Characterization and' Taxonomy

of

Historic Brass Musical Instruments

from ae

Acoustical Standpoint

Arnold Myers

Ph.D.

The University of Edinburgh

1998

I" V *\- Abstract

The conceptual bases of existing classification schemes for brasswind are examined.

The requirements of a taxonomy relating to the character of brass musical instruments as experienced by players and listeners are discussed.

Various directly and indirectly measurable physical parameters are defined.

The utility of these parameters in classification is assessed in a number of case studies on instruments in museums and collections.

The evolution of instrument design since 1750 in terms of these characterization criteria is outlined. Declaration

I declare that this thesis has been composed by me and that the work is my own.

? r % *} Acknowledgements

I have been encouraged and helped by many in my investigations.

My supervisors, D. Murray Campbell in the Department of Physics and Astronomy

Christopher D.S. Field, and John Kitchen in the Faculty of Music have provided wise guidance whenever needed.

Raymond Parks, Research Fellow in Fluid Dynamics, Department of Physics and

Astronomy, University of Edinburgh, has given unfailing support, and has been

responsible for much of the measuring equipment I have used.

David Sharp has used the pulse reflectornetry techniques developed in the course of his

own research to obtain bore reconstructions of numerous specimens for me.

Herbert Heyde kindly discussed the measurement of historic brass instruments with me.

Stewart Benzie has carried out instrument repairs for me and made the crook described in

Chapter 5.

I am grateful to the curators of many museums for allowing me access to the historic

instruments in their care. They include:

Joanna Archibald, Bate Collection, University of Oxford Otto Biba, Gesselschaft der Musikfreunde Wien, Vienna Margaret Birley, Horniman Museum, London James Borders, Stearns Collection, University of Michigan, Ann Arbor Philippe Bruguiere, Musee de la Musique, Paris Marie-France Calas, Musee de la Musique, Paris Joel Dugot, Musee de la Musique, Paris Eszter Fontana, Musikinstrumentenmuseum, University of Leipzig Monika Jäger, Steiermärkisches Landesmuseum Joanneum, Graz Sally Jewell, Leblanc Corporation, Kenosha, Wisconsin Peter Andreas Kjeldsberg, Ringve Museum, Trondheim Darcy Kuronen, Museum of Fine Arts, Boston Helene La Rue, Bate Collection, University of Oxford Jeremy Montagu, Bate Collection, University of Oxford Frances Palmer, Horniman Museum, London Gerhard Stradner, Kunsthistorisches Museum, Vienna David Surber, Holton Co., Elkhorn, Wisonsin Elizabeth Wells, Museum of Instruments, Royal College of Music, London Robert Woosnam-Savage, Burrell Collection, Glasgow Museums and Art Galleries

I am also grateful to many private collectors and owners of individual instruments, for

allowing me access to instruments in their care. These include:

Christopher Baines, Burford Mole Benn, London Dave Butcher, Edinburgh D. Murray Campbell, Edinburgh Simon Carlyle, Edinburgh John R.T. Davies, London William Giles, Rosyth Bruno Kampmann, Paris Jonathan Korzun, U.S.A. Jeremy Montagu, Oxford Steve Reed, London Gerhard Stradner, Vienna Frank Tomes, London John Webb, Padbrook The City of Edinburgh Band Newtongrange Silver Band The Salvation Army Heritage Centre, London The Department of Physics and Astronomy, University of Edinburgh

I should also like to record that it has been indispensable to have frequent and ready

access to the substantial and varied holdings of the Edinburgh University Collection

Historic Musical Instruments (EUCHMI) and to the acoustics laboratories of the

Department of Physics and Astronomy, University of Edinburgh.

Arnold Myers Contents

Chapter 1 Introduction 9

1.1 Scope 9

1.2 Basic acoustics of brass instruments 10

1.3 Historical background 15

Chapter 2 History of brasswind classification 18

2.1 Simple classifications 18

2.2 Heyde's bore characterization 24

Chapter 3 Purpose and expectations of taxonomy 30

3.1 Uses of classification 30

3.2 The taxonomic problem 30

3.3 Requirements of taxonomy 32

Chapter 4 Ranking of factors 34

4.1 Factors of possible taxonomic significance 34

4.2 Impedance measurements on trombones 36

Chapter S Air column bends 43

5.1 Effects of tube bends 43

5.2 Practical tests 45

Chapter 6 Considerations of the Horn Function 48

6.1 The horn function 48

6.2 Bessel homs 53 Chapter 7 Considerations of the mouthpiece volume and profile 64

7.1 Methods of mouthpiece description 65

7.2 The acoustical functions of the brass instrument mouthpiece 67

7.3 The anatomy of the mouthpiece 70

7.4 Method of mouthpiece cup profile measurement 71

7.5 Taxonomic parameters 74

7.6 Measurements of resonance frequency 76

Chapter 8 Considerations of mid-length bore 79

8.1 Data from pulse reflectometry 79

8.2 Results for certain historical models of instrument 81

8.3 Comparison of cornets and trumpets 84

8.4 Taxonomy of the proximal half of the air column 95

8.5 Taxonomy of the distal half of the air column 98

8.6 Taxonomy of the overall air column 101

Chapter 9 Synthesis of criteria 103

9.1 Scaling of designs 103

9.2 Case study: the saxhorn families 104

9.3 Case study: the trombone in different sizes 106

9.4 Case study: the early history of the modern trombone 108

9.5 Case study: valve trombone and bass trumpet 110

9.6 Case study: Wagner tuba and cornophone 112

9.7 The evolution of instrument design since 1750 113

Bibliography

Publications

Appendices

A. Brass instruments sold by Henry Distin, 1857 127

B. Instruments ranked by peak horn function value 129

C. Instruments grouped by nominal pitch and ranked by cut-off frequency 141 D. Minimum shank diameters of mouthpieces in EUCHMI 151

E. Mouthpieces ranked by cup volume 160

F. Mouthpieces ranked by Shape Quotient 168

G. Mouthpieces ranked by Resonance Factor 175

H. Instruments ranked by value of parameter K 182

I. Instruments ranked by value of parameter C 189

J. Sources of specimens 196

K. Table of tube lengths 197 Chapter 1

Introduction

1.1 Scope

The scope of this study is the whole field of what may be called 'European' brass instruments made for musical purposes. This includes instruments made in the European tradition on other continents, but excludes purely signalling instruments and instruments of folk traditions that have not been to some extent integrated into the mainstream of 'art' music.

General criteria for consideration are:

1. The instrument is essentially tubular, sounded by a player exhaling through

vibrating lips applied to one end of the tube. The terms 'brasswind' and 'brass

instruments' do not denote the material of construction, which can be metal, wood,

plastic, etc. or composite.

2. The instrument is designed to play a range of notes, typically over one to four

octaves.

2. The instrument is designed to play notes which are intended to be 'in tune' with the

prevailing conventional framework of pitch standards and temperament.

3. The instrument is normally assigned a nominal pitch (Myers 1994), i.e. is in a key

such as B b.

Thus discussed in this study are all the brass instruments used in orchestras and bands

playing from written music, with the addition of instruments only occasionally so used

but built with this possibility, e.g. bugles in Bb, alphorns in Gb. By analogy with woodwind instruments, a term which is not normally used for signalling whistles and folk flutes and reed-pipes, the instruments satisfying these criteria may be termed

'brasswinds'.

Excluded are instruments such as the short English hunting horn, burgmote horns and

oliphants (not designed to play a range of notes); didgeridoos (not intended to be assigned

a nominal pitch); and ancient instruments such as the buccina, carnyx, lur (pitch

framework and playing range not adequately known). The instruments of the Russian

horn band, though each designed to play a single note, might be considered as a group to

meet the criteria - however no set was readily available for study.

There are inevitably some of the many hundreds of kinds of brasswinds past and present

with some kind of established identity which have not been mentioned because of lack of

availability. However, the types most commonly used in music making since the period

of the Renaissance have been studied, and there is no reason to believe that the methods

of classification investigated here will not be applicable to any of the other kinds.

1.2 Basic Acoustics of Brass Instruments

The acoustics on which this study is based is thoroughly dealt with in textbooks such as

Campbell and Greated (1987) and Fletcher and Rossing (1991), and may be summarised

as follows.

All brass instruments consist of a tube, at one end of which is a mouthpiece shaped so

that the player can make an air-tight seal when the lips are placed against it. The

acoustical properties of brass instruments depend on the interactions of the player (in

particular the oral cavities and lips), the air column inside the instrument, and the

ambient air at the other end of the instrument. The column of air inside the tube is set

into vibration when it is excited by the player buzzing the lips, which are placed against

the mouthpiece. A sustained sound on a brass instrument requires 'standing waves', i.e.

soundwaves travelling from one end to the other and reflected from each end like water

waves in a bath. Although the player opens the lips by blowing air through them, because

10 the lips are buzzing they are effectively closed for enough of the time to reflect most of the sound waves travelling towards them through the instrument. Whether the other end of the instrument terminates abruptly (as in a bugle) or terminates in a flaring bell (as in a trumpet), sound waves are reflected by the bell mouth or by the flare. The sound inside an instrument is much more intense than the sound produced by the instrument in the surrounding air. The bell of an instrument has to be carefully designed so that it reflects enough sound to allow standing waves to build up, yet allows enough sound to escape to be audible at an appropriate intensity to be useful in music. For this reason, brass

instrument bells are of a limited range of patterns - one shaped like a gramophone horn, for example, would not work.

The standing waves lose some of their energy to the ambient air as audible sound, some in friction with the walls of the instrument, and also a small part to the player's lips, which are coerced to vibrate at a frequency to some extent dictated by the instrument. At the same time, the player adds energy to the vibrating air column at just the right frequency by blowing through the buzzing lips to replace the sound energy being dissipated.

The air inside a brass instrument, which is effectively closed at one end by the lips and

open at the other, can sustain standing waves at certain quite well-defined frequencies,

known as the frequencies of the 'modes of vibration' of the air column. If the frequency

of the wave is a very slightly higher or slightly lower than one of these frequencies,

standing waves are still possible, but will be weaker. These mode frequencies form a

series which is more extensive for a narrow tube such as in a french horn or a natural

trumpet than for a wide tube such as in a bugle or an ophicleide. For a perfectly conical

tube, the frequencies would correspond numerically to a harmonic series, which is

defined as a series of numbers (here, frequencies) which are exact integer multiples of the

lowest member (the fundamental). For a perfectly cylindrical tube, the frequencies would

correspond to the odd-numbered members of a harmonic series. Real brass instruments

are neither perfectly cylindrical nor perfectly conical, and the modes of vibration depend

on the internal shape of the instrument. Tubes are musically most useful if several of the

frequencies of several of the modes of vibration approximate to members of a harmonic

series. In the case of instruments with large cylindrical portions of tubing such as

trumpets and trombones, the mouthpiece and bell need to be carefully designed to make

11 this possible. Even so, the lowest one or two members of the series of modes of vibration

of trumpets and trombones diverge considerably from the harmonic series. The art of the brass instrument maker is to give the modes the most advantageous frequencies, strengths

and tolerances.

When a sustained sound is produced on a brass instrument, not only does the air inside

the instrument vibrate at the frequency of vibration of the players' lips, but also at exact

integer multiples of this frequency. These are the spectral components of the sound,

sometimes called 'overtones'; the lowest component (whose frequency is that of the lip

vibration) is the fundamental. The frequencies of the spectra! components of the sound

when a sustained single note is being played without vibrato form a harmonic series. The

sound which escapes from the bell of the instrument also contains these spectral

components, and it is the relative strengths of these components that determine the timbre

of a sustained sound on the instrument. However, different notes played on the same

instrument will have different spectra: a high note may have a significant amount of

acoustic in energy only two or three components whereas a low note may have a rich

spectrum with significant amounts of energy at fifteen or more frequencies. It is always

easier to distinguish two brass instruments by comparing low notes than high. Loud notes

not have only energy at each spectral component, but also a more extensive spectrum.

Because of this, a recording of a loud note can be recognised as such even if reproduced

at low volume.

The series of fundamental frequencies of the notes which can be sounded by a player

form only an approximation to a harmonic series, though they are sometimes loosely

called 'the harmonics'. If the frequencies of the modes of vibration of the air column

formed a harmonic series, then the 'note centre frequencies' available to the player would

also form a harmonic series [Figure 1.1]. However, this is an ideal case and the

behaviour of real instruments is more complicated. In order for the instrument to 'speak'

and produce a 'well-focused' sound, several of the overtones (harmonics) of the note

being played need to resonate with modes of vibration of the tube. In most cases, the

fundamental of the note is very close to one of the mode frequencies; in addition, to

produce the tone quality expected of brass instruments, its spectral components

(harmonics) also resonate with higher modes of vibration of the air column inside the

12 tube. The interaction of the harmonic components of the sound with the air column, termed a 'co-operative regime', is a strong effect. On one hand, a co-operative regime can allow a sustained sound even if the fundamental does not match a mode of vibration

of the air - column this is how a trombonist can sound a pedal note or a tuba player can sound 'factitious' notes not in the usual series [Figure 1.1]. On the other hand, if the modes of vibration have a poor match with the overtones (harmonics) of a note a player is sounding, the note will be 'stuffy' in quality, difficult to produce, and possibly out of tune. Since the air column can sustain standing waves at frequencies very slightly higher or slightly lower than the mode frequencies, the player has some latitude to 'lip' a note up or down in pitch and to use pitch vibrato.

-©-

Figure 1.1: The pitches of the first 20 modes of vibration of air at 25 C in an ideal cone of length 2.645 metres (approximately 8ft): the mode frequencies departing most from the equally-tempered scale are indicated in black. A well-in-tune instrument pitched in 8-ft C will allow a portion of this series of notes to be played without extending a slide, operating valves or opening tone-holes, depending on the bore proportions and the ability of the player. An ophicleide, for example would normally use members 1 to 6; a natural trumpet can sound members 3 to 20.

In the case of wide-bore signalling instruments such as a bugles, there are only a small number of modes of vibration of the air column which are of sufficient strength to contribute to the generation of sustained sound; therefore the 'co-operative regimes' are

less extensive than those which allow in-tune production of the lower notes of narrow-bore instruments such as the french horn and the trombone; as a result many

instruments of the bugle family are not well in tune. In the case of instruments with tone-holes such as cornetts and serpents, the situation is complex: the series of notes

which can be produced with a given fingering are not generally a close approximation to

a harmonic series. On these instruments, for example, a note and a note an octave higher

13 usually have different fingerings (Campbell 1996).

So far, only sustained sounds have been discussed. In order to sound a note, the brass player has to set the lips in vibration, sending a pulse of sound towards the bell. By the

time the initial pulse is reflected back and can interact with the lips to establish a stable

sustained sound, the lips will have gone through at least one cycle (many cycles for high

notes). A large part of the skill of the brass player consists of the ability to buzz the lips

at the right initial frequency; it is to acquire this ability that many teachers recommend

the practice on mouthpiece alone. The length of unsupported time is longer for a given

note on, say, a natural trumpet in 7-ft D than a piccolo trumpet in 21/4-ft Bk With a

longer tube length, the nearest playable notes above and below the desired note are closer

in pitch than with a short tube length. For these reasons, the trend in instrument design

since the invention of the valve has been to make shorter instruments.

The sound characteristics of instruments depend to a large extent on their behaviour in

the initial build-up of a note. If tape recordings have these 'starting transients' cut out, it

is almost impossible to identify the instrument being played, sometimes even to tell if it

is wind or string. Another characteristic of an instrument can be the presence of

formants. These are regions of the spectrum where the components are consistently

strong regardless of the exact fundamental frequency of the note being sounded.

Formants are the mechanism whereby vowels can be recognised in speech and song; they

make an important contribution to woodwind character, and are less important for brass but still significant (Meyer, 1978).

Opinions differ as to the importance of the material of a brass instrument. The vibration

of the walls has little effect on the sound spectrum produced by a brass instrument, and

the character of what the listener hears is principally determined by the shape of the bore

profile of the instrument and of the oral cavities of the player. Factors such as material

and wall thickness may in some cases have effects that can be sensed by the player, who

is in physical contact with the instrument and who perhaps hears sound radiated from the

body of the instrument. The bore profile, however, is the principal determinant of the

character if the instrument - for example whether it is a french horn, a flugelhorn or a

saxhorn.

14 Mode Frequency C2 c3 G3 C4 E4 G4 C5 Ds E5 number (Hz)

1 42.2 66.4 2 124 133 133 3 198 199 199 4 265 265 265 265 5 332 332 332 6 395 398 396 398 398 7 461 465 8 529 529 529 529 529 9 599 597 597 597 10 663 664 664 664 664 11 732 730 12 801 796 796 796 796 796 796 13 872 863

Figure 1.2: Example of Mode Frequencies and Spectral Components. The second column shows the frequencies of the modes of vibration of a bass trumpet in 8ft C by Alexander (Model 19) with a Bach 7C mouthpiece belonging to W.A. Giles, the tuning-slides fully closed and with no valves operated, measured at 18 C using the capillary input impedance method as described by Campbell (1987). The other columns show the spectral components (harmonics) of the notes playable on this instrument with no valves operated [Figure 1.1]. The pedal note, C2, which is rarely used on the bass trumpet receives no

support for its fundamental, and can be sounded only because of the support of modes 3 - 13 for its harmonics 3-13. The second mode (124 Hz) is a semitone flatter than the fundamental of the note C3 (133 Hz), which note can therefore be sounded only because

of the support of modes 4, 6, 8, 10 and 12 for its harmonics 2 - 6. On this instrument,

modes above the 13th are not strong enough to help a player 'centre' on a desired note. In fact, the compass of the bass trumpet is not usually regarded as extending above G5.

The playable notes are a little sharp compared with the pitch standard A4 = 440 Hz

(middle C = 265 Hz is equivalent to A4 = 446 Hz), and will be sharper still when the instrument is warmed up; however, the instrument is normally used with the tuning-slide drawn.

1.3 Historical Background

The history informing this study is based is dealt with in detail in textbooks such as

Baines (1976) and Heyde (1987b); the phenomenon of the proliferation of brasswind

models may be summarised as follows.

