UNIVERSITI PUTRA MALAYSIA

SIGNIFICANCE OF HARMONIC CONTENTS WITH RESPECT TO THE TIMBRE OF THE VIOLONCELLO

LIU LI YOON

FEM 2002 3

SIGNIFICANCE OF HARMONIC CONTENTS WITH RESPECT TO THE TIMBRE OF THE VIOLONCELLO

LIU LI YOON

MASTER OF SCIENCE UNIVERSITI PUTRA MALAYSIA

2002

SIGNIFICANCE OF HARMONIC CONTENTS WITH RESPECT TO THE TIMBRE OF THE VIOLONCELLO

By

LIU LI YOON

Thesis Submitted to the School of Graduate Studies, Universiti Putra Malaysia, in Fulfillment of the Requirement for the Degree of Master of Science

September 2002

Abstract of thesis presented to the Senate ofUniversiti Putra Malaysia in fulfillment of the requirements for the degree of Master of Science

SIGNIFICANCE OF HARMONIC CONTENTS WITH RESPECT TO THE TIMBRE OF THE VIOLONCELW

By

LIU LI YOON

September 2002

Chairman: Dr. Minni Ang Kim Huai

Faculty: Buman Ecology

Harmonic contents (harmonic or inharmonic partials) is an important

waveform characteristic that influences the timbre of musical tones. The first part of

this research is aimed at finding out (through waveform analysis) the harmonic and

inharmonic partials of four sampled violoncello (or cello) C#3 tones, each played

using a different technique. The four different techniques studied are 'arco',

'spiccato', 'pizzzicato' and 'tremolando'. From the results of the waveform analysis,

the difference in timbre between the four different playing techniques of the cello

could be understood by comparing the harmonic contents of the four cello tones. The

results of the waveform analysis generally showed that the four different playing

techniques have different number of harmonic and inharmonic partials in their

spectra. Both the 'spiccato' and 'tremolando' techniques produced more inharmonic

compared to harmonic partials while the 'arco' technique produced more harmonic

11

compared to inharmonic partials. The 'pizzicato' technique produced only harmonic

partials. The results of the waveform analysis is then used in the second part of this

research that is aimed at finding out the significance of various groups of harmonic or

inharmonic partials in contributing to the timbre of the cello through a listening test.

For this test, the results of the waveform analysis are used to modifY the harmonic

contents of the four cello tones. The timbres of the modified cello tones are then

compared with the original cello tones by using short music sequences. Comparisons

are then made between the four different techniques by using tables and graphs.

Results indicate that different groups of harmonic or inharmonic partials affect the

timbre of the cello in different ways. In other words, some groups of harmonic or

inharmonic partials are more significant to the timbre of the cello compared to other

groups. Besides, the timbres of the four different playing techniques are influenced by

the harmonic contents modifications differently. The results generally showed the

'spiccato' technique as the technique that is influenced most significantly and the

'pizzicato' technique as the. technique that is influenced least significantly in timbre

by the harmonic contents modifications executed. The timbres of both the 'arco' and

'tremolando' techniques are influenced moderately by the harmonic contents

modifications. However, the timbre of the cello 'arco' technique is influenced more

significantly by the harmonic contents modifications compared to the 'tremolando'

technique.

iii

Abstrak tesis yang dikemukakan kepada Senat Universiti Putra Malaysia sebagai memenuhi keperluan untuk ijazah Master Sains

KESIGNIFlKANAN KANDUNGAN HARMONIK KEPADA KUALITI BUNYI VIOLONCELLO

Oleh

LIU LI YOON

September 2002

Pengerusi: Dr. Minni Ang Kim Huai

Fakulti: Ekologi Manusia

Kandungan hannonik (separa hannonik atau inharmonik) merupakan ciri

gelombang yang penting dalam mempengaruhi kualiti bunyi nada-nada muzikal.

Bahagian pertama kajian ini adalah bertujuan mendapatkan separa hannonik dan

inharmonik (melalui analisis gelombang) untuk empat nada C#3 violoncello (atau

cello), masing-masing dimainkan dengan menggunakan teknik yang berlainan.

Teknik-teknik yang dikaji adalah 'arco', 'spiccato', 'pizzicato' and 'tremolando'.

