one pitch from another particularly when they are separated by a small interval is fundamental to the appreciation of music. But the magnitude of separation, called as the Just Noticeable Difference (JND), cannot be uniquely determined, as explained below.

l.3. JUST NOTICEABLE DIFFERENCE (JND)
Just Noticeable Difference (JND) is a psychophysical unit used to determine the minimum detectable change in pitch. It is the minimum amount of change in pitch that can be perceived. JND depends on several factors such as the frequency range, intensity, duration of the tone and suddenness of frequency change. More importantly, it varies from person to person. It also depends on the method of measurement (Roederer, 1995). JND increases proportionally with the magnitude of the stimulus (Goldstein, 1996). Since JND increases with frequency, it is not the same across octaves.

Between any two musical tones in a given scale, the ear can detect many intermediate pitches (Roederer, 1995). The number of pitches that may be detected by the ear within the octave far exceed the number of musical notes that make up a scale. That is, all these intermediate pitches are not taken as musical notes in a given scale. JND is not applicable to the selection of pitches in a musical scale and by extension, cannot be the basis for pitch selection whether it is Bharata's two-vinya experiment or Sarngadeva's twenty-two-stringed sruti experiment. As explained in sect. 3.3 (under Discrimination), there can be more than 4 pitches that can be distinguished in a semitone. Burns (1999) reported discernment of intervals separated by 30 cents or about 6 to 7 just noticeable intervals in a whole tone. Of course, this number is not unique and depends on several factors as explained above. Therefore, JND should not be equated to sruti.

It must be noted further that JND does not necessarily relate only to musical pitch, for, it is the ability to detect a change in the pitch of any sound stimulus within the audible range. The range applicable to music lies below 5 kHz and is smaller than the audible range, which can extend up to 20 kHz, in a healthy young adult with hearing mechanism intact.

The average ear can hear up to 1400 discrete frequencies over 16 to 16000 Hz. And sensitivity to frequency changes increases with the frequency (Olson, 1967). Winckel (1967) however says that the ear can distinguish about 850 different pitches. The ear can discriminate between two frequencies that are about 0.3% different and this discrimination ability diminishes with the frequency (Pickles, 1988; Backus, 1969; Mathews, 2001).

In addition to the concept of JND, even for the perception of a single pitch, there is a minimum time duration that is required. This is explained in chap. 4, sect.4.4.2.

 

Contents

 

5.4

  List of Tables xi
  List of Pitch profiles xiii
  Foreword xvii
  Acknowledgments xix
  Transliteration xxiii
  List of Symbols, Abbreviation, and Formulae xxv
1 Introdcution 1
1.1. Tuning and Temperament 3
1.2 Pitch of Musical Sounds 4
1.3 Just Noticeable Difference(JND) 5
1.4 Pitch and Frequency 6
1.5 Pitch and Sruti 7
1.6 Intonation 7
1.7 Impetus and Purpose 9
1.8 Scope of Research 12
1.9 Terminology and Organization 13
2 Sruti 15
2.1 A brief Background in musical Treatises 15
2.2 Bharata's two-vina experiment 16
2.3 Bharta's tw o-vina experiment with various configurations 17
2.3.1. The Sarana Process with Equal intervals 17
2.3.2. The Sarana Process with Unequal Intervals 21
2.3.3. the Sarana Process with Svara-s as Positions 27
2.3.4. Physics of Vibrating Strings 35
2.3.5. Bharata's Two-vina Experiment with Variable intervals 37
2.3.6. Position Analysis 39
2.3.7. Practical Problems with Bharata's two-vina experiment 42
2.4 Sarangadeva's Interpretation 43
2.5 Sruti and Svara 45
2.6 Suddha and Vikrta Svara-s 45
2.7 Ahobala's Approach 46
2.8 Venkatamakhi's View 47
2. 9 Govinda and Subbarama Diksitar 49
2.10 Summing Up 49
2.11 Modern Theroies of 22 Sruti-s 50
2.12 Theories of placement of Sruti-s in Raga-s 60
2.13 Related Issues 62
2.13.1. Octave 62
2.13.1.1. Octave Equivalence 62
2.13.1.2. Octave Stretching 64
2.13.2. Intervals 65
2.13.3 Scales 66
2.13.3.1. Pythagorean Tuning 67
2.13.3.2. Just Tuning 68
2.13.3.3. Equal Temperament 69
2.13.4. Modal Shift of Tonic 71
2.13.4. Consonance and Samvaditva 76
2.13.5. Effect of Tambura 77
3 Factors Affecting Pitch Perception 77
3.1. Physics of Music 78
3.2. Physiology of Hearing 80
3.2.1. Non-linearity in Hearing 81
3.3. Psychoacousitcs of Perception 83
3.4. Holistic Appreciation 84
3.5. The Role of Mathematics 89
4 Empirical Pitch Anlaysis 89
4.1 Overview of Pitch Analysis 92
4.2 Experimental Setup and Methodology 92
4.3 Software and Validation 93
4.4 Parameters-Assumptions and Limitations 93
4.4.1. Maximum Acceptable Pitch Deviation, p+_ 93
4.4.2. Minimum time for pitch perception 94
4.4.3. Establishing Pitch 95
4.4.3.1. The issue of Averaging 96
4.4.4. Plotting Pitch Profiles 97
4.4.5. Typical frequency range in Karnataka music 97
4.4.6 PRAAT parameters 97
4.4.7. Sampling Rate 97
4.5 Pitch Analysis Schedule 98
4.6 Results and Analysis 99
4.6.1. Gaula 99
4.6.2 Saveri 109
4.6.3. Bhairavi 122
4.6.4. Hindolam 129
4.6.5. Hamsanandi 137
4.6.6. Nata 144
4.6.7. Begada 144
4.6.8. Mayamalavagaula 145
4.6.9. Discussion 145 145
4.7 Intonational Imperatives 146
5 Conclusions 148
5.1. Recapitulation 148
5.2 Original Contribution Made 451
5.3 Suggested Further Research 151
Conclusions 152
  Epilogue 154
  Appendices:  
  A: 22 Sruti-s 159
  B: Various Suddha and Vikrta Svara Positions 164
  Empirical Pitch Analysis Results 170
  Noes 188
  Glossary 195
  References 204
  Index 210

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