Through the eighteenth century and the early years of the nineteenth, both the trumpet

and the horn were increasingly used in orchestral and band music. Despite the

15 of widespread use hand-stopping in horn playing and the rarer use of slide trumpets or keyed trumpets, composers and arrangers were very restricted in the kind of music they

could write for brass instruments. Makers had to provide sets of crooks - up to four or

five for the keys commonly used for trumpet music and ten or eleven for horns. Parts

written for these instruments were closely related to the natural series of notes; and if the

music changed into a different key, time had to be allowed for the player to change

crooks.

These limitations prompted the invention of the valve, which had the effect of an

instantaneous change of crook. The first successful valve was that of the musicians

Heinrich Stölzel and Friedrich Blühmel in Prussia in 1814. Other designs followed; these

achieved a similar effect by different mechanisms. It was soon realised that valves, when

mechanically capable of being operated with sufficient speed, could be used not merely to

change crook simply and rapidly, but to play tunes and ensemble parts with great facility

- more evenly and easily than by handstopping a horn and with greater rapidity than with

the slide of a trombone or slide trumpet.

Not only did the invention of valves revolutionise horn and trumpet technique, but it also

permitted the development of new kinds of brass instrument. The use of a slide in a

trombone or in a trumpet necessitated a bore profile that included considerable lengths of

cylindrical tubing. The use of finger-holes or keys for the cornett, serpent, keyed bugle

and ophicleide was most satisfactory for instruments with an almost purely conical bore

profile. The use of handstopping was effective only with instruments of the bore profile

of the french horn - narrow at the mouthpipe, wide at the bell throat and pitched not too

far from F (12-ft tube length). With valves, however, instrument makers had complete

freedom to introduce instruments with any bore profile that resulted in an instrument that

was acceptably in tune with itself.

Within a few years of the invention of the valve, instruments in various sizes and shapes

were being produced, particularly in Germany, which were the forerunners of the cornet,

the tuba and other instruments. In the course of nineteenth century the adoption of the

valve led to a proliferation of viable bore profiles for acceptable brass instruments. In

addition to unambiguously new instruments such as the tuba, many types of instruments

16 with intermediate bore profile were developed, such as the saxhorn. The established repertoire for existing instrument types (especially the horn and the trumpet) required

instrument designs capable of performing this repertoire, with sufficient performance characteristics remaining intact through each design development. This study is an

investigation of the properties which continued through the evolution of established types

to the present day, and which distinguish them from the newly invented models of the

nineteenth century.

Before the nineteenth century, instruments were made by hand-craft techniques, and

makers are considered to have used instrument designs incorporating proportions

expressible by the ratios of small integers, as will be discussed in Chapter 2, Section 2.2.

Generally, these methods were replaced in the nineteenth century by mechanised

techniques, an empirical approach to design and factory production; in the twentieth

century there has been some practical application of acoustical theory.

One important technique which has continued throughout is the use of mandrels in

instrument making. A mandrel is a piece of iron or steel of the exact shape required for

the interior of a part of an instrument, on which that part can be worked to bring it into

its correct shape. If not actually made by the instrument maker, mandrels are made to the

maker's specification. The mandrels form an essential, but usually unwritten, part of the

'recipe' for making an instrument. The mandrel on which the bell is made is particularly

important, since it determines exactly the shape of the bell flare of the instrument and

much of its acoustic character, as will be discussed in Chapter 6. Mandrels can be used

for many years, allowing continuity in the production of individual models of brass

instrument design over time.

Several manuals (Nodi 1970, Bahnert et al 1986, Dullat 1989) provide detailed

descriptions of brass instrument construction techniques, including many measurements of

components of contemporary instrument models. However, comparable measurements are

not readily obtainable for historic instruments, and for consistency fresh measurements

have been made for this study on old and new instruments alike using the same

techniques and equipment.

17 Chapter 2

History of classification

2.1 Simple Classifications

Classification, the systematic grouping of objects or ideas to facilitate their treatment, has

been used by authors to arrange material in books, and by museums to arrange displays

and catalogues. The best-known musical instrument classification is the Hornbostel-Sachs

classification of 1914 (Hornbostel and Sachs 1914, translation into English 1961). Its

treatment of brasswind [Figure 2.1] is rather superficial: the purpose of the scheme is to

allow curators to arrange objects even if they know nothing about the music or culture of

origin. Such a classification may, however, lead to discoveries about the migration of

instrument types from one region or people to another.

423 Trumpets 423.1 Natural trumpets 423.12 Tubular trumpets 423.121 End-blown trumpets 423.121.1 Straight end-blown trumpets 423.121.12 With mouthpiece

423.121.2 End-blown horns (tube is curved or folded) 423.121.22 With mouthpiece

423.2 Chromatic trumpets 423.21 Trumpets with fingerholes cornetti, key bugles 423.22 Slide trumpets trombone 423.23 Valve trumpets 423.231 Valve bugles (conical tube throughout) 423.232 Valve horns (predominantly conical tube) 423.233 Valve trumpets (predominantly cylindrical tube)

Figure 2.1: Western brass instruments in the Hornbostel-Sachs classification, 1914.

Here all brass instruments are 'trumpets', coming in the general class 423. The primary

division is into natural and chromatic, divided morphologically (natural instruments) or

by mechanism (chromatic instruments). These are the easiest attributes to be recognised

18 by someone with no specialist knowledge of kinds of brass instrument. For valved

instruments only, however, there is a simple categorization by bore profile. This

classification would (for example) separate natural, slide, keyed and valved trumpets

which might at one time have been used for the same repertoire.

This division into three classes by bore profile has been adopted by several present-day

writers on musical acoustics such as Eargle (1990). Here, a euphonium is regarded as a

valved bugle, almost entirely conical. Bb and F horns are predominantly conical, and

trumpets and trombones are cylindrical. It is not immediately obvious where to place

some modern instruments, such as a Wagner tuba or a cornet, let alone historical

instruments.

A division into five families [Figure 2.2] has been outlined by Edward Tarr (1984) which

he attributes to the collector Wilhelm Bernoulli. This is based on subtler distinctions

between bore profiles and bore diameters.

Wide conical bore

absent or minimal bell flare cornett, serpent, bass horn

Narrow mainly cylindrical bore medium bell flare medium throat wide mouthpipe trumpet (except modern piston valve trumpet), trombone

Narrow half conical half cylindrical bore medium bell flare medium throat

narrow mouthpipe cornet, post horn

Narrow to wide conical bore

absent or minimal bell flare very large throat formerly wide, now narrow mouthpipe flugelhorn, ophicleide

Very narrow, slightly conical bore very large bell flare medium throat

very narrow mouthpipe horn

Figure 2.2 Five families of western brass instruments (Tarr, 1984).

19 A much more detailed scheme was proposed by Adam Carse (1939) This introduces mouthpiece profile as a principle of division. Note that modern french horns are now

'mainly conical' and the intermediate class is given to cornets. There are consistent

for natural and designations modern trumpets. This classification is satisfactory for many

purposes. However, in the Carse scheme [Figure 2.3], the Wagner tuba is still unplaced,

and many other distinctions are not made, such as the difference between a valve

trombone and a bass trumpet.

20 No mechanism Mainly cylindrical bore Narrow bore Cupped mouthpiece Old trumpets Deeper cupped mouthpiece Cavalry and fanfare trumpets Conical bore Wide bore Various mouthpiece Bugles Narrow bore

Cornet or bugle mouthpiece Coach and post horns Cone or funnel mouthpiece Hand horns and French hunting horns

Finger-hole or key-hole (shortening mechanism) Conical bore Wide bore Cup mouthpiece Cornetts .

% Very wide bore Cup mouthpiece Serpents Wide bore Intermediate mouthpiece Bass-horns, Keyed bugles, Ophicleides

Valve (lengthening mechanism) Mainly cylindrical bore Narrow bore Cup to intermediate mouthpiece Valve trumpets Intermediate mouthpiece Valve trombones Conical and cylindrical bore Narrow bore

Intermediate mouthpiece Modern cornets Conical (lily-shaped) mouthpiece Old cornets Mainly conical bore Narrow bore

Cone or funnel mouthpiece Valved french horns Wider bore Intermediate mouthpiece Fliigelhorns, alto, tenor and baritone saxhorns and bugle-horns Wide bore

Intermediate mouthpiece Euphoniums, tubas or bombardons

Slide (lengthening mechanism) Mainly cylindrical bore Narrow bore Cup mouthpiece Slide trumpets Intermediate mouthpiece Slide trombones

Figure 2.3: Carse's 1939 classification.

Carl Schafhäutl (1854) introduced the concepts of 'whole-tube' and 'half-tube' brass

instruments, the former being able to sound the pedal notes and the latter only the octave

of the pedal note and higher members of the series of natural notes. This criterion

21 depends, however, to a large extent on the abilities of individual players, and is not strictly related to musical practice. For example, the pedal notes of bugles and other soprano brass instruments may be able to be sounded, but they are not much required in the usual musical repertoire.

Nicholas Bessaraboff (1941) in his catalogue of musical instruments in the Boston

Museum of Fine Arts collection which includes much of Canon Galpin's Collection, gives considerable attention to the taxonomic problems of brasswinds. Bessaraboff was an engineer by training, and was perceptive about the nature and roles of brass instruments.

He realises the limitations of the 'whole-tube' and 'half-tube' concepts, but retains them

as a tertiary principle of division. A further failure of the 'whole-tube' and 'half-tube'

division which he recognised is that a french horn crooked in 12-ft F or lower cannot

readily sound the pedal but a french horn crooked in 11-ft G or higher can, so this

principle of division separates two very closely related instruments. Worse still, a tenor

trombone in position 1, 2 or 3 can sound the pedal but a tenor trombone in position 4, 5,

7 6 or cannot, so this instrument changes its class in the course of being played. (Players

of modern wide-bore trombones, it should be mentioned, can and do play pedals in all

positions, and even notes an octave below the pedal as 'privileged notes' on occasion.)

In Bessaraboff's classification [Figure 2.4], the primary principle of division is into

conical and cylindrical instruments; his secondary principle is into 'two-octave',

'three-octave' and 'four-octave' instruments, depending on the highest in the series of

natural notes available to the player. This also, of course, depends to some extent on

individual playing abilities. Sounding tessituras do not necessarily vary much in practice:

trumpets and french horns, for example, have been built in widely differing tube lengths

to play the same orchestral parts. With band instruments there has been a tendency for

instruments to be used with a 2^-octave range. Thus Bessaraboff's divisions cut across

families and even the identity of individual instruments.

22 A. Conical 1 Two-octave Shofar, Oliphant, Forester's horn Cornett, Serpent, Bass horn Key bugle, Ophicleide

2 Three-octave i With pedal tone Bugle, Lur, Alphorn ii Without pedal tone Cornet, Post-horn, Ballad horn

3 Four-octave i With pedal tone ii Without pedal tone Hunting horn (trompe), french horn

B. Cylindrical 1 Two-octave

2 Three-octave With pedal tone Trombone, Trumpet

Figure 2.4: Bessaraboff's 1941 classification.

Herbert Heyde (1975, 1987a) proposed a classification of instruments following Linnean

taxonomy. His scheme uses successive division into Komplex, Abteilung, Stamm, Bereich,

Ordnung, Gruppe, Familie, Gattungskries, Gattung, and Art; these levels being

subdivided or omitted as necessary. The principles of division for 'Labialinstrumente'

are:

Lengthening, shortening or no mechanism

Overall bore profile ('Kornoide' or 'Tromboide')

Bell shape (flared, funnel or 'hyperbolic')

Degree of cylindricality (weak or strong) Type of mechanism

The classification can be considered to be an outline only, since the terms are not

sufficiently well defined and not enough examples are given to apply the scheme without

establishing further rules. It has not been developed in Heyde's later work, discussed in

Section 2.21 below.

These broad-brush classifications have no precisely stated criteria or tests. The terms

'conical' and 'cylindrical' have intuitive meaning but are not satisfactorily defined.

Simple schemes may distinguish satisfactorily between the types of instrument in use

before the invention of the valve, but fail to give clear places to new types such as the

cornet, the bass tuba, the saxhorn, the bass trumpet and the Wagner tuba.

23 2.2 Heyde's bore characterization

The greatest body of detailed and consistent measurements so far made of brasswind has been for the series of catalogues by Herbert Heyde of the museums in Eisenach, Halle,

Leipzig and Frankfurt an der Oder (Heyde 1976, 1980a, 1980b, 1982, 1989). These

collections together hold most types of German brasswind from all periods, including

early examples by Nuremberg makers. As well as the lengths of the various conical,

cylindrical and flaring sections, Heyde has measured the bore diameter at certain points.

Among the measurements he gives are:

d = the minimum diameter, usually a short distance in from the mouthpiece

receiver

D = the bell diameter and

D3 = the tube diameter in the bell at the depth of one bell diameter.

Heyde has found that when expressed in terms of the units in use at the time and place of

the instrument's making, the measurements of pre-industrial instruments are frequently

simple numbers and the various lengths often turn out to be related by simple

proportions. For example, in a Viennese trombone of 1794 in Edinburgh University

Collection of Historic Musical Instruments (EUCHMI 3205) examined by Heyde in 1991,

the upper section is two-fifths of the total tube length, the slide section three-fifths. The

diameter of the cylindrical tubing is 5 Viennese Linien (five-twelfths of a Zoll or

Viennese inch). D3 is three-and-a-half times d. The end of the bell divides the overall

length by the golden section. These observations may have little acoustical significance,

but they could point us to the models, the design ideal, adopted by the makers.

Heyde designates the relative lengths of the conical, cylindrical and flaring sections of an

instrument the Anteilverhältnis or AV, and in his catalogues gives this as two or three

fractions whose sum is unity. The 1794 trombone for example, is seven-ninths cylindrical

plus two-ninths 'hyperbolic'. This proportion is often cited as the principal distinction

24 between a trombone and a trumpet. However, a simple plot of this ratio against nominal pitch for the trumpets and trombones described in Heyde's catalogues shows consistency. among Renaissance and baroque examples but reveals that both trumpets and trombones have evolved to contain less cylindrical tubing. The picture presented by valved instruments is not so simple. What was a valid distinction between, say, an alto

Renaissance trombone in ö^-ft Et and a natural trumpet in 6%-ft Eb is not so straightforward when we look at valved instruments. There are other limitations of this measurement as a guide. A trombone is still a trombone, whichever position the slide is in. As the slide is extended, however, the effect is to increase the proportion of cylindrical tubing. Similarly, operating the valves of a trumpet increases the proportion of cylindrical tubing, but does not make the instrument sound like an alto trombone.

Heyde has suggested that the ratio of D3 to d is particularly valuable. It is a measure of the increase in diameter over the tube length up to the start of the final flare. This ratio can be plotted against D for some different kinds of instrument. Considering instruments widely used before the invention of keys or valves, the different kinds occupy different areas (Figure 2.5). With specimens immediately prior to the general adoption of valves, an altered pattern appears (Figure 2.6). Considering instruments of the valve era (Figure

2.7) there is a proliferation of bore profile design made possible by the invention of the valve.

25 # 10

; Serpents

t *

-

- : D3 Mute d Tenor '. (

- cornetts cornett

-T0Z :'* \ Bass !'

' * sackbuts e .--!'.

e .' Natural '. ,*/ Tenor sackbuts Cornetts horns

- .8" ";. Alto

: .:' Sackbuts

.' '. . 6 i> *:

Natural trumpets 1 . t 0 D (mm) 300

Figure 2.5: P/o? ofD3/d against D (millimetres) for early instruments.

26 10 *

Ophicleides ..' §

Russian bassoons ..& bass horns

D3 d

' .'-'"" #-.' .' ** . Keyed (, e ### . '.._ '. bugles . .

-. f ,'

Hand horns & Keyed /' inventionshorns trumpets *

D 0 (mm) 300

Figure 2.6: P/of ofD3/d against D (millimetres) for pre-valve era instruments.

27 -

Helicons 10 -

Wagner ...

tubas ' - @ .' e

;

i

.' * t i Tubas

''--' * \ i * f /

* Euphoniums \ ,:"-.

Tenorhorns D3 *" * ' * ä

d Althorns ./-. # '. .#-..#

s : $ Flugelhorns... eea

. -i .'t ' : Valved .. -

' * ':-. orchestral # '' ' ;, \Cornets ' horns

Valved \ # ;'

trumpets ''' Trombones

1 < ~ r ~~i D 0 (mm) 300

Figure 2.7: Plot ofD3/d against D (millimetres) for valve era instruments.

28 Although prior to the invention of valves, signalling instruments such as posthorns could be made with any viable bore profile, instruments for musical purposes were restricted to those with usable high registers (french horns and natural or keyed trumpets) those with slides (necessarily with much cylindrical tubing), horns that could be hand-stopped (long and with a pronounced bell-flare) or those playable with finger-holes or keys (conical throughout). The valved versions of these are in Figure 2.7 along with cornets, tenorhorns, tubas etc.

However, the wide-bore trombone, the design introduced by Sattler and adopted by

Wagner, has moved some way from the Renaissance trombone. The main orchestral instalments have changed a considerably. At each point of change they have carried with them an established repertoire, and enough of their character for the new design to be recognised as being in the same class as the old. If, however, someone had invented the modern valved trumpet without the intermediate evolutionary steps, one feels it would hardly share the same name as the old natural trumpet.

Figure 2.7, of course, omits other designs made possible by the invention of valves such as the ballad horn, the cornophone, the tenor cor and many others.

29 Chapter 3

Purpose and expectations of taxonomy

3.1 Uses of Classification

Classification of instruments has been used for many purposes (Kartomi 1990). These can

include managing material in catalogues and text books, the main purpose of the systems discussed in Chapter 2 Section 2.1. A cultural or functional approach could be

appropriate for ethnographic purposes (Kartomi 1990, Devale 1990). A classification by

playing technique as proposed by Kvifte (1989) might be useful in pedagogic work.

Other purposes may require classifications that place emphasis on instruments' value,

their museum conservation requirements, their overall size or weight, or even their

sculptural qualities. The acoustical standpoint of this study is only one of many valid

approaches, and taxonomy as discussed below is only one purpose.