Daripada keputusan analisis gelombang, perbezaan dalam kualiti bunyi antara empat

teknik permainan ceHo yang berlainan tersebut dapat difahami dengan membuat

perbandingan di antara kandungan harmonik bagi empat nada cello tersebut.

Keputusan analisis gelombang secara keseluruhannya menunjukkan bahawa empat

teknik permainan tersebut mempunyai bilangan separa harmonik dan inharmonik

yang berbeza di dalam spektra mereka. Kedua-dua teknik 'spiccato' dan'tremolando'

lV

menghasilkan lebih separa inhannonik berbanding dengan separa hannonik manakala

teknik 'arco' menghasilkan lebih separa hannonik berbanding dengan separa

inharmonik. Teknik 'pizzicato' menghasilkan hanya separa barmonik sabaja.

Keputusan analisis gelombang yang diperolebi akan digunakan di dalam bahagian

kedua kajian ini yang bertujuan untuk mengetahui kesignifikanan beberapa kumpulan

separa harmonik atau inharmonik dalam mempengaruhi kualiti bunyi cello melalui

suatu ujian pendengaran. Untuk ujian ini, keputusan analisis gelombang digunakan

untuk mengubah kandungan harmonik keempat-empat nada cello tersebut. Kualiti

bunyi nada-nada cello yang telah diubah kandungannya akan dibandingkan dengan

nada-nada cello asal dengan menggunakan beberapa sekuens muzik yang pendek.

Perbandingan kemudian dibuat diantara kempat-empat teknik tersebut dengan

menggunakan jadual dan gra[ Keputusan ujian menunjukkan bahawa kumpulan

separa hannonik atau inhannonik yang berbeza mempengaruhi kualiti bunyi cello

dengan cara berbeza. Dengan kata lain, sesetengah kumpulan separa harmonik atau

inharmonik adalah lebm signifikan kepada kualiti bunyi cello berbanding dengan

kumpulan yang lain. Selain dari ito, kualiti bunyi teknik permainan yang berlainan

dipengaruhi oleh perubahan-perubahan kandungan hannonik tersebut dengan cara

berlainan. Secara kesuluruhannya, keputusan yang diperolehi menunjukkan bahawa

teknik 'spiccato' adalah teknik yang dipengaruhi paling banyak dan teknik 'pizzicato'

adalah teknik yang dipengaruhi paling sedikit dalam kualiti bunyi oleh perubahan­

perubahan kandungan harmonik tersebut. Kualiti bunyi kedua-dua teknik 'arco' and

'tremolando' dipengaruhi secara sederhana oleh perubahan-perubahan kandungan

harmonik tersebut. Bagaimanapun, kualiti bunyi teknik 'arco' dipengaruhi lebih

banyak oleh perubahan-perubahan kandungan harmonik tersebut berbanding dengan

teknik 'tremolando'.

v

ACKNOWLEDGEMENTS

I would like to thank my principal supervisor, Dr. Minni Ang for spending her

precious time in guiding and helping me and also providing me with lots of valuable

suggestions, resources and infonnation. I would also like to thank my second

supervisor, Dr. Veeraghavan Prakash, for his help especially in the section on

spectrum analysis and also the last member of my supervisory committee, Ms Martha

Lee Jin Ai for providing me useful suggestions during the course of my research. I

also appreciate the UPM Graduate School for supporting my course of study here in

UPM through the PASCA Siswazah scheme. Also, I would like to express my

appreciation to my lecturers and friends, especially Ms Ong Bee Suan from the

Nanyang Technological University of Singapore, for spending her time in answering

my questions, explaining to me in detail and clearing my doubts. Besides, my utmost

appreciation goes to the students of the music department who have spent their

precious time in helping me with the cello timbre survey listening test and making

this research a success. I would also like to thank my research colleagues Yoke Fun,

Pei Sze and Zek Chew for providing a cheerful atmosphere in the graduate lab and

help me enjoy my work. Last but not least, I would like to thank my parents for their

love, support and understanding in everything that I do.

