71-7522

MOORE, James Loyal, 1934- ACOUSTICS OF BAR PERCUSSION INSTRUMENTS.

The Ohio State University, Ph.D., 1970 Music

University Microfilms, A XEROX Company, Ann Arbor, Michigan

Copyright by

James Loyal Moore

1971

THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED ACOUSTICS OP BAR PERCUSSION INSTRUMENTS

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

By

James Loyal Moore, 3. Mus., K.Mus

******

The Ohio State University 1970

Approved by

i Adviser School of Music PLEASE NOTE;

Some pages have small and indistinct type. Filmed as received.

University Microfilms ACKNOWLEDGMENTS

I would like to express my appreciation to the members of my dissertation committee. Professor Norman F. Phelps of the School of Music, Professor Wave H. Shaffer of the

Department of Physics, and my adviser Professor William

Poland for their encouragement and guidance. The interest shown by Dr. Donald E. McGinnis, Head of the Instrumental

Music Area of the School of Music is appreciated, as is the cooperation of Professor Karl F. Graff of the Department of

Engineering Mechanics and the technical assistance of

Louis J. Kiraly which made possible the experimental por­ tion of this investigation. Appreciation is also extended to Mr. Richard J. Richardson, President of Musser-Kitching

Division of Ludwig Industries, who provided the bsir material for testing and willingly shared the problems and concerns of the industry. A special thanks is due Pro­ fessor James D. Salmon, of the University of Michigan, my teacher some years ago, who first inspired my curiosity about the bar percussion instruments. Finally, the en­ couragement and concern shown by my wife, Lyn, helped greatly to bring this dissertation to completion. VITA

May 2, 1934 Born— Jackson, Michigan

1956 . . • B.M. Mus. Ed., University of Michigan, Ann Arbor, Michigan

1957 . . • M.M. Mus. Ed., University of Michigan, Ann Arbor, Michigan

1957-1960 • Percussion Instructor, Army Element U.S. Naval School of Music, Washington, D.C.

1960-1964 • Percussionist,Indianapolis Symphony Orchestra

1961-1962 • Percussion Instructor, School of Music, DePauw University, Greencastle, Indiana

1962-1964 • Percussion Instructor, School of Music, Butler University, Indianapolis, Indiana

1964-1967 • Teaching Associate, School of Music, The Ohio State University, Columbus, Ohio

1967- . . • Percussion Instructor, School of Music, The Ohio State University, Columbus, Ohio

1964- . . • Principal Percussionist, Columbus Symphony Orchestra

FIELDS OF STUDY

Music Theory: Professors William Poland and Norman F. Phelps

Music History: Professor Keith Mixter

Musical Acoustics: Professor Wave H. Shaffer

iii TABLE OF CONTENTS

Page

ACKNOWLEDGMENTS ...... il

VITA ...... ill

LIST OF FIGURES ...... vi

Chapter

I. INTRODUCTION ...... 1

Purposes op the Investigation ...... 1 Outline or the Investigation ...... 4

II. NOMENCLATURE OF THE BAR PERCUSSION INSTRUMENTS . 6

Bar Percussion Instruments ...... S Modes of Vibration of the B a r s ...... 9 Cross Sect.r ...... 13 Bar Materials ...... 15 R e s o n a t o r s ...... 20 M a l l e t s ...... 28 Ranges of the Instruments ...... 31 Other Terminology Factors ...... 3^ Summary . 35

III. LITERATURE REVIEW ...... 38

B a c k g r o u n d ...... 38 C h l a d n i ...... 38 H e l m h o l t z ...... 39 Twentieth Century Musical Acoustics Texts . . 40 R i c h a r d s o n ...... 4l Bartholomew ...... 43 C u l v e r ...... 44 Taylor ...... 45 O l s o n ...... 48 J o s e p h s ...... 50 Le varie and L e v y ...... 51 S u m m a r y ...... 53 Literature on Experimental Research and T u n i n g ...... 54 S u m m a r y ...... 63

iv TABLE OF CONTENTS— Continued

Chapter Page

IV. BAR TUNING ...... 66

Tuning Standards ...... 69 Shaping the B a r ...... 74 S u m m a r y ...... 84

V. IDENTIFICATION OF STEADY STATE AND TRANSIENT RESPONSES ...... 86

Description of Experimental Work ...... 8? Steady State Testing ...... 91 Transient Testing ...... 94 S u m m a r y ...... 96

VI. RESULTS OF EXPERIMENTAL W O R K ...... 97

Steady State Measurements ...... 97 Transient Measurements ...... 125 Resume of Steady State and Transient R e s u l t s ...... 131

VII. SUMMARY AND RECOMMENDATIONS ...... 135

Summary of the Investigation ...... 135 Recommendations for Further Work ...... 147

APPENDIX A ...... 162

REFERENCES ...... 175 LIST OP FIGURES

Figure Page

1. Distinguishing Factors of Bar Percussion Instruments ...... 8

2. Harmonic Series and Ideal First Three Modes of Vibration of Uniform Theoretical Bar, Marimba Bar, Xylophone Bar, Vibe Bar, and Orchestra Bell Bar Expressed in Musical Notations and as Frequency Ratios of the Fundamental ...... 10

3. Resonator with One-quarter Wavelength C o n t a i n e d ...... 23

4. Length of Resonator for Bar of Ag = 220 Hz C o m p u t e d ...... 24

5. Sounded Scale Ranges Musser Mallet [Bar] Percussion Instruments ...... 32

6. Mode of Vibration of Supported Bar According to R i c h a r d s o n ...... 42

7. Mode of Vibration of Fundamental of B a r ...... 67

8. Ideal Ratios of Modes of Vibration and Musical Note Representation for Percussion Instrument B a r s ...... 68

9. Fundamental and Second Partial of Marimba and Vibe Bars Represented on Stroboconn ...... 72

10. Cross Section View of Basic Tuning Arch of Percussion Instrument Bar ...... 76

11. Effect of Material Removed from Bar in Various A r e a s ...... 7 8

12. Cross Section View of Second Partial Tuning Arch ...... 80

13. Cross Section Views of Typical Marimba and Xylophone B a r s ...... 82

vi LIST OF FIGURES— Continued

Figure Page

1^. Testing Apparatus for Percussion Instrument B a r s ...... 88

15. The Mechanical Striker ...... 88

16. Bars Used In Acoustics of Percussion Bar Experiment (No. EM6X, I969) ...... 90

17. Equipment Used In Steady State Testing ...... 92

18. Modes of Vibration and Musical Note Represen­ tations of Partial Tone Structure of a Rose­ wood Marimba Bar 110 Hz ( A g ) ...... 105

19. Modes of Vibration and Musical Note Represen­ tations of Partial Tone Structure of a Rose­ wood Marimba Bar 220 Hz ( A g ) ...... IO6

20. Modes of Vibration and Musical Note Represen­ tations of Partial Tone Structure of a Rose­ wood Marimba Bar 440 Hz ( A % ) ...... 107

21. Modes of Vibration and Musical Note Represen­ tations of Partial Tone Structure of a Rose­ wood Marimba Bar 880 Hz (A5 ) ...... IO8

22. Modes of Vibration and Musical Note Represen­ tation of Partial Tone Structure of a Rose­ wood Xylophone Bar 440 Hz ( A % ) ...... Ill

23. Modes of Vibration and Musical Note Represen­ tation of Partial Tone Structure of a Rose­ wood Xylophone Bar 880 Hz ( A ^ ) ...... 112

24. Modes of Vibration and Musical Note Represen­ tation of Partial Tone Structure of an Aluminum Vibe Bar 220 Hz ( A ^ ) ...... 115

25. Modes of Vibration and Musical Note Represen­ tation of Partial Tone Structure of an Aluminum Vibe Bar 440 Hz ( A % ) ...... II6

26. Modes of Vibration and Musical Note Represen­ tation of Partial Tone Structure of an Aluminum Vibe Bar 88O Hz ( A g ) ...... 117

vll LIST OP FIGURES— Continued

Figure Page

27. Modes of Vibration and Musical Note Representa­ tions of Partial Tone Structure of a Steel Orchestra Bell Bar 880 Hz (A5 ) ...... 120

28. Modes of Vibration and Musical Note Representa­ tions of Partial Tone Structure of a Steel Orchestra Bell Bar 1760 Hz ( A g ) ...... 121

29. Modes of Vibration and Musical Note Representa­ tions of Partial Tone Structure of a Steel Orchestra Bell Bar 3520 Hz ( A y ) ...... 122

30. Summary of Frequencies of Modes of Vibration of Marimba, Xylophone, Vibe, and Orchestra Bell B a r s ...... 123

31. Comparison of the Frequencies of the Modes of Vibration of Marimba, Xylophone, Vibe, and Orchestra Bell Bars Tuned to Nominal 880 Hz (A5 ) ...... 124

32. Oscilloscope Trace of Waveform Produced By 220 Hz (Ao) Rosewood Marimba Bar Struck at Center with Soft Mallet ...... 126

33. Oscilloscope Trace of Waveform Produced By 220 Hz (Ao) Aluminum Vibe Bar Struck at Center with Soft Mallet ...... 126

34. Oscilloscope Trace of Waveform Produced By 220 Hz (Ao) Rosewood Marimba Bar Struck 1/2" from Centa* with Soft M a l l e t ...... 126

35. Oscilloscope Trace of Waveform Produced By 220 Hz (A3) Aluminum Vibe Bar Struck 1/2" from Center with Soft M a l l e t ...... 126

36. Oscilloscope Trace of Waveform Produced By 220 Hz (A3) Rosewood Marimba Bar Struck 1" from Center with Soft M a l l e t ...... 127

37. Oscilloscope Trace of Waveform Produced By 220 Hz (A3) Aluminum Vibe Bar Struck 1" from Center with Soft Mallet...... 127

viii LIST OF FIGURES— Continued

Figure Page

38. Oscilloscope Trace of Waveform Produced By 220 Hz (A3) Rosewood Marimba Bar Struck 2" from Center with Soft M a l l e t ...... 127

39. Oscilloscope Trace of Waveform Produced By 220 Hz (Ao) Aluminum Vibe Bar Struck 2" from Center with Soft M a l l e t ...... 127

40. Oscilloscope Trace of Waveform Produced By 220 Hz (Ao) Rosewood Marimba Bar Struck at Node 01 Fundamental (0.224 from end of Bar) with Soft Mallet ...... 128

41. Oscilloscope Trace of Waveform Produced By 220 Hz (A3) Aluminum Vibe Bar Struck at Node of Fundamental (0.224 from end of bar) with Soft Mallet ...... 128

42. Location of Striking Point of Producing Strongest Response of Fundamental of Percussion Instrument Bars ...... 130

43. Cross Section Views of Unusual Bar Shapes .... 154

44. Drawing of Multiple Resonators for a Bar .... 157

45. Drawing of Bar with Double Resonator ...... 157

ix CHAPTER I

INTRODUCTION

Purposes of the Investigation

In the twentieth century percussion instruments have been used to a greater extent in the music of the Western world than in any previous era. While some serious efforts have been made by manufacturers and acousticians to obtain an understanding of the acoustics of new and improved per­ cussion instruments, most musicians and particularly percussionists have not attempted or had the mesins to explore the acoustical bases and principles of percussion instruments. Percussionists often have voiced and written their thoughts and views on percussion acoustics without an understanding of the acoustical principles and construc­ tional problems of their instruments and without any serious attempt to measure and evaluate the actual audible phenomena.

Very little reliable information exists on the topic of the acoustics of percussion instruments. Most text and reference sources that might be expected to contain helpful information are unsatisfactory because they either, (1) state general idealized uniform or theoretical characteris­ tics which, however, are not present in percussion

1 2

instruments (Taylor, 1965), (2) present incomplete and even

inaccurate descriptions of percussion instruments in use

(Olson, 1967), or (3) dismiss the problem of percussion

acoustics on the grounds that sufficient musicality is

Judged to be lacking in these sound sources for the appli­

cation of standard acoustical theory (Bartholomew, 19^2).

This investigation is specifically concerned with the

acoustics of bar percussion instruments— (1) marimba,

(2) xylophone, (3) vibe, also known by the trade names

"vibraphone” and "vibraharp" (Reed and Leach, 1969, p. 1%),

and (4) orchestra bells, often called by their German name.

Glockenspiel— instruments that possess a chromatic arrange­

ment of tuned bars of wood or metal. The sound is produced

on these instruments by percussionists manually striking

the bars with objects called mallets , the term "hammer" is

also used for these objects (Olson, 1967, p. 196).

Emphasis has been placed upon accurately describing the

modern bar percussion instruments being manufactured and

used in the United States at present. Historical problems

concerning older bar percussion instruments and their per­

formance practices are not dealt with in this investigation.

The concept of striving to be a "total percussion­ ist" is gaining a firm standing in the pedagogy of percus­ sion at all levels from grade school through the college-

conservatory and into the professional field. Therefore, students, educational institutions and professional players 3

are buying and using bar percussion instruments in greater

numbers than in the past. This has taxed the production

capacities of the relatively few manufacturing firms that

produce these instruments to the point that they are search­

ing for ways of updating production methods in order to

meet the demand for bar percussion instruments.

I'he tuning processes for the bars used in the mar­

imba, xylophone, vibe, and orchestra bells have been

traditionally carried out by skilled tuners on an empirical basis. Little published information is available that

describes these processes which, until recently, have been based entirely upon the aural perception and Judgment of

an experienced tuner. Production of bar percussion instru­ ments by this process is time consuming and expensive.

Manufacturers have experienced difficulty in meeting the quantity and quality demands for these bar percussion instruments.

The specific purposes of this investigation are to:

(1) present a nomenclature for the bar percussion instru­ ments that will clarify the terminology and characteristics for these instruments, (2 ) review (a) musical acoustics reference literature concerning percussion instruments, especially bar percussion instruments, and (b) literature on' tuning and experimental work of relevance to bar percussion instruments, (3) describe the manufacturing and tuning processes of percussion instrument bars, pointing out in 4

particular the influence of bar shape on the modes of

vibration of the bars, (4) report the results of experi­

mental work that measured the steady state and transient

vibrational characteristics of percussion instrument bars,

and (5) present suggestions for improving the manufacturing

processes of bar percussion instruments.

While this investigation is concerned specifically

with bar percussion instruments, the review of literature

and the methodology employed in the experimental work are

relevant to other areas in the field of percussion instru­

ment acoustics. It is felt that this investigation will be

of value and application in the manufacture, performance,

and teaching of bar percussion instruments, and of interest

to those involved in the theoretical aspects of the

measurements of steady state and transient sounds.

Outline of the Investigation

Chapter II presents a nomenclature for bar percussion

Instruments. Terminology is clarified by defining six

factors— (1) modes of vibration of the bars, (2) cross

section of the bars, (3) bar materials, (4) use of reson­

ators , (5 ) types of mallets used, and (6) ranges of the

instruments.

Chapter III reviews those portions of musical

acoustics reference texts that are concerned with percussion instruments; in particular, the bar percussion instruments. 5

Critical evaluations of the scope and validity of these

portions of the texts are presented. The concluding sec­

tion of the chapter discusses literature on tuning and

experimental investigations of relevance to bar percussion

instruments.

Chapter IV describes the manufacturing and tuning

processes of the bars. Details of shaping the bars to produce the desirable modes of vibration for each bar type

are given.

Chapter V describes the experimental work done to identify the steady state and transient responses of a group of representative percussion instrument bars.

Chapter VI reports the results of the experimental work and discusses the relationship between these results and the ideal characteristics of percussion instrument bars.

Chapter VII contains a summary of the investigation and recommendations for further work in developing improved bar percussion Instruments. CHAPTER II

NOMENCLATURE OP THE BAR PERCUSSION INSTRUMENTS

There are four bar percussion instruments— marimba,

xylophone, vibe, and orchestra bells; instruments that

possess a chromatic arrangement of tuned bars of wood or

metal which are played manually by a percussionist striking

these bars with various kinds of mallets. Each of these

four instruments has distinct individual characteristics.

It is the purpose of this portion of the investigation to

describe each of these bar percussion instruments.

Bar Percussion Instruments

The term "bar percussion instruments” is felt to

best describe as a group the marimba, xylophone, vibe, and

orchestra bells. This was the terminology used by

MacCallum (1969), whose recent book is an excellent source

of information on these instruments, the marimba in particu­

lar. Describing the marimba, but relevant to all of the

instruments regardless of bar material, MacCallum stated,

"... a musical instrument consisting of a series of wooden bars graduated in size, tuned to a scale, and mounted in such a manner thac they are free to vibrate when struck with mallets held in the performer's hands" (p. 11).

6 7

Some authorities and many percussionists call these same

instruments "keyboard percussion instruments." Among these

authorities Peters (1962) stated, "Keyboard percussion

instruments, that is, a series of homogeneous different-

toned [pitched] struck materials, . . ." (p. 178). The

term "mallet percussion instruments" is also used by some

musicians to describe these instruments.

The term "keyboard percussion instrument" creates

confusion with instruments that have a keyboard and a

mechanism which in turn activates the sound generating por­

tion of the instrument. This would include such instru­ ments as the piano, celesta, carillon bells, and harpsi­

chord. The term "mallet percussion instrument" could include a variety of percussion instruments, such as the timpani, that are struck with "mallets." Therefore these terms should not be used for the bar percussion instruments.

The factors that distinguish each of the bar percus­ sion instruments are: (1) modes of vibration of the bars,

(2) cross section of the bars, (3) material of the bars,

(4) characteristics of resonators where present, (5) types of mallets used to strike the bars, and (6) ranges of the instruments. Figure 1 presents these distinguishing fac­ tors for i,he four bar percussion instruments. Each of these factors will be discussed to clarify the characteristics of the instruments. Ideal Ratios of First Three Modes of Vibration of Cross Bar Types of Range of Instrument Bars Section Material Resonators& Mallets Used Instrument MARIMBA f, 4:1, 10:1 Non- Rosewood Must have Soft rubber Ag—Cy^ uniform or yarn over (C3-C7 )® rubber core

XYLOPHONE f. 3 :1 , 6:1 Non- Rosewood Optional Hard rubber, uniform plastic or F 4-C8 wood VIBE (Also known f, 4:1, 10:1 Non- Aluminum Must have Yarn or cord F 3-F6 as vibraphone uniform (contains over rubber or vibraharp) motor core driven ro­ tating fans) ORCHESTRA BELLS f. 2.75:1, Uniform Steel None Hard rubber, G 5-C8 (Also known 5.4:1 plastic or as brass Glockenspiel) All resonators of bar percussion instruments manufactured in the United States are cylindrical aluminum tubes, closed at the lower end, \ / k wave length resonators of the fundamental of their respective bars.

^Identification of tones is based upon a system using Cq = 16.352 Hz; thus Ag = 110 Hz, Ao = 220 Hz, A% = 440 Hz, A5 = 88O Hz, Ag» 1?60 Hz, Ay = 3520 Hz. For a comparison of this and seven other systems of identifying tones see Olson (1967, p. 28).

°Some models are only four octaves. 00 Fig. 1.— Distinguishing Factors of Bar Percussion Instruments. Modes of Vibration of the Bars

American Standard Acoustical Terminology (i960) is

used as the basis for a discussion of the modes of vibration

of percussion instrument bars.

1) a mode of vibration is a characteristic pat­ tern assumed by a system in which the motion of every particle is simple harmonic with the same frequency. Two or more modes may exist concur­ rently in a multiple-degree-of-freedom system (ASAT, 3 .18).

2) the fundamental mode of vibration of a system is the mode having the lowest natural frequency (ASAT, 3.20).

3) a partial is a physical component of a complex tone LandJ is a component of a sound sensation which may be distinguished as a simple tone that cannot be further analyzed by the ear and which contributes to the timbre of the complex sound. [A partial] may or may not be an integral multi­ ple or submultiple of the basic frequency. If the frequency is not a multiple or submultiple, the partial is inharmonic (ASAT, 13.5).

4) a harmonic is a partial whose frequency is an integral multiple of the fundamental fre­ quency (ASAT, 13.6).

5) a harmonic series of sounds is one in which each basic frequency in the series is an inte­ gral multiple of a fundamental frequency (ASAT, 13.7).

A complete harmonic series is a series of whole number integral multiple number ratios of a fundamental extending from 2:1 to infinity. For purposes of compari­ son with the modes of vibration of bars, the harmonic series is shown through the 10th harmonic in Figure 2.

Neither bars of uniform cross section nor non- uniform cross section produce a complete harmonic series as Uniform Theoret- Marimba Xylophone Orchestra Bell Harmonic Series ical Bar Bar Bar Vibe Bar Bar

lO.'l

t o : i m ■Q— 4J: :a ~ 4» I 2 .75 *:/

I 2E=p: a : 331 zee T = =

&The musical notation indicates the tones which most nearly approximate the fre­ quencies of the members of the harmonic series. The 7th harmonic is considerably lower than the note G.

^Approximate musical notation is given for inharmonic partials. Second mode of 2,75:1 is decidedly low for comparison to the 3rd harmonic which is being 51 cents (hundredths of a semi-tone) above Dij and ^9 cents below Third mode of 5.4:1 Is decidedly low for comparison to 6th harmonic which is E^, being 19 cents above musical note D5 .