3.2 The TaxoEomic Problem

How many different types of brass instrument are there ? A typical nineteenth-century

maker's catalogue offers an impressive choice. For instance, Henry Distin's catalogue of

1857 lists 76 kinds [see Appendix A]; although some models are stated to be the same

instrument but in differently wrapped forms for cavalry use etc, it is not explicitly stated

that they are made using the same mandrels but differently bent afterwards. Similarly, the

Zimmermann catalogue of forty years later (Zimmermann 1899) includes 79 varieties of

brass instrument, counting in each case raw brass and silver-plated versions as the same

instrument. In preparing the first edition of the catalogue of the brass instruments in the

Edinburgh University Collection of Historic Musical Instruments (Lewis, Myers and

Parks 1992; Myers and Parks 1993; Myers and Parks 1994) it was found necessary to

use 185 type names. In several cases the same name can be applied to instruments that

are separated by an appreciable evolutionary distance, such as the varieties of tenor

trombone in B \>.

30 It is a valid question whether these hundreds of nominally different instruments really all

respond to the player and sound differently. After discussing valved brass instruments in

some detail, Carse (1939, p.315-6) states provocatively:

"No doubt other instruments, all in varying degree akin to the cornet, bugle or ophicleide, could be found if the records, catalogues and patent files of last century were searched and the museums ransacked. The collection of varied types could be enlarged by including some solitary instruments made only in one size and named according to register, kinship to type, or perhaps with the idea of perpetuating the

name of some optimistic inventor. Most of these would probably fail to establish a claim to any individual existence, for the field is limited, and there is not room for any great variety between the tone-quality of the cornet and that of the bugle, whether large or small; nor does the admixture of trumpet-, horn-, or trombone-bore, and their characteristic mouthpieces, supply sufficient variety to

provide very many new and clearly different tone-qualities. Many claimants to a separate existence within this restricted field have had to give up their pretended individuality and throw in their lot with the common types that are in use today. The flügelhorns and contralto saxhorns, the tenorhorns and baritones, the tubas and

bombardons may be differently named in each country, or may even be differently named in the same country, but their nomenclature is always more varied than their tone-qualities. Different widths of bore and diversity of mouthpiece-cup will give variety of tone-quality within a certain radius, but that radius is limited in extent. In the highest register, the field of brass instruments in high E flat, it matters little to

the hearer whether the instrument be a trumpet, cornet, saxhorn or flugelhorn. In the contralto or B flat register, there is room enough for the cornet and the flugelhorn, but hardly for anything in between the two. So it is in the tenor or E flat

register, the baritone and the bass registers; we can admit instruments which are large-sized cornets or large-sized bugles, but anything between these two makes the distinction too fine for ordinary ears, and therefore too fine for practical use ..."

Carse may be correct in suggesting that 'ordinary ears' can distinguish no more than two

differing types of brasswind in each register. A psycho-acoustic survey of the general

population to test this contention is outwith the scope of this study. There is no doubt that

trained musicians can recognise more than two types, if not as auditors then certainly as

performers. The continued production by individual manufacturers of a wide range of

instruments as well as differing models of the most popular instruments, nominally the

same type, is commercially justified only by purchasers perceiving differences.

The use of the word 'taxonomy' implies, of course, an analogy with biological

scholarship. In the field of natural history, taxonomists do not merely wish to classify

species for convenient handling of museum specimens and written descriptions, but also

31 to suggest the evolutionary relationships between species. With artefacts, as opposed to natural entities, there is no requirement for a new species to have evolved from a previous species: objects can be new inventions. However, completely new musical instruments are rare. Although some brasswind types such as the keyed bugle, cornet, ophicleide and tuba could have been claimed to be new, many developed while keeping the name and some of the character of a predecessor. The instruments designed for the purpose of performing, say, orchestral trumpet parts have been very varied, but each (if successful) has to do justice to the existing trumpet repertoire. The concepts of evolution and taxonomy are more than metaphor in this situation.

Taxonomy can be regarded as reflecting a classification by sound ideal. To belong to the same taxa, instruments should convert a similar output from a player into a similar input for a listener.

We should distinguish between classification and taxonomy for the purposes of this study.

There are many possible ways of classifying musical instruments; taxonomy is only one

form of classification.

3.3 Requirements of Taxonomy

We require principles of division consistent with acoustical theory, for economy

involving the minimum necessary number of parameters. The parameters should relate to

factors under the control of instrument makers (e.g. properties of their patterns and

mandrels), to the audible character of the instruments (e.g. the radiation characteristics of

the bell flare) and the feel to the player (e.g. the input impedances).

We would seek some quantity that is constant for all sizes of the family of saxhorns, for

instance, or for all trombones from soprano to contrabass. One would expect this quantity

to remain constant, or at least to change slowly and continuously with time, when an

instrument undergoes an 'evolutionary' change.

Although direct measurements of the acoustical behaviour of instruments, and indeed

playing them, are useful for testing taxonomic criteria, for historical purposes we require

32 criteria that can be applied to museum instruments. These are often fragile, damaged or

even incomplete, and thus not amenable to acoustical testing. A taxonomy would ideally

be applicable to surviving fragments, also to surviving mandrels and designs.

Although acoustically measured quantities may provide the key to consistent

characterization of instruments, direct physical measurement should be sufficient to

identify the maker's model. Manufacturers have offered ranges of instruments made to

certain specifications: it should be possible to ascertain these specifications in recent

history, and to reconstruct those of earlier periods. Performers have chosen certain

instruments for a particular repertoire; organological research aims to identify what

instruments have been used for the various parts in music of interest to us.

Such a measurement-based taxonomy should prove useful to instrument makers,

performing musicians, composers, organologists and museum curators.

33 Chapter 4

Factors and ranking of factors

4.1 Factors of possible taxonometric significance

As in other areas of musical acoustics, it is a delicate task to prioritise the many factors which can, in different circumstances, appear important to instrument makers, players and audiences. Some of these factors may be used to distinguish between good instruments and bad, but in attempting a rigorous taxonomy, it is a greater priority to distinguish, say, a bass trumpet from a valve trombone than to distinguish between a superb french horn and a poor one.

For nearly all brasswind, it is possible to consider the bore divided into mouthpiece, main length of the tube, and the bell. Very generally speaking, the mouthpiece shape governs the coupling with the player, the main body determines the playing pitch, and the

bell controls the radiation of sound and thus the character of what the listener hears. This

model is too simple for any detailed analysis, but may serve for taxonomic purposes.

The factors considered by various authors to affect the character of brasswinds include:

1. Bore profile (which can be varied in one instrument by use of slides, valves or

placing the hand in the bell). In Chapter 2, authors of published classification

schemes used various principles of division: cylindrical/conical; degree of flare in

bell; narrow/wide mouthpipe; whole tube / half tube; compass. These issues are

discussed in Chapters 6 and 8.

2. The profile of the mouthpiece proper to the instrument. In Chapter 2, authors of

published classification schemes distinguished between cupped and funnel cup

shapes. This is discussed in Chapter 7.

34 3. The of properties a particular player's lips and vocal tract. This is undoubtedly a

very significant factor in the character of brasswinds, but since performing

technique is entirely dependent on the player and completely independent of the

instrument, it cannot form part of a taxonomic scheme.

4. Wall thicknesses, particularly in the bell flare. This is considered to be a noticeable

factor by some players. The effect of wall thickness, particularly in the bell section

of trombones has been investigated by Smith (1981) and Watkinson and Bowsher

(1982) and is at most a second-order factor in determining tone quality. How the

brass is stress-relieved or coated (Pyle 1981) may make the difference between a

and good trumpet a bad, but not the difference between a trumpet and a horn.

5. Bends in the tubing. It would be useful to be able to take as a premise that the most

important determinant is the interior profile of mouthpiece and instrument bore

viewed if as the instrument were straightened out, so that the taxonomy did not

depend on the shape a tube is coiled in (the 'wrap'). Although from an ethnographic

and organological viewpoint the manner of folding, looping or coiling instruments

may be significant, it will be suggested in Chapter 5 that the wrap is of

second-order importance in the acoustical behaviour of instruments.

6. Bore perturbations (e.g. water-keys, dents, valve misalignments). Widholm (1989)

also discusses the effects of valve type on transitions between notes in legato

passages.

7. Temperature and humidity; thermal gradients.

8. The steady (or unsteady) flow of air through the instrument.

Several of these factors have been investigated in previous research and can be discounted

as forming primary principles of division in a taxonomy. Pratt & Bowsher (1978a)

ranked the factors determining the perceived tone quality of trombones as (1) the

instrument (2) the player and (3) the mouthpiece.

35 4.2 Impedance measurements on trombones

In order to test the hypothesis that the bore profile of the bell flare is of prime

importance, the acoustic impedance of a considerable number of trombones of different

sizes and models was investigated. This continued the work of Campbell (1987) and

relates directly to relevant work reported elsewhere (Backus 1976, Pratt & Bowsher

1978b, Pratt & Bowsher 1979, Causse et al. 1984). The trombone has been used with a

wider variety of mouthpiece than other brass instruments, ranging from the shallow cup

of the jazz era to the deep cone of the nineteenth-century French trombone; this makes it

particularly suitable for investigation.

The experimental part of this study has consisted of input impedance measurements of

trombones of various sizes (alto, tenor, bass and contrabass) and various styles and

periods (reproduction Renaissance models, baroque, nineteenth-century and modern). The

apparatus was that described by Campbell (1987), similarly calibrated. Peak envelopes

were similarly derived. The instruments measured included:

FT Alto Renaissance model trombone in E b (Tomes) bore 11 .Omm.

EUCHMI 2782 Alto trombone in Eb (Besson, London, c 1940) bore 11.5mm. SSC Tenor Renaissance model trombone in Bb (Tomes) bore 12.0mm. EUCHMI 3205 Tenor trombone in Bb (Huschauer, Vienna, 1794) bore 10.8mm.

EUCHMI 606 Tenor trombone in Bb (Courtois, Paris, c 1880) bore 11.2 - 11.5mm.

EUCHMI 214 Buccin trombone in Bb (probably France, c 1840) bore 11.1 - 11.4mm. CEB Tenor trombone in Bb (Boosey & Hawkes Imperial model) bore 12.4mm.

EUCHMI 3207 Tenor trombone in Bb (Schopper, Leipzig, c 1920) bore 13.0 - 13.3mm.

DMC Tenor trombone in Bb (King 2B model) bore 12.2 - 12.5mm. AM 159 Tenor trombone in Bb + F (King 3B model) bore 12.9mm. AM 171 Tenor trombone in Bb (Conn 8H model) bore 13.8mm.' AM 960 Bass Renaissance model trombone in G (Tomes) bore 12.0mm.

EUCHMI 3671 Bass trombone in G (Higham, Manchester, c 1935) bore 12.0mm. EUCHMI 3255 Bass trombone in G + D (Boosey & Hawkes wide bore model) bore 13.4mm.

AM 764 Bass Renaissance model trombone in Eb - D (Meinl) bore 13.0mm.

EUCHMI 3208 Contrabass trombone in Eb + Bb (Germany, c 1925) bore 13.5mm.

The input impedances were measured with each instrument equipped with an appropriate

mouthpiece and in several cases with alternative mouthpieces. It was found that the peak

envelope is seriously disturbed only if a mouthpiece of radically different volume is used.

A deep conical traditional French mouthpiece (virtually a scaled-up french horn

mouthpiece) gave a peak envelope differing little from that given by a shallow jazz era

36 mouthpiece [Figure 4.1]. Campbell (1987) discussed the effect of using a reproduction

Renaissance model trombone mouthpiece of much smaller cup volume.

100

: z (Mß) 3

X it VY^ \K > 10: \>

:

a P O

b n is

c

t l ,i(M r * till

0.1 f (kHz)

(a) DD conical traditional French mouthpiece (b) O O Jazz era mouthpiece (c) modem American mouthpiece

Figure 4.1: Peak envelopes of Courtois narrow-hore trombone with (a) Courtois deep cone mouthpiece EUCHMI 3100, (b) Selmer 23Djazz mouthpiece EUCHMI 665, (c) Bach 6V2 AL mouthpiece of greater volume than (a) or (b), AM 189.

The tenor and bass Renaissance model trombones by Tomes are equipped with removable

tapered leadpipes. The tapered leadpipe is not an authentic feature of the Renaissance

sackbut, but this maker supplies them for present-day players who find the instruments

speak more readily when the leadpipe tapers as does that of the modern trombone. It was

found that the taper has the effect of levelling the peak envelope slightly, raising the

peaks of modes 3-7 and lowering the peaks of modes 8-12 [Figure 4.2].

37 100

z (Mil)

10 -

1 _

fa) D D without tapered leaclplpe fb) - with tapered leadplpe

Figure 4.2: Peak envelope of Tomes bass Renaissance model trombone in G (a) without tapered leadpipe and (b) with tapered leadpipe.

The effect of moving the slide on the trombone is more pronounced than the effects

discussed above. A slide shift of 500mm, increasing the tube length by lm, gives

approximately the player's sixth position on a B t> trombone (in practice, a trombonist

varies the position from one note in sixth position to another). The introduction of so

much extra cylindrical tubing into the instrument constitutes a drastic modification of

bore profile, which has the effect of lowering the peaks of the first six to eight modes

and raising the peaks of the higher modes; the use of the thumb valve lowering the

overall pitch by a perfect fourth has a comparable effect [Figure 4.3]. This effect can be

regarded as that of a formant at the resonant frequency of the mouthpiece; moving the

.slide lowers the frequencies of all the modes, the mouthpiece formant at constant

frequency subsequently enhancing peaks of higher mode number. Also, the increase in

the proportion of cylindrical tubing increases the frequency intervals between the lowest

modes. This is not so noticeable to the player because of the accompanying enhancement

of the higher mode peaks which can support co-operative regimes; for a trombone in

38 sixth position, the lowest three tones should be regarded as 'privileged' notes [Figure

4.4].

100 -

fa) D D Bb trombone, slide in fb) O O Bb trombone, slide extended 500mm (c) using F valve, slide in

Figure 4.3: Peak envelope of King 3B trombone with (a) slide in, (b) slide extended 500mm and (c) thumb valve used to put instrument into F.

39 1 5089 6972 2 3282 4495 3 3099 4288 4 2951 4083 5 2947 3970 6 2961 3958 7 2942 3975 8 2947 3988 9 2988 3947 10 2998 3979 11 2957 3972 12 2970 4012 13 2973 4010 14 4015 15 3970 16 3977 17 3972

Figure 4.4 Table of effective cone lengths (in millimetres) of trombone by Joseph Huschauer, Vienna, 1794 (a) slide in and (b) slide out 500mm.

The greatest and most irregular variations in peak envelope are found between trombones of different model, especially those of different bore size. The Tomes Eb alto

Renaissance model trombone has a similar envelope to that of the Besson alto trombone;

the King 2B tenor trombone has a similar envelope to that of the King 3B model; the

Tomes G bass renaissance model trombone has a similar envelope to that of the Higham

G bass trombone. The main traditional schools of trombone design, however, show

distinctive peak envelopes [Figure 4.5].

40 100 ~

z

(MO)

10

a o o

b o o

i -irr -T-rr- 0.1 f (kHz)

(a) ? D narrow bore traditional French trombone (b) O O medium-wide bore traditional German trombone (c) # wide bore modem American trombone

Figure 4.5: Peak envelopes of (a) Typical narrow-bore French trombone (Courtois), (b) Typical Sattler model German trombone with wide bore and bell (Schopper), (c) Typical modern wide-bore orchestral trombone (Conn 8H); all with appropriate mouthpiece and with slides in.

the Thus investigations of the input impedances of a varied sample of trombones suggest

hypothesis that the bore profile of the bell flare is a factor of great significance in

characterizing brass instruments: it will be discussed further in Chapter 6. Other features

also but such as the presence of a tapered leadpipe and the mouthpiece shape are factors,

second-order. The input impedance curve can act as a 'fingerprint' of instrument design,

the slide the if like slide and valve positions are compared. The effect of extending on

that of different trombone is pronounced, and can give a peak envelope similar to a

instrument with slide in closed position.

Compared with completely different instruments, the peak envelopes of the trombones

instrument with have much in common. Figure 4.6 shows the envelope for an a

41 pronounced conical bore. A study comparable with the above treatment of trombones was

made by Krüger (1983) for natural and valved trumpets.

100

Figure 4.6: Peak envelope of ophicleide in Bb (EUCHMI 2158) with mouthpiece by Higham (EUCHMI 2159), all keys closed except the lowest (the open-standing A key).

42 Chapter 5

Air column bends

5.1 Effects of tube bends

In order to compare and classify instruments, it would be helpful to be able to discount

the effects of the bends in the tube. The bows in trumpets and the coils in french horns

are sufficiently accounted for by the practicalities of holding and transporting the

instruments, and do not need to have any acoustical purpose.

In general, when faced with a historic brass instrument in a museum, it is necessary to

know how to measure round the bows, loops and other bends so that it can be usefully

compared with another instrument which might for example, have fewer, more gentle, or

differently spaced bends.

This raises two other questions: how, acoustically, does a bend affect the response of the

instrument, and how, practically, does bending a straight tube affect its length ?

Instrument makers have long been concerned to reduce the sharpness of bends in valve

pistons and rotors, an area currently being re-visited by trombone makers with

'open-wrap' Bb +F trombones and revivals of nineteenth-century concepts such as disc

valves and Blühmel's wide-rotor valves. In this chapter, the effects of tube bending are

assessed in practical terms, leaving until Chapter 6 the problems of measuring flaring

tubes and the acoustical effects of flare.

Different authors have assumed different answers to these questions. Most, in measuring

the sounding length of a wind instrument, calculate the path which follows the centre of

the bore: we might call this the 'mid-line' approach. Webb (1991), for practical

instrument-making purposes, has measured along the outer surface of the tube following

its outside extreme round bends. Albertson (1984) following a suggestion of Gary Karp

takes a more subtle approach by calculating the lengths of lines in the bore on both the

43 inside and the outside of the bend and then taking the geometric mean. One can also consider measuring the shortest path from one end of an instrument to the other: threading inelastic string through the instrument, pulling it tight, and measuring.

The acoustical theory has been presented by Keefe and Benade (1983), who also tested it by experiments using highly bent tubing (series of baritone horn tuning-slide bows joined end-to-end). Brindley (1983) also carried out practical tests. The effect of a bend in a tube is to reduce the wave impedance and to increase the phase velocity. The speed of sound is increased, so the result of the bend is to make the air column effectively shorter than its mid-line length. This effect is greater for higher frequencies, so the 'in-tuneness' of the air column's modes of vibration is potentially affected and hence the instrument's response to the player. The effect is, as one would expect, greater for more acute bends.