VI

I certify that an Examination Committee met on 20th September 2002 to conduct the final examination of Liu Li Y oon on her Master of Science thesis entitled "Significance of Hannonic Contents with Respect to the Timbre of the Violoncello" in accordance with Universiti Pertanian Malaysia (Higher Degree) Act 1980 and Universiti Pertanian Malaysia (Higher Degree) Regulations 1981. The Committee recommended that the candidate be awarded the relevant degree. Members of the Examination Committee are as follows:

Chan Cheong Jan, Ph.D. Faculty of Human Ecology Universiti Putra Malaysia (Chairman)

Minni Ang Kim Duai, Ph.D. Faculty of Human Ecology Universiti Putra Malaysia (Member)

Veeraghavan Prakash, Ph.D. Faculty of Engineering Universiti Putra Malaysia (Member)

Martha Lee Jin Ai, M.A. Faculty of Human Ecology Universiti Putra Malaysia (Member)

SBAMSRER MOBAMAD RAMADILI, Ph.D. ProfessorlDeputy Dean School of Graduate Studies Universiti Putra Malaysia

Date:

Vll

This thesis submitted to the Senate of Universiti Putra Malaysia has been accepted as fulfillment of the requirements for the degree of Master of Science. The members of the Supervisory Committee are as follows:

Minni Ang Kim Huai, Pb.D. Faculty of Human Ecology Universiti Putra Malaysia ( Chairperson)

Veeraghavan Prakasb, Ph.D. Faculty of Engineering Universiti Putra Malaysia (Member)

Martha Lee Jin Ai, M.A. Faculty of Human Ecology Universiti Putra Malaysia (Member)

AINI IDERIS, Ph.D. ProfessorlDean School of Graduate Studies Universiti Putra Malaysia

Date:

Vlll

DECLARA nON

I hereby declare that the thesis is based on my original work except for the quotations and citations that have been duly acknowledged. I also declare that it has not been previously or concurrently submitted for any other degree at UPM or other institutions.

LIULIYOON

Date:

IX

TABLE OF CONTENTS

Page

ABSTRACT ... ... ......... ... ...... ... ...... ... ... ... ...... ... ... ..... , ... ... ... ............. ii ABSTRAK. ... ... ...... ... ... ... ... ...... '" ... '" ... ... ... ...... '" ... ... '" .. , ... '" ., . .. , IV

ACKNOWLEDGEMENTS... ...... ... ... ............... ... ... ......... ...... ............. vi APPROVAL SHEETS ...... ... ... ... ... ... ....... , . ... '" .. , '" .. , '" .. , '" '" ... ........ vii DECLARATION FORM .... , ... , ..... , '" ...... '" '" ... '" .. , ... ... ... ... ... ... ... ...... ix LIST OF TABLES ... '" .. , '" ... '" ... ... ... ... ... ............ ... ........ , '" .. , ... ... ... xiii LIST OF FIGURES ..... , ., . .. , '" .. , ... .. , ..... , ..... , ..... , ...... '" ... ... ... '" ... ..... XIV

CHAPTER

ONE INTRODUCTION...... ............ ...... ... ... ... ... ... ... ... ...... 1 Statement of the Problem ..... , ... ......... . , . ... ... '" . .. ......... .. . 5 Objective of the Study... ... ... ... ... ... ... ... ... ... ... ... ... ... ..... 6 Significance of the Study . . . ... '" ... ... '" ... ... ... ... ... ... ......... 6 Design of the Study ... '" ...... .... , . ........ , ... ... ........... , ... .. 7

Organization of the Thesis ... ...... ...... ...... ... ... ... ... '" .. , ... 8

TWO LITERATURE REVIEW ... ...... .. , ... ... ... ... ... ... ... ... ... ..... 10 How Harmonic Contents and Waveform Envelope Influence

THREE

the Timbre of Musical Instruments...... ...... ... ......... ... ..... 10 Waveform (Spectrum) Analysis... ... ... ... ... ... ... ... ... ... ...... 14

Harmonic Analysis ... ... ... ... ... ... ... ... ... .. , ... ... ... .. 14

The Significance of Waveform (Spectrum) Analysis. 15 Past and Current Research ... ... '" ... ... ...... ... '" ... ... ... . .. ... 18

Spectrum and Timbre of Musical Tones ..... , .,. ... .... 19 Waveform (Amplitude) Envelope and Timbre of Musical Tones...... ... ... ... ... ... ... ... ......................... 30

Conclusion .. . ... ... ... ... .. . '" ... ... ... ... ... ... ... ... .. . ... ... ... .... 33