Fig. 2.— Harmonic Series and Ideal First Three Modes of Vibration of Uniform Theoretical Bar, Marimba Bar, Xylophone Bar, Vibe Bar, and Orchestra Bell Bar Ex­ pressed in Musical Notation and as Frequency Ratios of the Fundamental. 11

found in theoretical thin strings or narrow uniform cross

section pipes. A comparison of the harmonic series, and

the ideal first three modes of vibration of a uniform bar

and marimba, xylophone, vibe, and orchestra bell bars is

given in Figure 2.

In this investigation the terms mode of vibration

or partial rather than a given member of a harmonic series

will be used. The modes of vibration of percussion instru­

ment bars do not correspond to adjacent members of a

harmonic series. However, harmonic partial tones as

represented by the first three modes of vibration of the

marimba, xylophone, and vibe bars (Fig. 2) are created by

the particular non-uniform shaping of the cross sections of

these bars. Comparing these harmonic partial tones to the

harmonic series, the first mode of vibration (fundamental)

of marimba and vibe bars is the frequency of the 1st

harm.snic, the second node of vibration (second partial)

approximates the 4th harmonic, and the third mode of vibra­

tion (third partial) approximates the 10th harmonic. The

first mode of vibration (fundamental) of a xylophone bar is

the frequency of the 1st harmonic, the second mode of

vibration (second partial) approximates the 3rd harmonic,

and the third mode of vibration (third partial) approxi­ mates the 6th harmonic. The first mode of vibration (funda­ mental) of an orchestra bell bar is the 1st harmonic, but the second amd third modes of vibration (second and third 12 partials) are inharmonic partials and do not approximate members of a harmonic series.

In Figure 2 a nominal A2 110 Hz fundamental is used to facilitate a direct comparison of the ratios of the modes of Vibration of the several bar types. However, only the marimba bar of instruments currently manufactured pro­ duces a 110 Hz fundamental. The musical note "A" was chosen as this is the pitch letter name of a series of bars

(A2 - Ay) used in this investigation (infra Chapter V).

The ratios of the modes of vibration of the bars shown in Figure 2 are ideal ratios for each bar type. Ex­ perimental work done in conjunction with this investiga­ tion (infra Chapter VI) showed the actual ratios of most second modes of vibration to the fundamental to be very close to the ideal ratios, while for reasons to be dis­ cussed in Chapter VI the actual ratios of the third modes of vibration may be quite far from the ideal ratios.

Modes of Vibration of Marimba and Vibe Bars

The second mode of vibration of the marimba and vibe bars is a harmonic partial at a ratio of 4:1 to the funda­ mental, or the musical note two octaves above the funda­ mental. The third mode of vibration of the marimba and vibe bars is a harmonic partial at a 10:1 ratio to the fundamental or the musical note three octaves and a major third above the fundamental. 13

Mode of Vibration of Xylophone Bars

The second mode of vibration of the xylophone bar is

a harmonic partial at the ratio of 3:1 to the fundamental

and the third mode of vibration is a harmonic partial at

the ratio of 6:1 to the fundamental. These partials cor­

respond to the musical notes one octave and a perfect fifth

and two octaves and a perfect fifth above the fundamental.

Modes of Vibration of Orchestra Sell Bars

Orchestra bell bars, the only percussion instrument bars of a uni form cross section, produce modes of vibra­ tion that are inharmonic partials. The ratio of the second mode of vibration to the fundamental is 2 .75:1 and the ratio of the third mode of vibration to the fundamental is

5.4:1. The approximate musical notation given in Figure

2 (p. 10) shows the extent to which these inharmonic par­ tials depart from those available in the superparticular harmonic series of sounds.

Cross Section

Most musical acoustics reference sources fail to distinguish between the modes of vibration of percussion instrument bars and the modes of vibration of idealized, theoretical bars of homogeneous material and uniform cross section and attempt to use the general characteristics of the uniform bar to represent the characteristics of all 14 percussion instrument bars regardless of cross section.

Further, most brief definitions of the bar percussion

Instruments fall to account for the acoustical differences among the four bar percussion Instruments caused by the differing non-uniform arch characteristics of the bars which

In turn control the modes of vibration of the bars (Infra

Chapter III).

Bars of non-uniform cross section with a deep arch cut In the underside of the bar produce upper partials at relatively high frequencies. Bars of non-uniform cross sec­ tion with a shallow arch cut In the underside of the bar produce upper partials at relatively lower frequencies.

Bars of uniform cross section produce upper partials at frequencies lower than either bars with deep or shallow arches.

A thorough description of the non-uniform shaping of percussion Instrument bars Is given In Chapter IV, Bar

Tuning. The characteristic cross sections of each of the four bar types, however, may be summarized as follows:

Cross Sections of Marimba and vibe Bars

A deep arch Is cut in the underside of the bars particularly In low and middle register bars of the Instru­ ments, producing second and third partials with frequency ratios of 4:1 and 10:1 to the fundamental. 15

Cross Section of Xylophone Bars

A shallow arch is cut in the underside of the bars

producing second and third partials with frequency ratios

of 3:1 and 6:1 to the fundamental.

Cross Section of Orchestra fee11 Bars

The cross section of the bars is uniform producing second and third partials with frequency ratios of 2.75:1 and 5.4:1 to the fundamental.

Bar Materials

Rosewood, aluminum, and steel are the materials presently used in the United States for percussion instru­ ment bars. The characteristic sound produced by each of these materials differ from the others when the bars are struck.

Rosewood bars produce tones of relatively short audible duration with a strong fundamental and weak upper partial tones. Metal bars produce tones of relatively long audible duration with strong upper partial tones in addition to the fundamental. The tone of the aluminum bars tends to be mellow and the tone of the steel bars bright.

The most important criteria that a piece of material must meet for use as a percussion instrument bar are:

(1) durability, (2) resonant quality (a term used by musi­ cians to describe the ringing quality of sound produced by a struck piece of material) and (3) ability to hold pitch. 16

No matter how well shaped the bar during the tuning

process and how well controlled the other manufacturing

processes, an instrument must have material meeting the

above criteria in order to produce an acceptable sound.

Durability of a bar is particularly important for xylophone

bars where the bar must tolerate rather heavy beating with

hard mallets over a period of years.

The density and internal structure of rosewood bars

varies considerably from bar to bar and even within the

same bar, while metal bars have a structure that is rela­

tively consistent for =^11 bars of a given material specifi­

cation. Thus, an expected resonant quality will occur more

consistently for a given metal material than for rosewood.

For the instrument manufacturer quality control is less of

a problem with metal bars than with wooden bars, and metal

bar material is readily obtainable from suppliers of

industrial metals in the United States.

Marimba and Xylophone Bars

The marimba and xylophone both use wooden bars. The

term marimba or one of its many close derivatives used in

the African languages , from where the instrument may have

originated (Chenoweth, 1964, p. 54), refers to an instru­ ment consisting of wooden bars. The term xylophone is

composed of two Greek word elements, xylo meaning "wood"

and phone meaning "sound." In a literal sense the term 17

xylophone should be applied only to instruments with wooden

bars. Educational toy instruments called "xylophones" are

manufactured using either wood or metal bars.

The bar material used for the manufacture of fine

quality marimbas and xylophones in the United States is

rosewood, obtained from Honduras in Central America. A

handbook published by the United States Department of

Agriculture (No. 207, pp. 101-102) contains information on

Honduras rosewood. This wood is found only in British

Honduras and is very hard and heavy with a pinkish brown to dark purple coloring and irregular black markings or zones which are independent of the growth rings. These alternating dark and light bands give the wood an attrac­ tive figured appearance. Air-dry rosewood weights on the average 62 pounds per cubic foot and has a very low shrinkage rate after being cut and shaped into marimba and xylophone bars.

One of the prime considerations is the age of the rosewood used for bars. Wood that has been dried from six to eight years after it has been cut was said to be pre­ ferred by one leading manufacturer.

The Honduras rosewood selected in the tropical forests of Central America is sent to Belize and barked there for shipment to the States. These logs are graded on arrival in underground storage chambers and then dated before placing them in special humidifying rooms for curing. The wood is cut into slabs for the drying process. Later another curing operation takes place. The raw bars are taken to a third drying kiln, this time 18

under thermostatic control. This last process may take anywhere from six to eight years before the manufacturers are ready to tune them for key­ board perfection (Jackson, 1952, from a 1937 commercial pamphlet of J. C. Deagan, Inc.).

The specifications for rosewood used by the Musser

Division of Ludwig Industries are,

1) Quarter sawed to produce greatest yield of

straight grain wood.

2) Ripped into long strips of predetermined widths

and thicknesses.

3) 7-9? moisture content.

Dried wood has a more resonant quality than freshly cut wood and produces the desired sound for marimba and xylophone bars. Marimba bars are ideally formed from the slightly softer logs of rosewood or the outer layers of a log, whereas the xylophone bars require the very hard logs or the inner layers of wood from near the core of the log.

Xylophone bar stock is often subjected to pressure under heated rollers in an effort to produce a more durable sur­ face. Woods other than rosewood, such as Asian birch and redwood, have occasionally been used for marimba and xylophone bars, but generally the tonal and durability characteristics have not proven satisfactory for profes­ sional quality instruments in the United States.

While the harder grades of rosewood are best for use as xylophone bars, they still do not stand up well under heavy beating by performers in large bands and 19

orchestras. The author feels that a synthetic bar material

of better durability and comparable or better tone quality

might well be developed for use as xylophone bars. Further

comments are given on this topic in Chapter VII in discus­

sing improved manufacturing processes and recommendations

for further work in the area of bar percussion instrument

acoustics.

Vibe Bars

Vibe bars are made from aluminum which is obtain­

able from suppliers of industrial metals in the United

States. The aluminum bar material used by the Musser

Division of Ludwig Industries for the manufacture of their

vibe bars is obtained from the Aluminum Company of America

(ALCOA) and is known as material #2024-T4. Its chemical

composition and mechanical properties are as follows :

Silicon 0.50 maximum Iron 0.50 maximum Copper 3.48-4.9 Manganese 0 .30-0.9 Magnesium 1.2-1.8 Chromium 0.10 maximum Zinc 0.25 maximum

Mechanical Properties

Tensile Yield Thickness Strength Strength Elongation

.125- .495 inch 62,000 psi 45,000 psi 10% .500-4.5000 inch 62,000 psi 42,000 psi 10% 20

Orchestra Bell Bars

Orchestra Bell bars are made from high carbon con­

tent Steel which is obtainable from suppliers of indus­

trial metals in the United States. The steel used by the

Musser Division of Ludwig Industries for manufacture of

their orchestra bell bars is known as AISI-10M2. Its

chemical and physical properties are as follows:

Chemical Properties— Typical

Carbon , k O to .47 Manganese .l60 to .190 Phosphorus .04 maximum Sulpher .05 maximum

Physical Properties

Tensile Strength 102,000 psi Yield 89,000 psi % of elongation in 2 in. l 6 % % Reduction of Area 40% Brine11 Hardness 207 Machlnability 63

Inaccuracies found in reference sources in describ­ ing bar material of the four bar percussion instruments are discussed in Chapter III which reviews musical acoustics literature pertaining to bar percussion instruments.

Resonators

Resonators of bar percussion instruments made in the

United States are cylindrical aluminum tubes slightly larger in diameter than the width of the oars above them and are suspended vertically close to the underside of the percus­ sion instrument bars. The resonators are stopped at the 21

lower end, open at the top end, and their length is a

quarter wavelength of the fundamental frequency of their

respective bars. Resonators placed under the percussion

Instrument bars increase the power of available energy in

a shorter period of time and aid in the production of the desired tone quality. Resonators are an essential part of the marimba and vibe, optional on the xylophone, and not used on the orchestra bells. Resonators project the sound of the bar percussion instruments and a complete instrument needing resonators is only "tuned" when the bars and the resonators function properly together.

Sounding by itself a bar emits energy at a relatively low rate for a long period, but when coupled with the cor­ rect length air column of the resonator the intensity of the sound is increased. Near resonance will occur between a bar and a resonator of incorrect length, but resonance occurs only when the resonator is tuned to the correct length relative to the fundamental frequency cf the bar above it. The resonator is designed to the correct length to achieve coupled resonance with the fundamental of the bar in order to strengthen this part of the complex tone.

The fundamental is judged to sound relatively louder than the partial tones, which causes the listener to judge the tone to be mellow and in tune.

The importance of the resonator may easily be dem­ onstrated by covering the top of a resonator with a piece 22

of cardboard, which in effect removes the influence of

resonator. When the bar is struck a thin, weak sound will

be noted, one lacking carrying power and loudness. Also

if the tone is subjected to a stroboconn analysis the

second mode of vibration will show greater relative ampli­

tude than the fundamental. When the covering is removed

from the resonator and the bar is struck a tone will be

noted that has a greater loudness and more mellow quality,

caused by the coupling of energy between the fundamental

mode of vibration of the bar and the air enclosed in the

properly tuned resonator.

The length of a cylindrical tube resonator of the

type used on bar percussion instruments in the United

States is determined in the same manner as the length of a

closed organ pipe. The length of the resonator is approx­

imately one-quarter of the wave length of the fundamental

frequency of the bar (L = %/4) and is closed at the lower end. The resonator contains one-quarter of a wavelength of the sound wave, with a node at the closed end of the resonator and an anti-node at the open end (Pig, 3).

A node is a point, line, or surface in a stand­ ing wave where some characteristic of the wave field has essentially zero amplitude (ASAT, I960, 4.21).

An anti-node is a point, line, or surface in a standing wave where some characteristic of the wave field has maximum amplitude (ASAT, I960, 4.22). 23 L-

Fig. 3.— Resonator with One-quarter Wavelength Contained.

Closed resonators for a given frequency need be only one-half as long as open resonators. Practical reasons for the closed resonator are, (1) the resonators are short enough that the bars of the instrument need not be an extreme distance above the floor, and (2) the cost of tubing is less.

By taking the fundamental frequency (Hz) of a given bar, dividing it into the speed of sound in air (approxi­ mately 1128 feet per second) and then dividing by four, the approximate length of a resonator can be obtained (see

Pig. 4).

5.12 feet 220/ 112'8.00 1100 ~ 5 F 0 220 60 0 440

1.28 feet, or approximately 15 inches 4 / 5 7 1 ? 4 IT 8 ■32 32 24 T ^ i IS iU

Fig. 4.— Length of Resonator for Bar of Ag=220 Hz Computed.

There is an end correction factor present in all con­

tained air columns. If the anti-node were exactly at the

end of the resonator the waves would have to change from

plane to spherical with sudden discontinuity (Richardson,

1953, p. 167). The boundary of the anti-node is not a flat

cover over the open end of the resonator, but is more in

the shape of a hemispherical cover (Joseph, 1967, p. 113).

The effective length is increased by a factor of

O.58R (R = radius of resonator) for a cylindrical resona­

tor, and this length must be added to the actual length of

the resonator to obtain the effective length. Practical

considerations in the construction of the bar percussion instruments must also allow space between the underside of the bars and the tops of the resonators for the removal of the resonators when the instrument is disassembled. Sus­ pension of the resonators on some models of bar percussion instruments, the marimba in particular, allow for a slight upward or downward adjustment of the resonators to effect small tuning changes made necessary by temperature changes 25

In the environment. Based on the above calculations and by

empirical standards manufacturers of bar percussion Instru­

ments have developed optimum lengths for resonators for

each bar frequency.

The radius of the resonator Is dependent upon the width of the bar above It, being slightly larger than the width of the bar. The maximum allowable radius possible In the construction of the Instrument Is preferred because a wide radius resonator Is most conducive to the production of a tone with a desirable strong reinforcement of the fundamental frequency (Richardson, 1953, p. 172).

Marimba and Xylophone Resonators

All marimbas, and those xylophones equipped with resonators, manufactured In the United States today use cylindrical tubular resonators made of aluminum. In years past nickel plated brass tubing was used for resonators.

The better quality xylophones manufactured In the United

States possess resonators, while Inexpensive xylophones and educational toy xylophones are made without resonators. It

Is not correct to distinguish between marimbas and xylo­ phones by the presence or absence of resonators. It Is rather the shaping of the bars and the subsequent modes of vibration that determine whether an instrument Is a marimba or a xylophone (supra, p. 10).

In making Intercultural distinctions some authori­ ties do, however, differentiate the marimba and xylophone 26

by the presence or absence of resonators. Chenoweth (1964)

held this position.

The marimba then Is a struck Idlophone of the xylophone group (from Its wooden keys [bars]), differentiated from other xylophones by having a resonator under each key [bar] which Is tuned to that key [bar] (p. 52). It Is these resonance chambers that differentiate the marimba from Its close relative the xylophone, which, strictly, does not have them. . . . Manufacturers In North America have confused the distinction by adding resonators to the xylophone to Improve Its tonal quality while continuing to call It a xylophone (pp. 2-3).

Vibe Resonators

A new bar percussion Instrument was conceived and

manufactured in the 1920*s. Both J. C. Deagan, Inc. In

Chicago and the Leedy Manufacturing Company In Indianapolis

were experimenting with a metal bar Instrument that used a

motor driven set of pulsating disks in the resonating

tubes. This Instrument was called a "vlbraharp" by the

Deegan firm and a "vibraphone" by the Leedy firm (Wechter,

1962, p. 4). Through complexities of trade mark registra­

tion Deagan retains to the present the name vibraharp and

Leedy (now the JenCo brand) the name vibraphone. The shortened term vibe which Is used by the Musser firm has In recent years gained acceptance as a concise name for this

Instrument. The vibe Is not a "harp" and a companion term

'"marlmbaphone" passed Into disuse long ago, therefore the shortened term vibe seems appropriate and is used for this instrument in this investigation. 27

Resonators are an essential part of the vibe, both

for ançlifying the sound and for containing the electri­

cally driven pulsating disks that give the instrument its

characteristic pulsating vibrato tone quality and its name.

The resonators contain the air column that is subjected to

the compressing action of the motor driven pulsating disks

at the top of each resonator. These disks, slightly smal­

ler than the interior radius of the resonators, connect to

a horizontal shaft positioned in the resonator tubes near

the top of the tubes, and rotate slowly (1 to 9 revolutions

per second) powered by an electric motor with a belt and

pulley mechanism. This action causes an intensity vibrato

since the top of the resonators are alternately open and

closed by the rotating disks. Wechter (1962, p. 39)

described this action.

When the bar is struck the sound waves travel downward, reverberating against the "tuned” column of air and producing the familiar Vibra­ harp [vibe] sound. By employing the revolving pulsators at the top of the resonators, the sound wave is repeatedly broken up and emerges in a series of short, rapid pulsations. This then, is the "vibrato” which gives the Vibraharp [vibe] its unique sound and name. . . . On many models, the vibrato can be adjusted for variable speeds from very slow to very fast. This is accom­ plished on more expensive models by a rheostat control and on less expensive models by a multi-speed pulley hub.

Orchestra Bells

Orchestra bell bars are never resonated. The length of resonators for bars of the high fundamental frequencies 28

of this instrument would be so very short that the en­

closed amount of air in the resonators would be an insuf­

ficient amount to appreciably affect the sound.

Mallets

Mallets are the objects held in the hands of the

performer of bar percussion instruments for the purpose of

striking the bars to produce sound. The term "hammer” is

also encountered for these objects. Olson (1967, p. 196)

described them as follows, "A hammer [or mallet] consists

of a heavy head fastened to a light shank. It is used to

strike strings, bars, rods, bells, etc., to produce the

musical tone."

The shanks or shafts of these mallets or hammers are

made of thin round dowels of rattan cane or fiberglass. A

great variety of mallet heads are used by performers of the

bar percussion instruments. The mallet head type has con­

siderable effect on the sound produced by the instrument.

A mallet head of soft material and relatively large contact

area with the bar will produce a tone with a strong funda­ mental and less prominent partial tones. A mallet head with this large surface contact area tends to damp out partials whose anti-nodes occur in the striking area, thus producing a tone less rich in partials and generally described as mellow and smooth. A mallet head of hard material and a smaller contact area with the bar will pro­ duce a tone with more and stronger partial tones. Fewer 29

higher partials will be damped since the area of contact Is

smaller on the surface of the bar. The tone quality pro­

duced with this type of mallet head Is generally described

as harsh and percussive. The generally accepted types of mallets used for each of the bar percussion Instruments

can be stated with the understanding that the Individual player can exert considerable Influence over tone quality by his choice of mallets and his own characteristic means of striking the bars. The results of experimental work done In conjunction with this Investigation on the transi­ ent responses of bars struck In different positions with different mallets are discussed In Chapter VI.

Marimba Mallets

The marimba Is played with soft rubber or yarn cov­ ered rubber core mallets. These mallets produce varying degrees of a mellow, blending quality of sound character­ istic of the Instrument, one which emphasizes the funda­ mental of the bar rather than the upper partial tones. In marimba playing the various mallets are used In somewhat specific portions of the Instrument’s reinge. The softest and largest headed mallets, usually yarn covered, are used

In the lower portion of the Instrument’s range, while the slightly harder grades of mallets, usually the rubber tipped ones with no yarn covering, are used In the upper portion of the Instrument’s range. 30

Xylophone Mallets

The xylophone is played with hard rubber, plastic,

or wood headed mallets, These mallets produce varying

degrees of a harsh, brittle tone quality characteristic of

the inetriment. In comparison to the softer mallets used

on the marimba, the hard xylophone mallets produce a tone

with a more intense noise factor at impact and more and

stronger upper partial tones.

Vibe Mallets

The vibe ts played with yarn or cord covered rubber

core mallets. These mallets produce varying degrees of a

generally mellow blending sound. The hardness of the rubber core, upon which is wrapped the yarn or cord cover­ ing, effects the tone quality. The harder the core, the more percussive and harsh the sound with a greater presence of upper partial tones.