Keefe and Benade define a 'bend parameter' to measure the severity of a bend [Figure

5.1]. For a tube of radius r0 bent so that the 'mid-line' has a radius of curvature Ro, the bend parameter B is defined as

T

B = (5.1)

Figure 5.1: Bow of radius Ro in a tube of radius r0.

44 The bend parameter can be calculated for some instrument components:

French horn D crook: B = 0.06

French horn A crook: B = 0.11

Trumpet crook (described below): B = 0.16

Trumpet 2nd valve tuning-slide bow: B = 0.57

Baritone horn tuning-slide bow: B = 0.73 (Keefe and Benade's test specimen)

Ophicleide large bow: B = 0.76

Ei> bass tuning-slide with L.P. 'kink': B = 0.91

The shortening effect also depends on the position of the bent section in the whole tube.

However, the shortening effect is not large. Even for Keefe and Benade's experimental

highly curved tube, it was found that the effects of the curvature were less than the

effects of the rise in temperature caused by handling the tube.

For taxonomic purposes, therefore, the mid-line convention remains satisfactory. The

geometric mean calculation of Albertson and the 'shortest path' technique both

over-correct the very slight shortening of the path (or increase in the speed of sound)

round a bend.

5.2 Practical tests

In order to test further the practical effects of tube bending, some experiments were

carried out using a straight trumpet in 4 V^-ft Bb by Hawkes & Son (EUCHMI 877). This

particular instrument has a detachable central section stamped "Bb"; the model was quite

possibly originally provided with an alternative piece for A, but this specimen lacks this

'corps de rechange'. The Scottish brasswind specialist, Stewart Benzie, was

commissioned to make two new sections with matching internal diameter and the correct

external diameters for fitting into the instrument. Various tests were carried out to see if

they could be distinguished - both by laboratory measurements of acoustic impedance and

also by playing tests. No difference could be detected, though it was possible to detect

small differences in response between either of the two new A sections and the trumpet

with the Bb section and the second valve operated, which gave approximately the same

45 tube length.

Mr Benzie was then asked to bend one of the tubes into a loop, using the conventional method of filling with metal, pitch (as in this case) or ice and bending round a form. The joint-fitting ends were removed while the bending took place, and carefully re-fitted afterwards in the same positions on the tube. The looped A section has two approximately semi-circular bows, and is the shape of a standard D crook for a trumpet in 6-ft F. Measurements on the looped corps de rechange showed that the external length of the tube on the outside had, at the bends, increased by 23%; the external length of the tube on the inside had, at the bends, decreased by 17%; and the length of the bent sections along the mid-line had increased by 3.5%. The length of tube actually bent was

200mm, the total length of instrument and mouthpiece some 1500mm, so the overall

effect on the instrument of looping the crook was a lengthening of the air column by

0.45%, equivalent to a flattening of 8 cents. Acoustic impedance tests showed no perceptible difference between the bent section and the unbent section, and playing tests

showed no significant difference: the shortening acoustical effect of bending was

cancelled out by the increase in tube length.

If a maker chooses to make a much-coiled instrument such as a post-horn or a trompe de

Lorraine by starting with a straight version and bending it, however, he could expect the

length to increase, although the effective acoustical length will not increase as much as

the mid-line length.

Mention could also be made of the tendency of the cross section in a bowed tube to

become slightly elliptical with bending. Since the internal volume of a bend does not

change, the cross-sectional area decreases slightly. This may also have an effect on the

acoustical length of the air column.

There are, of course, other ways of bending a tube. A century ago, the makers Silvani

and Smith (1895) developed a method for bending without heating or cooling the tube at

all, by inserting a flexible steel mandrel. Today, the large manufacturers make bows by

hydraulic expansion of the tube in a mould.

46 In the above we have been considering the 'steady state' behaviour of air columns with bends and finger-holes or other vents. The pitches of the notes that can be satisfactorily sustained on an instrument depend on the resonance frequencies of all the modes, not just the mode with frequency closest to the fundamental frequency of the note being played.

These pitches are relatively little affected by bends, but much affected by openings.

However, the response of an instrument to the player's attack, the 'starting transient' of a note, is another matter, as also is playing at such high volume that the wave propagation is non-linear, the 'tearing linen sheet' effect when a narrow-bore trombone is played loudly (Hirschberg et al. 1996). The effects of bends do not appear to have been investigated in the non-steady state case, but they may account for trombonists' problems with the common rotary valve.

47 Chapter 6

Considerations of the horn function

6.1 The horn function

Bell designs fall between two extremes, the virtually conical and the acutely flaring,

approached, for example, by the alphorn and the natural trumpet respectively. If a small

section is cut off the end of a conical bell, the pitch of the instrument is raised but the

tone quality is hardly affected; if a small section is cut off a bell that goes beyond an

acute flare and approaches a flat disk, such as a sousaphone's, the pitch is unaltered, the

only effect being to change very slightly the sound radiation properties of the bell.

For taxonomic purposes it might be desirable to find parameters for measuring bell flares

that relate to their acoustical function and which would place them on a scale ranging

between these two extreme cases. One well-established parameter is the Horn Function,

introduced by Benade and Jansson (1974) and further discussed by Amir et al (1993).

The horn function is defined as U in Equation 6.1 where r is the 'radius' of the tube - not

the geometric radius but the distance from mid-line to tube wall measured over the

surface of a wavefront, shown in Figure 6.1.

i#L (6.1) U(z) = r dz2

48 Figure 6.1: A spherical wavefront in a bell flare for a tube with a circular cross-section, like most brass instrument bells.

the In a region where the bore is not expanding too rapidly, a good approximation to value of the horn function is the product of the two curvatures which characterize an axially symmetrical flare given in Equation 6.2 where in Figure 6.2, KL is the reciprocal

of the longitudinal radius and KT is the reciprocal of the geometric radius of the tube

(Benade and Jansson 1974).

U KTKL (6.2)

49 Figure 6.2: The radii of curvature of an axially symmetrical horn.

Jansson and Benade This is an approximation assuming that the wavefronts are spherical;

brass instruments fall between and (1974) found that actual wavefronts in plane spherical . surfaces. The advantage of making the approximation in Equation 6.2 however is that it gives the horn function entirely in terms of the geometry of a bell flare. with The horn function varies along the length of a brass instrument, and for instruments

short distance before the end of the bell. For a developed flare there is a peak value a example, the bell of the trumpet by Joseph Huschauer of 1794 in the Edinburgh

University Collection of Historic Musical Instruments is shown (dashed line in

The horn function reaches a Figure 6.3) with a plot of its horn function (solid line). peak

also in the of 615 m2. Similarly, the bell of a trombone by Robert Schopper of c 1910,

Edinburgh University Collection of Historic Musical Instruments, is shown (dashed line

The horn function reaches a in Figure 6.4) with a plot of its horn function (solid line).

50 peak of 312 rrr

Trumpet in D (Huschauer)

600

CD (1) 500 D i CD CT3 03 400 c O rH

O 110 300 , 1 c O3 - C

- So C 200 CD o c

iOO

100 150 200 250 300 350 distance from bell end origin

Figure 6.3: Se// o/a natural trumpet (EUCHMI 3247), bore diameter in millimetres, with plot of horn function (rn2). The curves stop at the end of the bell: this is not the origin of co-ordinates, for reasons explained in Section 6.2.

Tenor trombone (Schopper)

600 - ,

l-tro lete

O3 \S0 rH T33

WO I1 O3 C

90 CD

4}, } r

50 100 150 200 250 300 350 distance from bell end origin

Figure 6.4: Bell of a trombone (EUCHMI 3207), bore diameter in millimetres, with plot of horn function (m2). The curves stop at the end of the bell: this is not the origin of co¬

ordinates, for reasons explained in Section 6.2.

51 A flare reflects sound waves of different frequency to a different extent. A low frequency wave is almost completely reflected in a region of instrument tube with a high value of the horn function, whereas a high-frequency wave is hardly affected by a flare. The effect is analogous to the potential barrier effect in quantum physics. The peak value of the horn function corresponds to a cut-offfrequency, given by

(6.3) cut-offfrequency = \ftj 2%

where c is the speed of sound in free air (typically 346 ms"1) and shown schematically in

Figure 6.5 (Fletcher and Rossing 1991). Sound waves of frequency higher than the

cut-off frequency are not reflected by the potential barrier; waves of lower frequency are

reflected rather than transmitted to a degree depending on how far they have to 'tunnel'

through the barrier and the height of the barrier. This reflection of waves at different

places is required in instruments such as trumpets and trombones with substantially

cylindrical sections of bore in order to bring the frequencies of the modes of vibration

into an approximation to a harmonic series, necessary for centred, in-tune notes.

400

High frequency

Cut-off frequency CD D 300

c o

200 o c Z5

C i_ o 100 sz

400 500 600 100 200 300 distance from bell end origin

Figure 6.5: Schematic diagram of the barrier effect of a horn function peak and the cut-offfrequency. For a peak value of horn function of 312 m2 as shown here, the cut-off frequency is 970 Hz.

52 6.2 Bessel horns

In order to compute the horn function (and thus the cut-off frequency), for actual historic

instruments, some mathematical model is needed in order to smooth out the local

irregularities common in old instruments and which would unduly affect the peak value

of the horn function. It has been suggested (Pyle 1975) that the bore profile of a flaring

bell can be modelled by a 'Bessel horn' for which the radius R of the horn at a distance z

from the origin of co-ordinates is given by

+ (6-4) R = RF1 az'a

where RF is a characteristic radius of the horn and a is a dimensionless 'flare parameter'.

(Typical values of a are 0.5 for a baroque trumpet, 1.0 for a modern trombone and 1.5

for a french horn.)

No actual brass instrument exactly follows the profile of a Bessel horn, since the

mandrels used by instrument makers have always been designed by trial and error, not by

plotting the curve of Bessel horn. Nevertheless, a Bessel horn can usually be found which

fits closely a portion of a real bell flare; for the purpose of this study, close fits have

been found for the portion of the bell flare containing high values of the horn function

and thus virtually all of the 'potential barrier'. Applying the approximation of

Equation 6.2 to the Bessel horn of Equation 6.4 gives the horn function in terms of the

characteristic radius and the flare parameter:

"*Vi ""' "'Z| r ' v"-5) 1 ' U(z) ~ z2

In practical terms, the computation of the horn function is achieved by taking

measurements of the bore diameter and depth at a series of different depths into the bell

of an instrument. The interior of a bell mouth is measured using a logarithmically graded

series of rod probe gauges, each made from perspex rod to a tolerance of 0.1mm. These

are attached in turn to a prepared rule allowing the depth of insertion to be read directly.

Where possible, areas of obvious denting are avoided. Normally, the maximum and

53 minimum depths of insertion of each rod gauge are made; these generally occur at orientations approximately 90 to each other. The average of the two depths is recorded as the axial distance from the bell end, and half the difference (plus a basic tolerance in the measurement of lmm) is recorded as the spread in the axial distance measurement.

An isolated high spread value can thus be interpreted as a discrepancy due to a minor dent or ripple in the bell wall surface, whereas consistently high spread values result

from an overall ellipticality (squashing) of the bore. If the bell rim itself is squashed, the

subsequent readings will have high spread values (unless the effect is cancelled out by

ellipticality in the opposite sense further into the bell mouth); any systematic error in

determining the position of the end of the bell is eliminated by the subsequent data

processing: a discussion of the accuracy of the process is given in Appendix B.

The results can be presented as a table with four columns. As an example, the bell flare

of the ex- Galpin trombone by Neuschel in the Kunsthistorisches Museum, Vienna

(extensively used as a model for reproductions) has the bell flare of Figure 6.6

Location Interior Axial Spread Tolerance diameter distance in in from axial interior bell end distance diameter Bell end 102.5 0 0.1 1.5 99.48 5 2 0.1 90.17 19 2 0.1 81.45 34 2 0.1 73.70 47 2 0.1 66.69 59 2 0.1 60.43 71 2 0.1 54.60 85 2 0.1 49.40 101 2 0.1 44.70 120 3 0.1 40.45 140.5 3.5 0.1 36.60 163 3 0.1 33.12 189 5 0.1 29.96 219 4 0.1 27.12 250 3 0.1 24.23 282.5 2.5 0.1 22.20 317 2 0.1 20.08 346 4 0.1 18.17 387 9 0.1 16.44 434 5 0.1

Figure 6.6: Bell flare measurements for trombone by J. Neuschel dated 1557 (WSAM 706), all in millimetres. With this measuring technique, the diameters are fixed and the depth of insertion is the dependent variable.

54 The overall diameter at the very end of the bell has been ignored in most of the horn function computations in this study, and only the measurements made by the gauges used, i.e. with the measurements starting at a depth of a few millimetres from the end of the bell. To each depth measurement has to be added a distance z0 since bell flares never extend to the origin of co-ordinates (at the asymptotic plane of the Bessel horn) where the diameter would be infinite. (Typical values of z0 are 10mm for a modern trumpet, 30mm

for a trombone and 100mm for a french horn.) The depths are then transformed

logarithmically, and the logarithms of the augmented depths plotted against the logarithms

of the diameters. It is necessary to adjust z0 until the logarithmic plot is as near as

possible a straight line for a substantial portion of the bell, an iterative process. The slope

and intercept are computed for the least-squares fit to this portion of the bell. Then the

two Bessel horn parameters can be taken from the slope and the intercept of the straight

line fitted to the transformed data. The least-squares curve fit will minimise the influence

of the various dents and squashes picked up by most old instruments.

A plot of ten or eleven appropriately spaced points can be sufficient to cover the region

where the horn function is significantly high. It is necessary to take at least twenty-two

bore measurements from an instrument to achieve a satisfactory fit of eleven points.

Figures 6.7 to 6.10 show two examples of the fit of a Bessel horn to actual bore profiles.

The bell of the Huschauer natural trumpet in D of 1794 in the Edinburgh University

Collection of Historic Musical Instruments (EUCHMI 3247) is closely fitted by a Bessel

horn of flare parameter 0.6983 and characteristic radius 49.35mm. The fit is good from

the end of the bell as far as the ball sleeve, 200mm from the bell end. Figures 6.7 and

6.8. show linear and logarithmic plots respectively of the actual bell measurements

(dotted line) and the Bessel horn (solid line).

55 Bessel horn: flare 0.6983, size 49.35

I 3 i i i i i i i i i i i i i i i r

350 B0.698f49 eu3247w

300

en rH

o 250 "O c cu

200

E O

CU Ü c CO +j> CO "-a loo

co rH X CO 50

I _L_I I I 1 I I I I I I L I I I I I I I I 0 20 40 60 80 100 120 140 Internal diameter

Figure 6.7: Bell of a natural trumpet (EUCHMI 3247) with plot offitting Bessel horn, axial distance and bore both in millimetres, linear co-ordinates.

56 Bessel horn: flare 0.6983, size 49.35

i i T T l r

B0.698f49 eu3247vi

10

O

"D C CD

_Q

E O

CD O C co -p V) rH TD

CO 10 iI X CO

10' Internal diameter

Bessel Figure 6.8: Bell of a natural trumpet (EUCHMI 3247) with plot offitting horn, axial distance and bore both in millimetres, logarithmic co-ordinates.

57 The Bessel horn flare parameter and characteristic radius are stated precisely at this stage; rounding of figures to reflect the accuracy of the measurement is done later (see

Appendix B).

The bell of the B \> valved trumpet by Vega is less closely fitted by a Bessel horn.

Nevertheless, a useful fit can be obtained over the region 15.5mm from the bell end to

148mm from the bell end by a Bessel horn of flare parameter 0.426 and characteristic

radius 41.69mm: Figures 6.9 and 6.10 show respectively the linear and logarithmic plots

of the actual bell measurements (dotted line) and the Bessel horn (solid line). The failure

of a Bessel horn to model the whole of a brass instrument's bell section is the reason that

the flare parameter and the characteristic radius cannot themselves be used to classify

instruments.

58 Bessel horn: flare 0.426, size 41.69

i r T7T T l r i i i 1 i i I i r

350 B0A26f42 eul701w

300 c "en rH L_ o 250 XD C CD

ii ii CD 200

O

CD O C CO

-O 100

f1 03

X CO 50

) i 0 20 40 60 80 100 120 140 internal diameter

with Bessel Figure 6.9: Bell of a modern trumpet (EUCHMI1701) plot offitting horn, axial distance and bore both in millimetres, linear co-ordinates.

59 Bessel horn: flare 0.426, size 41.69

B0A26f42 eul701x

o

c CD

CD JD

E O

CD Ü C CO -P

"Ö

2 |T X CG

10 internal diameter

with Bessel horn, Figure 6.10: Be// of a modern trumpet (EUCHMl 1701) plot offitting axial distance and bore both in millimetres, logarithmic co-ordinates.

60 The peak horn function and thus the cut-off frequency can then be calculated by inserting

the Bessel horn parameters numerically in the appropriate expressions. The position zPEAK

of the maximum value of the horn function is obtained by differentiating the right-hand

side of Equation 6.5 with respect to z which is then zero when

(6-6)

If this does not fall well within the portion of the bell used for curve-fitting, then a

the bell end has be sequence of measurements either nearer to or further away from to

used instead, and the process repeated. When the best-fit Bessel horn matching the

portion of the bell which comfortably includes zPEAK has been found, the maximum value

of the horn function is then given by

_2 ~*, 2 U (6.7) PEAK 2 ZPEAK

and include Appendices B and C show some of the results of these calculations a note on

the sensitivity to errors in measurement. These results are mostly for museum

The instruments; but some modern instruments have also been measured for comparison.

results presented in Appendices B and C are those from mainstream brasswind: they can

be used for comparison when investigating unusual or experimental instruments.

far is We can see, for example, that the highest cut-off frequency found so (not

the which have surprisingly) for a piccolo trumpet. For instruments such as alphorn

negligible bell flare, the sound is reflected by the abrupt termination rather than by any

flare. The value of the horn function is low overall (a maximum of only 7 m2 at the bell

end), and does not reach a peak before the distal termination (bell end) of the instrument.

It has generally been found that the instruments with acutely flaring bells, and thus those

with the highest horn function values, are those best modelled by Bessel horns.