METHODOLOGy... ... ... ... ...... ...... ... ... ...... ................. 35 Spectrum Analysis... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. . 36

Data Conversion ... .. , ... ... ... ... ... ... ... ... ... ... ... ..... 36 Harmonic Analysis ... ... ... ... ... ....... ... '" ... ... .. , ... . 37

Waveform Modification... ... ... ... ...... ... ...... ............ ..... 47

Harmonic Contents Modification... ... ...... ......... ..... 47

Using the Notch Filter... ... ... ... ... ... ... ... ... ... ... .... 47

Listening Test Methodology . .. ... ...... .. . ... . ,. ... ... ... ... ....... 49

Identification of Test Subjects, Test Samples and Candidates... ... ... ... ... ... . .. ... ... ... . .. ... ... ... ... ... ... ... ... .... 49

Test Subjects ... ... .. , ... ... ... ... ... ... ... .. .............. ..... 49

Test Samples... ... ... ... ... ... ... ... ... ... ... ............. ... . 50 Test Candidates ... . ..... ...... .. , ... ... ... ... .... ... ... ... .. 51

Designation of Test... ...... ...... ... ......... ... ...... ... ...... ..... 52 Test Environment......... ... ... ... ... ... ... ............ ..... 52 Test Procedures... ... ... ... ... ...... ... ... ... ... ... .... ..... 52

Preparation of Test Samples ... '" ... ... ... ... ... ... ... .. .............. 53

X

FOUR

FIVE

Loading the Original and Modified Cello Samples as Soundfonts ... ... '" ... .. , '" ...... .... ,. ... ... ... ... ... ... .. 53 Attaching the Original and Modified Soundfonts to Short MIDI Sequences for the Comparison Test ....................... , . . ,. ... ... ... ... ... ... ... ... ... .... 58

Conducting the Listening Test ... ... ... ... ... '" ... '" '" .. , ... .... 62 Analysis of Test Results ... ... '" ... .. , .. , .. , .. , ... ... ... ... ... ...... 64 Conclusion .. . . .... . ..... . .. . ... ... '" ... ... ..... , ... ... ... ... .. . ... ... 64

RESULTS AND DISCUSSIONS 65 Identification of the Harmonic and Inharmonic Partials ... '" " 65 Results of the Harmonic Analysis ... ... ... ... ..... , .. , ... ... ... .... 65

Spectrum Components of the Cello 'Aroo' Tone...... 67 Spectrum Components of the Cello 'Spiccato' Tone.. 68 Spectrum Components of the Cello 'Pizzicato' Tone. 69 Spectrum Components of the Cello 'Tremolando' Tone................. ... ... ... ... ... ............ ......... ... ..... 70

Discussion on the Results of the Harmonic Analysis ... '" ..... 71 Cello'Arco'Spectrum......... .................. ... ... ... 71 Cello 'Spiccato' Spectrum................................ 73 Cello 'Pizzicato' Spectrum ... ... . ,. ... ... ... ... ... ... .... 75 Cello 'Tremolando' Spectrum...... ... ... ......... ....... 77 Comparisons between the Spectra of the C#3 Cello Tone played using the 'Arco', 'Spiccato', 'Pizzicato' and 'Tremolando' Techniques... ............... ... ... ... 79

Results of the Listening Test.. .... .... " ... .. , ... ... ... ... ... ....... 84 Discussion on the Results of the Listening Test... ... ... . .. ...... 103

Comparisons between the Order of Significance of the 13 Groups of Partials to the Timbre of each Technique... ... ... ........................................................ 103 Comparisons between the Techniques that are Influenced Most to Least Significantly in Timbre by each of the 13 Groups of Partials ...... '" ... ... ............ 117

Summary of Findings... ... ... ...... ... ...... ............................... 123 Conclusion ... '" ... '" ... ... .. , ... .. , ... ... ...... ... '" ... '" '" ... ... 128

CONCLUSIONS AND SUGGESTIONS FOR FURTHER STUDy... ... ... ... ... ...... ...... ......... ... ... ...... ...... ... ........ 129 Summary of the Thesis...... ... ... ... ... ... ... ...... ... ...... ........ 129 Conclusions ... ...... ... .. , ... ... ... ... ... ... ... ... ... ... ... ... ... ..... 131 Suggestions for Further Study... ... ... ... ... ... ... ... ... ... ... ... .. 134

BIBLIOGRAPHY. . . . . . . . .. . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . ...... 135

APPENDICES A B C

Definitions ... ... ... ......... ............ ... ...... ... ... .............. ..