Orchestra Bell Mallets

The orchestra bells are played with hard rubber, plastic or brass mallets, A rather wide range of tone qualities is possible, from the rubber headed mallets which produce a somewhat mellow tone, to the brass headed mallets which produce a very bright, ringing tone characterized by a percussive impact sound. 31

Ranges of the Instruments

The sounding ranges of the bar percussion instru­

ments have in past years lacked standardization. Some

reasons for this lack of standardization are, (1) it is

easy to make, within reasonable limits, a bar percussion

instrument of any desired range, (2) instruments were built

with sufficient range to play parts written in musical

compositions, and (3) the cost of construction of a given

size instrument is considered in relation to its sales

potential. The lack of standardization of ranges has caused

difficulties for manufacturers, composers and performers

of these instruments. Gradually, and not completely even

today, standardization of the ranges of each of the bar

percussion instrument types has come about in professional

quality instruments in the United States. The ranges of

these bar percussion instruments currently manufactured by

the Musser Division of Ludwig Industries, a leading firm in

the United States, is given in Figure 5. It is an accurate

source of information on the sounding ranges of modern bar percussion instruments regardless cf manufacturer. A recent definitive text by Reed and Leach (1969) on scoring

for percussion instruments uses these ranges.

The notational practices for bar percussion instru­ ments in relation to their sounding ranges often cause confusion. A one or two octave transposition down from sounding pitch is used in some cases to place the notation ;

1 I :

p \ i* \ P p I # tt tt tt # # » it I H ClD F G IClD; F G A C D 3 -UUL 4 ♦ - * Orchestra âe,f/s -Xylophone, #- V/Ae. ■Alan’mb ^ ------* I c,| (I ; I ^ = 261.63 cps )

Piér. 5.— Sounded Scale Ranges Musser Mallet [Bar] Percussion Instruments

LO rv> 33

on or near the treble staff for ease of reading. These

transpositions are discussed below under the appropriate

instruments.

Marimba Range

The full size "concert grand" marimba (Musser #250) has a sounding range of Ag to Cy, or four and one-third octaves. Other first line marimbas have a sounding range of Cg to Cy, or four octaves. The marimba is notated at sound pitch using both treble and bass clefs. Passages sounding in the top octave of the marimba's range are some­ times notated an octave below sounding pitch for ease of reading. The marimba is the only bar percussion instru­ ment whose sounding range extends significantly downward into that portion of the musical scale where bass clef notation is used for the lowest notes.

Xylophone Range

The full size xylophone has a sounding range of Fij to Cg , or three and one-half octaves. Some small models are also in common use. Often term "piccolo" xylophones, they have a range of to Cg, or only three octaves. The xylophone is written in treble clef one octave below sound­ ing pitch and this transposition is understood, with no specific designation given on the music. This practice avoids numerous ledger lines that would result from writing a xylophone part at sounding pitch. 34

Vibe Range

The range of the vibe is standardized at Pg to F6,

or three octaves. The notation for the vibe is at sounding

pitch and conveniently fits the position of the treble clef

without an excess number of ledger lines above or below

this clef.

Orchestra Bell Range

The range of the orchestra bells is standardized at

Gç to Cg, or two and one-half octaves. This sounding range

corresponds to the extreme upper two and one-half octaves

of the piano keyboard therefore the orchestra bells are notated in treble clef two octaves below sounding pitch

for ease of reading. This transposition is understood and need not be designated in the music (some composers and

arrangers have, on occasions, used only a one octave transposition rather than two octaves).

Other Terminology Factors

It is not the purpose in this investigation to describe historical and cultural deviations of the bar per­ cussion instruments. However, there are problems of terminology that exist in the translation of the names of the instruments from language to language within the

Western world and problems regarding the intended instru­ ment in musical compositions by composers from different countries. 35

Some of the European names for the bar percussion

instruments are occasionally used In the United States.

The orchestra bells are often called Glockenspiel (German),

and less frequently Jeu de timbres (French) or campanelll

(Italian). Conçosers and arrangers sometimes write only

the single word bells on a percussion Instrument part. This

requires that the percussionist make an aesthetic Judgment

as to whether the composer wanted orchestra bells or the

chimes, which are long hollow brass tubes which give the

sound of church bells. In England the chimes are called

tubular bells thus making the necessary clarification. The

German term for chimes Is Glocken, which must not be con­

fused with Glockenspiel for orchestra bells.

Summary

Each of the four bar percussion Instruments— marimba,

xylophone, vibes, and orchestra bells, possess distinct

Individual characteristics. Their modes of vibration

differ, their cross sections vary, different bar materials

are used, some use resonators, some do not, certain types

of mallets are used for each instrument, and the ranges of

the Instruments differ.

The Marimba produces second and third modes of vibration at ratios of 4:1 and 10:1 to the fundamental. A deep arch Is cut In the underside of the bars. The bars are of Honduras rosewood Ideally formed from the less hard 36

grades of this wood. Tubular aluminum resonators are

essential for producing the desired tone of the instrument.

Soft rubber or yarn covered rubber core mallets are used to

play the marimba. The full size instrument possesses a

range of four and oie-third octaves— A2 to Cy (some models

only Cg to Cy). Notation is at sounding pitch with both

the treble and bass clefs used.

The Xylophone produces second and third modes of

vibration at ratios of 3:1 and 6:1 to the fundamental A

shallow arch is cut in the underside of the bars. The

bars are of Honduras rosewood of the hardest grades.

Tubular resonators are used on the high quality instru­

ments and not used on less expensive models. Hard rubber,

plastic or wood mallets are used to produce the desired

sound of the instrument. The full size instrument possesses

a range of three and one-half octaves— Fi^ to Cg (smaller

models C^ to Cg). Notation is one octave below sounding

pitch in the treble clef.

The Vibe, also known as "vibraphone" or "vibraharp,"

produces second and third modes of vibration at ratios of

4:1 and 10:1 to the fundamental. A deep arch is cut in the

underside of the bars. The bars are of high grade commer­

cial aluminum. Tubular aluminum resonators containing motor driven rotating fans are essential for producing the desired tone of the instrument. Mallets with y a m or cord covering over rubber cores are used on the instrument. 37

The range of the vibe is standardized at three octaves—

Pg to Pg. Notation is at sounding pitch in the treble

clef.

The Orchestra Bells, also known as Glockenspiel, produce second and third modes of vibration at ratios of

2.75:1 and 5«4;l to the fundamental. The bars are of uniform cross section. The bar material is high carbon content commercial steel. Resonators are not used on the instrument. Hard rubber, plastic or brass mallets are used to play the orchestra bells. The range of the orches­ tra bells is standardized at to Cg. Notation is proper­ ly two octaves below sounding pitch in the treble clef. CHAPTER III

LITERATURE

Background

The harmonic series produced by a theoretical thin

string or narrow pipe had for centuries furnished the

basis for the evaluation of the musicality of a sound.

Each harmonic or mode of vibration of these vibrators cor­

responds to an integral multiple of the frequency of the

fundamental mode of vibration of the string or pipe. This

concept of the idealized, thin, narrow vibrator whose seg­

ments vibrate as perfect integral divisibles of the whole

was the basis for the development of broad theoretical

systems of music and musical acoustics spanning centuries

(Mersenne, I636, Rameau, 1722, Helmholtz, I863, and Hinde­ mith, 1937). An extensive historical investigation of the harmonic series has been done by Green (1969).

In the latter part of the eighteenth century the acoustician Ernst Plorens Friedrich Chladni (1756-1827) became very aware of the limitations of the theories which used an idealized vibrator, such as a narrow string, to explain the vibration of all sonorous bodies. He recog­ nized that sonorous bodies such as rods, plates and bells

38 39

produce quite a different order of partial tones than those

of an Idealized string. In his celebrated treatise

Entdeckungen uber die Theorle des Klanges (1787) Chladni

did the first scientific study with vibrating plates. This

study became the basis for subsequent research on vibrators

that depart greatly from the Idealized conditions of thin narrow strings and pipes. Chladni made visible the nodal patterns for many danqjed conditions of circular and rectan­ gular plates of metal by sprinkling sand on plates and setting them Into steady state vibration by bowing the edge of the plate with a string Instrument bow. When a plate Is set Into vibration In this manner, the sand col­ lects along the nodal lines of the plate. While these

Chladni plates were thin brass plates quite unlike real percussion Instrument vibrators, they did furnish evidence of an early concern for the characteristics of percussive type vibrators.

Investigators In the nineteenth century such as the respected acoustician Helmholtz (1821-1894) were aware of and commented on the problems of Inharmonlcity of uniform three dimensional vibrators. Helmholtz (1863) stated:

Nearest to musical tones without any upper par­ tials are those with secondary tones which are Inharmonic to the prime, and such tones there­ fore, In strictness, should not be reckoned as musical tones at all (p. 70).

Helmholtz did present some explanation of the more "musi­ cally pleasant" tone that we associate with the bar 40

percussion instruments such as the xylophone.

In wood the mass is small, theinternal struc­ ture comparatively rough, being full of count­ less interstices, and the elasticity also com­ paratively Imperfect, so that-the proper tones [upper partial tones], especially the higher ones, rapidly die away. And for this reason the strawfiddle [xylophone] is perhaps more sat- Isfactory to the musical ear, than harmonicons formed of steel or glass rods or plates, with their piercing inharmonic partial tones . . . (p. 71).

The modes of vibration produces by uniform cross section percussive vibrators do not form a harmonic series.

This basic characteristic of percussive type vibrators, which produce inharmonic partial tone relationshipsj has long been recognized as an extremely important aspect of the tone quality of percussion instruments. Prom the time of Chladni to the present, writers of most musical acoustic texts have assumed these conditions of inharmonic partials to exist in all situations for all percussion instrument vibrators. There has been a tendency for many writers to arbitrarily dismiss any consideration of the musicality of percussion instrument tone quality on this basis.

Twentieth Century Musical Acoustics Texts

An adequate description of the acour> ical properties and nomenclature of modern percussion instruments is needed. Musical acoustics texts written in the twentieth century should accurately describe instruments currently in use. Not one present, in detail, the characteristics of the refined instruments (such as the bar percussion 41

instruments) that have evolved in the present century.

These texts that might be expected to contain detailed

information (1) state the general conditions found in a bar of homogeneous material and uniform cross section,

(2) present incomplete and even inaccurate descriptions of bar percussion instruments in use, (3) dismiss the problem on the grounds that sufficient musicality is Judged to be lacking in these sound sources, or (4) sts;e that the solution is too complex to be presented. A representative group of musical acoustics textbooks was critically examined in regard to the scope and validity of those por­ tions of the texts concerned with percussion instruments, the bar percussion instruments in particular.

A text by Richardson (1929), one of the first writ­ ten non-technically for the musician with an interest in acoustics, discussed percussion instruments (Chapter V, pp. 89-104). Richardson stated, "the xylophone is the only orchestral example of the 'supported' bar instrument"

(p. 90). It is possible that Richardson used the term

"xylophone" in a very general sense to include all of the four bar percussion instruments, however, this is not clarified by his further discussion. No mention is made of the orchestra bells, which were common in the orchestra of that time, nor of the marimba or the newly invented vibe.

A figure titled "mode of vibration of supported bar" is given by Richardson (p. 90). He described anti-nodes. 42

or points of maximum vibration as occurring "at the ends and

intermediately,” however, his figure shows a node point, or

point of minimum vibration at the middle of the bar (Fig. 6)

Pig. 6.— Mode of Vibration of Supported Bar According to Richardson.

Richardson's figure is not the correct representation of a

percussion instrument bar vibrating in its fundamental

mode of vibration (infra. Fig. 7, p. 67).

Richardson spoke of the "pure tone" of the xylo­ phone (p. 90). The struck tone of a xylophone bar contains many • artial tones that cause a harsh, percussive quality to be heard, and should not be described as a "pure tone."

Acoustically a pure tone is defined as only one sinusoidal mode of vibration with no upper partial tones present

(ASAT, i960, 13.2 ).

The tuning of percussion instrument bars is not described by Richardson. However, in his discussion of carillon bells (p. 100) the applicable principle of adjust­ ing the thickness of various sections of the bell to make the partials harmonic is described. This principle is used in tuning percussion instrument bars (infra Chapter

IV). 43

In a brief section devoted to percussion instru­ ments, Bartholomew (19^2, pp. 129-139) stated that, "since percussive vibrators give rise to inharmonic upper par­ tials these instruments are of less Importance as orches­ tral instruments" (p. 130). Later in the same paragraph he concluded:

It is easy to understand why percussion instru­ ments have only a limited use musically when we remember that frequently not a single strong over­ tone [partial] may be consonant with the funda­ mental, while in other instruments the fundamental and the first five overtones lie in a major chord, while many higher overtones duplicate the tones of this chord (p. 130).

This judgment of the musicality of a tone based upon the extent of the components of the complex tones departure from the harmonic series is not appropriate for percussive vibrators. It is now well established that percussive tones consisting of only harmonic partials may not be judged to be good musical tones. This is particularly true of the tone of the piano, whose tone source is a percussive — vibrator. As described by Blackham (1965):

. . . the Inharmonicity of the piano’s tone must not be neglected. Some believe that the tone quality of the piano could be improved merely by making the tones more harmonic. Our tests have proved that synthetic tones built of harmonic partials lack the quality of warmth that is associated with the piano as it exists today (p. 99).

Bartholomew presented a brief discussion of rods (p. 131) in which he mentioned only basic matters such as :

pitch depends on dimensions and other character­ istics of the metal, . . . loudness depends on 44

the force of the blow, and on the manner of reinforcement . . . tone quality depends on such factors as the dimensions, characteristics of the metal or other material, point of strik­ ing, material and shape of the striking point, and the manner of reinforcement.

The material of the bar and the material of the

"striking point" which Is the mallet for bar percussion

Instruments Is not'discussed further by Bartholomew and no bars are shown by way of illustration. The "manner of reinforcement" likely refers to resonators for the bar percussion Instruments, but this is not brought out in his discussion.

In his widely used text on musical acoustics. Culver

(1956) mentioned the transverse vibration of rods (p. 237).

He stated, "Since rods used In musical and related devices commonly have a rectangular cross section, we shall con­ sider only that geometric form." He did not mention any possible cross section irregularities while diagramming and discussing the position of the nodal polr.ts of the fundamental of a bar or rod of uniform cros? section (p.

239). He presented the usual series of upper partial tone ratios "1, 2.75, 5.4, etc." and stated that they are "In­ harmonic" and "though the overtones [upper partials] do not form an harmonic series, they are not all dissonant, though some are decidedly so" (p. 240). He did not attempt to explain which partials are "not dissonant" and which par­ tials are "decidedly so" and why and how this Is the case. 45

Culver mentioned that one use of transverse vibra­ tion of bars Is found In the xylophone, "this organization

[sic] consists of a series of flat strips of metal or wood"

(p. 240). He stated that, 'In some cases the sonorous bars are associated with tubular resonators for the purpose of augmenting the Intensity of the emitted sound. Such an assembly Is called a marimba" (p. 240). He stated that the "compass" or range of the marimba «as three and one-half octaves from C3 to Fy, yet the plate given (Fig. 14-6, p. 240) clearly shows a photo of a marimba beginning on a low note of "F" rather than "C".

Culver discussed the Important aspect of percussive excitation of tones. He described the change In tone quality of a percusslvely generated tone after the vibrat­ ing element has been excited:

The timbre of a musical sound may undergo a decided change within a small fraction of a second after the vibrating element of the instrument has been excited. This is particularly true in those cases where the sound is initiated by a percussive stroke, the upper partials in general are found to be relatively strong, . . . these partials tend to decrease rapidly in amplitude, the most pro­ nounced change occurring in less than 1/10 of a second after the initiation of the sound. . . . As a result of the fading out of these high fre­ quency partials, the character of the sound under­ goes an appreciable change (p. 107).

A thorough treatment of musical acoustics topics is given in a recent text by Taylor (1965). The subject Is more technically and mathematically treated than by

Richardson, Bartholemew, or Culver. Taylor's description 46

of percussive vibrators Is theoretical or idealized more

than based upon measurement of real percussion instruments.

This text does contain pertinent information on percussive

vibrators, but no cohesive description of the acoustics of

these instruments is found in any one portion of the text.

The classic Chladni plates are used to illustrate several percussive phenomena. In the section on modes of vibration (2.5, p. 13) Taylor presented a description of

Chladni plate vibration and pointed out that the frequen­ cies of the various modes of vibration do not bear a simple ratio to each other. A method of producing steady state excitation of these plates through the use of a vibration transducer with a signal fed from a variable fre­ quency signal generator was described in the same section.

In his section on vibration of membranes and plates

(2.9, p. 23) Taylor stated, "The analysis for transverse vibration of rods will not be attempted." Percussive excitation is referred to in a section on vibration in several modes at o, ce (3.2, p. 33). Oscillograph traces of a Chladni plate that was struck shows the complicated wave form produced by percussive excitation.

While discussing resonance amplification (5.3, p.

70), Taylor mentioned that:

The use of tuned resonators as amplification is not very common in modem musical instruments. It occurs in the xylophone, marimba and other similar instruments in which the sound produced by striking a wooden or metal plate of specific 47

dimensions is amplified by a long tube suspended beneath it and adjusted to be of resonant length. The purpose here is not so much to amplify the whole sound as to amplify that part of the rather harsh noisy sound of the initial note which is musically desirable.

The above is the clearest and most lucid description of

acoustical resonance in connection with the bar percussion

instruments to be found in the reference literature.

"Impulsive excitation" is the title of the section

(6.4, p. 89) that contains a description of the struck tone of percussive vibrators. The effect of the shape of the striking object is well stated: "The broader the dis­ turbing object the less rich in harmonics will be the resulting sound." The effect of the place and manner of excitation are likewise mentioned: "If a plate . . . is struck at a point at which a node would occur for a par­ ticular partial, that partial would be absent from the subsequent vibration" and "it is necessary to pay special attention to the rapid removal of the hammer to prevent interference with the subsequent free vibration of the string or plate."

Chapter Ten (pp. 156-177) "The Physical Characteris­ tics of Conventional Instruments" does not include any mention of percussion instruments. Useful information is found in the earlier chapters concerned with types of excitation and acoustical principles connected with per­ cussion instruments. The discussion of items relating to 48 percussion instruments given on the above pages indicates that Taylor's text does contain helpful information on percussion instrument acoustics when it has been located.

The failure of most musical acoustics texts to acknowledge the importance of (1) preferred material, and

(2) non-uniform cross sections of percussion instruments bars is the major criticism of these reference sources.

Olson (1967) stated, "The xylophone consists of a number of resonant metal or wood bars . . ." (p. 172). This is fol­ lowed by a perspective drawing of a xylophone and a brief discussion of its properties. He ignored the fact that a non-uniform cross section shape is used for xylophone bars.

The equation for a uniform bar is given as characteristic of xylophone bars.

The range of the xylophone given by Olson is C-j to

Ey. The range of xylophones currently manufactured is

to Cg. He indicated the range of the marimba to be

?2 to Py, which is a range found on no instrument manu­ factured in the United States and might possibly be found only among the large Guatemalan marimbas noted for their extensive range. The largest marimba manufactured in the

United States has a range of A? to Cy.

Olson did not correctly define the bar material of the orchestra bells or xylophone. The "glockenspiel"

(orchestra bells) Is described by Olson (p. 173) as con­ sisting of "resonant bars with frequencies corresponding to 49

the musical scale and arranged like the keyboard of a

piano." "Resonant bars" does not define the material of

the bars, one can assume that "resonant bars" are bars

that ring, and while this is true of the steel bars used in

the orchestra bells, the xylophone was also described by

Olson as having "resonant metal or wood bars" (p. 172).

The rosewood bars used in the xylophone are "resonant" in quite a different sense, they produce a crisp, percussive tone of very short duration. The range of the glocken­ spiel is stated as being "somewhere between to Cg."

The instrument in use today has a range of G5 to Cg

(supra Fig. 1, p. 8).

In discussing resonators (p. 173), Olson stated they, "thereby increase the sound output," and in a pre­ vious section concerned with the basic principle of resonance he used the phrase, "a larger sound output." No details of the construction of the resonators are given.

Olson described hammers used to set the bar percus­ sion instruments into vibration, ones with felt heads for xylophone and wood heads for orchestra bells. These are not the materials most commonly used by performers today

(see supra Fig. 1, p. 8).

Under the topic of growth and decay characteristics of musical instruments (6.6, p. 237), Olson gave a graphic representation of the growth, steady state, and decay characteristics of percussion Instruments of definite 50

pitch (Pig. 6.45 F) and showed that the "build-up time of

the emitted tone Is very short" and "the decay time Is

exceedingly long." He did not mention that the material would have considerable effect on the decay time; for If

the bar were of metal the decay time would be consider­

ably longer than if the bar were of wood. Olson discussed in some detail growth, steady state, and decay character­ istics of tones and concluded that, "percussion instruments do not produce a steady-state output during any portion of the sounding time" (p. 240).

Olson's treatment of bar percussion instrument acoustics has been discussed in some detail for, (1) inac­ curacies exist in his presentation, (2) despite these errors his treatment of the acoustical properties of percussion instruments is one of the better attempts currently avail­ able in musical acoustics reference sources.