Instruments with little flare such as alphorns or with a significant flare only at the very

end of the bell such as the Swedish kornett and most tubas are not well modelled by

61 Bessel horns.

Schnitzer trombone in For an instrument with a truncated flaring bell, such as the 1594 the Edinburgh University Collection, the horn function [solid line in Figure 6.10] does

the maximum is not quite reach what would, in a longer flare, be its peak value, and

This lower barrier anyway not as high as that of a modern tenor trombone. potential reflects high-pitch components less effectively, thus contributing to the Renaissance trombone's mellower sound.

Tenor trombone (Schnitzer, 1594)

600 -

CD -p CD 500 D CD E CO 03

400 i) C o

300 110 03 functi C L_ CD c 200 -P o C

iOO

0 50 100 150 200 250 300 350 distance from bell end origin

bore diameter in Figure 6.11: Bell of a Renaissance trombone (EUCHMI2695), millimetres, with plot of horn function (m2).

of The cut-off frequency is not found to have a precise value for recognised types

extent with those of other instrument, but a spread of values which overlaps to some taxonomic types of instrument [see Appendix C]. Thus it cannot be the sole criterion in a values of scheme. However, it can be one element: instruments with drastically differing

UpEAK cannot be expected to respond similarly to the player or sound the same to an

auditor.

maximum horn function The diameter (or cross sectional area) of the bell at the point of

and could value is sufficiently well-defined to be a taxonomic parameter [Appendix B],

62 brass instrument well give a more satisfactory measure of bore size at the distal end of a than the parameter D3 of Heyde (Chapter 2).

bell wall Modelling bell flares as Bessel horns can also allow the position of maximum

curvature to be computed. In terms of the characteristic radius RF and the dimensionless

from the 'flare parameter' a, the distance zMC of the point of maximum curvature

asymptotic plane is given by

(6.8) ZMC 2+a

By the definition of the horn function, this point is always nearer to the end of the bell

than the point of maximum horn function. Although it corresponds to a feature of a flare

has been which is visible to the eye, it has no known acoustical significance and not

systematically computed in this study.

63 Chapter 7

Considerations of the mouthpiece volume

and profile

No topic is discussed more by brass players than mouthpiece preference, especially by

trumpet and trombone players. However, the subtleties of mouthpiece design are features

of musical instruments which are of no interest to audiences or even to other musicians.

The lay person can appreciate the distinction between, say, a trumpet and a cornet, and

the difference between one model of mouthpiece and another can have an effect on the

sound comparable to the effect of such a change of instrument. In this chapter the

acoustical functions of the mouthpiece are briefly reviewed and parameters are suggested

which can be used to characterize mouthpieces, together with priorities in the use of these

parameters.

There are specialists in matching mouthpieces to players, in making tiny adjustments to

series. the design, or selecting a mouthpiece from a finely graded commercially-produced

These 'clinicians' satisfy a recognised need of student and other players. In this study,

however, answers are sought to questions such as whether particular mouthpiece

how associated with an instrument is likely ever to have been supplied with it or for it, or

to identify what possible instruments an unattached mouthpiece might have been made

for.

The problem is that to describe a mouthpiece fully requires a great number of

measurements. Even to specify a mouthpiece that performs the same acoustical function

(but does not necessarily look the same) requires many measurements. An analytical

approach to mouthpiece taxonomy is very much needed.

64 7.1 Methods of mouthpiece description

The exact shape of the mouthpiece is considered by most players of brass instruments to be critically important in performance, both for the tone quality achieved and for the

player's endurance. The design of the mouthpiece is often believed to be more important

than the design of some of the features of the instrument such as leadpipe taper or bell

flare. The study of brasswind mouthpieces has mostly been subjective in nature, based on

clinical experience in selecting mouthpieces matched to players' individual anatomies and

desired playing styles. Such an account of mouthpiece 'tailoring' criteria has been given

in publications and brochures by many mouthpiece manufacturers, for example Bach

(1952), Elliott (1995), Hall (1963), Himes (1982), Schilke (1952) and Stork and Stork

(1989); these writers discuss the relative benefits of different sizes of cup and bore and of

different profiles of rim and throat. The concepts introduced by most writers of such

mouthpiece lore do not stand up to scientific scrutiny. It has to be admitted, however,

that acoustical investigation has yet to yield an analysis of mouthpiece function which

reflects at all adequately the fine control of detail in design which makers exercise.

Specialist mouthpiece makers will offer a range of, say, a dozen slightly different cornet

in mouthpieces or a similar variety of trombone mouthpieces. Developments mouthpiece

design have been neglected by most historical organologists: most written histories of

instruments rarely go further than the most obvious differences such as those between

early and modern trumpet mouthpieces or between cornopean and modern cornet mouthpieces.

Previous accounts of systematic measurement of mouthpieces have been given for a wide

for range of instruments by Heyde (1980, pp. 196-204 and 1982, pp. 199-211), early

British trumpets by Halfpenny (1967, 1968, 1971) for modern trumpets and cornets by

Rohner(1952,1953).

Rohner (1952) suggested a standardised system of describing mouthpieces using seven

parameters, the measurements being graded and given code numbers (the T-V-D CRIB

code, Figure 7.1) which he proposed should be stamped on mouthpieces by

manufacturers.

65 T-THROAT- DIAMETER.-

OCt-*| 0 * 1 & 4 > 1 1 Ö 9

T- mow 29 I 26 zs 24 23 zz 21 20 ~~* "is*. V- VOLUME IS 16 17 18 21 22 23 14

p. IAME.TE* S3 6 41 11 63 64 >S* 66 67 68 _JC> C-tURV*HlE 9 10 II .13 14 15 16 1? Iß

a HIM u< 23 2.4 25 26 27 28 R"TWICKMtii 19 20 i I I? RßSlON 76 77 78 79 SO 'SI* 82. 83 84 85 111 1 & 2 3 4* 5 6 7 8 Bent Z^ I 26 I Z7 I i& I 25 I 24 I 23 I 2. I 21 I 20 I 18

* o< Swu Dn.U Site targe Mi atme and bei which an an equal Hunter mouthpieces.

V- Cup VOLUME D- Gip (inside rim) &IAMETER Sß 42 1 44

I I D 1 Is !* it 10

li n tt 2 2 s 1

14 i<; li. ir Iß 19 2,1 22 24 IS 24 27 t s t< t te & t I I I 145 SS 17. t les ras a Hi ZIS US 2 .58 [Sß ].6O [.61 1.62 [.63 | .66 | .67

Swell --Large Sm*U hiwidred+hs of sn inch.-- Urge

C- Rim CUfWATURE R - R.IM Thickness

SO

§20

t z 1 0 & li

0 \ to I U \il 113 [l4 \\S I t6 |(7 |t8 |!9 [20 | i 11 (FUt

Htm WeU r

wmfeers 0 -Hireu.gk ZZare I 64-fto$ ^ 1^cy mdlcste ö circle whose r&dius t% thai -m&.nv 64fhi. Thin- in fractions of a inch. Thick

I - Rim SMPRESSION B- BITE

TO &> 1 A I 4 1 30 i t| zs 20 -I1 1 lO 1 1. Z|3|4|5|6|7|8 .78 .75 .80 .81 Jbi .84 Sharp In&lde rim rmind.nesi Roondd.

Nu.vbrs 2 -through 8 are in 64thi; they indicate in hundredths of an Lnck - Wiie s ctrde whose raditt* liHietmsny &4-H1&.

Figure 7.1: T-V-D CRIB code of Rohner (1952, from The Instrumentalist 7 Nov-Dec 1952).

66 However, the range of graded measurements covered only trumpet and cornet

of the mouthpieces, and his code numbers were unfortunately not adopted by any manufacturers, who have continued to use their own inconsistent and idiosyncratic code numbers and letters. Moreover, his method of cup volume measurement (the average of

transferred to the cup depths at two fixed distances from the axis) cannot be mouthpieces for other sizes of instrument. Halfpenny used ten measurements to describe trumpet

mouthpieces, but conveyed information about cup shape, rim contour and 'bite' (meaning

the curvature of the edge between rim and cup) solely by illustration. Heyde provided a

in the useful diagram of 28 cup shapes, which enabled him to assign the mouthpieces

Leipzig University collection to 28 classes. He used six measurements, from which he

extracted ratios expressing cup conicity and cup depth as a proportion of overall length.

7.2 The acoustical functions of the brass instrument mouthpiece

that the A mouthpiece is necessary to provide support for the player's lips, so player can

that suitable area of make an air-tight seal when the lips are placed against it, and so a lip

is coupled with the instrument air-column. However, the acoustical functions are rather

is and more complex than this. A review of mouthpiece acoustics given by Campbell

Greated (1987).

The behaviour of the air in the mouthpiece cavity depends on the frequency of the

component of the sound being considered. Further, the function of the mouthpiece is not the bore of solely dependent on its own physical properties, but also depends on profile

in the rest of the instrument. To a first approximation, for low frequency waves a

conical-bore instrument such as an alphorn, the primary effect of the mouthpiece cavity

end. volume is to compensate for the fact that the cone is truncated at the narrow

its the so-called Helmholtz resonance The cavity itself has a resonance frequency of own,

the of the frequency. In the case of a cavity vented by a cylindrical tube, square

S of the and resonance frequency is proportional to the cross-sectional area cylinder

inversely proportional to the volume V of the cavity and the length L of the cylinder

(Fletcher and Rossing 1991)

67 S (7.1) f = J rex 2tt\ VL

where c is the speed of sound in free air.

Area S

Volume V

Figure 7.2: 27ze Helmholtz resonator, a simple mouthpiece model.

backbore of the When a mouthpiece is placed in the instrument for use, the mouthpiece

continues into and forms part of the bore of the instrument. In some instruments the taper

of the backbore is continued (after the inevitable small discontinuity) by the taper of the

the bore leadpipe. The resonance frequency of the cavity depends to some extent on

profile of the whole instrument. The acoustic impedance response of a detached

mouthpiece follows an approximately Gaussian curve as does a Helmholtz resonator

[Figure 7.3].

68 dB

to -

Hz

Besson Figure 7.3: Acoustic input impedance for a trombone mouthpiece by at 565 Hz, measured at 19 C using (EUCHMI 2830) with a peak or resonancefrequency the capillary input impedance method as described by Campbell (1987).

of the fundamental of the The resonance frequency is usually in the range frequencies

For near the resonance notes in the normal tessitura of the instrument. notes mouthpiece affects the frequency, the mouthpiece cavity boosts the response of the instrument and of the whole air column. A mouthpiece with exact positions of the resonance frequencies

of an instrument of being played a suitable resonance is essential for the design capable

of a Helmholtz well in tune. The parameters reflecting the behaviour a mouthpiece as

resonator are:

1. Cup volume 2. Minimum cross-sectional area 3. Length and shape of throat 4. Shape of backbore and instrument

69 7.3 The anatomy of the mouthpiece

fits into the instrument, An essential requirement of a mouthpiece is that it mechanically

is the minimum shank diameter. so the first (though not the most interesting) parameter

Interchangeability of mouthpieces is generally desirable; also the bore in the instrument kind just beyond the end of the mouthpiece shank is itself acoustically significant, so each diameters. There of instrument tends to have mouthpieces with a narrow range of shank

which to take cornet are exceptions, such as the few models of trumpet are designed

mouthpieces. Appendix D gives the minimum shank diameters for the 435 mouthpieces in

the Edinburgh University Collection (Myers and Parks 1996a and 1996b).

its influence on the The parameter most often cited is the cup diameter, because of great cornettino embouchure and the feel to the player. It varies from 12mm or less in limits dictated by the size mouthpieces to 30mm or more in the largest tuba mouthpieces, role of the human lip rather than by the nature of the instrument. Its taxonomic may, which therefore, be accomplished better by cup volume and shape, parameters might

and and are not constrained in any way by the have a greater effect on timbre response

size of the human lip.

further At least one manufacturer of mouthpieces (Denis Wick) uses a categorization,

medium the backbore shape. This is classified as either barrel, v-type, or open. Although of the instrument's shape of the backbore is important, continuing as it does the profile

leadpipe, its description has not formed part of this study.

of information on the nature of the A deficiency of existing museum catalogues is lack known association between mouthpiece and instrument. A trumpet mouthpiece may be to

have been used a have been supplied with the trumpet when new, may be known to by

been known to have been 'thrown in with' former player with the trumpet, or may have

This even when known to the catalogue the trumpet when it was last sold. information,

author, is rarely given.

70 7.4 Method of mouthpiece cup profile measurement

of all kinds for this The purpose of the measurements of brass instrument mouthpieces

study has been to generate data of sufficient quality to allow direct comparison of

acoustically significant parameters. The bite has been measured at its maximum curvature

has been measured to using a set of curvature gauges; the minimum radius of curvature

the bite the nearest 0.25 millimetres. For the purpose of cup profile measurement,

minimum radius cross-section is modelled as the quadrant of a circle having as radius the

of of curvature of the bite, and the inside cup diameter is measured by caliper at a depth

one bite radius [Figure 7.4].

minimum bore

'bite

minimum bore, Figure 7.4: Anatomy of a mouthpiece cross-section (solid line) showing bite radius and the inside bite as modelled by a quadrant (broken line), rbite, cup diameter.

For each mouthpiece studied, the minimum bore diameter and its position have been

a set has been measured . measured using an expanding bore gauge. The cup profile using

with of simple plug gauges, a series of aluminium cylinders logarithmically graded e13 e14 e15 (4.48) e34 (29.95) millimetres. The tolerance in diameters, (3.67), (4.06), ...

with of 0.2 mm. The diameter is 0.02 mm; the depth of insertion is measured a spread

table with two columns as in 7.5. gauge measurement can be presented as a Figure

71 Internal diameter in millimetres Axial distance from rim in millimetres

6.69 17.36 7.39 17.26 8.17 17.00 9.02 16.87 9.97 16.67 11.02 16.50 12.18 16.45 13.46 16.15 14.88 15.92 16.44 15.37 18.17 14.61 20.09 13.62 22.20 12.10 24.53 10.21 27.11 6.83 29.97 0.23

Figure 7.5 Cup profile of mouthpiece for serpent (probably France, c 1750; the EUCHMI 3304) as measured by plug gauges. With this measuring technique, variable. The tolerance in diameters are fixed and the depth of insertion is the dependent is less than internal diameter is 0.1 millimetre or less; the spread in axial distance not rounded 0.25 millimetres. Since the data are used in subsequent calculations, they are at this stage.

Scale 111

France, c 1750; Figure 7.6 Plot of cup profile of mouthpiece for serpent (probably minimum diameter measured an EUCHMI 3304) as measured by plug gauges. The by 17.35mm 1mm; the bite radius expanding bore gauge is 6.7mm 0.1mm at a depth of 0.75mm and the diameter at a as measured by a curvature gauge is 0.25mm, cup 29.5mm 0.1mm. depth of 0.75mm as measured by a caliper is

The data for a number of mouthpieces have been manipulated using a computer-aided

constructed which touches the drafting software (AutoCAD). For each, a cone has been

mouthpiece rim and throat. The point where this reference cone touches the rim is a

72 of bite radius. In small distance into the mouthpiece cup, a little less than a depth one

volume which lies outside cup-shaped mouthpieces, there is an annular part of the cup

For shape there is this cone; for a conical cup shape, there is no annulus. a cuspoidal cup inside at the of minimum bore; the cup walls lie no throat - the cone apex is placed point

a value. the reference cone and the annulus volume can be regarded as taking negative

and annulus. Figure 7.7: The three types of mouthpiece cup shape with reference cone

is as a measure of the The volume of the cone plus the annulus volume adopted

acoustically effective volume of the mouthpiece. The fact that the cone terminates at a

rather than on the face of the rim can be point a small distance into the mouthpiece cup

fact that a part of the volume regarded as an allowance made for the player's lips occupy varies of the mouthpiece. The protrusion of the lips into the mouthpiece considerably

embouchures for notes to embouchures for low from one player to another and from high

with confirms that notes; inspection of embouchure formation transparent mouthpieces is this allowance is of the right order of magnitude. That the apex of the cone not exactly

73 of minimum bore is often at the point of minimum bore reflects the fact that the position not well defined and can be at some distance from the throat.

7.5 Taxonomic parameters

measurements The construction of this cone and annulus readily gives two well-defined

that can be used in taxonomic studies:

('-2) + Volume annulus Cup volume = Volume of reference cone of

\ ( Volume of annulus in c, t J- \> Shape Quotient = 1 + \ Volume of reference cone)

minimum all directly These parameters, together with the cross-sectional area of bore, of known related to acoustical function, have been determined for a sample mouthpieces

instruments. The results are to be associated with and historically appropriate for specific

presented in Appendices E and F.

used for The results support the view that similar mouthpieces are in practice frequently reveal quite different instruments. For example, this study has been unable to any

distinction between mouthpieces for keyed bugles and mouthpieces for cornopeans.

Mouthpieces for baritone and for tenor trombone are almost completely overlapping be made between mouthpieces for categories. Similarly, no distinction can consistently

bass trombone and for euphonium.

of is well Whereas the function of the mouthpiece cup in supporting modes resonance

of the known and generally accepted, the 'popping frequency' (Benade 1973) mouthpiece

of the Helmholtz resonance frequency of in isolation can be only such a rough indication

than not to be misleading. the mouthpiece when in the instrument that it is more likely

surface such as the The pitch of the sound obtained by slapping the mouthpiece cup on a

the volume and throat cross-sectional area, palm of a hand does not only depend on cup

backbore. This can be tested by extending but also on the length and shape of the simply

74 can be the backbore with a shank or even a rolled slip of paper. The 'popping frequency'

and therefore in an considerably lowered by a small extension of the backbore, depends

When is unmeaningful way on the length and shape of the backbore. a mouthpiece placed into and forms of in the instrument for use, the backbore of the mouthpiece merges part continued the bore of the instrument. In most instruments the taper of the backbore is

(after the inevitable small discontinuity) by the taper of the leadpipe. The column of air whole of inside the backbore in isolation is not a critical feature of the system instrument,

mouthpiece and player.

will The mouthpiece backbore is not in general cylindrical, but the popping frequency

the is in in the clearly depend strongly on backbore length. When mouthpiece place

instrument, the calculation of the cavity resonance is not simple: the resonance frequency

the effective of the associated with the cup volume is substantially lowered, as length

and to some extent from backbore receives an additional contribution from the leadpipe

the main air-column. Causse, Kergomard and Lurton (1984) report such discrepancies

modes of resonance between popping frequency and the frequency of peak support for the

of various mouthpieces attached to cylindrical tubes.

be useful in A further parameter, which can be called the 'Resonance Factor', may

and the minimum cross-sectional area, taxonomy. This is derived from the cup volume

Helmholtz resonance but not related as they would be in calculating the frequency,

backbore: involving any measure of length of grain or

Minimum area of bore cross-section n As _, 1./.4). Resonance Factor = Cup volume

and values can conveniently be given This parameter has the dimensions of inverse length

an increase in the Resonance Factor in nr1. For a mouthpiece of given backbore length,

of correlation between will increase the resonance frequency. Appendix G shows a degree

Resonance Factor and normal playing tessitura of the associated instrument.