Sample of Questionnaire ... ... ...... ... ......... ... ... ... ............ .. Types of Instruments the Modified Cello Tones Sound Like .. .

Xl

140 147 149

Table

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4

5

6

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8

9

10

1 1

12

13

14

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LIST OF TABLES

Order of the 13 Modified Cello Soundfonts played using the Four MIDI Sequences for the Four Different Techniques . . . . . . . . . . . . . .. . . . . Harmonic and Inharmonic Partials of the Recorded C#3 Tone played on the Cello using the 'Arco' Technique .. . ... ... . . , .. . . ..... ... . Harmonic and Inhannonic Partials of the Recorded C#3 Tone played on the Cello using the 'Spiccato' Technique .. . ... . .. .. , ........ . Harmonic Partials of the Recorded C#3 Tone played on the Cello

. h 'p" 'T hn' usmg t e lZZlcato ec lque ... ... . . , . . . . . . . . , . . . ' " . . . . .. . . . . . . ... . . .

Harmonic and Inharmonic Partials of the Recorded C#3 Tone played on the Cello using the 'Tremolando' Technique ... . . . . . . .. , .. . Ratings for the 13 Modified Cello Sequences played using the Four Different Techniques .. . . .. .. . . . . . . . . . . .. . .. , . . . . . . ... ... . ...... ....... . Average Ratings for the 13 Modified Cello Sequences played using the Four Different Techniques ... . . . . , . .. . . .. . . . . . . . . ... . ... . . . . .. . Sequences that Still Sound Quite Similar in Timbre to the Original (average ratings of below three) and also Sequences that Sound Very Different in Timbre from the Original (average ratings of three and above) Cello Sequences for the Four Different Techniques . .. ... . . . . , . . .. . . . . , . ' " . . . . . . . . . ... . . . . . , .. . ... . . . . . . ' " .. , ' " .. . Average Ratings of the Four Different Techniques Arranged in Order from the Highest to the Lowest Rating for the 13 Modified Cello Sequences Showing the Technique that is Most to the Technique that is Least Significantly Influenced in Timbre by each of the Harmonic Contents Modifications Executed . . . ... .. , ' " .. . .. , .. The General Order of Significance (most to least significant) of the Various Groups of Partials to the Timbre of the Cello played using the Four Different Techniques .. . ... . , . . . . .. . . , . ... . . . . , . .. . ... . . . . Average Ratings of the Modified Cello Sequences in Order from the Highest to the Lowest Rating for the 'Arco' Technique . . . ... . . . . Average Ratings of the Modified Cello Sequences in Order from the Highest to the Lowest Rating for the 'Spiccato' Technique .. . .. . Average Ratings of the Modified Cello Sequences in Order from the Highest to the Lowest Rating for the 'Pizzicato' Technique .... . Average Ratings of the Modified Cello Sequences in Order from the Highest to the Lowest Rating for the 'Tremolando' Technique. Number and Percentage of Participants who Agreed and also Disagreed that the Modified Cello Sequences Still Sound Like a Cello for the Four Different Techniques .. . .. . . , . . . . ... . .. . . . .. . . , . . . . .. .

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Figure

1 2 3 4 5

6

7

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9

10 11 12

13 14

15 16 17 18 19 20 21

22

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LIST OF FIGURES

A Typical ADSR Envelope ...... ... ............ ... ...... ............ ... ..

The F3 Spectrum Representing the Chalumeau Register ... ... . , . . . ,

The D5 Spectrum Representing the Clarion Register ... ... ...... .... . The F#6 Spectrum Representing the Altissimo Register ..... , . . . . . . .

The Spectrum of the C#3 Cello Tone played using the 'Arco' Technique ... ............ ......... ...... ... ...... ...... ... ... ............... .

The Spectrum of the C#3 Cello 'Arco' Tone Showing the First 20 Partials (selected by using the Mouse Zoom Button} ... ... ... ....... , .

The Spectrum of the C#3 Cello 'Arco' Tone Showing the Fundamental Harmonic (selected by using the Mouse Zoom Button} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

The Fundamental Harmonic of the C#3 Cello 'Arco' Tone with its Peak Point Indicated by the Small Circle and Triangle ... ... ' " . , . . . . .