A recent publication by Josephs (1967) devoted a chapter to percussion instruments (Chapter 8, pp. 127-134), but due to the brevity of this chapter has very little detail on bar percussion instruments. Transverse vibra­ tions of rods [bars] free at both ends are mentioned (p.

128), with the frequency ratios for a uniform bar given

(p. 129). Joseph stated that these are the type of bars used in xylophones and marimbas. While xylophone and marimba bars are free at both ends, they are not of uni­ form cross section and the frequency ratios given by 51

Joseph are Incorrect for percussion instrument bars. Men­

tion is made that pipes [resonators] tuned to the funda­

mental frequencies of the corresponding bars are placed

under the bars. The manner in which the length of these

pipes or resonators is determined or their acoustical

function is not explained.

A brief description of how to obtain sand patterns

on Chladni plates excited by bowing is included (p. 130)

along with some forty of the approximately 250 different

possible Chladni patterns. Writers of musical acoustics

texts seem obligated to place these geometrically appeal­

ing patterns in the percussive excitation section of their

texts, but usually do not attempt to explain how these

might relate to acoustical properties of percussion

instruments.

Levarie and Levy (1968) assumed quite a different

approach to the topic of musical acoustics than any other

known to this author. They purported to speak about

"investigating tone in terms of musical values" (vii). A brief chapter (Chapter 11, pp. 150-162) is devoted to the acoustics of percussion instruments in which they dis­ cussed the properties and perception of percussive tones.

In keeping with the approach of the text, one does not find the usual tables of frequencies and the terse over­ simplified statements about percussive tone quality characteristic of many texts. Rather some explanation of the manner in which we hear percussive sound is given along 52 with references to specific orchestral works and orches- trational procedures.

The body of literature on the acoustics of percus­ sion instruments is not large, and one goal or task of an investigation on this subject Involves collecting the bits of information into some definable whole. In this regard two statements made by Levarie and Levy concerning the tone quality of percussion instruments bear inclusion here!

(1) a Justification for the lack of research on percussion instrument tone quality, and (2) a specific comment on partial tone structure and its relationship to the musi­ cality of a percussive sound.

The musicians' interest in the acoustics of in­ struments may justifiably be most intense for the specifically "musical" ones, that is, those capable of providing definite tones; and it may gradually diminish as his studies approach the noise makers, that is, the mere rhythm instruments. A music an would learn little of value and use to him by i vestigating the acoustics of, say, the triangle p. 153).

Because the sound of all percussion instruments contain a large share of inharmonic partials, the definiteness of pitch (i.e., "musicality" of the sound) depends on how far removed from the fundamental these inharmonics lie. The higher up they are, the more quickly they fade than the more powerful fundamental, thus permitting the tone to become definite, the nearer they are to the fundamental, the more they obscure the exact pitch and approach noise (pp. 152-153).

These statements rather accurately reflect a reason for the lack of research at present into the tone quality of percussion instruments and the difficulties inherent in evaluating the "musicality" of percussive tones. A 53

comment of perhaps only incidental interest except to those

deeply immersed in percussion acoustics is that Baldwin

(1970) has Just completed an exhaustive study of triangle

and cymbal tone qualities (infra p. 58).

A Selective Bibliography of Material Pertaining to

the Acoustics of Percussion Instruments (1969) compiled by

the acoustics committee of the Percussive Arts Society is

a fifty entry annotated bibliography of basic references

on the acoustics of percussion instruments. Included are

musical acoustics texts, some of which are discussed in

this chapter. Other books and articles that deal in

particular with bar percussion instruments are found in

this bibliography. Some of these are mentioned in this

investigation. In general they do not go into adequate

detail.

Summary

The recognition that the modes of vibration or partial tones of percussive vibrators depart greatly from

a harmonic series was of importance to the early study of this class of vibrators (Chladni, 1787). Later investi­ gators continued to describe this deviation, stressing particularly the inharmonic nature of the partial tones

(Helmholtz, 1863).

Musical acoustics texts of the present century

(Richardson, 1929, Bartholomew, 19^2, Culler, 1956, Taylor,

1965, Olson, 1967, Joseph, I967, and Levarie & Levy, 1968) 54

carry on the concept of solely Inharmonic partial tones

existing In the tone of percussion Instruments. Many bar

percussion Instruments and bells are tuned, through manip­

ulation of their cross sections, to produce partial tones

with harmonic relationships to the fundamental. Accurate

descriptions of the modes of vibration, cross sections, bar

material, use of resonators, striking Implements (mallets),

and ranges of the four bar percussion Instruments— marimba,

xylophone, vibe, and orchestra bells— In use today are

either not attempted or are given Incorrectly In musical

acoustics texts.

The review of selected literature on the acoustics

of percussion Instruments, specifically the acoustics of bar percussion Instruments, Indicates that the authors of musical acoustics texts have not completely Ignored this type of percussion Instruments. However, they have not presented detailed discussions of the acoustical properties of these Instruments. The many Incomplete, Inaccurate and even erroneous statements make It Impossible to obtain an accurate and complete description of the acoustics and nomenclature of bar percussion Instruments of the type manufactured and used today.

Literature on Experimental Research and Tuning

Very little experimental research on the acoustical properties of bar percussion Instruments has been done. 55

If any acoustical investigation on these instruments has

been carried out by manufacturing firms in this field it has

not been made available for scholarly study.

Literature giving detailed information on the tuning

processes of marimba, xylophone, vibe, and orchestra bell bars is not available. These tuning processes have been

carried out for many years on an empirical basis by skilled tuners using their aural perception and judgment. Brief accounts of bar tuning do not describe the details of shaping the bars to produce the desired harmonic partial tones. Descriptions of bar tuning given in manufacturers sales literature often are incomplete and contain little technical information.

Literature describing experimental research and tuning for other percussive vibrators is relevant and of value to an investigation in an area such as bar percus­ sion instrument acoustics, where specific information is lacking. Reasons for this are: (1) all percussive vibra­ tors have partial structures that are unique in that they depart greatly from a harmonic series, (2) many percussive vibrators are shaped to non-uniform cross sections to pro­ duce particular desired partial tone structures, (3) the tone quality of percussive vibrators is influenced by the type of striker and manner of excitation, (4) sympathetic vibration or resonance effects occur between parts of many percussive vibrating systems, and (5) there are similarities 56

of apparatus and procedures that may be used for the inves­

tigation of the tone qualities of various percussive

vibrators. Therefore, in addition to literature on bar

percussion instruments, literature on the following related

areas was examined: (1) membrane and metallic percussion

instruments such as tom-toms, drums, triangles, cymbals,

and carillon bells, (2) piano tone quality, and (3) vibrat­

ing qualities of violin body plates.

The act of manually striking a percussive vibrator

with a mallet involves a rather complicated physical

process. In a detailed study of percussion technique

Stauffer (1964) discussed physiological principles and

their acoustical implications, pointing out variables in

the stroke, and the mallet. These variables can be sum­

marized as follows: (1) weight, shape, size and material

of the striking agent, (2) speed with which striking agent

comes in contact with the vibrator, (3) point of contact of

striking agent with vibrator, (4) angle at which striking

agent comes in contact with vibrator, (5) total area of

striking agent that comes in contact with vibrator, and

(6) flexibility or elasticity of striking agent.

Stoutmeyer (1968) presented some clarification of

the acoustical differences between the marimba and the xylophone. His findings support the subjective Judgment

of bar percussion instrument tuners regarding the presence of strong octave partials in the marimba tone and strong 57

fifth partials in the xylophone tone. His studies, imple­

mented with a spectrum analyzer, in which selected marimba

and xylophone bars were struck with mallets ranging from

those considered to be hard xylophone mallets (plastic

Musser M5 and hard rubber Musser M4) to those considered

to be soft marimba mallets (yarn Musser M8 and soft rubber

Musser Ml) also showed that the harder mallets produced a

more intense noise factor at Impact, more partial tones,

and greater duration and intensity of these partials.

McConnell (letter to author) has investigated the

change in tone quality of steel bars that he felt occurred

with a change in pitch. He mentioned two hypotheses re­

garding the tone quality of these bars.

(1) Internal stress or inclusion defects in the steel affect the tone quality, (2) Energy is robbed from desired modes by vibration by unde­ sired vibration and possibly the dissipation of such undesired vibration by the supports [manner of suspension of the bars].

In an early study Obata and Tesima (1935) reported

their findings concerning the acoustical properties of

primitive Oriental membrane percussion instruments with

tacked on heads,rather than heads secured by means of modem counterhoop tension. They described the occurrence

of sympathetic vibration when both heads of a shallow drum were tuned to the same frequency. The acoustical proper­ ties of drumheads of calfskin and the newer mylar plastics were investigated by Hardy and Ancell (1961). Their study 58

showed that a homogeneous material such as plastic produced

a tone quality characterized by the presence of more

strong upper partials in the sound of the drumhead, than

from a less homogeneous material such as calfskin. A

dissertation written by Henzie (I960) investigated the

amplitude and duration characteristics of snare drum tones.

Henzie’s study is significant because it was one of the

first attempts to use electronic apparatus to measure the

acoustical properties of snare drum tones.

Baldwin (1970) investigated, measured and compared the "overtones" [partials] produced by six different triangles struck with three different Implements at three different points on the surface of the triangles. Also five different cymbals were struck with three different implements at two different points on the instrument’s surface at three different dynamic levels. The influence of variations in instrument size, striking point and angle, size and material of implement, and dynamic level were determined with a Bruel and KJaer Frequency Analyzer and Level Recorder. A mathematical investigation of the triangles, made with the Structural Analysis and Matrix

Interpretive System (SAMIS) produced a set of predicted frequencies for each triangle plus the Information neces­ sary to diagram each frequency’s mode of vibration. The predicted frequencies were compared to the actual 59

frequencies the triangles produced. This investigation is

significant in that desirable parameters are defined for

the design and manufacture of these instruments.

Grutzmacher (1965) provided a description of pro­

cedures used in analyzing carillon bell tones. His studies

were concerned with the influence of the striker. Graphs

from tests were given that compared the harmonics [par­

tials] produced by strikers of different sizes, materials,

and speeds of striking motion. Green (1969, Chapter VII)

surveyed the history of the art of bell making and traced

in particular the practice of shaping the bell and removing material at critical points to obtain desired partial tone relationships.

Fletcher (1962) and Blackham (1965) reported the results of their extensive investigations that showed the inharmonicity of the tone of the piano. They found that the high partials of a piano tone depart considerably from a harmonic relationship with the fundamental and that this is a distinguishing characteristic of the piano’s tone quality. Synthetic tones built of only harmonic partials were not judged to be "good" piano tones by auditors.

Studies begun by Frederick Saunders and carried on by Hutchins (1968) on the many aspects of violin tone qual­ ity, including wood plate resonances, have shown that desirable parameters of violin tone quality may be isolated 60

and quantitatively measured. In her report Hutchins

described experiments in which they investigated the

resonant vibrations of individual top and back plates of

violins that were driven sinusoidally. Their testing

apparatus was described and pictured (pp. 36-38). In their

tests they attempted to give analytical Justification to

the practice of identifying and cutting wood from the

plates until the tuner aurally hears what he Judges to be

the correct ®tap-tone?‘ resonance. A similar method of

removing small amounts of wood from the underside of the

percussion bar is used to obtain the correct tuning of

these percussion instruments.

Hutchin’s described the process of tuning and

testing violin plates.

We concentrate mainly on observing plate resonances and their effect on final tone quality. We test top and back plates of violins and the larger in­ struments in the course of construction, thus observing changing resonances as wood is progres­ sively removed (pp. 35-36).

. . . the first strong resonance appears when the frequency is scanned from low to high— the resonance known as the "tap-tone.” A traditional violin maker can approximate this resonance by tapping the wood with his fingers and listening for pitch and quality of sound. By experience he works by careful removal of wood to achieve a certain "ringing" in each completed plate (p. 37).

. . . We have tried to correlate these tapping and listening methods with the measured fre­ quencies and amplitudes of free plates and the resultant resonances and tone qualities of each completed instrument (p. 37).

"Pine tuning" of the plates is further described as,

"the process whereby the wood is carefully scraped thinner 61

In certain areas to achieve the best subjective tap-tone

and high amplitude smooth resonances* (p. 38). Hutchins

also stated:

. . . only experience and intuition help us decide where wood should be shaved. . . . This process of tuning plates by tap-tone resonance is still incom­ pletely documented since alterations in the wood are reflected by changes in the many resonances in the spectrum (p. 39).

A brief report on xylophone bar tuning by Gentil

(1919) appeared in a German publication. The report con­

cerning the xylophone and the physical laws of trans­ versely vibrating bars described the basic principles of

tuning, including the influence of the length, thickness

and elastic modulus of the wood, but contained no mention

of the relation of the partial tones to the fundamental and of any possible non-uniform cross section deviations of the bars. Jackson (1952) in his thesis on the history of the marimba, which placed emphasis on the acoustical properties of the instruments, briefly mentioned tuning.

The actual tuning is done with the utmost care by men with a good ear and special equipment to assist in this delicate process. Each bar is checked against a metal bar in the master key­ board for pitch and hand-filed for the finishing touches. . . . It is, . . . a scientific process the end result of which gives pleasure to the performer and listener alike (pp. 63-64).

Mention of tuning is to be found in a commercial pamphlet issued by the Musser firm about 1950.

Musser Marimba Bars are made from the finest Rose­ wood grown on the mountains in Honduras, and kiln- dried to less than 5% moisture. They are perfectly 62

tuned by a master tuner In a special temperature controlled room at 70® fahrenheit. This guarantees a balanced scale throughout at all times.

Vibe Bars are made of a special aluminum alloy and are tuned by a master tuner under strict tempera­ ture control to guarantee perfect intonation and balance under all conditions. You are sure of perfect tuning when you purchase a MUSSER.

The musical range of four and one-half octaves, from A in the lower bass clef [A^] to C [Cy] is perfectly voiced due to the stientifically graded parabolic tone bars with their exclusive contour design.* Thermodyne temperature control, an exclusive CanterFury f^eature, permits perfect resonance, balance and tonal clarity at all times. Iso-tone resonator shock mounts prevent extrane- ous vibration (from Musser catalog, date ca. 1950). *Model #500 Canterbury Marimba.

MacCallum’s (1969) informative book on the marimba contains a description (pp. 75-77, 89-92) and diagrams of bar tuning (Plates III and IV, pp. 106-107). It indicates the importance of tuning the upper partials as well as the fundamental of the bar, and states that the second mode of vibration should produce a musical note two octaves above the fundamental and that the third mode of vibration should be three octaves above the fundamental. This text is one of the first to stress accurate tuning of the upper par­ tials, the second and third modes of vibration, as well as the fundamental. These aspects of the tuning process are increasingly being refined in the production of quality

Instruments today. This work will be described in the following chapter (infra Chapter IV). 63

A brief account of the tuning of modern handbells

(Markey and Malta, 1966) indicates the care being taken by

the manufacturers of one type of percussion instrument.

In the traditional English handbell there are two prominent tones or partials— the fundamental or strike tone, and the twelfth. . . . Although the skill and touch of the craftsman plays an impor­ tant role in the tuning of the bell, he uses precision instruments to guide and check his judgement in his work with the bronze casting. One of these instruments is the StroboConn which permits a visual check on the audible partials of the bell to 1/lOOth of a semitone. Schulmerich is now using an instrument which visually shows the frequency of the sound even beyond the audible range, and to an accuracy of up to 1/lOOOth of a cycle. Obviously, this permits an exactness which goes far beyond the capabilities of the human ear and has been largely responsible for the tremendous strides which have been made in handbell tuning over the past few years (n.p.)

Summary

A small amount of research has been done on the

acoustical properties of bar percussion instruments. Due

to the limited amount of experimental research done on

these instruments and the 3ack of detailed descriptions of

the tuning processes for these instruments, literature

concerning related areas of percussive tone quality was

consulted in an effort to obtain relevant material and some basis for the study of bar percussion instrument acoustics.

Studies concerned with the manner of excitation and the material of the striker have been done by Stauffer 64

(1964), Stoutmeyer (1968), and Grutzmacher (1965). The partial tone content of various percussive vibrators has been investigated by Stoutmeyer (1968), marimba and xylophone bars; Hardy and Ancell (I961), calfskin and plastic drumheads; Baldwin (1970), triangles and cymbals ;

Green (1969, Chapter VII), church and carillon bells;

Fletcher (1962) and Blackham (1965), piano tones; and

Hutchins (1968), violin plate tap-tones.

Tuning of percussion instrument bars has been described by Gentil (1919), Jackson (1952), and MacCallum

(1969). These sources do not treat the topic in adequate detail. The descriptions of the tuning of carillon bells

(Green 1969, Chapter VII) and handbells (Markey and Malta,

1966) to produce desired harmonic relationships is rele­ vant to the tuning of percussion bars, as is the descrip­ tion of selective removal of wood from violin body plates to produce desired "tap-tone resonances" (Hutchins, 1968).

Experimental methods and apparatus used by Obata and

Tesima (1935), oriental drums ; Henzie (1960% snare drum; and Hutchins (1968), violin body plates, may be applied to the study of the tone quality of percussion instrument bars.

In the absence of detailed acoustical literature on bar percussion instruments, literature drawn from related areas of research on the acoustics of percussive vibrators provided the best presently available basis for 65 the study of the acoustics of bar percussion instruments.

The need exists for accurate descriptive literature and published research studies concerning the acoustics of bar percussion instruments. CHAPTER IV

BAR TUNING

The objective of this chapter is to provide a des­

cription of the manner in which percussion instrument bars

are tuned. Accurate written information on this topic

that goes into sufficient detail is practically non­

existent (supra, pp. 54-55). The description of the tuning process for percussion instrument bars is based upon (1) an examination of the small amount of available literature,

(2) personal consultation with, and observation of, the manufacturers of these bar percussion instruments, and

(3) practical application of the principles of bar tuning.

The process of tuning a percussion instrument bar involves shaping a rectangular, three dimensional piece of wood or metal in such a manner that a desired fundamental mode of vibration, which is heard as the pitch of the bar, and desired upper partial tones are obtained. This process involves selective removal of material from the underside of the marimba, xylophone and vibe bars to pro­ duce a bar shape of non-uniform cross section. The cross section of the orchestra bell bars is left essentially uniform.

66 67

Any percussion instrument bar vibrates in its funda­

mental mode of vibration in a manner common to all three

dimensional free-free bars where length is considerably

greater than width. Nodal points of the fundamental mode

of vibration occur at 0.224 of the length from either end

of the bar (Olson, 1967, p. 77). The first mode of

vibration, the fundamental of the bar has a vibrational

pattern that can be represented as shown in Figure 7.

anti-nodes - N ( \

nodes' . 0.224

Pig. 7.— Mode of Vibration of Fundamental of Bar.

The node points of the fundamental, where the holes are drilled to insert the cords for suspending the bars in position on the completed instrument, are points of mini­ mum vibration. The center and ends of the bar are anti­ node points of the fundamental where maximum vibration occurs and it is at these points that the bars are struck to produce the desired sound.

Upper partial tones must be present in the sound of a three dimensional vibrator such as a percussion 68

Instrument bar. Partial tones influence what is perceived to be an "in tune" bar, and must be tuned carefully during the manufacturing process.

The second partial of marimba, xylophone, and vibe bars must be tuned at or very slightly sharp to a harmonic relationship with the fundamental of the bar. It is also desirable to tune the third partial to a harmonic relation­ ship with the fundamental. The ideal ratios of the modes of vibration and their musical note representation for marimba, xylophone, vibe, and orchestra bell bars are giien in Figure 8. It will be noted that the upper partials of the orchestra bell bars are not harmonic, this due to the essentially uniform cross section of this type of bar. A more detailed discussion of modes of vibration of bars and their relationship to the harmonic series was given in

Chapter II, pp. 9-13.

2 S

Orchestra Bell Marimba Bar Xylophone Bar Vibe Bar Bar Fig. 8.— Ideal Ratios of Modes of Vibration and Musi­ cal Note Representation for Percussion Instrument Bars. (^Nominal A2 110 Hz is used for purposes of direct compari­ son. ) 69

The use of the proper material of a high quality

grade for each bar type was previously described (supra,

pp. 15-20. Marimba and xylophone bars are Honduras rose­

wood, vibe bars are aluminum alloy, and orchestra bell

bars are high carbon steel. The important criteria that

these materials must meet are, (1) durability, the ability

to tolerate heavy beating with mallets, (2) resoneint

quality, a ringing tone of definite pitch when struck, and

(3) ability to hold a musical pitch, over a period of many

years.

Tuning Standards

Before a description of the process of shaping the bars is given, a brief consideration of reference tuning

standards is necessary. It is from a reference standard that the tuner obtains the Information necessary to make the Judgments relative to shaping the bar to produce a particular frequency relationship.

In past years professional tuners used only sets of metal bars termed "master bars" for reference checks in the tuning process. Experienced tuners used an aural matching process based upon their Judgment of the accuracy of the tuning of a bar in relation to these master bars.

In recent years a device developed by the G. C. Conn Cor­ poration in 1942, called a Stroboconn, has become widely used as an aid in the tuning of percussion instrument bars. 70

A msuiual by the Conn Corporation (1963) describes in detail

the use of this instrument.

The Stroboconn is an electronic device for instan­

taneous and accurate visual measurement of sound frequen­

cies. The scanning unit of the Stroboconn contains twelve windows arranged like the black and white keys of a piano,

thus allowing the instant representation of any sound in relation to the nearest semi-tone.