75 7.6 Measurements of resonance frequency

obtained In order to check the assumptions made above, the resonance frequency was directly for several mouthpieces using the capillary techniques of acoustical impedance

of were measurement described in Campbell (1987). If the actual backbore a mouthpiece

to the minimum bore replaced by a cylindrical tube of diameter equal mouthpiece's the diameter, the equivalent length LEC of this cylindrical tubing is that required to give

the volume as calculated same resonance frequency as the actual mouthpiece. Using cup

using equation 7.2 and direct measurement of the minimum bore, the equivalent length

7.1 LEC can be calculated using Equation [Equation 7.5]

c (Minimum area of bore cross-section^ ^ ^\ j I I " I^T^i EC y Cup volume J

end-correction has been The equivalent cylinder length is over-estimated because the

volume to ignored, and also because the experimental apparatus uses the complete cup makes allowance for the plane of the mouthpiece rim, whereas the calculated cup volume since the backbore is mostly the protrusion of the player's lips and is smaller. However, cross-sectional the actual backbore larger in cross-sectional area than the minimum area,

than the length. The results given length can be expected to be longer equivalent cylinder

at the backbore length, in Figure 7.8 show that LEC is of the same order of magnitude

though the correspondence is imperfect.

76 o so vi im © oo ^o 1 CN 00 in m rN t^ in SO OS oo in OO oo 5;! El 35, VI En" in VI VI SO u mi vi SO mi

Bac

._ H _ in in Os lO SO CN o. C3s" in 00 m m o SO ^^ ' O CN o Os in SO MM iCN VI --^ in SO VI "^ in in SO VI OS r<1 r<1 r<1 r<1 mi in 00 u uiv O"

11^ oo vi Os OS in , , vi jo 00 ^o oo in 00 so OS o O OO t ri CN ,1 OS oo in on CN SO (N OS SO CN ;so SO SO SO so ^ VI in VI VI VI in "^f Os 00 00 00 oo ! 'S, a

o o O io o o CN CN CN CN CN , t^ o ^. o in , o in o OS Os OS OS 195 00 CN 1984 1.19/e 11.19/e 11.19/e 11.19/e fri9/e |m.2O 1.19/e OS [cJ98; [Date 11.19 j1.20 : S |e.2O je o CJ o

iter /~^ P : -*. -^ ^. ( ( German} Place Spain Spain German} German} Manche; German" German^ Luton Paris Austria London London Britain Austria 00 London ,USA

i j l 1 I j 1 wkes

Cß I J a

c IN Q en 'S SO 1 cj 1 c er. Ivatio sson Imer ein iker o O 'e c G o Cß O CJ o O :3 Cß o tan CQ H s X CQ 00 !U pa 00 oa

rho o ! CO i i> c c c r c 3 o ( i CJ c o o O x> X x> x> ; hoi qui x> E S a 'S S CD u , CJ I : S tri he tro c c i 4m tro tro c sack x> s c Bass ast-horn rumpet rench enor romboni c enor 1 ass ugle ugle ugle ornet c I enor a CJ s H H H CQ 03 03 Oh 03 U 2 tu orIt f H ^<: ^CQ _ o SO SO Os =? Os sc es o SC oc m in es i© Os in CN oo SO m SO CN SO 'a\ SC o s v~ 00 so oc CN 00 CN OS oo m !os O o f SC SC> a CN m m 1 CN CN OS os OS SO oc c^ CN m SOjCN

_

- s - T^ D s D D 3 D D "Z D D EI W tu <^ PJ < PJ W PJ PJ ft1 P.i PJ

and Figure 7.8: The popping frequency (Hz), equivalent cylinder length (millimetres) measured hackbore length (millimetres) for some mouthpieces.

have been measured in A further source of error is that backbore lengths assuming many

backbore at the of maximum curvature at the cases that the cup ends and the begins point Parks the throat (further discussed in Myers and Parks 1996a or Myers and 1996b); better than few measured backbore lengths cannot necessarily be given to an accuracy a

millimetres.

77 also than a The effect of mouthpiece cup resonance on the sound quality is more complex

these are simple dependence on cup volume and throat cross-sectional area, though

factors. For low notes on an instrument, the support given by the mouthpiece cup

will indeed be For resonance for the upper harmonics in the sound spectrum significant. the high notes, however, the Helmholtz frequency will be not far removed from

fundamental frequency of the note being played; here the effect of the mouthpiece cup

of the and the to resonance is to support the production of the fundamental note, support

its overtones (harmonics) will be negligible. This is confirmed by subjective experience

brass instruments of the same basic as a listener: it is difficult to distinguish the sounds of

when size playing high notes; instruments show their own character much more playing

low notes.

The listener's perception of 'brightness of sound' also depends on the starting transient

and throat seems characteristics as well as on the spectrum of the sustained sound, shape

of likely to affect transients even if steady state sound is largely independent cup shape

detail. Some players consider that throat curvature affects the response of the system to

further research. the 'attack' of a note. This is an area very ripe for

78 Chapter 8

Considerations of mid-length bore

relating to In Chapters 6 and 7 methods of characterization of brasswind by parameters terminations of the bore the acoustically-important proximal (mouthpiece) and distal (bell)

alone do not unambiguously characterize all were discussed. However, these parameters

the overall of the instruments investigated, and it has been necessary to consider profile

amenable to instrument bores although the relevant acoustical theory is not as yielding

readily determinable parameters.

8.1 Data from pulse reflectometry

that substantial of the air column Many historic brass instruments are so constructed parts

Recent advances in the use of pulse reflectometry are inaccessible to direct measurement. 1996; Sharp, for bore reconstruction (Sharp, Myers, Parks and Campbell 1995; Sharp

and allowance for Myers and Campbell 1997) in particular compensation for losses tool for measurement of historic musical multiple reflections, have provided a useful

instruments.

effect on the The question of musically inconsequential leaks having a disproportionate The bandwidth of the pulse spectrum utilised bore reconstruction is a potential problem.

of in musical in reflectometry does not necessarily match the range frequencies employed

found that these techniques require instruments to be use of the instrument. It has been

so are clearly not applicable to leak-free to a higher degree than players require, they

for those that are (or can safely be made) many museum instruments. However, of the view of the effective leak-free, the resulting degree of accuracy, the completeness make the investment in interior, and the reduction in tedious direct physical measurement

pulse reflectance apparatus an attractive option.

79 have at one end a The bore profiles which have proved to be viable for brass instruments followed the narrowest part of mouthpiece, which may be cupped or funnel-shaped, by the the windway, the 'mouthpiece throat'. From the throat, the windway passes through

or valves, finally mouthpiece backbore, the mouthpipe or leadpipe, any tuning-slide The of coupling with the free air at the widest part of the tube, the bell. area

there can be some localised cross-section in most cases increases monotonically, although The traditional narrowing (e.g. at slides and at valves, or due to some slight damage). cross-section is bore cross-section is circular; where (rarely) a deliberately elliptical

in the the bore profile can for introduced, or in the slight deformation at bends tube,

that of tube of the same most purposes be considered to be equivalent to a cylindrical

cross-sectional area.

for Much of the sounding length of the instrument can, however, pose severe problems with coils. In Chapter 5 it direct physical measurement, particularly in instruments many

between instruments, a coiled was established that for the purposes of comparison

instrument with the same instrument can be treated as equivalent to a perfectly straight

the centre of the cross-sectional area at each point along a line drawn through geometric of actual instruments bore, the 'mid-line'. The bends encountered in the great majority

.will give rise to second-order discrepancies only.

reconstruction already in use in The extension of the pulse reflectance techniques for bore useful of the medical field (Marshall, 1990) to brass instruments is a potentially means

to investigating brass instruments for the purposes of classification. Existing applications Bowsher 1988, Bowsher musical instruments (Krüger 1979, Smith 1988, Watson and would be in 1989) have been directed to other purposes. A particular advantage coiled establishing the bore profile of instruments with substantial portions of tubing measurements of without the difficulties of making large numbers of precise physical

measurements could be made and bore curved tube: a smaller number of direct physical

reconstruction techniques used for interpolation.

80 8.2 Results for certain historical models of instrument

Rudall Carte without mouthpiece Figure 8.1 shows the bore profile of a Bb cornet by measured and the (EUCHMI 2988), without any valves operated. The directly profile initial is profile reconstructed from reflectance measurements are superimposed. The dip

the bore when a the mouthpiece receiver taper, and does not represent part of sounding bore mouthpiece is inserted. The small-scale fluctuations in the reconstructed are mostly

small discontinuities at the ends of accounted for by features such as water-keys and

the cross-sectional area tuning slides and at the valves; no attempt was made to measure

at these features physically.

Pulse reflectometer Direct measurement

14 -

12

E 10

1.4 0.8 1.0 1.2 0.2 0.4 0.6 Distance/m

with reconstruction obtained by Figure 8.1: Comparison of directly-measured bore profile pulse reflectometry.

scale for both axes it would The bore (y axis) is exaggerated here: drawn with the same

final flare of the bell (bore radius greater than 16mm) has been appear as Figure 8.2. The in flared omitted: bore reconstruction by pulse reflectometry is not reliable highly tubing

for the final and the techniques discussed in Chapter 6 are more appropriate plotting

section of the bore.

81 Courtois

1400 1r ir

1200

to CD

+ 1000

TD C CD

800

CD ID

E O 600

J L i i i I L i i i 1000 200 400 600 800 interior diameter

distance and bore Figure 8.2: Plot of Courtois cornet (EUCHMI 2560) to scale, axial both in millimetres.

82 that the bore through the Inspection of the central part of the bore in Figure 8.1 indicates

indeed the case: the Rudall Carte valves is not cylindrical, but expands gradually. This is with incremental bore cornet is the 'Patent Conical Bore' model (Tomes and Myers 1995) cross-section in the windways through the pistons and in the tuning-slide bows.

Carte 'Conical Bore' cornet Figure 8.3 shows a comparison of the Rudall 2704), all three valves of (EUCHMI 2988) with a standard cornet by Boosey (EUCHMI its both instruments operated. The Boosey cornet has at some time had playing pitch the lowered by extension of each leg of its tuning-slide; this accounts both for greater

overall length and for the two peaks around 0.5 metres from the mouthpipe.

Conical bore Standard bore

rH

15 2.0 0.5 1.0 Distance/m

Bore' cornet line] and Figure 8.3: Reconstructions of Rudall Carte 'Patent Conical [solid both with all three valves standard cornet by Boosey & Co [broken line], operated.

with bores The method of pulse reflectance is of potential value for coiled tubes

reconstruction of a inaccessible to direct measurement. Figure 8.4 shows the successful and coiled posthorn (EUCHMI 561). Only the mouthpipe (sliding for tuning purposes)

the bell flare could be reached for direct measurement.

83 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Distance/m

in Bb Morhange, Figure 8.4: Reconstruction of coiled posthorn or cornet simple by c 1895.

between instruments, bore reconstructions of For purposes of comparison of bore profile with corrections for attenuation offer a the accuracy now possible (see Appendix H)

the mid-line in coils are avoided, useful tool for taxonomy. The problems of measuring is ensures that the acoustically defined path since the use of sound waves in measurement what is measured.

8.3 Comparison of cornets and trumpets

1976 and It is commonly stated in the literature of musical instruments (Baines

a of the - it was virtually elsewhere) that the cornet was a development post-horn in Bate 1978) that since the post-horn with valves added. It is also stated (for example and the have evolved to development of the cornet in the mid 1820s, the cornet trumpet in the performance of become virtually indistinguishable. This has practical application

others: if it is desired to approach the original cornet parts by Berlioz, Elgar and if should be performed on modern originally intended sound, it is necessary to know they

cornets, modern trumpets, or if antique cornets are necessary.

84 'cornet simple' by Figure 8.5 shows the bore profile of a coiled posthorn or natural of the Kretzschmann, Strasbourg (EUCHMI 3052), the supposed predecessor cornet. It has tapered crooks.

1.2 1.4 1.6 1.8 0.2 0.4 0.6 0.8 1.0 Distance/m

1830. Figure 8.5: Reconstruction ofposthorn by Kretzschmann, c

85 made c 1845. The Figure 8.6 shows the bore profile of a cornopean - an English cornet

The Stölzel valves have acute bends in the crooks are virtually cylindrical in this model. windway, with irregularities in the bore radius of + lmm.

1.6 1.8 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Distance/m

Figure 8.6: Reconstruction of cornopean by Pace (EUCHMI 2485).

86 modern which have a fixed These early cornets can be compared with more cornets, 1930s mouthpipe (i.e., without crooks): Figure 8.7 shows an American cornet of the the (EUCHMI 3275). The windway is much smoother, but there are inevitable ripples at tuning-slides and valves.

16 I r

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

1935. Figure 8.7 : Reconstruction of cornet by York, c

87 of the same 4 to 4V ft tube length. A A further comparison can be made with trumpets of and Astronomy, modern trumpet by Amati (belonging to the Department Physics

University of Edinburgh) is shown in Figure 8.8.

~C0

XJ CO tr

1.6 1.8 0.2 0.4 0.6 0.8 1.0 1.2 Distance/m

Figure 8.8: Reconstruction of trumpet by Amati, c 1992.

to distinguish between trumpets and We can immediately discount any simple attempt

of 'conical' (meaning the bell section) to cornets by comparing the ratio of lengths tubing and the Amati 'cylindrical' tubing. The only distinction between the York cornet trumpet end of the windway, the so-called is in the steepness of the taper at the proximal for 'leadpipe'. This is reflected in the different external design of the mouthpieces 7. trumpets and cornets, discussed in Chapter 8.7 and 8.8; The distinction in leadpipe taper is not always as clear as between Figures

between the modern and the modern some instruments seem to come half-way trumpet cornet in bore profile, as in Figure 8.9.

' ' ID 1 ' ' 1 1 / - 14 / 12

10

13 8 y (XS / '- Av - 6 - ^_^>\j- rs*^.^

'

- 4

2 -

I L_J 1 1 1 I I I 1 1 1 j > 1 l j j 1.2 1.4 1.6 1.8 9)0 0.2 0.4 0.6 0.8 1.0 Distance/m

Figure 8.9: Reconstruction of cornet by Conn, 1924 (EUCHMI 3273).

Rudall Carte, based on a patent of 1903 Figure 8.1 showed a 'conical-bore' cornet by

bore cornets was taken out by E.A. (Klussman et al, 1903). Another patent for conical

Couturier in 1913 (Couturier, 1913) in which the concept of a smoothly tapered leadpipe taken the and expansion of the bore through the valve section passages was to greatest took out extent found in the course of this study [Figure 8.10]. (Couturier subsequently

89 including one for a slide trombone.) patents for other conical bore instruments,

1.8 1.0 1.2 1.4 1.6 0.2 0.4 0.6 0.8 Distance/m

1913 or soon after Figure 8.10a: Reconstruction of cornet by Couturier, (EUCHMI 3274).

16 r

12 b

10 00 D

co u

CD u. O

_J _J IJ- I- 1- 'J i_ t__ 0 -J i.O DO 02 04 0.6 0.8 axial distance (m)

1913 or soon after Figure 8.10b: Reconstruction of cornet by Couturier, (EUCHMI 3694).

90 'Patent Conical Bore' There have also been models of valve trumpet employing the

earlier this Rudall Carte, the 'Webster concept. One of these was introduced century by

endorses its design as Trumpet'. The subjective appraisal of this instrument by players

and 1995). The unusual design includes a being acceptable as a trumpet (Tomes Myers

cornet mouthpiece [Figure 8.11] with leadpipe so tapered that the instrument accepts a air column than usual. The profile of the valves placed closer to the proximal end of the

it has the horn function value the bell, however, is so acutely flared that highest peak for EUCHMI 3460) of all (1062 nr2 for EUCHMI 3460) and cut-off frequency (1789 Hz

the instruments in 4xh-ft B \> studied.

16

I

14

12

10*- e=

0)

8 -

"a a3

e -

1.2 1.4 1.8 0.4 0.6 0.8 1.0 Distance/m

Rudall Carte, 1926. Figure 8.11: Reconstruction of a Webster trumpet by

Bb and Hawkes Figure 8.12 shows the bore profile of a trumpet in by Boosey the standard modern Bb trumpet. The (EUCHMI 3212), not significantly different from

and cornet is made more apparent by relative similarity between a modern trumpet a 8.13]. comparison of their bore profiles with that of a flugelhom [Figure

91 CO D

"O CO

CD

o

axial distance (m)

1931. Figure 8.12: Reconstruction ofBb trumpet by Boosey & Hawkes, c

00

03

CD

O 3

8 10 0 2 0.4 0.6 0 axial distance (m)

3592). Figure 8.13: Reconstruction offlugelhorn by Besson, c 1900 (EUCHMI

92 the French model, developed by Paris The cornet widely used over a long period was

and still in use recently. This model makers such as Besson and Courtois circa 1850 quite

which inserted between the had detachable shanks or crooks of different length were different mouthpiece and the body of the instrument to put the instrument into keys.

Courtois with a shank for Bb. The Figure 8.14 shows a cornet by (EUCHMI 3710) rather increase in bore where the shank is not significantly tapered and there is a abrupt section. shank is inserted into the body of the instrument, in turn followed by a tapering

D F~H

03

CD

O n

axial distance (m)

Figure 8.14: Reconstruction of cornet with Bb shank (Courtois, 1862-71).

of the model sometimes Figure 8.15 shows the bore profile of an early British cornet

c 1840. This employed an known as a "cornopean" (EUCHMI 215) by Glen, Edinburgh, in the earlier form of valve (the Stölzel valve) which has noticeably more irregularities

The feature is the lack windway due to the abrupt bends in the valve passages. significant

of the crooks is of approximately the same radius as of any tapered leadpipe. The tubing is thus similar to the tubing of the body of the instrument. The overall topography very

that of the modern trumpet.