The Second Partial of the C#3 Cello 'Arco' Tone with its Peak Point Indicated by the Small Circle and Triangle ... ... ... ... ..... , . . . . Example of a Line Spectrum Graph ...... ...... ' " . . . .. . . " . .. . . . . . . . . .. .

Example of a Continuous Spectrum Graph ... ............................... . .

The Notch Filter Window used for Filtering Out Specific Partials (Harmonic or Inharmonic) from the Four Cello Tones ... . , . . , . . . . . . ,

The MIDI Sequence used for the 'Arco' Technique ... ... ... ........ . .

The MIDI Sequence used for the 'Spiccato' Technique ......... ... ..

The MIDI Sequence used for the 'Pizzicato' Technique ... .......... . The MIDI Sequence used for the 'Tremolando' Technique .......... .

Spectrum of the C#3 Cello 'Arco' Tone ... ... ... ... ... ... ... ... ... ... . .

Spectrum of the C#3 Cello 'Spiccato' Tone ...... ...... ... ... ... ..... .

Spectrum of the C#3 Cello 'Pizzicato' Tone ... ... ... ... ... ...... ... .. .

Spectrum of the C#3 Cello 'Tremolando' Tone ... ...... ......... .... .. Comparison between the Spectra of the C#3 Cello Tone played using the 'Arco', 'Spiccato', 'Pizzicato' and 'Tremolando' Techniques ... ......... ........ , . . . ... . .. . . . . . . . . . . .. ... ... . .. ... . . . . . . .. . .. .

Comparison between the First 14 Partials of the C#3 Cello Tone for the 'Arco', 'Spiccato', 'Pizzicato' and 'Tremolando' Techniques ... ......... .... , . . , . ... . .. . . . . .. .. . .. . . , . .. , . . . ... . . . .. . . , . . . . .. . Comparison between the Average Ratings of the 13 Modified Cello Sequences played using the Four Different Techniques ...... .

Comparison between the Number of Participants who Agreed that the Modified Cello Sequences Still Sound Like a Cello for the Four Different Techniques ...... ' " .. . . . . . , . .. , .. , . . . . . . . .. . . . .. . ... . . . .. .

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59 60 72 74 76 78

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CBAPTER ONE

INTRODUCTION

Musical timbre or tone quality is defined as the way in which musical sounds

differ once they have been equated for pitch, loudness and duration (Krumhansl,

1989). Thus, timbre enables us to recognize two different instrument sounds with the

same pitch, loudness and duration. Music researchers like Helmholtz (1877), Risset

and Mathews (1969), Houtsma (1989), Handel (1995), and Wessel (1999) have all

defined timbre in their own views or perspectives. According to Brown (1999),

studies on how human beings perceive timbre have been performed over the past four

decades with the indefinable goal of correlating the results of perceptual experiments

with a small number of acoustical properties of the sounds studied. Many of these

studies were performed by first modifying acoustic signals and then experiments were

done to determine whether listeners could distinguish or perceive the difference of

timbre between the altered signals and the original signals.

Helmholtz carried out the first significant studies on timbre in the 19th century

(Hourdin, Charbonneau and Moussa, 1997). The various investigations performed by

Helmholtz proved that the timbre of a sound is influenced by its harmonic contents

(hamonic or inhannonic partials). [Harmonics are defined as the several different

frequencies present in a sound, in addition to the frequency that corresponds to the

note being played which is the fundamental harmonic. These harmonics above the

fundamental, also known as partials or overtones are integer multiples of the

fundamental harmonic (Huber and Runstein, 1995). Harmonics are integer multiples

of the fundamental harmonic while partials could be either integer or non-integer

1

multiples of the fundamental harmonic. Partials that are integer multiples of the

fundamental harmonic could also be referred as harmonic partials while partials that

are non-integer multiples of the fundamental harmonic are known as inharmonic

partials]. For example, an extremely nasal timbre stresses on different harmonics as

compared with a mellow timbre. The timbre of the tuning fork and of the stopped

diapason organ is clear and pure because the sound they produce is almost without

overtones (Encyclopedia Britannica, 2000). Thus, timbre is the result of the unique

harmonic content that each sound produces (Rubin, 1995). In other words, timbre is

the combination of fundamental frequency, harmonics, and overtones that gives each

voice, musical instrument, and sound effect its unique colouring and character (Mott,

2001).