The Conn manual explains the use of the Stroboconn as an aid in piano tuning. This is the method now used for the tuning of percussion instrument bars as well. The

JenCo Musical Products Company, a major manufacturer of bar percussion instruments supplies the following information with each instrument sold:

The tuning on this instrument has teen checked by an electric Stroboscope [Stroboconn! and incorpor­ ated in the tuning is the stretched octave, the same as the best piano tuners uf.e. That is the hJ.gh notes show exceedingly sha;-p on the Strobo­ scope, although the instrument is tuned to the concert pitch, A=440. . . . If the purchaser should have occasion to check this instrument with the Stroboscope, we would advise getting the piano tuners chart as furnished with the Stroboscope, and check the instrument accordingly. Zero setting on the Stroboscope, although mathematically correct, does not sound in tune to the human ear.

A basic tuning standard of A n = 440 Hz is widely accepted as the correct reference frequency for musical organizations. However, there is a decided tendency for musical organizations to play higher fhan A ^ = 440 Hz. For this reason the xylophones and orchestra bells manufactured 71 by the Musser Division of Ludwig Industries are tuned to

» 442 Hz. Musser supplies the following information with each of these instruments sold:

This instrument is tuned to A » 442 ops [Hz] to produce a crisper, clearer, more penetrating sound preferred by top professional studio and symphony orchestras.

Accurate tuning to + 1 cent may be carried out by means of the Stroboconn because of the ease of adjusting the reference frequency of this device. With the scale pointer set at "zero,” the Stroboconn is in exact tune with the equally tempered scale based on = 440 Hz. The tuning scale is calibrated in hundredths of a semitone, referred to as cents. By changing the pointer setting to any position other than zero all notes are equally changed in cents. Pour cents deviation from A » 440 Hz is equal to approximately 1 Hz, therefore to tune to a standard of

A « 442 Hz, the pointer would be moved to the right to plus eight setting.

In addition to displaying the fundamental of a bar the Stroboconn can show the second mode of vibration, the second partial, for fundamentals up to (marimba and vibe bars) and Eg (xylophone bars), and will indicate their tuning relationship to the fundamental. For marimba and vibe bars both the fundamental and the second partial have the same musical note letter but two octaves apart

(supra. Fig. 8) and will appear in the same window of the 72

Stroboconn as shown in Figure 9. For xylophone bars the second partial has a musical note letter an octave and a fifth above the fundamental and will appear in the appro­ priate window (examples, "A" window for fundamental, ”E" window for second partial). An apparent rotating movement of an octave band to the left when the bar being tested is sounded indicates a frequency lower than the reference frequency and an apparent movement to the right a frequency higher than the reference frequency. It is desirable to have the apparent motion of the octave band stopped for the fundamental and stopped or revolving very slowly to the right or sharp direction for the second partial.

Fundamental

Second partial

Fig. 9.— Fundamental and Second Partial of Marimba and Vibe Bars Represented on Stroboconn.

Second partials are of considerable importance paz ticularly in the low registers of the marimba, xylophone and vibe. Fundamentals of bars below C]| are rather weak and accurate tuning of the second partial is of critical 73

importance in the tuning process. A representation of the

third partial can be obtained on the Stroboconn only for

bars whose fundamentals are or below.

The Stroboconn is of value in accurately carrying

out the important and necessary process of octave stretch­

ing (Railsback, 1938, p. 86; Conn, 1553, p. 10). Partial

tones produced by vibrators such as wide, stiff strings

in the low register of the piano are sharp to the funda­ mental and as such are not harmonic. These partial tones

of one string must be unison tuned with the fundamentals

of the strings in the higher octaves if the instrument is to sound "in tune." With the use of tii

The same process of octave stretching is necessary in tuning percussion instrument bars. Thus, as indicated by the information from the Jenco firm (supra, p. 70), a zero Stroboconn setting will show the higher bars, especi­ ally Cy to Cg as being very sharp. In actual practize the pointer on the Stroboconn is advanced a predetermined num­ ber of cents to the right to correctly "stretch" the octaves as the higher register bars are tuned. The funda­ mentals of well tuned bars in the upper register of the bar percussion instruments will produce frequencies a few cents sharp to the exact frequencies given for the equal tempered scale (ASAT, I960, 13.2). Also for a bar to be 74

correctly tuned, the ratio between the fundamental and the

second partial must be slightly more than that given as

the "ideal" ratio. For example a marimba bar with a 110 Hz

fundamental will have a second partial of about 444 Hz

rather them an exact 4:1 ratio frequency of 440 Hz. A

marimba bar of 2 2 0 Hz fundamental will have a second

partial of about 885 Hz. The above frequencies are those

found on bars tested in this investigation (infra. Chapter

VI). Tuners for the Musser firm use a chart of octave

stretching, that they have developed, expressed in cents

for each bar frequency of the instruments they manufacture.

The amount of octave stretching may vary according to the

Judgment of different firms, and no one established pattern is recommended (Conn, 1963, p. 12).

Shaping the Bar

The shaping of the bars to achieve the desired funda­ mentals and upper partial tone relationships is explained in this portion of the chapter. Industrial tools such as power saws, milling machines, and belt senders along with specially developed tools are used for the various steps of the shaping of percussion instrument bars.

The first step in the manufacturing process of the bars is to cut the bar material to appropriate lengths for particular pitches, termed bar blanks, from the bar stock material. For aluminum and steel bars u ed in the vibe and 75

orchestra bells this is a simple operation as the bar

stock material is of the correct width and thickness when

purchased and need only be cut into desired lengths.

Rosewood stock is selectively obtained for use as marimba

and xylophone bars, using the specification previously

described (supra, pp. 16-19). According to tuners of the

Musser firm even this stock has only an approximate 30%

yield of material that is suitable for bars. Rosewood of

poor quality by the standards of this industry (i.e.,

containing knots, curved grain and worm holes) must be

discarded or if of mediocre quality used on less expensive

models of instruments.

Largely through an empirical process, predetermined

lengths, thicknesses and widths, have been assigned to each

bar of each model instrument. Once established, the width

of the bar is not changed and is not a factor in the

tuning process of the bar. Only the length and thickness

are adjusted during the tuning process. In the early stage

of the manufacturing process little concern is given to

checking individual rosewood bars for the desired resonant

quality, this will be done later by the master tuners who will accept or reject each bar. Customers usually desire

an Instrument with a somewhat consistent color and grain to the set of rosewood bars. This visual factor will be given consideration in the later stages of manufacture when a given set of rosewood bars is selected for a 76

particular instrument. Metal bars will be given a satin

surface finish of consistent texture.

The second step in the manufacturing process of the

bars is to cut the basic arch in the underside of the bar.

Since the initial dimensions of the bars are approximations

and do not determine the exact final tuning of the bar, the removal of material from the underside of the bar, and if necessary from the ends of the bar, determines the final tuning of the bar. Material is removed with a band saw on rosewood bars, and with a milling machine on aluminum bars

(Pig. 10).

basic arch

Fig. 10.— Cross Section View of Basic Tuning Arch of Percussion Instrument Bar.

The basic arch does not extend quite to the node points of the fundamental mode of vibration of the bar as this area will require special attention in tuning the second partial at a later stage in the tuning process. The holes are drilled through the bar at the node points of the funda­ mental for suspending the bar on the framework of the 77 instrument at a later assembly stage. It is know that these node points are 0.224 of the distance from either end of the bar and this distance can easily be established for each bar length thus allowing for a preset drill loca­ tion on an appropriate drilling machine.

At all stages of tuning from this point on the

Stroboconn is used as an aid in the tuning of the bars

(see supra, pp. 69-74). By tapping the bar lightly with a mallet while holding the bar close to the Stroboconn microphone, an instantaneous visual reading of the fre­ quencies of the bar can be obtained on the Stroboconn scanning unit. Each step in the tuning process brings the bar downward in frequency, nearer to its eventual funda­ mental. using this method, all removal of material is from the underside of the bar avoiding the necessity of removing material from the end of the bar to raise the frequency of the fundamental (see Pig. 11— Effect of Material Removed from Bar in Various Areas), The bar is brought to one-half step above the eventual desired fundamental of the bar at this stage of tuning. For example, a bar destined to be an A|| on an instrument would at this stags appear as Bbij fundamental bar. At this stage, concern is for the tuning of the fundamental more than for the second partial or any other upper partials.

The third step in the tuning process begins the more critical aspects of shaping the bar. This step brings the 78

fundamental to 5 cents above the eventual frequency. Small

amounts of material must be removed by sanding or grinding

in selected areas of the underside of the bar to effect

changes in frequency of the fundamental mode of vibration

and the upper partials of the bar. Removal of material

from the underside of the bar is a critical adjustment, particularly at the center of the arch. A small amount of material removed lowers the fundamental frequency of the bar considerably. Removal of material from the ends of the bar will raise the frequency of the bar and is a less critical adjustment requiring the removal of more material to effect a given amount of change in frequency. A bar made thin in relation to its length will produce a lower fundamental than a bar that is thicker in relation to its length. The effect of the removal of material from various areas of a bar is shown in Figure 11.

material removed material removed material removed at either end raises near nodal points at center of arch fundamental frequency lowers second lowers fundamental and partial tones partial frequency

Fig. 11.— Effect of Material Removed from Bar in Various Areas. 79

The fourth step, the final step, in the tuning

process for regular production bars involves the very care­

ful removal of small amounts of material from carefully

selected areas of the underside of the bar to obtain the

desired frequencies of the fundamental and the second

partial of the bar.

By altering the cross section of the bar in the man­

ner shown in Figure 11 the fundamental of the bar and the

second partial of the bar may be tuned. It is possible to

change the frequency of one of these with only minimal

effect on the frequency of the other by carefully selecting

the area where material is removed.

The practice of tuning partial tones of marimba,

xylophone, and vibe bars is a relatively recent development.

Until approximately fifty years ago only the fundamental of

each bar was tuned. Little concern was shown for the

relationship of the upper partials to the fundamental and

the upper partials were not tuned. As musicians became

critical of the tone quality of the bar percussion instru­ ments, a concern developed for tuning not only the funda­ mental or first mode of vibration, but also the second partial or second mode of vibration. MacCallum (1969) stated what he believed to be the date that concern was first given to the second partial. 80

Until the 1920's only the fundamental was tuned. Such a marimba is passable if the clank note (the most prominent overtone partial) [second partial] is tonally some distance away from the funda­ mental in terms of the lettered names of the notes. But co have the fundamental C, and the clank C#, a B or a D- cannot be tolerated (p. 89).

"Octave tuning" is in keeping with the high stand­ ards of marimba manufacture. . . . With octave tuning the bar will sound harmonious wherever it is struck (p. 90).

The higher octave percussion instrument bars are easily tuned, their fundamentals are strong and the partial tones are not prominent. However, in the low registers of the marimba, xylophone, and vibe the second partials are very strong and are heard clearly when the bars are struck.

Thus in keeping with the MLgh standards of tuning carried out today, the second partials of these bars are carefully tuned. This is done by enlarging the portion of the arch near the node points of the fundamental or by forming a secondary arch near these node points as shown in Figure 12.

\

Pig. 12.— Cross Section View of Second Partial Arch Tuning.

For particularly accurate tuning, the third partial as well as the second partial may be tuned to a desirable harmonic relationship with the fundamental. Tuning of the 81

third partial requires extreme care and skill on the part

of the tuner and is done only upon special request from

the customer. Tuning of the third partial is done only in the low register of the instruments, on bars with funda­ mentals of Cij downward. For marimba and vibe bars the desirable ratios of the second and third partials to the fundamental are 4:1 and 10:1. For xylophone bars the desirable ratios of the second and third partials to the fundamental are 3:1 and 6:1. Representative musical nota­ tion for these partials was given in Figure 8. To change the frequency of the third partial independently of the first and second partials is a difficult task as very small amounts of material must be removed from the underside of the bar without changing the tuning of the first and second partials. Rosewood bars in particular must be of exceptionally fine material, relatively free of imperfec­ tions and uneven grain, to allow tuning of the third mode of vibration. Aluminum vibe bars that are made of a material more consistent and homogeneous than rosewood, produce a tone of longer audible duration and may be more easily tuned to a desirable third partial.

Marimba and Xylophone Bar Tuning Contrasted

The basic differences between a marimba bar and a xylophone bar are the proportions end arch characteristics 82 of the bar, which in turn determine the modes of vibration of the bar. The marimba bar is shaped thin in relation to its length, particularly at the center of the arch— its anti-nodal point. The xylophone bar is shaped thicker in relation to its length at the center of the bar which is its anti-nodal point. Figure 13 contrasts the cross sec­ tions of a marimba bar and a xylophone bar.

Marimba bar Xylophone bar (side view) (side view)

Pig. 13.— Cross Section Views of Typical Marimba and Xylophone Bars.

Chenoweth (1964) stated the tuning differences of marimba and xylophone bars in the following manner :

In practice there is a difference in tuning which serves to further distinguish them. The xylophone . . . is tuned with a predominant partial heard an octave and a fifth above the fundamental note. . . . the marimba, as manufactured in North America, is tuned with a predominant partial heard two octaves above the fundamental (pp. 2-3).

The second partial of a marimba bar is a partial whose fre­ quency is at a 4:1 ratio with the fundamental, or a musical note two octaves above the fundamental as indicated by

Chenoweth. It has become standard practice in bar percus­ sion tuning to call the tuning of the second partial of the 83

marimba bar, octave tuning. The second partial of a

xylophone bar Is a partial whose frequency Is at a 3:1

ratio with the fundamental, or a musical note an octave and

a perfect five above the fundamental. This relatively

lower frequency second partial of the xylophone bar,

produced by the thicker cross section of the bar Is also

carefully tuned, and can be called fifth tuning. It Is

not uncommon to refer to the tuning of the second partials

of both marimba and xylophone bars as "overtone" tuning.

However, the term "overtone" Is not a precise term. It

creates considerable confusion, and Its use In acoustical

terminology should be avoided (American Standard Acoustical

Terminology, I960, 13.6, note 2).

The second partial of a bar can be checked by

lightly pressing a mallet or the fingertips Into the top

center of a bar and at the same time striking the bar

firmly near the nodal point of the fundamental. The

second partial will be heard clearly and will establish whether the bar Is xylophone or marimba tuned.

Vibe Bar Tuning

The second partial of a vibe bar Is a partial whose

frequency Is at a 4 :1 ratio with the fundamental, or a musical note two octaves above the fundamental. As des­ cribed for marimba bars this relationship of the second partial to the fundamental is termed octave tuning. 64

Orchestra Bell Bars

Orchestra bell bars have a uniform cross section and

produce partial tones as previously shown (Figure 8) that

are not harmonics. The bar material is cut into bar

blanks that are usually within a few vibrations of the de­

sired fundamental frequency and only a touch on a grinding

machine at the center of the underside of the bar is

required to bring the bar to the exact desired frequency.

Since the cross section of the orchestra bell bars are

left essentially uniform the frequency ratios of the

second and third partials are the same as those of any

uniform cross section bar (2.75:1 and 5.4:1).

Summary

Bar blanks of predetermined materials and dimensions are prepared for use as percussion instrument bars by,

(1) cutting the bar material to the proper uniform cross section dimensions, (2) cutting a basic arch on the under­ side of all bar types except orchestra bells, and ( 3 ) selec­ tively removing material from portions of the underside of the bars to produce desired partial tone relationships.

This process is carried out by experienced tuners using their skill and Judgment to determine the desirable quali­ ties of the tuning of the bars. Their Judgments are aided by the use of reference standards including master sets of 85 tuned metal bars and the Stroboconn, an electronic device for visual measurement of sound frequencies.

Fundamental frequencies of the bars are tuned to the equal tempered scale incorporating the principle of octave stretching. Second partials of percussion instrument bars are tuned to harmonic relationships with the fundamental for marimba, xylophone, and vibe bars. Tuning of the third partial of low register marimba, xylophone, and vibe bars to a harmonic relationship with the fundamental is an exacting tuning step done only on special request. CHAPTER V

IDENTIFICATION OP STEADY STATE AND

TRANSIENT RESPONSES

The purpose of this chapter Is to describe the ex­

perimental work done to identify the steady state and

transient responses of a representative group of percussion

instrument bars.

The testing procedure used was essentially that used

by Hutchins and Fielding (1968) in which they tested the

resonant vibrations of individual top and back plates of

violins by driving them sinusoidally and determining their

responses electronically. Justification for this procedure was found in the relationship between steady state patterns

of these plates and dynamic patterns of complete instruments.

The procedure used for steady state testing was to mount a percussion instrument bar in a vibration fixture

consisting of a massive base plate and steel uprights. The bar was held in place between the uprights with cord support similar to that used in \ > a r percussion instruments. The bar was vibrated from beneath using an electrodynamic shaker. The vibrations of the bar were monitored with a

86 87

condenser mlcorphone and displayed on an oscilloscope, and

a frequency counter. The vibrational mode was observed by

sprinkling sand on the surface to show the nodal pattern

(Fig. 14).

To test for the transient response produced by a

mallet striking the percussion instrument bar, a mechani­

cal striker was built to provide a uniform stroke (Pig,

15). A storage screen oscilloscope was set for a single

sweep and a laser beam trigger was used. Photographs of

the oscilloscope traces were obtained and used in compari­

sons of bar responses to show the influence of the

location of mallet stroke on the bar surface and type of

mallet used.

Description of Experimental Work

The Department of Engineering Mechanics Vibrations

Analysis Laboratory at The Ohio State University has

facilities where accurate measurements of the characteris­

tics of vibrating bars may be obtained. A study of the

steady state and transient characteristics of percussion

instrument bars was proposed by the author and members of the School of Music faculty in cooperation with members of the Department of Engineering Mechanics. The general

objective of this work was to carry out research that would support and augment the limited empirical information available about bars used in the marimba, xylophone, vibe 88

Pig. lA.— Testing Apparatus for Percussion Instrument Bars.

;î>LlDi/0O, BASE &(jipe HOD

Pig. 15.— The Mechanical Striker. 89 and orchestra bells. Initial work was to determine the modes of vibration of selected bars of rosewood, aluminum

and steel of the type used in bar percussion instruments,

and to investigate the transient responses of these bars.

Funding for the experimental work was provided by the Engineering Experiment Station (Project EM6X). The carrying out of the experiments was done by technically competent personnel provided by the Department of Engineer­ ing Mechanics, with apparatus provided by this department and the School of Music Sound Laboratory. The project extended from January 1, to June 30, 1969.

Frequencies of the bars of each material were chosen so that all parts of the range were represented and so that comparisons among the three materials could be made (Fig. l6). The frequency range included bars of the musical note

"A" whose nominal fundamentals were from Ag (110 Hz) to

Ay (3520 Hz). These frequencies include the extreme limits of the musical note ”A" of currently manufactured bar per­ cussion instruments. The bars necessary for this experi­ ment were obtained through the cooperation of the Musser

Division of Ludwig Industries, Chicago, Illinois. These bars were Judged by their tuners to be "well tuned," and representative of the type used on their regular produc­ tion first line bar percussion instruments. "Well tuned" means, (1) fundamentals accurately tuned employing the practice of octave stretching, and (2) second partials 90

tuned for bars in the low registers of the marimba.

xylophone, and vibe. None of the bars were subjected to

the exacting step of third partial tuning.

Octave and Steel Nominal Rosewood Rosewood Aluminum Orchestra Frequency (Marimba) (Xylophone) (Vibe) Bell) A^ (110 Hz) X

A3 (220 Hz) XX

Ail (440 Hz) X XX

Ar (880 Hz) X XXX

Ag (1760 Hz) X

Ay (3520 Hz) X

Fig. 16.— Bars Used In Acoustics of Percussion Bar Experiment (No. EM6x, I969).

A testing fixture was constructed that would allow

the bars to be mounted as they are on the bar percussion

instruments. The fixture was basically an adjustable sup­ port, capable of mounting all of the four types of bars.

Four sliding blocks on two elevated tracks were the adjust­ ments which allowed the mounting of the different bar types.

The marimba, xylophone and vibe bars were mounted with a nylon cord passing through the holes drilled in the bars. This cord was guided by running against the adjust­ able sliding blocks which provided accurate alignment.

Rubber grommets were placed on either side of the bar, in a manner similar to that found in bar percussion instrument 91

frames, to loosely constrain the bar from vibrating

against the metal support. The orchestra bell bars were

supported underneath at the node points of the fundamental

by two cross pieces which were affixed to sliding blocks.

One cross piece had a tapped hole into which was inserted

a bolt with a rubber bumper. The other cross piece left

the bar laterally free and was insulated with crossed cord,

as in orchestra bell frames, to suppress any extraneous

noises.

Figure 17 shows the equipment and equipment orien­

tation used in the testing. A velocity pickup was mounted

above the bars at about a third of the bar's length from

the bar's end. The pickup was used in all testing of the

bars.

Steady State Testing

In finding the bar's modes of vibration three main

methods were used in conjunction with a continuous vari­

ation of the driving frequency. These methods were: (1)

maximum sand motion and pattern formation on the bar's

surface, (2) maximum intensity of response as observed on

the oscilloscope screen, and (3) production of Lissajous

patterns on the oscilloscope screen formed by driving and

response signals. Of the three methods used, the third was most effective and indicated all resonant points found by the first two methods as well as many more, most of rAûBe-

hAKKOPHOWE dODKL S4N1 Do^v. WOKi. ReSF’OM5E sweep

P£K'.o££.! j& 6 A R oecinjoscope' - r ^ ^ \êKT\ SWEEP ALT vAOOe

00886 GEÜSK TOK, SHAMED FREQ COUNTER

Fig. 17.— Equipment Used in Steady State Testing.