93 CO

03

(D

O .Q

08 10 0.2 04 06 axial distance (m)

in Bb. Figure 8.15: Reconstruction of a cornopean

the was of a longer It should be pointed out that in the mid-nineteenth century trumpet discussed above, and basic tube length, and thus is not comparable with the instruments

different so the that the mouthpieces for cornet and trumpet were of markedly designs,

have been at that similarity between trumpet and cornet now observed would not apparent

time.

'inside information' about Pulse reflectometry can thus quickly and accurately provide It is non-invasive brass instruments and reveal the hidden differences and similarities. a .

of instruments with a degree of technique and hence is very useful in the measurement

instruments. inaccessibility, and can be safely used on museum

94 8.4 Taxonomy of the proximal half of the air column

C and 41/2-ft A variety of instruments of approximately 1.25 metre tube length (4-ft Bb) the have been regularly used: bugles, cornets, flugelhorns, trumpets and others. Of from the others by their common types, bugles and flugelhorns are readily distinguished the Webster bell flare shapes, but modern Bb trumpets and cornets are not: apart from the Trumpet, the examples shown in Figures 8.1 to 8.10 do not differ markedly in profile B \> of the distal half of the air column, and the cut-off frequencies for modern trumpets for and cornets [Chapter 6] do not provide a clear distinction. Mouthpiece cup shapes but cornet and trumpet were distinct in the nineteenth century [Chapter 7], present-day

for cornet and It is mouthpieces are made with exactly the same cup shapes trumpet. the overall therefore useful to examine the bore profile of these instruments considering

topography of the tube.

air in tube with circular The longitudinal wave behaviour of a column of a symmetry

about the z axis is given by the "Webster" equation (8.1):

(8.1) lA(s) + k2p = 0 S dz{ dzj

and is the acoustic where S is the area of a wavefront, k is the wave number p pressure

bore 5 be taken as the (Fletcher and Rossing 1991). For a gently expanding profile, may

of this for the air column cross sectional area of the tube. The solution equation It contained by the actual instruments described above is beyond the scope of this study. the acoustical is clear, however, that the variation of 5 with z is of critical importance to

on these behaviour of a brass instrument, and an appropriate parameter dependent

corresponding to the quantities can be defined to facilitate quantitative comparisons qualitative comparisons of the instruments in the above discussions.

95 its minimum (which occurs at or near the If S^ is the cross-sectional area of the bore at

the bore at the mid-way mouthpiece receiver) and SM is the cross-sectional area of point dimensionless K between the two ends (ignoring local irregularities), then a parameter can be defined such that

(8.2) K =

K is little more. For For instruments conventionally regarded as cylindrical, unity or

is for a instruments conventionally regarded as conical, K significantly greater. Clearly of the whole bore profile full consideration of an instrument design, a detailed description and readily is needed; this parameter is a candidate for a simple, widely applicable classification of instrument models. determinable measure which can be useful in the

towards the end of the The mid-point of the air column occurs in cornets and trumpets of the bell flare. approximately cylindrical part of the tube, before the marked expansion

of basic tube length and comparable Figure 8.16 gives for some instruments comparable and normal tessitura the values of K derived from pulse reflectometry physical

8.5 measurements. (The parameter C is discussed in Section below.)

96 3jSnq p3Ä9^ L0(, na CITÜ 1 TJBIBH oe-* 890 or* 08T 3 luoiipSnjij Z6S na qa ß-y* uopuoq oo Tg uossag OL'O OL'Z 006T3 *99 na ZJBlSSlUO^i ÄU9AJ33 qa ß-y* S L90 Z9T 006T3 pduiTuj Bpjv na g e-yt ^* SUBd XBS PV IBituBii -6, OL'O 8T 0Z,8T3 01JBIJU03 ao ß-y* uoioqxBS 05 SUBd XBS PV qa L90 6ZT 0Z-8T 3 s,Ä3|ÄBg LL na ß-y* pmoo opsnooB uopuoq i3iqo^ qa 080 60T S98T 3 pdiutuj jsjsqsy^ 88*9 cm ß-y* nopuoq 3WB3 n^pn-a qa 6/.0 TOT 8Z6T 3 PUJ03 ez,re na ß-y* yBqJiig UU03 qa 080 TOT tZ6l 'pdiutux TTL ao ß-y* ppoui god uopuoq 3UB3 iiBpn^j qa 80 OOT SZ6T 3 PUJ03 TTZ; oe-* 3 spsstug XBS HO WO OOT 0*8T J3UJ03 OTL na ß-y* SUBd siownoo qa WO 861 TZ,-Z98T PU103 I asN uosssg qa ß-y* WO Z.61 L66T PUJ03 "XIO mi qae-y* uopuoq 080 881 S98T3 puioo sptjS 8T Id ß-y* yBi[5[|3 UU03 qa T80 S81 or9 PUJ03 SLl na 5[ioaI qg ß-y* 3 ubSihoij^ LL'O 081 S6T 3JOq-IB3lUO0 '13UI03 *69 na vsn jsunjnoo ^^^^qgj-ytj 6L0 SL'l 0Z6T3 pdratuj jgjsqg^ 09* na ß-y* uopuoq 3JJB3 IIBpn^ qa T80 L'l LZ61 3 pmo3 VOLZ na Ässoog qa ß-y* 3 uopuoq 03 ig 080 091 ZZ6T UJOIJ ISOd ZSO na oe-* 3 gjnoqsBJJS uuBuiqoszpj^j 080 08T 'Pduillfl 3A]BA 9^ ano li ß-y* PPOUI .UBippUBH, uopuoq qa T80 L'\ "^68^3 pduitux T Hd qa ß-y* s 3 Diiqnds^i vpvzj E^Yj 6L'O Z\ Z66T pduitux IOZ,T na S ß-y* uojsog B§3A qa LL'O Tl SS6T3 'uBsdoujoo SST na e ß-y* gdtdipnoui avojjbu Tiopuoq J31Z19J^ qa *Z/0 LZ'l Z*8T 3 pduiTUx ZTZ na uopuoq ss^AVBH 18 Ä3soog qae-y* LL'O 9Z1 T6T3 'suojsxd b PUJ03 69Z na ß-y* gdidqjnoui 9ptA\ 30UBJg qa 6L0 9Z1 0*8T3 iBflsgqoio ZOSZ na ß-y* pujoo uojsog Äquinf) Tg ||Bfj qa 890 *Z1 0Z.8T3 uB9domo3 8TZ na qa ß-y* 3 puB^äug 9L'O Z\ S*8T na X/Wip3lpS qae-y* plünux|66S 3 SatiqsSiAvpnq ZL'O OZl U6l pduiTUx 8*Z na 31S3UX BU§BJUO]/\I-JO0Ip\J qae-y* 080 *I1 OZ UB9dOUJIO3 STZ na o6 U9I9 qae-y* WO en 0*8T 3 qSitiquipg

pjauHU*sui 33BM a D 3|B(I models of instrument which it is Some of these (such as those by Rudall Carte) are rarer models, the values interesting to compare with common models. Considering only typical of K are as follows:

K = 1.13-1.23 Cornopean

K = 1.14-1.32 Valve trumpet

K= 1.98 - 2.00 Comet

= - 2.70 Flugelhorn K 2.62

Further This demonstrates the value of parameter K in distinguishing instrument types.

in 9. H gives a further listing of use of the parameter is made Chapter Appendix

instruments ranked by K.

8.5 Taxonomy, of the distal half of the air column

and which have similar bell profiles The capacity to distinguish between cornets trumpets of the K. The capacity to has been used in this study as a test of the usefulness parameter bore distinguish between different trombone models which have similar (i.e. cylindrical)

been used in this study as a profiles for the proximal half of the air column has similarly characterize the distal half of the air test of the usefulness of a parameter C used to

column.

division between the part of the For early instruments there is often a clear cylindrical

tube made on a cylindrical tubing and the expanding part, with one section of being However this is not the mandrel and the adjoining section made on a tapered mandrel.

instruments. To trombones of the case for nineteenth- and twentieth-century compare Anteilverhältnis nineteenth century with earlier models, it is not possible to use an

defined. There are [Chapter 2 Section 2.2] since this ratio is no longer clearly many

is not well- instruments for which the transition from cylindrical bore to expanding between defined, including all valve trombones. Gai (1984) attempted to distinguish

similar to a upright model valve trombones and 'flicorni tenore' (a brasswind type conical tube baritone saxhorn) by comparing the proportions of cylindrical tube,

98 conical tube expanding at a rate of expanding at a rate of approximately 0.5%, facilmente determinabile"). approximately 1.0%, and bell section ("forma geometrica non

wider use would be hampered by Gai's approach succeeded in its immediate aim, but for

rather than internal and (b) imprecision in determining (a) use of external diameters where the division between the sections of the windway occur.

and modern trombones is that the One of the most striking differences between early

ferrule at the start of the bell-pipe, tubing of the early trombone is cylindrical until the of the main slide ascending whereas the modern trombone tubing expands from the top bell bow is considered by bore. This expansion through the main tuning-slide at the intonation of the instrument. In the modern makers to be important for the response and

in the narrow-bore French model trombone, there is also a wider bore, but even this earlier is trombone of the nineteenth century and early twentieth century expansion

pronounced.

view to characterizing the bore profile in this area A parameter C can be defined with a and has already been of the instrument. The region of the bell has its own properties

worth while investigating the part of the bore just investigated, so it would seem to be bore of the main slide of the beyond the mid-point (which is near the top of the ascending of the overall of the air column up to trombone). C is defined as the proportion length

is double that at the mid-point. the point in the air column where the cross-sectional area

This proportion is necessarily between 0.5 and 1.0.

this in the windway can be For instruments measured by pulse reflectometry, point of the beyond the directly located from the reconstruction. Otherwise, for portions tubing

the rod measurements of the exterior diameter reach of, or outwith the range of, gauges,

insertion of the an estimate of the bell wall are made. At a point near the deepest gauges, valve thickness is made. A further estimate can often be made at a tuning-slide or interior diameters tube wall thicknesses are used to estimate the passage, and interpolated

at intermediate points.

of basic tube length and comparable Figure 8.17 gives for some instruments comparable in Section 8.4 above): normal tessitura the values of C (and also of K, discussed

99 JOU3X 1 Id lUBqgiH qa-6 9U0qUI0JJ 9A[BA 08813 J31S3qDUBJ/\[ 680 181 9pI|S '9U0qUI0Jl J0U3X SXd XBS 'PV qa-6 3 SUBjJ 18 980 *01 0L81 9uoquiojj JOU9X 81* 91 gizdpq J9J11BS qa-6 n 1*81 JOU9X ZZl 3d 980 qa-6 9U0qUI0Jl 3-id SUBrf S9J3JJ SIO^JJTIO^) 901 *81 JOU9X 0Z na 80 qa-6 9UOqUIOIl BUU3IA JlSTlBUOSTlT-I 80 001 *6Z1 9U0qUI0Il JOU3X 909 na CTTT> T SpiiTKQ qay-6 3 3 14. t> ^ 01 0881 jousi SI'O 8Z. na 80 qs-6 JB3J 01 ipq 'auoquioji umiSpa jo 90UBJj 001 613 (l) JOU9X LfL na 80 qa-6 9U0qUI0Jl SUBJ sioynoQ ZOl 981 louai S'l'O 8Z. na 80 qay-6 luojj 01 ipq '9uoqujoii uitiiSpg jo 30UBJJ 001 613 (l) JOU3X Uli 3d 80 qa-6 9U0qUI0Jl SUBc[ AJBIBH 901 Z.81 jousx OiLl na OO 80 qay-6 auoqmoji uopuoq UOS 19 S3J[MBH 911 Z61 3 JOU9X * na 80 qafr6 9UOqUIOJi SIJBJ J35J3Olp9fa LO'l 01813( na *80 qa-6 uopuoq uossaa 601 0061 3 3d *80 3 -8 SUBd XBS PV 801 81 3 9ai[ba jou9x *6 Id <3 uiBqgiji 3 -8 auoquioji S 3 J9}S9XpUB]AI *80 TÖ1 981 auoquioji jou9X 9681 91 9ija qa-6 8991 gjgqujiijsi O 80 001 9A|BA"9 '9U0qUI0Jl 9A]B/^ \\L 3d S SUB(J XBS PV qa-6 in 0813 jousx 6681 Ol 80 qa-6 auoquioji U9qOJX>pi9U5lJBM qoBqu9qosg 80 901 96/1 9uoquiojj ssBqjou9X 61* 91 Sizdpq J9J1TBS [ qa -6 901 15?1j jou9X oai na 80 qajy>6j auoquioji 681 3 uopuoq 91 80 IVI 1 qälFö 9uoquiojijou9x|/,681 1 0ZX13 gj3qujtiM :Ma Z80 ZOl 3A|BA"9 '9U0qUI0Jl 9A|By\ lOZ XBS PV qa-6 3 180 6Z1 A981 9uoquioji J0U91 S'1'0 IIPll 9a ujtiigiaa USpSug UByV 3 -8 180 001 0*813 9uoquioji ssBq/JOU3x 80* aa3 SIJBJ sioyno3 qa"6 180 811 0613 gUtlBSOjJ 99UIJV ILYi na anSBJd IBuiBqos qa-6 180 0*1 08813 9UOqUIOJl JOU9X 69Z na jszjraqos qa-6 *61 gjaqujtijsi 180 001 H8 '9uoquioji JOU9x in jArv UU03 qa-6 ppoui 8Z/0 8Z1 8L61 9U0qUI0Jl JOU9X LOU na gizdpq J9ddoqos "a qa-6 6Z/0 11 01613 9uoquioji ssBqjousx dÖd A\f pzuaj qa-6 gizdpq jagjojqoBjsi oö & LL'O 001 00613 J0U9X /. na qa-6 9U0qUI0Jl fei AUBUIJ3O Ä5[siiBqDS{v guiqosjijAj 9//0 001 613 S luauijujsuj qajij luoM PU 6, 3JBQ LJ X which it is interesting to compare with Some of these are rarer models of instrument

models, the values of C are as follows: common models. Considering only typical

C = 0.76 - 0.79 German model trombones

C = 0.78 American trombones

C = 0.84 - 0.85 French trombones

- 0.88 C - 0.81 Early trombones

instrument models. Further This demonstrates the value of parameter C in distinguishing

in 9. I gives a further listing of use of the parameter is made Chapter Appendix

instruments ranked by C.

8.6 Taxonomy of the overall air column

minimum cross-sectional area, the The parameters defined above are derived from the and the of the point in cross-sectional area at the mid-point of the air column, position

the latter. the air column where the cross-sectional area is double

is the area of the bell mouth. The final (and maximum) cross-sectional area of the bore

on two This, however, has to be discounted as a taxonomically significant parameter with substantial flares has grounds: firstly, the final portion of the bell of instruments bell is not critically little acoustical significance (the exact diameter of a sousaphone

surfaces but are important); secondly, the wavefronts in flared bells are not plane and Jansson 1974). In the intermediate between plane and spherical surfaces (Benade such those used in defining portions of the tube which are locally close to cylindrical, as

the cross-sectional area of the tube. K and C, the area of a wavefront is effectively

the distal end of the tube which can be of value Determining a cross-sectional area near

cross-sectional areas is not For in comparisons with the minimum and mid-point easy.

has been to the horn function (using a this reason in this study more attention given of the windway. It spherical wavefront approximation) in characterizing the final portion value of the horn function is a is shown in Appendix B that the position of the maximum

of the and that the cross-sectional area at that well defined point near the distal end tube,

nevertheless this area cannot point can be computed to an acceptable accuracy: of the tube with little necessarily be usefully compared with the areas in the portions

101 flare.

102 Chapter 9

Synthesis of criteria

in and collections in which This chapter gives some case studies on instruments museums developed the capabilities and limitations of the methods of characterization previously

to the of making a detailed are tested. Some conclusions can be drawn as possibility discussed in Chapters 6, history of brasswind design presented in terms of the parameters of these 7 and 8, and the evolution of instrument design since 1750 in terms

characterization criteria is outlined.

9.1 Scaling of designs

such alto, tenor and bass When it is desired to make instruments in a range of sizes, as

baritone saxhorns, the maker needs to decide how trombones or soprano, alto, tenor and

the notes need to be scaled to give to scale the dimensions. The pitch centres of playable

needs to be scaled so that the correct pitch, so the effective cone length LEC

(9.1) LEC = EC 1f

For example, where/; is the frequency of the pedal note in the series of playable notes.

closed will have of the effective tube an alto trombone in E b with slide three-quarters

B with slide closed (the exact proportion may differ length of a tenor trombone in \> of This applies in slightly from 0.75 depending on considerations temperament).

comparable settings of slide or valves.

overall tube is scaled similarly, but effects of factors To a first approximation, the length

and bell flare on effective tube- such as bore diameter, mouthpiece cup volume properties

103 length will mean that the tube length is not necessarily scaled by such a simple formula.

In practice makers will have had to adjust the tube length of a prototype empirically. The other factors such as cross-sectional area of minimum bore and mid-length bore and the mouthpiece and bell flare parameters may also need to be scaled, but it is not necessarily to be expected that they will vary in simple proportion to effective tube length. The

factors discussed in Chapter 4 that are dependent on the player (lip and vocal tract) can

only be changed within limits. The range of frequencies used by the human ear for pitch

recognition do not change at all.

Extensive measurements of matched sets would be needed to establish scaling rules;

examples of sets of museum instruments intended to be a family by the maker are rare or

conjectural. Psychoacoustic assessment of the performance of different instruments, even

if sounded by artificial lips to remove variations due to human players, is beyond the

scope of this study, but would be of great value.

There is no reason why one type of instrument in (say) 9-ft B b should not sound

indistinguishably like a different type of instrument in 6-ft E \> with valves 1 and 3

operated or slide extended. For simplicity and consistency in making comparisons, the

measurements for this study involving tube length (those for calculating K and Q have

unless otherwise stated been made without any slides extended, keys opened or valves operated.

9.2 Case study: the saxhorn families

Adolphe Sax did a great service to taxonomy by marking many of his instruments with

their model name, and requiring other makers who produced saxhorns in the period

between the imposition of licensing in 1855 and the expiry of his patent in 1865 to do

likewise. Thus included in this study are a number of instruments marked "SAXHORN

BARYTON" or comparable name. Figure 9.1 gives values for the principal parameters

for such saxhorns, and other instruments which are indubitably saxhorns.