Different types of timbres are associated with different harmonic contents. For

example, 'bright' timbres are likely to contain high-level upper harmonics; 'bell-like'

sounds are rich in inharmonic contents; many 'percussive' timbres have high noise

(Cary, 1992) as well as inharmonic contents (Runas, 1998); open, warm and filled-out

timbres have spectra that emphasize on even-numbered (second, fourth and sixth)

harmonics and closed, harsh and stopped-down sounds emphasize on odd-numbered

(third and fifth) harmonics (Alten, 1996). The second harmonic, an octave above the

fundamental, adds fullness to sound, the third harmonic softens sound while

harmonics above the seventh harmonic give sound edge, bite and definition (Alten,

1996). Some sounds are made up of only harmonic partials while others are made up

of a combination of both harmonic and inharmonic partials.

2

Two notes of the same pitch, loudness and duration would also sound

different if the shape of their amplitude or ADSR envelope (refer to Figure 1) is

different. This means that different instruments would produce different ADSR or

amplitude envelopes with different ADSR parameters that lead to the difference in

their tone qualities or timbres.

Amplitude

Sustain

Time

Figure 1 : A Typical ADSR Envelope

Different techniques of playing also affect the timbre of an instrument. For

example, a similar note would sound different if it is played on a violin using

different techniques like bowing, plucking, tremolo etc even though it is played with

equal loudness. This is because the shape of the amplitude envelope would be

different when different techniques of playing are used.

Of the two important factors that contribute to the timbre of musical tones

mentioned, only the significance or importance of harmonic contents would be

studied in this research. Besides contributing to the timbre of musical instruments,

these two factors are the most common waveform characteristics that allow one

3

waveform to be distinguished from another. Other waveform characteristics include

velocity, wavelength and phase (refer to Appendix A).

Many research projects on instrumental timbre have been performed by music

researchers worldwide. Some of these researchers include Charbonneau (1981),

Wolfe (1998), Conklin (1999) and recently Mellody and Wakefield (2000).

The aim of this study is to find out the influence and significance of various

groups of partials (harmonic or inharmonic) to the timbre of the violoncello which is

more commonly known as the cello, an instrument from the strings family played

using four different techniques that are 'arco', 'spiccato', 'pizzicato' and

'tremolando'. A listening test would be carried out to compare the timbres of the

original sampled tones and their modified versions (modified in terms of harmonic

contents). A similar note, C#3 (middle C#3), is analyzed for all the four different

techniques. Studies on other types of instruments have also been performed widely by

researchers in the past. Some of the instruments studied include piano and

harpsichord (Weyer, 1976), plucked-strings (Karplus and Strong, 1983), double bass

(Abbas, 1989), winds (Keefe, 1992) and violins (Miller, 1993� Mellody and

Wakefield, 2000).

4

Statement of the Problem

Tone color or timbre is the subjective quality of a sound that allows us to tell

the difference between musical instruments (Phenomena Cross Reference, 1995).

When a similar instrument is played using different techniques, different timbres are

produced. Thus, waveform analysis is required to find out the harmonic contents

(hamonic or inharmonic partials) that represent the four different playing techniques

('arco', 'spiccato', 'pizzicato' and 'tremolando') of the cello. The significance of the

contribution of specific harmonic or inharmonic partials to the timbre of the cello bas

yet to be documented. The difference in timbre between the 'arco', 'spiccato',

'pizzicato' and 'tremolando' playing techniques, not fully explained as yet, may be

better understood and explained with this information.

In theory, every sound has its own harmonic contents (harmonic or

inharmonic partials) that distinguishes it from any other sound. By modifying the

harmonic contents (harmonic or inharmonic partials) of a musical waveform, the

timbre of the sound also changes. The significance of harmonic contents (harmonic or

inharmonic partials) in contributing to the timbre of the cello played using different

techniques needs to be determined through the listening test, whereby the timbres of

the original cello tones may be compared with their modified versions (various

groups of harmonic or inharmonic partials filtered out).