*0 93

which were left unrecorded because of their slight

intensity.

Sand sprinkled on the bar visually displayed the

nodal patterns of each mode of vibration. A dual hori­

zontal trace on the oscilloscope of driving and driven

signal was used to determine if there was a 1:1 sinusoidal

response. In the terminology of engineering mechanics any

1:1 sinusoidal response of this nature is termed a

"harmonic" response, whether or not these response fre­

quencies bear an integral number relationship with the

frequency of the lowest mode of vibration of the bar. To

avoid a possible terminology problem, the author will

continue to call these 1:1 sinusoidal responses modes of vibration or partial tones rather than harmonics.

For each bar the driving frequencies which caused the maximum relative response intensity were noted. The modes of vibration of the bars are those modes that elicited this sinusoidal response on the dual oscilloscope, thus showing an equal amplitude of input and response.

Numerous other non-sinusoidal responses were obtained, ones in which the driving and response frequencies differed. With the steady state tests the mere presence of the shaker tip at the center underside of the bar imposed additional constraints on the bar that would not be present in actual musical performance. Also the fluctuating magnetic field of the operating 94

electrodynamic shaker was received by the velocity pickup.

These effects may have caused some of the non-sinusoidal

responses noted on the data sheets (Appendix A).

Lissajous figures were produced on the oscillo­

scope screen when one of the voltages was derived from a

standard frequency generator and the other from another

audio frequency, in this case the bar in driven sinusoidal

vibration. This offers a precise method for identifying

the phase, frequency, and amplitude of two frequencies

(Josephs, 1967, pp. 14, 63). The standard frequency was

varied until an appropriate figure was formed, and in that

way the exact frequency of the bar sinusoidally driven was

obtained.

Transient Testing

Rather small changes in the striking location on a

percussion instrument bar will produce important differ­

ences in tone quality. If the point of contact between the mallet and the vibrator is at the anti-nodal point of the

fundamental, the tone produced will emphasize this compon­ ent and the partial tones will be less prominent. By moving the point of contact away from this anti-node point of the fundamental the higher partials will become increasingly prominent.

The effect of different strikers on the marimba and xylophone bar tone quality had been previously investigated 95

by Stoutmeyer (1968). A study of the effects of different

forces of strokes would require the efforts of physiologi­

cally trained personnel that would be beyond the scope and

intent of this investigation. For these reasons it was

decided that the variable most closely investigated in the

tests would be that of the location of the striker along

the surface of the percussion bar.

The variables inherent in a manually produced stroke

were so numerous that it was felt that some mechanical means of striking the bars was advisable. The possibility

exists that this means of tone production is not exactly

like a manually produced stroke. However, it was felt

that uniformity of stroke and precise placement could best be obtained with a mechanical striker.

In testing for this struck or transient response of the bars a storage screen oscilloscope was set for a single sweep and a laser beam trigger was used. A mechan­ ical striker was built to provide a uniform stroke. The mallet mounted in the striker was pulled up to a stop and released. The falling mallet head broke the ray of light from the laser and provide a trigger for the observation of starting transient response. The downward motion of the mallet head from a fixed pivot was facilitated by both gravity and spring action. The elasticity of the mallet handle and an angle stop snapped the mallet head back from the bar after initial contact to prevent the 96 mallet head from damping out bar responses. The striker was built so that the bar could be struck at many different

locations along Its length. Photographs of the waveforms generated by the strokes were obtained by a polarold camera attached to the storage screen oscilloscope.

Summary

A testing apparatus was devised to drive percussion

Instrument bars sinusoidally and determine their modes of vibration. A mechanical striker was constructed to Imple­ ment testing of the transient responses caused by percus­ sive excitation. The purpose of this work was to carry out testing that would support and augment the empirical Infor­ mation on tuning of percussion Instruments bars. Test bars were chosen which were considered to be of high quality by present bar percussion Instrument Industry standards. The results of the testing are presented In the following chapter. CHAPTER VI

RESULTS OF EXPERIMENTAL WORK

Steady State Measurements

Excitation of a bar by a means other than striking,

such as steady state excitation, is of value in that it of­

fers a stable means of identifying the modes of vibration

of a percussion instrument bar. However, this is not the

sound of the instrument when played in the normal fashion.

The tone produced in performance is a struck tone and, for many of the instruments, a resonator is present under the bar (supra. Fig. 1, p. 8). Conclusions drawn from steady

state experiments must be carefully evaluated in light of this divergence from actual percussive excitation.

However, steady state excitation can provide an accurate means of studying the relationship of the frequencies of the modes of vibration or partial tones of the bar.

Justification for this type of measurement is found in related areas of research on musical instrument tone qual­ ity such as that done on violin plates (Hutchins, supra, pp. 61-62) in which desirable steady state characteristics were directly related to desirable tone quality and response of a completed violin. In a like manner a

97 98

percussion Instrument bar whose modes of vibration are

tuned so as to produce desired frequencies in steady state

measurement, will likewise produce a desirable sound when

struck by mallets in the completed bar percussion instru­

ment .

Basically, the tested bars produced the modes of vibration expected of their group type. The testing pro­ vided verification of the stated acoustical differences between marimba, xylophone, vibe and orchestra bell bars.

The differing non-uniform cross section characteristics of the four bar types accounted for the differing modes of vibration which form the partial tone series of each bar.

The mathematics involved in an analytical solution to define the optimum shapes of these non-uniform bars would be complex. The complexity arises from the on- uniform cross section formed in tuning the bar. The experimental work reported does provide a summary of some of the basic responses from which analytical study might at some later time proceed.

Figures 18-29 give the modes of vibration for each percussion instrument bar tested (1) in vibrational fre­ quencies, and (2) in musical notation to the nearest semitone. The nominal fundamental frequency for each bar is given in the title of the figure, while the measured frequencies are given within each figure. The number of modes of vibration obtained for the bars varied from three 99

to five, and these are Indicated in the upper left column

of each figure. Center columns contain the frequency of

each mode of vibration with fundamentals given to the

nearest .0 Hz and other partials to the nearest Hz. The

corresponding musical note letter name and octave designa­

tion follows each vibrational frequency, and the number of

cents above or below the exact frequency of the nett in iX equally tempered scale based on = 440 Hz (A .S.A.T.,

i960. Table 13.2) is given. Relative intensity,as indi­

cated for each mode of vibration in the right hand column, refers to the response to the amplitude of the driving signal. A response obtained at a low amplitude driving signal was termed "very strong" and a response requiring a high amplitude driving signal "weak."

The lower portion of each figure contains musical notation to the nearest semitone for the first three modes of vibration with plus or minus number of cents indicated above and below the frequencies of the equal tempered scale. Accompanying square headed notation repre­ sents the frequencies of the ideal partials for each bar type so that these may be compared to the musical notation for the actual frequencies. The translation of frequencies into musical notation is intended to clarify this material for readers who would have difficulty in converting fre­ quencies into musical notation. Those familiar with the harmonic series (see Chapter II, p. 10) can in this manner 100

relate the modes of vibration of the bars (partial tones) to certain harmonics of a series if desired.

In an effort to keep the musical notation on the great staff as much as possible all first modes of vibra­ tion (fundamentals— the actual letter name and octave of the bars) have been notated on the A space in the bass clef with the appropriate indication given as to the sounding range of the tones. It should also be noted that even though frequencies above 4l86 Hz (Cg) are above the range of all standard musical instruments including the piano keyboard, these frequencies have been translated into a representative musical notation. For convenience in making direct comparisons of vibrational frequencies.

Figure 30 gives a summary of the frequencies of the modes of vibration of all bars tested.

Figure 31 gives the frequencies of the modes of vibration of all four bar types, marimba, xylophone, vibe, and orchestra bells for the nominal 880 Hz fundamental.

This is the only nominal fundamental frequency level at which a l l four bar types may be directly compared.

Data work sheets, found in Appendix A, contain all sinusoidal responses obtained for each of the twelve bars tested. In addition, non-sinusoidal responses obtained are given for the 110 Hz and 220 Hz Rosewood Marimba Bars, the 220 Hz Aluminum Vibe Bar, and the 880 Hz Steel

Orchestra Bell Bar, On these sheets are given the 101

frequencies of the responses together with sketches of the

nodal patterns. The bottom portion and the right hand

column of the data sheets contain additional notes, coded

comments and information on the availability of polaroid

photos. Information contained on these data sheets is of

possible value especially for a technically oriented

thesis in engineering mechanics or a related field. The

steady state or driven responses were obtained for each bar

using the apparatus and procedure described in Chapter V.

Marimba Bars

The 110 Hz Rosewood Marimba Bar (Fig. l8) produced

the ideal tuning relationships. The actual frequency of the fundamental was 110.1 Hz only +1 cent above the nominal fundamental. The actual frequency of the second partial was 444 Hz, +15 cents high, to a 4:1 ratio to the nominal fundamental. This relationship produced the second par­ tial two octaves above the fundamental slightly sharp which is desirable and in keeping with the practice of octave stretching.

The third mode of vibration produced the musical note C#g three octaves and a major third above the funda­ mental being the desired 10:1 ratio of the third partial to the fundamental. The relative intensity of the second and third modes was "very strong," while the first mode was

"strong." It was characteristic of low frequency bars to 102

have more strength in the second partial than in the

fundamental further indicating the importance of accurate

tuning of this partial.

The 220 Hz (A3) Rosewood Marimba Bar (Fig. 19) pro­

duced the ideal tuning relationships. The actual frequency

of the fundamental was only +3 cents high to the nominal

fundamental and the second partial +13 high to the equally

tempered double octave frequency. This relationship pro­

duced the slightly sharp double octave between the funda­

mental and second partial which is desirable. The third

partial was three octaves and a major third above the

fundamental, but -5 cents too low to produce the exact

frequency of C#y at a 10:1 ratio with the fundamental. The

relative intensity of the second partial was "very strong"

while the fundamental and third partial were "strong."

The 440 Hz ( A ^ ) Rosewood Marimba Bar (Fig. 20) pro­

duced the ideal tuning relationship for the second partial,

but not for the third partial. An ideally tuned third

partial would be a partial at a 10:1 ratio to the funda­

mental or 4400 Hz (C#g). The third partial produced by

this bar was 4026 Hz + 32 cents above By. Only three modes

of vibration were obtained for this bar compared with

four or five modes of vibration for the lower register marimba bars. As the cross section of the rosewood bars increased it became difficult to obtain driven responses 103

and thus only three modes were measureable for some high

register bars.

The 880 Hz (A^) Rosewood Marimba Bar (P:g: 21) did

not produce the ideal tuning relationships. The actual

fundamental of 883.1 Hz was +6 cents high to the nominal

880 Hz fundamental, indicating the presence of octave

stretching. A second partial at a ratio of 4:1 to the

fundamental would be 3520 Hz (Ay). The second partial pro­ duced by this bar was 2928 Hz -19 cents below P#y. A third partial at a 10:1 ratio would be 8800 Hz, the third partial produced by ^his bar was 5675 Hz +23 cents above

Fg. The thicker cross section of this bar caused the second and third modes of vibration to occur at lower frequencies. The characteristic "marimba" bar tuning changed with the 880 Hz marimba bar. The second mode of vibration was much too low for the 4:1 ratio that was desirable in the lower registers of the marimba. The third mode of vibration dropped to nearly a 6:1 ratio or, as will be seen upon examination of the xylophone bars, the same third mode as found in the xylophone bar with an 880 Hz fundamental. The upper register marimba bars were no longer "marimba" tuned in the ideal sense but started to have second and third modes of vibration characteristic of xylophone bars. Their thicker cross sections caused the upper modes of vibration to occur at lower frequencies than for bars of thinner cross section (supra, pp. 81-83). 104

The relative intensity of the second partial of the

880 Hz marimba bar was "strong to weak" rather than

"strong" or "very strong" as found in the lower register bars. Upper partials of the high register marimba bars that depart considerably from the ideal relationships to the fundamental are not perceptually obvious in the struck tone of the bar, for they c o n t a i n relatively little energy and die away quickly, leaving only the sound of a strong fundamental clearly heard.

In summary, low register marimba bars (A2 and A3) produced second and third partials at the ideal frequency ratios. The middle register marimba bar (A^) produced a second partial at the desired frequency ratio, but a third partial lower than the Ideal frequency ratio. The high register marimba bar (A^) produced both second and third partials lower than the ideal frequency ratios. 105

Frequencies of Relative Mode Modes of Vibration Intensity

1st 110,1 ( A n + 1 cent) Strong

2nd 444 i A n + 15 cents) Ver” Strong

3rd 1109 ° cent) Very Strong

4th 1971 (Bg - 4 cents) Strong

Musical Notation

3rd Mode ■ +0 cent

2nd Mode ii — +15 cents

1st Mode I + 1 cent A2 (110 Hz)

sounding as written

Fig. 18.— Modes of Vibration and Musical Note Representations of Partial Tone Structure of a Rosewood Marimba Bar 110 Hz. 106

Frequencies of Relative Mode Modes of Vibration Intensity

1st 221 (A3 + 3 cents) Strong

2nd 887 (A, + 13 cents) Very Stronp

3rd 2211 - 5 cents) Strong

4th 3725 - 2 cents) Strong-Weak

cents) 5th 5558 (^8 — 9 Weak

Musical Notation

3rd Mode cents

2nd Mode +lj cents

1st Mode ■*■3 cents

A3 - 220 Hz Sound one octave higher

Fir. 1 9 .— Modes of Vibration and Musical Note Representations of Partial Tone Structure of a Rosewood Marimba Bar 220 Hz. 107

Frequencies of Relative Mode Modes of Vibration Intensity

1st 440.7 (Ai, + 3 cents) Strong 2nd 1780 Very Strong (^6 + 19 cents) 3rd 4026 (By + 32 cents) Very Strong

Musical Notation

S l 3rd Mode +32 cents

2nd Mode +19 cents

1st Mode i + 3 cents

Ai, 140 Hz

soundinp two octaves higher

Fip:. 20.--Modes of Vibration and Musical Note Representations of Partial Tone Structure of Rosewood Marimba Bar 4^4 0 Hz. 108

Frequencies of Relative Moàe Modes of Vibration Intensity

1 rît 883.1(A,^ + € cents) Stronp

?nci 2928 (F#y -19 cents) Stronp to weak

3rd 5675 (Fg +23 cents) Stronp

Musical Notation

3rd Mode +23 cents

2nd Mode -19 cents

1st Mode cents

BBO Hz A5 soundlnp three octaves up

Plp. 21 .— Modes of Vibration and Musical Note Representations of Partial Tone Structure of a Rosewood Marimba Par B80 Hz. 109

Xylophone Pars

The 4^0 Hz (A^) Rosewood Xylophone Bar (Fig. 22) produced the ideal tuning relationship of an octave and a perfect fifth musical Interval between the fundamental and the second partial. The actual fundamental of 444.5 Hz was +l8 cents above the nominal fundamental, and the actual second partial was +25 cents above a 3:1 ratio with the nominal fundamental. This apparent considerable sharping condition is accounted for by the stated practice of tuning xylophone bars to an - 442 Hz standard (supra, pp. 69-

70) rather than A ^ = 440 Hz. The third partial was +3 cents high to the musical note Py, higher than the desired 6:1 ratio for this partial. With consideration of the

A^i = 442 Hz tuning standard and the practice of octave stretching this sharpness of the third partial is less extreme.

The 880 Hz (A^) Rosewood Xylophone Bar (Fig. 23) produced an actual fundamental of 888.0 Hz, + 15 cents above the nominal fundamental. This apparent considerable sharpness of the fundamental is again accounted for by the stated practice of tuning xylophone bars to an A% = 442 Hz standard rather than A ^ = 440 Hz. The second partial was decidedly low, -32 cents below an equal tempered Ey. The third partial was much too low, being +24 cents above Dg.

This is nearly a whole tone too low, for the nominal pitch of this partial is Eg. The thicker cross section of this 110 bar causes the lower frequencies of the second and third partials. The second partial was Judged to be strong to weak in response. As with higher register marimba bars, the upper partials contain relatively little energy and when struck die away to inaudibility quickly, leaving only the sound of the strong fundamental.

In summary, the low register (Ay) xylophone bar pro­ duced second and third partial tones at the ideal frequency ratios. The middle register xylophone bar (A^) produced second and third partial tones lower than the ideal frequency ratios. High register xylophone bars (Ag, Ay) were not tested. Ill

Frequencies of Relative Mode Modes of Vibration Intensity

1st 444.5 (A|^ +18 cents) Stronp:

2nd 1338 (Eg +25 cents) Stronr to weak

3rd 2798 (Fy + 3 cents) Strong

Musical Notation

3rd Mode +3 cents

2nd Mode +25 cents

1st Mode I +l8 cents 440 Hz

sounding two octaves higher

Fi%. 22.— Modes of Vibration and Musical Note Representations of Partial Tone Structure of a Rosewood Xylophone Bar 440 Hz. 112

Frequencies of Relative Mode Modes of Vibration Intensity

1st 880.0 (A^ + 15 cents) Stronp:

2nd 2590 (E? -32 cents) Stronp: to weak

3rd 4765 (Dg +24 cents) Strong

Musical Notation

3rd Mode — +24 cents 2nd Mode I ~ -32 cents

1st Mode i +15 cents

880 Hz

sounding three octaves higher

Fig. 2 3 •— Modes of Vibration and Musical Note Representations of Partial Tone Structure of a Rosewood Xylophone Bar 88O Hz. 113

Vibe Bars

The 220 Hz (Ag) Aluminum Vibe Bar (Fig. 24) pro­

duced the ideal tuning relationship between the fundamental

and the second partial. The actual fundamental was only

+2 cents above the nominal fundamental, and the second

partial was +6 cents above an equal tempered double octave

Ag partial indicating octave stretching. The third partial was -19 cents below the musical note Dy. This is too high for the ideal 10:1 ratio of the third partial to the

fundamental which would be The second partial was judged to have very strong relative intensity. Performers have noted that when a vibe bar in the low register of the instrument is struck hard the second partial sounds out stronger than the fundamental. This prominence of the second partial in both steady state and struck conditions indicates the need for accurate tuning of this partial.

Five modes of vibration were produced by the 220 Hz Vibe

Bar. The aluminum bars were much more responsive to the driven force than the wood bars. The natural modes of vibration were more easily located on the metal bars and were obtainable usually at a lower amplitude of the driving frequency. Many other intermediate weak responses even occurred because of the greater responsiveness of the homogeneous light metal material of the bars.

The 440 Hz (A^) Aluminum Vibe Bar (Fig. 25) pro­ duced the desired double octave relationship between the 114

fundamental and the second partial. The actual fundamental

was only +1 cent above the nominal frequency, and the second

partial was +8 cents above an exact 4:1 freq' ^ncy ratio with

the nominal fundamental. This indicated tliat octave

stretching had been done. The relative intensity of the

second partiel was very strong. An ideal third partial at

a 10:1 ratio with the fundamental for the 440 Hz Vibe Bar would be the musical note C#g. The actual third partial produced by this bar was +25 cents above By, or nearly a whole tone too low.

The 880 Hz (A^) Aluminum Vibe Bar (Fig. 26) did not produce the ideal relationship between the fundamental and the second partial. The second partial produced a note +9 cents above G#y or nearly a semitone too low for the ideal double octave relationship. The third partial was -32 cents belovv or a musical interval of a fourth lower than the ideal C#g.

In summary, the low register vibe bar (A^) produced a second partial at the ideal frequency ratio to the funda­ mental and a third partial higher than the ideal frequency ratio. The middle register vibe bar (A%) produced a second partial at the ideal frequency ratio to the fundamental and a third partial lower than the ideal frequency ratio. The high register vibe bar (A^) produced second and third partials at frequencies lower than the ideal ratios. 115

Frequencies of Relative Mode Modes of Vibration

1st 220 .2 (A3 + 2 cents) Strone

2nd 883 (A5 + 6 cents) Very strong 3rd 2324 (Dy -19 cents) Strong

4 th 3815 ( + 39 cents ) Strong to weak

5th 5045 (D#g +26 cents) Strong

Musical Notation

3rd Mode -19 cents

2nd Mode +6 cents

1st Mode g +2 cents

220 Hz

sounding one octave higher

Fie. 24 .— Modes of Vibration and Musical Note Representations of Partial Tone Structure of an Aluminum Vibe Bar 220 Hz. 116

Frequencies of Relative Mode Modes of Vibration Intensity

1st 440.2 ( A^j +1 cents) Strong

2 n d 1768 ( f\f. +8 cents) Very strong

3rd 4010 ( i-iy +25 cents) Strong

iith 6109 ( -46 cents) Strong to weak

5th 8840 ( C ^ g -6 cents) Very strong

Musical Notation

3rd Mode +25 cents

2nd Mode +8 cents

1st Mode I + 1 cent

440 Hz

sounding two octaves higher

Fig. 25 «— Modes of Vibration and Musical Note Representations of Partial Tone Structure of an Aluminum Vibe Bar 440 Hz. 117

Frequencies of Relative Mode Modes of Vibration Intensity

1st 881.9 +4 cents) Strong

2nd 3340 +9 cents) Strong

3rd 6527 (G^g -32cents) Strong

4th 10,193 (D#g +40cents) Strong

Musical Notation

-Ul o - 3rd Mode -32 cents 2nd Mode ijlo +9 cents

1st Mode I +4 cents

A5 680 Hz

Sounding three octaves higher

Fig. 26 .— Modes of Vibration and Musical Note Representations of Partial Tone Structure of an Aluminum Vibe Par 88O Hz. 118

Orchestra Bell Bars

The 880 Hz (A^) Steel Orchestra Bell Bar (Fig. 27) produced an actual fundamental +7 cents above the frequency of an equally tempered A5. The second partial was at a frequency of 2^10 Hz, or +44 cents above Dy. The ideal

2 .75:1 ratio for this partial of a bar of uniform cross section would be 2435 Hz. The third partial was at a frequency of 4679 Hz or, -7 cents below Dg. The ideal

5.4:1 ratio for this partial of a bar of uniform cross section would be 4781 Hz. Five modes of vibration were obtained with the fourth and fifth modes showing very strong relative intensity.

The 1760 Hz (Ag) Steel Orchestra Bell Bar (Fig. 28) produced an actual fundamental +I6 cents above an equally tempered Ag indicating octave stretching tuning in the high register. Frequencies of the second and third par­ tiels were 4782 Hz and 9072 Hz, compared to the nominal frequencies of the second and third partials of a uniform bar of 4840 Hz and 9504 Hz. For this bar the third partial was 232 Hz lower than the nominal frequency. Four modes of vibration were obtained with the fourth mode showing very strong relative intensity.

The 3520 Hz (Ay)Steel Orchestra Bell Bar (Fig. 29) produced cin actual frequency +15 cents above the frequency of an equally tempered Ay. Frequencies of the second and third partials were 9299 Hz and 17,438 Hz, compared to the 119

nominal frequencies of 9680 Hz and 19,008 Hz. Only three

modes of vibration were obtained for this, the highest

frequency and smallest sized, percussion Instrument bar.

In summary, all orchestra bell bars tested (A5, A5,

and Ay) produced second and third partials at frequencies

approximating the Ideal frequencies for bars of uniform

cross section. The highest register bars showed a tendency

for the second and third partial to be slightly lower than

Ideal for a bar of uniform cross section.

A comparison of the frequencies of the modes of

vibration of all four bar types— marimba, xylophone, vibe

and orchestra bells— with the same fundamental or first

mode of vibration was possible at the nominal 88O Hz fre­ quency (Pig. 31). The actual fundamentals ranged from

881.9 to 888.0 Hz: vlbe-881.9 Hz, marlmba-883.1 Hz,

orchestra bell-885.3 Hz, and xylophone -888.0 Hz. The higher actual frequencies of the fundamentals of the orchestra bell and xylophone bars are accounted for by the practice of tuning these Instruments to an A^ = 442 Hz reference standard (supra, pp. 69-70).

A comparison of the frequencies of the second par­ tiale of the four bar types shows the influence of the bar shapes on this mode of vibration. The vibe and marimba bars being of thinner cross section produced second partials of higher frequencies (3340 Hz and 2928 Hz) than the xylophone bar of thicker cross section (2590 Hz) and 120

Frequencies of Relative Mode Modes of Vibration Intensity

1st 885.3 (A. +7 cents) Strong ‘J 2nd 2410 + 44 cents) Strong to weak ("T Strong 3rd 4679 (^8 -7 cents)

4th 7651 (A'g + 43 cents) Very strong

5th 11,224 ( ^ + 7 cents ) Very strong

Musical Notation

3rd Mode -7 cents

2nd Mode " M r + 44 cents

1st Mode Ë + 7 cents

A5 880 Hz

Sounding three octaves higher

Pig. 2 7 .— Modes of Vibration and Musical Note Representations of Partial Tone Structure of a Steel Orchestra Bell Bar 880 Hz. 121

Frequencies of Relative Mode Modes of Vibration Intensity + lC 1st 1777.1 (^6 cents) Strong

2nd H 7Q 2 (D7 +30 cents) Stronp,

3rd 9072 +38 cents Strong

'Ith 14,661 -31 cents) Very stronp;

Musical Notation

3rd Mode +38 cents 2nd Mode +30 cents

1st Mode I ~ +1( cents

1760 U z

founding four Octaves hirher

FiK. 28 .— Modes of Vibration and Musical Note Representations of Partial Tone Structure of a Steel Orchestra Bell Bar 1760 Hz. 122

Frequencies of Relative Mode Modes of Vibration Intensity

1st 3552.3 (A^ +15 cents) Strong

2nd 9299 (D,^ -19 cents) Stronp:

3rd 17,438 (C^io -30 cents) Very stronp:

Musical Notation

3rd Mode -30 cents -19 2nd Mode cents

1st Mode i +15 cents

A j 3520 Hz

Soundinp five Octaves hirrher

Pip:. 29.— Modes of Vibration and Musical Note Representations of Partial Tone Structure of a Steel Orchestra Bell Bar 3520 Hz. ROSKV/OOD ROSBV.’OOD ALUMIiJUM STEEL MARIMBA BARS XYLOPHONE BARS VIBE BARS ORCHESTRA BELL BARS Frequencies of Frequencies of Frequencies of Frequencies of Fundamental Modes of Vibration Modes of Vibration Modes of Vibration Modes of Vibration

110 Hz Ap 110.1 444/1109/ 1971

220 Hz Ap 221.0 887/2211/ 220.2 883/2324 3725/5558 3815/5C45

440 Hz A/4 440.7 1780/4026 444.5 1336/2798 440.2 1768/4010/ 6109/8840

880 Hz A- 883.1 2928/5675 888.0 2590/4765 881.9 3340/6527/ 585.3 2410/4679 10,193 7651/11,224

1760 Hz A; 1777.1 4782/9072 14,661

3520 Hz A 3552.3 9299/17,438 7

Fig. 30.— Summary of Freauencies of Modes of Vibration of Marimba, Xylophone, Vibe and Orchestra Bell Bars.

ru U) Rosewood Rosewood Aluminum Steel Marimba Xylophone Vibe Orchestra Bell Bar Bar Bar Bar

1st Mode 383.1 888.0 881.9 885.3 of Vibration 2nd Mode of 292s 2590 3340 2410 Vibration

3rd Mode of 5675 4565 6527 4679 Vibration 4th Mode of Vibration 10,193 7651 5th Mode of - -—— 11,224 Vibration

Fig. 31.--Comparison of the Frequencies of the Modes of Vibration of Marimba, Xylophone, Vibe and Orchestra Bell Bars Tuned to Nominal 880 Hz (A^).

fU 125

the orchestra bells bar of uniform cross section (2410 Hz).

A still greater divergence between the highest and lowest

third partials are found between these partials of the vibe

bar (6527 Hz) and xylophone bar (4765 Hz).

Rosewood bars at the 88O Hz frequency did not produce

modes of vibration above the third mode, while the aluminum

vibe bar produced four modes of vibration and the steel

orchestra bell bar five modes of vibration.

Transient Measurements

The transient responses produced by the percussion

Instrument bars were displayed on a storage screen oscill­

oscope and photographs of various waveforms were obtained.

The bars were excited by a mechanical striker equipped with mallets of the type used by players of bar percussion

Instruments. The apparatus and procedure used were des­ cribed in Chapter V. Figures 32-41 show oscilloscope traces of the transients produced by 220 Hz Marimba and

Vibe bars struck at various positions with a soft mallet

(Musser M-8, yellow yarn covered).

Comprehensive testing of the struck transient re­ sponses was not carried out for all bars used In the steady state tests. In a comparison of a 220 Hz Rosewood

Marimba Bar and a 220 Hz Aluminum Vibe Bar the variables of (1) position of stroke on bar surface, and (2) material of mallet head were tested. 126

Fig. 32.— Oscilloscope Trace of Fig. 33.— Oscilloscope Trace Waveform Produced by 220 Hz of Waveform Produced by (A3 ) Rosewood Marimba Bar 220 Hz (A3 ) Aluminum Vibe Struck at Center with Soft Bar Struck at Center with Mallet. Soft Mallet.

* . ... , — . . • f ■ t . A . \ , * V : ^^./ y % ; ^

/

Fig. 3^.— Oscilloscope Trace Fig. 35.— Oscilloscope Trace of Waveform Produced by of Waveform Produced by 220 Hz (A3) Rosewood Marimba 220 Hz (A3) Aluminum Vibe Bar Struck 1/2" from Center Bar Struck 1/2" from with Soft Mallet. Center with Soft Mallet. 127

Fig. 36.— Oscilloscope Trace Fig. 37.— Oscilloscope Trace of Waveform Produced by of Waveform Produced by 220 Hz (A3) Rosewood 220 Hz (A3 ) Aluminum Vibe Marimba Bar Struck 1" from Bar Struck 1" from Center Center with Soft Mallet. with Soft Mallet.

Fig. 38. — Oscilloscope Trace Fig. 39.— Oscilloscope Trace of Waveform Produced by of Waveform Produced by 220 Hz (Ag) Rosewood 220 Hz (A3 ) Aluminum Vibe Marimba Bar Struck 2" from Bar Struck 2" from Center Center with Soft Mallet. with Soft Mallet. 128

Fig. 40.— Oscilloscope Trace Fig. 41.— Oscilloscope Trace of Waveform Produced by of Waveform Produced by 220 Hz (A3) Rosewood 220 Hz (A3) Aluminum Vibe Marimba Bar Struck at Node Bar Struck at Node of of Fundamental (0.224 from Fundamental (0.224 from end end of Bar) with Soft of bar) with Soft Mallet. Mallet. , 129

The uniformity of the mechanical striker was first

validated Several photographs showing the initial re­

sponse of the same striking location were almost indistin­ guishable. The effects of striking location on the initial bar response was then tested. In general for all bars there was a predominance in the appearance of the funda­ mental (first mode of vibration) and the second partial

(second mode of vibration) in the waveforms. Marimba and vibe bars have a second partial at a ratio of 4 :1 to the fundamental. Therefore, the resultant waveform had four peaks to every repeating segment of the fundamental. The respective amplitude proportions of each were dependent upon the striking location. Generally the waveform appear­ ing was that of the fundamental modulated by the second partial. In all cases there were frequency components higher than the second partial. These were of much lower amplitude and damped out rather quickly. The second par­ tial decayed relatively quickly in the rosewood marimba bars and lasted for a relatively longer time in the aluminum vibe bars. The point of striking that produced the strongest response of the fundamental was the anti- nodal point at the center of the bar, midway between the two nodal points as shown in Figure 42. 130 /

Fig. 42.— Location of Striking Point Producing Strongest Response of Fundamental of Percussion Instru­ ment Bar.

Transient response is Influenced greatly by the

position of the striker on the bar's surface. Moving half

an Inch from the center on a fourteen inch bar showed

significant difference. Striking the bar at its center produced an Initial response of a strong fundamental and extremely complex high frequency components. One-half inch

from the center on the fourteen inch bar, in addition to the fundamental, a very strong second partial occurred.

Higher frequency components were of greater amplitude, and the total response had more Intensity. Response intensity was greatest, as well as high frequency response, midway between the supports and the center.

Moving the striking point further toward the supports, caused the fundamental response to be less apparent, the second partial relatively large in amplitude, and the other higher frequency components less apparent. At the supports, where the nodes of the fundamental are located, a strike caused an almost pure response of the second partial. Moving out from the supports toward the end, the 131

above effects reversed themselves until, at the end, the

response was almost identical to that of the strike

between the center and the supports, as described above.

In comparisons of the wave forms produced by hard

and soft mallet heads, the relations between the funda­ mental and second partial were the same. The differences

came with the higher frequency elements. The harder mal­

let displayed many quickly decaying, high frequency ele­ ments of a very complex nature and high amplitude.

It was noted from the photographs that it often appeared as if the amplitude increased slightly in the first few vibrations after the stroke. This effect may have been due to the supporting rope and its elasticity immediately after the strike. However, particularly with the marimba bar, higher frequency elements often became more pronounced after the first few vibrations as well.

This effect was mainly noted when the bar was struck at or near the nylon cord supports where the nodes of the funda­ mental are located.

Resume of Steady State and Transient Results

The results of the steady state measurements of the modes of vibration of the bars indicated that :

1) The ideal relationship between the fundamental and the second partial was achieved in the tuning of the bars in the low and middle registers of the instruments. 132

2) The Ideal relationship between the fundamental

and the second partial was not maintained for bars in the

upper registers of the instruments, this was caused by the

thickening cross section of the bars necessary to produce

the high frequency fundamentals.

3) The ideal relationship between the fundamental

and the third partial (third mode of vibration) did not

appear consistently in the tuning of the bars. The bars

tested were of regular production quality and were bars not

subjected to this additional exacting step of tuning

(supra, pp. 79- 80).

4) Modes of vibration higher than the third partial, where identified, also showed no consistent relationship with the fundamental.

5) Aluminum and steel bars as contrasted with rose­ wood bars produced more and stronger upper partial tones.

6) Bars of thin cross section, and consequently low register fundamentals, produced more upper partial tones than bars of thicker cross section.

7) The tuning of the fundamentals and the second partials showed octave stretching.

8) Bars of non-uniform cross section made thin by selective removal of material produced harmonic partials.

Bars of thicker cross section and less severe non-unifor­ mity of arch produced inharmonic partials. Bars of uni­ form cross section produced inharmonic partials whose 133

frequency ratios very closely approximated those of a

uniform theoretical bar.

9) Bars of thin non-uniform cross section produced

second partials of very strong relative intensity. Bars of

thicker cross section produced second partials of lesser

relative intensity.

10) Xylophone and orchestra bell bars produced

higher actual fundamental frequencies than marimba and vibe bars of the same nominal fundamental frequency.

The testing of the transient responses of the per­

cussion instrument bars supported empirical findings and previous investigation in that:

1) The relative amplitude of the fundamental is strongest when the bar is struck at the center or anti-node.

2) The second partial becomes more prominent as the striking point approaches the node of the fundamental, reaching an almost pure response of the second partial directly over the node of the fundamental.

3) The effect is reversed as the striking point approaches the ends of the bar, producing nearly the same relative amplitude of partials as at an equivalent point between the center and node of the fundamental.

4) Harder mallets produce a tone characterized by the presence of many quickly decaying high frequency par­ tials. Softer mallets produce a tone characterized by the presence of the fundamental and the second partial. 134

The frequencies of the modes of vibration of percus­ sion instrument bars can be precisely identified as demonstrated by the steady state testing. This furnished an exact means of analyzing the partial tone relationships of the bc's. However, the tone quality produced by percus­ sion excitation of these bars can undergo considerable variation through the place of excitation, the manner of excitation and the hardness of the striker. The percussive excitation experiments indicated that as little as a half­ inch deviation in striking location on the bar's surface produced a considerable difference in the waveform and a marked difference in the quality of the sound.

Control of tone quality by varying the place of excitation, and the striking object should be well under­ stood by performers and teachers of bar percussion instruments. CHAPTER VII

SUMMARY AND RECOMMENDATIONS

Summary of the Investigation

Restatement of the Problem

In the twentieth century percussion instruments have

been used to a greater extent in the music of the Western world than in any previous era. Many thoughts and views on

the acoustics of percussion instruments have been voiced

and written without an adequate understanding of the

acoustical principles and constructional problems of these

instruments and without any serious attempt to measure and evaluate the actual audible phenomena.

Musical acoustics texts and reference sources do not contain adequate or even accurate information on percussion instrument acoustics. These sources: (1) state general idealized uniform or theoretical conditions which, however, are not present in percussion instruments, (2) present

Incomplete or inaccurate descriptions of percussion instru­ ments in use, or (3) dismiss the problem of percussion instrument acoustics on the grounds that sufficient musicality is Judged to be lacking in these sound sources.

Present day pedagogy in the field of percussion in­ strument performance stresses the musical development of

135 136

the "total percussionist" at all levels from grade school

through the college-conservatory and into the professional

field. As a result, the bar percussion instruments— marimba, xylophone, vibe, and orchestra bells are being purchased and used in greater numbers than in the past.

Firms manufacturing these instruments are striving to find ways to improve their production methods and produce a more uniform, acceptably musical product.

The specific purposes of this investigation, stated in Chapter I, were to; (1) present a nomenclature for the bar percussion instruments that will clarify the termin­ ology and characteristics for these instruments, (2) review

(a) musical acoustics reference literature concerning per­ cussion instruments, especially bar percussion instruments, and (b) literature containing material on tuning and experimental work of relevance to bar percussion instru­ ments, (3) describe the manufacturing and tuning processes of percussion instrument bars, pointing out in particular the influence of bar shape on the modes of vibration of the bars, (4) report the results of experimental work that measured the steady state and transient vibrational characteristics of percussion instrument bars, and (5) pre­ sent suggestions for improving the manufacturing processes of bar percussion instruments. 137

Nomenclature of the Bar Percussion Instruments

The four bar percussion instruments— marimba, xylo­

phone, vibe, and orchestra bells possess a chromatic

arrangement of tuned bars of wood or metal which are

played manually by a percussionist striking these bars

with various kinds of mallets. The factors that distin­ guish the bar percussion instruments one from another are:

(1) modes of vibration of the bars, (2) cross section of the bars, (3) material of the bars, (4) characteristics of resonators (when employed), (5) types of mallets used to strike the bars, and (6) ranges of the instruments.

The Marimba produces second and third modes of vibration at ratios of 4:1 and 10:1 to the fundamental.

A deep arch is cut in the underside of the bars. The bars are of Honduras rosewood Ideally formed from the less hard grades of this wood. Tubular aluminum resonators are essential for producing the desired tone of the instrument.

Soft rubber or yarn covered rubber core mallets are used to play the marimba. The full size instrument possesses a range of four and one-third octaves— Aj to Cy (some models only Cg to Cy). Notation is at sounding pitch with both the treble and bass clefs used.

The Xylophone produces second and third modes of vibration at ratios of 3:1 and 6:1 to the fundamental. A shallow arch is cut in the underside of the bars. The bars are of Honduras rosewood of the hardest grades. 138

Tubular resonators are used on the high quality instruments

and not used on less expensive models. Hard rubber,

plastic or wood mallets are used to produce the desired

sound of the instrument. The full size instrument possesses

a range of three and one-half octaves— P4 to Cg (smaller

models C5 to Cg). Notation is one octave below sounding

pitch in the treble clef.

The Vibe, also known as "vibraphone" or "vibraharp,"

produces second and third modes of vibration at ratios of

4:1 and 10:1 to the fundamental. A deep arch is cut in

the underside of the bars. The bars are of high grade

commercial aluminum. Tubular aluminum resonators contain­

ing motor driven pulsating disks are essential for produc­

ing the desired tone of the instrument. Mallets with

yarn or cord covering over rubber cores are used on the

instrument. The range of the vibe is standardized at three

octaves— Pg to Pg. Notation is at sounding pitch in the

treble clef.

The Orchestra Bells, also known as Glockenspiel

(Ger.) produce second and third modes of vibration at

ratios of 2.75:1 and 5.4:1 to the fundamental. The bars

are of uniform cross section. Bar material is high carbon

content commercial steel. Resonators are not used. Hard rubber, plastic or brass mallets are used to play the orchestra bells. The range of the orchestra bells is 139

standardized at to Cg. Notation is properly two octaves below sounding pitch in the treble clef.

Literature

Percussive vibrators such as percussion instrument bars do not produce the same series of partials as the idealized string. Investigators in the latter part of the eighteenth century undertook research on vibrators that departed greatly from the idealized conditions of a thin narrow string. Writers in the nineteenth century continued to describe the Inharomonicity of partials produced by uniform three dimensional vibrators.

Twentieth century musical acoustics texts'do not accurately describe the modem bar percussion instruments, but rather continue to use as a basis for description, the condition of inharmonic partials produced by uniform vibra­ tors. The practice of non-uniform shaping of percussion instrument bars to produce desired harmonic partial tone relationships is not described in these texts. Bar materials, resonators, ranges, and mallets used are inac­ curately or inadequately described.

Very little experimental research specifically on the acoustical properties of bar percussion instruments has been done. Detailed information describing the tuning processes for bar percussion instruments is not available. Brief accounts of bar tuning do not give the 140

details of shaping the bars to produce the desired partial

tones.

Literature describing experimental research and

tuning for other percussive vibrators is relevant and of

value to an investigation of bar percussion instrument

acoustics. Reasons for this are: (1) all percussive

vibrators have partial structures that are unique in that

they depart greatly from a harmonic series, (2) many per­

cussive vibrators are shaped to non-uniform cross sections

to produce particular desired partial tone structures,

(3) the tone quality of percussive vibrators is influenced by the type of striker and manner of excitation, (4) sym­ pathetic vibration or resonance effects occur between parts of many percussive vibrating systems, and (5) there are similarities of apparatas and procedures that may be used for the investigation of the tone qualities of various percussive vibrators.

Ear Tuning

The process of tuning a percussion instrument bar involves shaping a rectangular, three dimensional piece of wood or metal in such a manner that a desired fundamental mode of vibration, which is heard as the pitch of the bar, and desired upper partial tones are obtained. This process involves selective removal of material from the underside of the marimba, xylophone and vibe bars to produce a bar 141

shape of non-uniform cross section. The cross section of

the orchestra bell bars is left essentially uniform.

In past years professional tuners used only sets of

metal bars termed "master bars" for reference checks in

the tuning process. Experienced tuners used an aural matching process based upon their Judgment of the accuracy

of the tuning of a bar in relation to these master bars.