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Objective of the Study

There are three objectives of this study that are to:

1) obtain and compare the harmonic contents (harmonic or inharmonic partials) of

the cello played using different techniques,

2) find out the difference between the significance of various groups of partials (both

harmonic or inharmonic) to the timbre of the cello in dependence on the playing

technique employed and

3) find out whether the timbres of certain playing techniques of the cello are

influenced more (or less) significantly by harmonic contents (harmonic or inharmonic

partials) compared to other techniques.

Significance of tbe Study

By finding out the harmonic contents (harmonic or inharmonic partials) of the

sampled tones that represent the cello through waveform analysis and knowing the

contribution of this waveform characteristic to the timbre of the cello (through the

listening test) in dependence on the playing technique employed and also by

understanding how the various playing techniques are affected or influenced by the

various groups of harmonic or inharmonic partials, we would have a better

understanding of the waveform features and acoustics of the cello. This enables us to

synthesize more natural and high quality sounding cello tones with different timbres

in correspondence with the various playing techniques by using the results of the

harmonic analysis.

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The results of the waveform analysis could also be utilised via filters designed

to produce many different types of creative and original sounds like the various sound

effects used in films and electroacoustic compositions and sounds that are not in the

repertoire of natural instruments.

Design of the Study

This study is divided into three parts. The first part is made up of two smaller

sections that are a) selecting the various cello samples for analysis and b) copying or

importing the samples into the waveform or spectrum analysis software for the

harmonic analysis.

The second part focuses on the modification of the harmonic contents

(harmonic or inharmonic partials) of the four cello waveforms (the results of the

harmonic analysis from the first part are used) using a digital audio editing software.

Modifications are executed by filtering out various groups of harmonic or inharmonic

partials from the four cello spectra, each played using a different technique ('arco',

'spiccato', 'pizzicato', 'tremolando')' Similar modifications are executed on the four

different cello spectra so that the significance of the various groups of harmonic or

inharmonic partials to the timbres of the four different techniques of the cello could

be compared.

The third part focuses on the listening test where both the original and

modified cello waveforms are loaded as soundfonts. A different MIDI sequence is

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played using the original and the modified soundfonts for each different technique of

the cello. In this way, the timbres of the original soundfonts were compared with the

modified soundfonts for each different technique. From the comparison, the

significance of the various groups of partials in influencing the timbre of the cello in

dependence on the playing technique employed is deduced. The playing technique

that is influenced most to least significantly in timbre by each of the various groups of

partials is also deduced.

Organization of the Thesis

In Chapter Two, the literature review is undertaken. This focuses on topics

like how harmonic contents and waveform envelope influence the timbre of musical

instruments; a brief history and definition of the waveform analysis method that is

used; the significance of waveform analysis and also past and current research on

spectrum and waveform envelope analysis and timbre of musical tones.

In Chapter Three, the methodology is discussed. The steps for executing the

harmonic analysis are explained. Besides that, the steps taken to modify the cello

waveforms for the listening test are explained. The procedures of the listening test are

also explained.

Chapter Four is focused on the results and discussion of the harmonic analysis

as well as the listening test. Graphs and tables are used in the discussion of the results

obtained.

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The last chapter presents the conclusions of the study. This chapter ends with

suggestions for further study. The literature review is now considered further.

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CBAPTER TWO

LITERATURE REVIEW

This chapter focuses on how the two most common factors: harmonic contents

and waveform envelope affect the timbre of musical instruments� a brief history and

definition of the waveform analysis method that is used and also the significance of

waveform (spectrum) analysis. Besides, past and current research on spectrum and

waveform envelope analysis and timbre of musical tones are documented

How Harmonic Contents and Waveform Envelope Influence the Timbre of Musical Instruments

Musical sounds have been traditionally viewed as a series of sinusoidal

components, each having an amplitude and frequency (McAdams, Beauchamp and

Meneguzzi, 1999). Each instrument sound has its' own unique waveform (spectral)

structure/envelope (approximated by using a continuous line to connect graphs of

amplitude versus frequency) and harmonic contents or spectrum components

(harmonic or inharmonic partials) that distinguishes it from all other sounds. These

two differences between sounds explain the difference in timbre or tone quality

between different instruments.

(Note: When the propagation of a sound wave is described by a graph of amplitude

versus time (time domain), it is known as waveform and when it is described by a

graph of amplitude versus frequency (frequency domain), it is known as spectrum�

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