In recent years a device, developed by the G. C. Conn

Corporation in 1942, called a Stroboconn has become widely used as an aid in the tuning of percussion instrument bars.

Fundamentals of the bars and second partials of certain bars are tuned with the aid of the Stroboconn. The prin­ ciple of octave stretching as practiced by piano tuners is applied to the tuning of percussion instrument bars. The following steps are carried out in the tuning of the percussion instrument bars:

1) The bar material is cut to appropriate lengths for particular pitches, from bar stock of predetermined widths and thicknesses. These pieces are called bar blanks.

2) Material is removed from the underside of the bar to form the basic arch, which leaves the bar one-half step higher than the eventual frequency of the fundamental.

3) Small amounts of material are removed from selec­ ted areas of the underside of the bar which leaves the bar

+5 cents above the eventual frequency of the fundamental. 142

4) Very small amounts of material are removed from

carefully selected areas of the underside of the bar to pro­

duce the exact fundamental desired, and the desired fre­

quency of the second partial for bars in the lower regis­

ters of the instruments.

5) A further step, tuning the third partial to a

desired frequency, is sometimes undertaken for low regis­

ter bars on custom-built instruments. ,

Experimental Work

Experimental work was done to identify the steady

state and transient responses of a representative group of

percussion instrument bars. The procedure used for steady

state testing was to mount a percussion instrument bar in

a vibration fixture and vibrate the bar from beneath using

an electrodynamic shaker. The vibrations of the bar were monitored with a condenser microphone and displayed on an

oscilloscope and a frequency counter. The vibrational mode was observed by sprinkling sand on the surface to

show the nodal pattern. To test for the transient response produced by a mallet striking the percussion instrument bar, a mechanical striker was built to provide a uniform stroke. A storage screen oscilloscope was set for a single sweep and a laser beam trigger was used. Photographs of the oscilloscope traces were obtained and used in compari­ sons of bar responses to show the influence of the location of mallet stroke on the bar surface and type of mallet used. 143

The general objective of this work was to carry out

research that would support and augment the limited empiri­

cal information available about bars used in the marimba,

xylophone, vibe and orchestra bells. Initial work was to

determine the modes of vibration of selected bars of rose­

wood, aluminum and steel of the type used in bar percus­

sion . instruments , and to investigate the transient responses

of these bars.

Frequencies of the bars of each material were chosen

so that all parts of the range were represented and so that

comparisons among the three materials could be made (Fig.

16), The frequency range included musical note "A" bars

whose nominal fundamentals were from A2 (110 Hz)to Ay

(3520 Hz). These frequencies include the extreme limits of

the musical note "A” of currently manufactured instruments.

These bars were judged by professional tuners to be well

tuned, and representative of the types used on regular production first line bar percussion instruments.

Summary of Results

Basically, the tested bars produced the modes of vibration expected of their group type. The testing pro­ vided verification of the acoustical differences between marimba, xylophone, vibe, and orchestra bell bars. The differing non-uniform cross section characteristics of the 144

four bar types account for the differing modes of vibra­

tion which form the partial tone series of each bar.

Modes of vibration for each bar tested were ex­

pressed as, (1) vibrational frequencies, and (2) in musical

notation. Relative intensity of response of each mode to

the amplitude of the driving signal was given for each

mode of vibration. Data work sheets, found in Appendix A,

contain all sinusoidal responses obtained for each of the

twelve bars tested. In addition, non-sinusoidal responses

obtained are given for the 110 Hz and 220 Hz Rosewood

Marimba Bars, and 220 Hz Aluminum Vibe Bar, and the 880 Hz

Steel Orchestra Bell Bar.

Steady state excitation of percussion instrument bars, while not the characteristic means of excitation used

in musical performance, provided an accurate means of determining the exact frequencies of the modes of vibra­ tion of the bars. Desirable steady state characteristics of percussion instrument bars are directly related to desirable dynamic patterns of tone quality and response of complete bar percussion instruments.

Low register marimba bars (Ag and Ag) produced second and third partials at the ideal frequency ratios to the fundamental. The middle register marimba bar (A^) produced a second partial at the desired frequency ratio, but a third partial lower than the ideal frequency ratio. 1^5

The high register marimba bar (A^) nroduced both second and

third partials lower than the ideal frequency ratios.

The low register (Ay) xylophone bar produced second

and third partials at the ideal frequency ratios. The

middle register xylophone bar (A^) produced second and third

partials lower than the ideal frequency ratios. High

register xylophone bars (Ag, Ay) were not tested.

The low register vibe bar (Ag) produced a second

partial at the ideal frequency ratio to the fundamental

and a third partial higher than the ideal frequency ratio.

The middle register vibe bar (Ay) produced a second par­

tial at the ideal frequency ratio to the fundamental and

a third partial lower than the ideal frequency ratio. The

high register vibe bar (Aq) produced second and third

partials at frequencies lower than the ideal ratios.

All orchestra bell bars tested (A5 , A5 , and Ay) pro­

duced second and third partials at frequencies approximat­

ing the ideal frequencies for bars of uniform cross section.

The highest register bars showed a tendency for the second

and third partials to be slightly lower than ideal for a

bar of uniform cross section.

A comparison of the partial tone structures of the

four bar types at the nominal 8 8 O Hz (A5 ) nominal frequency

showed the actual fundamentals of the xylophone and

orchestra bell bars to be higher in frequency than the marimba and vibe bars of this nominal frequency. This is 146

accounted for by the practice of tuning xylophone and

orchestra bell bars to an Ay = 442 Hz reference standard

and marimba and vibe bars to a A^=440 Hz reference stand­

ard. Upper partial tones of the xylophone and orchestra

bell bars occurred at lower frequencies than those of the

marimba and vibe bars due to the relatively thicker cross

sections of the xylophone and orchestra bell bars.

The results of steady state testing Indicated that

fundamentals and second partials were tuned to the Ideal

relationships for low and middle register bars, but that this relationship was not maintained for high register bars. Consistent tuning to any Ideal relationships for third and higher partials was not evident. Metal bars and bars of relatively thinner cross section produced more and stronger upper partials than wood bars and bars of thicker cross section. Bars of relatively thin cross section produced second partials at or very near to harmonic relationships with the fundamental. Bars of relatively thick cross section produced Inharmonic partials.

A mechanical striker equipped with mallets of the type used by players of bar percussion Instruments was used to excite selected bars to obtain oscilloscope dis­ plays of transient responses. Comparisons were made In relation to the variables of (1) position of stroke on bar surface, and (2) material of mallet heads. Testing support­ ed previous findings In that the relative amplitude of 14? the fundamental Is strongest at the center of the bar and that the second partial becomes more prominent as the striking point reaches the node of the fundamental. Hard mallets produce a tone characterized by the presence of many quickly decaying high frequency partials, and soft mallets produce a tone characterized by the presence of the fundamental and second partial.

Recommendations for Further Work

Meaningful recommendations and suggestions for fur­ ther work in the area of the acoustics of bar percussion instruments and for the development of new and improved instruments must be made with (1) an awareness of manu­ facturing processes, (2) a consideration of the needs of the performer of the instruments, and (3) a knowledge of the psycho-acoustics relating to the perception of musical sounds. Recommendations and suggestions are made in regard to the following areas of concern:

1) Further refinements of bar tuning, including the use of electronic aids.

2) New bar material

3) Innovative and experimental bar shapes

4) Resonator material

5) Extension of the marimba's bass range 148

Bar Tuning

As described by Barnett (1970) the quality of mallet

[bar] percussion instruments depends primarily upon three

important factors: "Intonation (Accuracy in tuning),

Materials (Quality standards in manufacture). Craftsman­

ship (Skill and care used in manufacture)" (p. 8). The

experimental portion of this investigation has shown that

present manufacturing processes produce percussion instru­ ment bars with accurately tuned fundamentals incorporating

the principle of octave stretching necessary to produce bar sounds Judged to be well in tune throughout the range

of the instrument. Second partials are tuned only on bars with fundamentals in the low registers of the instru­ ments where this partial is very prominent in the struck tone of the instrument. Third partials are not tuned unless this tuning is requested, and.then for only bars with fundamentals below Cj,. This degree of accuracy of tuning is seemingly satisfactory to players and listeners.

Experimental testing showed that the second partial of bars of high register fundamentals departed considerably from the ideal relationships found in low register bars.

Partials above the second showed no consistent relation­ ship with the fundamental. It has not been established in any reliable manner how much if any this lack of consis­ tent tuning of the higher partials affects the sound of the 149 bars In the Judgment of the player and the listener. If more exact tuning (nearer to Ideal ratios) of these partials In relation to the fundamental could be done and bars so tuned were Judged to be of superior tone quality to those presently manufactured, then this further refine­ ment of the tuning process should be Implemented by the manufacturer. It must be established which sound compon­ ents are perceptually Important to the listener. Certain upper partials that are measurable by the methods employed In this Investigation may be perceptually unim­ portant. The perceptual aspects of percussive sounds have been considered by those Involved In the electronic pro­ totypes of certain tone qualities. The comment given by

Hearne (196I) Is relevant:

The fact that a given Instrument has a peculiar characteristic, such as a strong unrelated over­ tone [Inharmonic partial]. Is not an adequate reason for adding It to the electronic prototype. The target to aim at. In the design of percus­ sion sound generators. Is the desired psycholog­ ical effect. We do not attempt to duplicate any component of a percussion sound unless we are reasonably convinced that this particular com­ ponent Is required to produce the aforementioned psychological effect (196I, p. 27).

A further aspect to consider Is the Inharmonlclty of the upper partials as a perceptually Important aspect of the desirable sound of percussive tone generators.

Blackham (1965) reported the results of extensive Inves­ tigation that showed: 150

The higher the frequency of the partial tones of any note on the piano, the more they depart from a simple harmonic series. . . . It is evident that the partials of the real piano tone become sharper— that is, higher in frequency— compared with the partials of a pure harmonic tone. . . . Above all, the inharmonicity of the piano’s tone must not be neglected. . . . [for] Our tests have proved that synthetic tones built of har­ monic partials lack the quality of warmth that is associated with the piano as it exists today (1965, pp. 88, 94, 99).

Aural perception has had and will likely continue

to have an important influence on the tuning practices of percussive vibrators. Exact harmonic ratios of frequen­

cies tuned into musical sound sources such as strings and bars are not always what the human ear accepts as pro­ viding the best tone quality.

The present tuning process makes considerable use of the Stroboconn at all stages of the manufacture of the percussion instrument bars. The use of this device has enabled the manufacturerto produce instruments of a con­ sistent tuning. Factory tuning personnel no longer are required to make aural Judgments during the tuning process. They are given a set of instructions for

Stroboconn settings that may be carried out simply by turning dials and visual observations of the instrument’s scanning unit. While the Stroboconn has enabled the manufacturante produce bar percussion instruments of con­ sistent quality with less aurally skilled tuners, the

Stroboconn does have limitations. Notable is the 151 instruments limited range— to By. Partial tones cannot be identified above By. Thus if future concern were to be given these upper partials o' a tone, a device for visual representation of high frequencies would be necessary.

Criteria for a device to aid in bar tuning are:

1) Frequency of a mode of vibration must be visu­ ally displayed clearly so that the tuner is not required to make a subjective Judgment. Information must be obtained instantly by glancing at some sort of display such as found on the Stroboconn. Reading and interpreta­ tion of oscilloscope traces would require skill and train­ ing beyond that presently found in tuning personnel in the industry.

2) The tuner must be able to handle the bar during the tuning process. Any apparatus must allow for the pick­ ing up and replacing of the bar in the test position without time consuming suspension of the bar with cords and mountings.

The procedure used to identify the modes of vibra­ tion of the bars tested in this investigation was to mount a bar in a vibration fixture with cord supports similar to that used in bar percussion instruments. The bar was vibrated from beneath using an electrodynamic shaker. The vibrations of the bar were monitored with a condenser microphone and displayed on an oscilloscope and a fre­ quency counter. This procedure allowed for the identifi­ 152

cation of frequencies far above the By upper limit of the

Stroboconn. An apparatus of this type might eventually be

used to Improve and accelerate the tuning process by the

Industry If the present suspension method could be changed

to allow for quick removal and replacement of the bars In

the test position. Component parts of the test apparatus would have to be developed Into a compact and financially

feasible unit.

Bar Material

Describing bar material Barnett (1970, p. 8) stated

"Marimba and xylophone bars should be made of selected genuine Honduras rosewood (although technological develop­ ments now hold promise of new materials for tone bars of excellent quality for these Instruments)." This paren­ thetical comment points out one of the most challenging innovations possible today In the development of modern bar percussion Instruments.

Rosewood of the quality required for marimba and xylophone bars Is difficult to obtain, much of the stock received Is unsuitable for bars and costly hand crafting hours are spent shaping and tuning the rosewood bars. If a suitable synthetic material could be molded to approxi­ mately the correct shape for each bar, then only "touch up" final tuning would be required of an expert tuner, rather than the time consuming process of cutting, shaping 153

and sanding now done on rosewood bars. Synthetics being

of a more consistent texture would eliminate most waste

bars as nearly all bars would be of suitable standards

for use on high quality bar percussion instruments. Pres­

ently after a rosewood bar has progressed through some of

the stages of tuning, flaws or imperfections become evi­

dent to the tuner and it often is or should be rejected

or relegated to inferior lines of instruments.

One problem likely to be encountered in the use of

a synthetic material to replace rosewood for marimba and

xylophone bars is that the uniformity of the internal

structure of some materials may cause a less rapid damp­

ing or Che modes of vibration than formerly obtained with

rosewood. Whether this would be Judged a desirable added

resonance to the sound by the player or a poor duplicate

of the natural product remains to be seen. Research by

Hardy and Ancell (I96I) has shown that the consistent

qualities of plastic drum heads allow the upper partials

to be heard more clearly and for a longer period of time

thus creating in the Judgment of some professionals a less

desirable sound from plastic timpani heads than from the more fundamentally oriented sound of a calfskin timpani head. Plastics are being used for the bodies of some musical instruments. Some professionals comment that instruments made of these materials lack the "warmth or flexibility" of a natural product. Zimmerman (1967, p. I6 ) 154

mentioned this in reference to the plastic clarinet body

as opposed to the traditional grenadilla wood body.

Bar Shape

If a practical molded bar process can be developed,

consideration should be given to innovative bar shapes that would yield a better "well tuned" bar. Of much theoretical and practical value would be extensive experi­ mental testing of a wide variety of bar shapes. If the optimum shape based on the presence of the desired modes of vibration can be identified for each bar this informa­ tion can then be used to further automate the manufactur­ ing process and eventually lead to the necessary programming for a molded synthetic bar to replace rosewood.

Bar shapes that utilize an uneven top surface cross section have been considered. Cross section views of unusual bar shapes proposed in two patents taken out in past years are shown in Figure 43.

Patent #1, 632,751— H. E. Winterhoof (June 14, 1927)

Patent #1, 838,502— H. J. Schluter (December 29, 1931).

Pig. 43.— Cross Section Views of Unusual Bar Shapes. 155

One problem in working on a bar of the shapes shown above

is the danger of splintering and chipping rosewood when­

ever v/orking diagonally to the bar's grain. If a practi­

cal molded bar process is developed, consideration should

be given to the possibility of finding acoustically

superior bar shapes, that are not feasible using rosewood.

Resonators

Resonator material may have some effect on the tone

quality of bar percussion instruments. Instruments pres­

ently manufactured in the United States use aluminum resonators. This material in light weight, easily obtain­

able, and economically practical for manufacture of resona­ tors. In years past, bar percussion instruments were manufactured with brass resonators, which were considerably heavier in weight than aluminum resonators. Some perfor­ mers feel that instruments with brass resonators produced a superior tone quality to those with aluminum resonators.

During and immediately after World War II, due to the shortage of metals for non-essential industries, bar per­ cussion instrument resonators were made of hard cardboard tube material. While the tone quality of instruments with cardboard resonators was generally described as "a bit less responsive and full," the tone was not entirely unacceptable to performers. 156

Recent studies on the influence of various types of

wall material of organ pipes (Backus, 1966) indicate that

the dimensions and interior surface conditions of the pipe

are more important than the specific wall material.

Applying these findings to bar percussion instru­

ment resonators it appears reasonable to project that

materials such as plastics might well be used for resona­

tors, Plastic materials have the advantage of being,

(1) light in weight, (2) relatively inexpensive, (3) easily

shaped into curved resonators necessary for bass marimbas,

and (4) of a smooth, durable and attractive finish.

Regardless of material used, the interior surface

of the resonator must be as smooth and non-porous as possible, to allow maximum reflection and minimum absorp­ tion of the sound waves in the resonator.

A patent was taken out in 1919 (Fig. 44) involving an elaborate system of resonators for each bar, tuned to the various partials of the bar. These several resonators were to be placed so that each resonator would accentuate a certain partial tone of the bar. The purpose was to produce a "rich tone." Each resonator, it will be noted, was placed directly under the spot where an anti-node would occur for that particular partial tone. 157

Fig. 44.— Drawing of Multiple Resonators for a Bar (Patent #1,304,435— H. E. Winterhoff [May 20, 1919]).

Most of the features of the above patent have never been developed into production bar percussion instruments.

One adaptation of the multiple resonator principle was used for a time on some models of vibes for the extreme low portion of the range (Pg to Ci^) as shown in Figure 45.

Second partial fundamental resonator resonator

Fig. 45.— Drawing of Bar with Double Resonator.

No bar percussion Instruments currently manufactured utilize multiple resonators for individual bars.

Electronic amplification now offers a possible means of controlling the respective amplitudes of partials of a 158

complex tone to produce a desired tone quality In somewhat

the same manner as projected by the multiple resonator

principle

Range

The bar percussion Instrument family possesses a

variety of tone qualities In the high frequency register

produced by rosewood, aluminum, and steel bars. However,

the ranges of Instruments presently being manufactured In

the United States emphasize the higher portion of the

frequency range and neglects the lower frequencies. Of the

bar percussion Instruments, only the marimba extends sig­

nificantly downward to the frequency range commonly

notated In the bass clef. The lowest note of the largest

marimba manufactured In the United States Is Ag, while

many other marimbas only extend downward to Cg. This lack

of a true bass Instrument In the bar percussion family

makes It Impossible to play transcriptions of music, such as

string ensembles at the composers Intended pitch levels.

Often a marimba quintet will resort to the use of a double

bass (string bass) to provide the needed bass sonority.

Some performer-craftsmen have built their own bass marimbas to fill their need (MacCallvun, 1969, p. 62). On rare occasions and at high cost manufacturers have custom built bass marimbas. 159

A Musser bass marimba, extending downward to C2, WcTs

custom built for the United States Navy Percussion Ensemble.

The instrument is over five feet tall, and a special plat­

form was built to accommodate the player. The resonators

are four inches in diameter, the lowest bar measures three

and one-half inches wide, one inch thick, and twenty-four

inches long. The range is an octave and one-half lower

than any production marimba on the market today. The

instrument took two months to build, and is an exact copy

of a standard Musser instrument except on a much larger

scale.

The bass marimba attempts to fill the need for a bass register instrument with a low range. At present it appears unlikely that a bass marimba will become a readily available production instrument, for as MacCallum (1967) noted:

Much research and effort have been expended to make the marimba perfect, but no attention has been given to the need for a greater extension into the bass register. Only marimbas of full range in ensemble playing can demonstrate the capabilities and uniqueness of the instrument and attract the attention more of serious com­ posers and musicians. As long as the "anti- bass” attitude of the manufacturers persists and is not countered. Central American marimbas will still be the only ones in the world dis­ tinguished for ensemble playing and versatility in all musical applications (p. 269).

Closing Comments

The research described in this investigation is intended to form a basis for additional study of modes 160

of vibration of percussive sound sources, for analyses of

transient sounds, for material studies, and for developing

ways of accessing the properties of new materials for per­

cussion instrument bars and other percussive vibrators.

It is hoped that this investigation has helped establish

the feasibility of doing acoustical research on percussion

instruments. Very little has been done in the area of the

acoustics of percussion instruments. There are now means

available to approach the problems of the acoustics of

percussion instruments from a scientific point of view.

Colleges and research centers now have or are developing

laboratories where accurate tone quality measurements and

tonal syntheses can be made. The artist-teacher-performer

of the percussion instruments, who has some understanding

of and a concern for the acoustical and constructional problems of these instruments, can express thoughts on

further developments of the instruments. However, only with the cooperation of those in the physical and behavioral sciences, and in the instrument industry itself, can answers and solutions be found that will be of value to all who perform on, teach and build the per­

cussion instruments.

To adequately meet the challenge in the area of percussion research, performers and teachers of percussion instruments must join forces with those whose knowledge and I6l technical skills are indispensable to obtaining signifi­ cant and accurate information. Encouraging evidences of these cooperative inter-disciplinary efforts are taking place now at leading educational and research centers. A great need exists for accurate, detailed descriptions of percussion instruments in musical acoustics texts. Pres­ ent coverage of this topic is inadequate, and often inac­ curate. For a text of this nature to accurately and in detail describe instruments in use and their underlying acoustical principles, an acoustician with a knowledge of and concern for musical instruments, as well as canpetence in the theoretical aspects of acoustics, should collabor­ ate with musician-performers of the instruments who possess competence in musical acoustics.

Further effort by all concerned cannot help but establish a greater understanding on the part of all who delve into the many fascinating, challenging aspects of the oercussion arts. A P P E N D I X A

STEADY STATE TESTING

DATA WORK SHEETS

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