104 r- en 00 © CN j "* 00 On 00 NO © © ~n ON NO *-M © 11 CN On tf NO NO a

en 00 r1 in p-H rt 00 © ©' ON in 00 © On ON On ON © ON © T- I

NO NO en en NO 00 1 CN ^. <* m CN in NO NO in in r- NO NO NO NO NO NO NO NO © © © © ©' ©' © © ©' © ©' © ©

On NO On © © n ON NO en en 00 CN r-M 00 On ON en © en in 00 en en CN tt * r< CN m "*' in On no' ©

© © © © © © © © © © © © bor in © 00 00 © 00 "*. NO © © l> © rn no' in no' oo' ON CN NO 00 CN in lid CN CN CN en en

© NO 00 *< © © © © © n in o © © © © © i> in in in NO NO On in NO f 00 NO f 00 00 00 00 00 00 00 00 00 in 00 NO 00 On 00 NO 00 00 00 o Ü o o o o o o o o rt o O o ^

w t^ o> o>

in w to o> o> ^ xx O o in m ul m in I Cß m CO in in y m in 'C "C fH i-I -< y u< s- 'd S3 'C S3 S3 S3 Cß c4 cd S3 ca s 6. P P Ph Oh P Oh Ph P Ph P P

Cß C^ artoi

i Sax O ker Sax Ltrot Sax Sax Sax Sax Sax uiBq S3 Sax S3 j=! Gau o> JMal lAd. |Ad. lAd. |Ad. jAd. lAd. PQ Hig Ad. |Hig |Hig <

I

x> x> x> w pa pa pj f-1 x> x> x> x> U m g x> Cß Cß Cß V I c % cd g o o s S3 o j5 s g 1 M o> 9A1 j=1 X X X ä cü S3 o o X X m c c C tf) in S3 S3 O a sa: m 8 8 o o X X x> g +3 sa sa rano 1 1 or or itone itone itone horn horn J horn horn I S3 c 'S a. g a c iH i^ X X x> X o o c O o> S3 re re s: S3 S3 CO U O o H H pa pa pa pa OO 00 w H 00 00

NO in in en r- in CN CN r- H CN in NO _! On On T 00 00 ON n NO On ,t T( en © CN NO p-M NO CN 00 NO en NO NO 00 -H !-H CN X ^< en en CN en en CN CN CN en

PQ N oa o D pa D p P D D i-j O PC o pa P o W 1 W W W W

Figure 9.1: Mid-length bore (millimetres), parameters C and K, bore at position of maximum horn function (millimetres), and cut-offfrequency (Hz) for various saxhorns. Not all measurements were made for each instrument.

105 This table includes data on several early saxhorns of Adolphe Sax's own manufacture, some made under licence from Sax (Gautrot, Besancon, Fischer and A.C.) and, for comparison, some typical English instruments by Higham. The fact that there are two distinct saxhorn families is immediately obvious from the values of K: from soprano down to baritone the proximal half of the bore is of moderate conicity, for the bass and

contrabass it is markedly expanding. The parameter C remains low for all saxhorns, an

indication that the bore expands rapidly from the mid-length point. The mid-length bore

is wider and the parameter K is larger for the later instruments, indeed the proportions of

the Higham baritone approach those of the Fischer instrument (which is inscribed

"SAXHORN BASSE").

Given that there is considerable variety even in this small sample, it appears that

parameters C and K are reasonably consistent for the two families of saxhorn. A

considerably larger sample and a statistical analysis would be required to draw confident

conclusions about the scaling of mid-length bore diameter and peak value of the horn

function (or cut-off frequency) with tube length (or nominal pitch).

9.3 Case study, the trombone in different sizes

One matched set of trombones has been studied, the set dated 1814 of alto, tenor and

bass formerly belonging to Reginald Morley-Pegge now in the Bate Collection,

University of Oxford. In addition, a number of late nineteenth-century and early

twentieth-century narrow-bore trombones, all either French or on the French model, have

been measured. Figure 9.2 gives the parameter values for these two groups.

106 H8 '! 6Z/0 11 0611 S68I3 SUBd siopno3 qa-8i auoquiofl ssBqBiiuo3 frZ: 5ta

980 6L1 06ZI 006T 3 SUBd Äureq-anTAnoqiiji 3-9T suoqiuojj ssBqBJjuo3 Ölt I s 0001 SZOI OfrXT 006 T 3 uopuoq OS ^> S35[AVBH O-TT auoquioji ssBg ZOZ.Z na Jsod 08 0 911 '! ZLSl SUBd siojjnoQ O-IT suoqiuon ssBg 09 3d ft,.S SL'O 801 'H 06813 uopuoq uossag os-ii suoquioj) ssBg 6ie na

ZL6 I'80I 080 TOI nzi 08813 uopuoq ayBO iiBpn^ D-II apijs aiqnop 'auoquioii ssBg ^Ild AVf tS8 LLOl 08II 69813 SUBd siojjnoQ 9 -11 auoquioj} sseg I8S na 80 601 09 II 00613 uopnoq uossag qa-6 auoqraon louax I66Z na u 980T 668 S80 SOT OSTT 08813 SIJBd siopnoQ qa-6 auoquiofl jousx 909 na ^ 8 0 ZYl SVU 6813 uopuc] 33Bd H'9 qa-6 auoquiojj louax \OLLl na 180 811 OVU 06 T 3 SUBd sioyno3 qa-6 auoquioij ssBq/ious^ 8017 ana S80 ZO'I OVU 981 SUBd siojjno3 qa-^j auoquiojj jouax LtL na 916 968 580 911 on i Z;6I3 uopuoq UOS Tg S3JIMBH qa-6 auoquiofl jouax OLZ na

066 806 oeii 0S8I 3 SIIBd siojjnoQ qaw-ViZ, auoquiojj o)iv |ui DOT

5 ?? ,** otn 9'69 09IT 611 iiopuoq uossaa j qa -2/i9 auoquiofl ojiy 58 3H1 A tOI 606 OSIT 0fr6I 3 uopuoq oo Tg uossag qa -s/i9 auoqiuojj O^? Z%LZ na Z80 11 O9'U 9-S88I uopuoq 03 ^ Ässoog qa-z/i9 auoquiojj ojjy 9?I na 0601 0061 3 uopuoq UOS 3? S35[MBJJ[ qa -z/i9 auoqraofl ojjv \Z9 na osn O'Z, 80 61 I 090T 08813 SUBd 9IIM / siopno3 qa -z/.9 auoquioij oj|y OVd AVf

UL 6811 tS'O OVU ' H8I ÄUBUU39 J -31 auoquiojj ssBg ZL ao ni\ fr'88 880 OT IT H8I ÄUBUIjgr) qa-6 auoquiojj jouaj[ UL ao Si 6I '89 0'6 t>181 ÄUBUIJ39 qa-2/i9 auoquiojj ojjv 0L ao I" yvzda J Regrettably the 1814 alto no longer has all its original slide tubing, so parameters C and

K cannot be obtained.

The average mid-length bore is for Eb altos 11.22mm, for Bb tenors 11.49mm, for G basses 12.24mm, for contrabasses 12.40mm. This suggests that there is no simple rule for scaling bore diameter for different sizes of instrument. Again, a larger sample might give a clearer picture.

9.4 Case study: the early history of the modern trombone

The period from 1750 to 1850 when the old form of trombone gave way to the standard

late-nineteenth century German and French models is not presented clearly in the

literature of the instrument. The values of the parameters discussed in Chapters 6 and 8

and bore size can be plotted against time in an attempt to chart the development of the

trombone in the period of transition (Figures 9.3, 9.4, and 9.5)

Bore (mm)

v<- L

\1 L

^-

P f P

w - A ft F u

w i 1 He

Figure 9.3: Mid-length bore diameter (millimetres) plotted against date for various

trombones. Places of manufacture are coded A = Austria, B = Belgium, E = England,

G = Germany (L = Leipzig, N = Nuremberg), U = U.S.A.).

108 c

oSg - q

oU - ^ f L A F

o^-

V u o$v- A

0-80- U

of A f

L 0-4

r~ r f

Figure 9.4: Parameter C plotted against date for various trombones. Places of

manufacture are coded A = Austria, B = Belgium, E = England, G = Germany (L

Leipzig, N = Nuremberg), U = U.S.A.).

fro

N

M.)

Figure 9.5: Maximum horn function value (m2) plotted against date for various

trombones. Places of manufacture are coded A = Austria, B = Belgium, E = England,

G = Germany (L = Leipzig, N = Nuremberg), U = U.S.A.).

109 Early and modern trombones are based on fairly well-established models. The period of transition, however, appears to be characterized by wide variation in design rather than an orderly process of evolution from old to new. The bore diameter (the parameter most familiar to players) increases slightly from the early trombone to the French model discussed in Section 9.3 above, and more markedly to the German and American models.

Parameter C and the cut-off frequency show wide variations before settling into recognisable ranges for French and German model instruments. A larger sample would allow conclusions to be drawn with more confidence; however, the use of parameter C and the cut-off frequency in addition to bore size already allows some interesting views to be given of this pilot sample.

9.5 Case study; valve trombone and bass trumpet

One of the least obvious distinctions between recognised instrument classes is that

between tenor valve trombone and bass valve trumpet, both being conventionally

regarded as 'cylindrical-bore' and both standing in 8-ft C or 9-ft B t>. The continuing

existence of both types and subjective experience attest to a perceptible difference in

response between tenor valve trombone and bass valve trumpet, though both have been

made in a variety of models. Baines (1976) recognises two models of bass trumpet, those

of the makers Moritz and Alexander, the latter now being the normal orchestral model.

The mid-length bore, parameters C and K, the bore at position of maximum horn

function, and the cut-off frequency for several specimens have been assembled in Figure

9.6.

Figure 9.6 [overleaf]: Mid-length bore (millimetres), parameters C and K, bore at position of maximum horn function (millimetres), and cut-offfrequency (Hz) for various bass trumpets and tenor valve trombones.

110 ui UOSS3Q qa-6 jspoui niSiidn 'auoquiofl 3Ajba I 3H1 0901 97.6 61 SUEd qa-6 SUOqUIOJJ 3AJBA T6I Id 680T 816 6T613 spsstug unjgaq qa-6 SUOqUIOZl 3A]BA SU mi 36 '6 00610 SUBd "J jÜBjBJJ 3 -8 auoquiojj sajba ZOZ.X ao KOI 17,01 61 SUEd qa-6 PPOUI 3piIS-3A{BA 'aUOqUIOJl JOU9X 01OZ oa eioi YZ6 611 iiossag qa-6 japoui 3AJBA-9 'auoquiojrj jouax I6Z na ZOOI Z/88 0T6TO spssma auoquiojj 3A{ba jouax id 680 181 T SI 0881 o J3JS9ipUBJ/\I uiBuSiH qa-6 3 anSBicj qa-6 SUtlESOd 33UUy zz-te na 8011 180 Of I ozn 0881 IBUIBqOS 'auoqmojj sajba 102 ^a 180 6Z1 OL'Zl Z.98I3 SUBd XBS 'PV qa-6 9AJBA-9 'auoqujojj sajba UL 3d 80 \Z\ ZYZl 0S8TO SUBd XBS W qa-6 3AJBA-9 o 3 -8 (S3AJBA uijjag ) auoquiojj sajba 17691 3d 001 8T6 t8"0 801 OOXT SS81 SUBJ XBS PV auoqiuoij sajba ioirax t6 Id t80 101 OSII 981 o isjsaipuepv uiBqSiH 3 -8 i

qa-6 pdujTU} ssBg LSZZ na 906 S'S6 80 061 OZZl 0E-636I yBqj[i3 UU03 ÄU3AJ93 qa-6 jaduitui ssBg 8S8Z na 8SII LOU ZL'O S91 06tT 00613 pduinj; ssBg 6ZZ na ZL'O 091 0ff[ 006 T 3 (i) ÄTIBUU99 qa-6 japuBxaiY 3 -8 jaduituj ssBg I OVM 6Z0I 888 Z80 11 oon S86I3 ZUIBp\[ ffoinj D JT Po Of these, the Alexander bass trumpet is distinguished by a higher value of parameter C than for typical German trombones; it is also normally used with a mouthpiece of smaller cup volume than average for a trombone. The Conn bass trumpet is built to receive a mouthpiece with a trumpet shank, hence the higher value of K. EUCHMI 229 and the

Cerveny bass trumpets appear to be Moritz model instruments, with both higher values of

K than most valve trombones and lower values of C. The valve trombones themselves show considerable variety in bore profile, some having low values of K like slide trombones, others being noticeably conical in the proximal half of the windway.

It is not possible to make a universal distinction between tenor valve trombones and bass valve trumpets, the differences between the various models of each being of the same order of magnitude as the differences between the two types.

9.6 Case study: Wagner tuba and cornophone

Given the historic use of cornophones to play Wagner tuba parts, it is interesting to compare examples of the two instruments to see how they differ. The following table gives a comparison of a Wagner tuba in B b by Alexander, Mainz, c 1930 with a

cornophone basse in C by Besson, Paris, c 1890.

instrument Wagner Cornophone tuba basse

Diameter of mouthpiece receiver 8.3mm 8.5mm Minimum bore diameter 7.7mm 7.3mm Mid-length bore diameter 21.7mm 20.0mm Bore at position of maximum horn function 167mm 149mm Bell diameter 236mm 200mm

Tube length 2758mm 2471mm K 7.94 7.51 C 0.65 0.63 Maximum horn function value 161 nr2 233 m-2 Cut-off frequency 697 Hz 838 Hz

Figure 9.7: Comparison of a Wagner tuba in 9-fl Bb (EUCHMI 2515) with a cornophone basse in 8-fi C (EUCHMI 3758).

Ill Thus the bore profiles of the two instruments are remarkably similar for the proximal

65 % of the air column length. The bell flare of the cornophone is more acute than that of

the Wagner tuba: the maximum value of the horn function is higher and as a result the

cut-off frequency is 320 cents higher. Simple playing tests of the two instruments (the

comparison is facilitated by operating the 1st valve of the cornophone so that it sounds

the B \> series) confirm that the overall tone quality and response to the player is very

similar, but the cornophone is perceptibly brighter. In situations where French-model

instruments were being used orchestrally, the slightly brighter sound of the cornophone

might well have balanced better with the other wind instruments than the German-model

Wagner tuba would have done.

9.7 The evolution of instrument design since 1750

Given the complexity shown in Section 9.4 by the evolution of a single instrument, the

trombone, it is not to be expected that a simple picture can emerge for the evolution of

brasswind in general. Nevertheless an overview can be given, drawing data from

Appendices C, H, and I, which could be developed into a treatment comparable to that of

Benade (1994) for woodwinds. As we saw in Section 1.3, not only did the invention of

valves revolutionise horn and trumpet technique, but it also permitted the development of

new kinds of brass instrument.

The natural trumpet and the trombone before 1750 have no significant leadpipe taper and

with their considerable lengths of cylindrical tubing have values of K very little over 1

and high values of C, over 0.8. Trumpets may have tended to have a higher cut-off

frequency than trombones of the same nominal pitch, but the difference was probably

mostly in mouthpiece design. French horns with their approximately conical bore profile

for much of their length had values of K between 2 and 4.5, values of C between 0.7 and

0.8, and very low cut-off frequencies. The cornett and serpent had almost purely conical

bore profiles and no bell flare at all.

The use of keys for the keyed bugle and ophicleide allowed a 'conical' bore profile with

higher values of K and lower values of C. With valves, instrument makers had complete

freedom to introduce instruments with any bore profile that resulted in an instrument that

113 was acceptably in tune with itself. In the course of the nineteenth century the adoption of the valve led to a proliferation of viable bore profiles for acceptable brass instruments.

This variety was also exhibited in the trombone. A new instrument, the cornet, had fairly low values of both K and C; other new instruments such as the smaller saxhorns were characterized by very low values of K and C, a bore profile with a marked expansion around the mid-length point which was not known in any pre-nineteenth century brasswind. The larger saxhorns and the tuba were also radical developments, with lower values of K than the ophicleide.

The established repertoire for existing instrument types such as the horn and trumpet

required instrument designs capable of performing this repertoire, with sufficient

performance characteristics remaining intact through each design development. Thus

these instruments have changed gradually to meet the requirements for higher dynamic

.levels and performance safety. However, the largely new repertoire for the trombone and

the necessarily innovative repertoire for newly invented instruments gave rise to an

apparent chaos in brasswind design in the nineteenth century from which the present-day

instruments have emerged by a process of 'survival of the fittest'.

The parameters developed in this study would enable classification schemes to be created

to meet museum and other needs which could use well-defined categories based on

practicable (though labour-intensive) measurements. Figure 9.8 shows one possible

classification. However, the inventiveness of instrument makers has been such that no

taxonomic system is likely to present in a simple structure the full diversity of brasswind design.

114 1 < K < 1.5

1 > C > 0.8

V < 2500 natural, slide and early valve trumpets

2500 < V German model and modem trombones

0.8 > C > 0.5

V < 2500 cornopeans, modern valve trumpets

2500 < y ear/y and French model trombones

1.5 < K < 2.2

0.8 > C > 0.5

z>^ < 12.5 comets

12.5 < DTOd higher saxhorns

2.2 < K <4

0.8 > C > 0.7

Z, < 1500 flugelhoms

1500 < L /renc/z horns

2.5 < ^?

1 > C > 0.6

V = 4500

L < 1500

' Dmid < 20 cometts

20 < bugles

1500 < L

4500 < V lower saxhorns, tubas

0.6 > C > 0.5

L^ < 100 serpents

100 < f/p^ ophicleides

Figure 9.8: A classification scheme based on measurable parameters. K and C are as defined in Chapter 8, V is the mouthpiece cup volume as defined in Equation 7.2, Dmid is the bore diameter in millimetres at the point mid-way between the two ends of the overall

air column, L is the overall air column length in millimetres (without extending a slide, operating valves or opening tone-holes), and U^ is the maximum horn function value in m2 calculated as described in Chapter 6. This scheme is not suggestedfor use in any

situation - it is given to demonstrate feasibility.

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124 Publications

LEWIS, P., MYERS, A. and PARKS, R., 1992. Horns and bugles: catalogue of the

Collection Volume 2 Part H Fascicle i. Edinburgh: Edinburgh University Collection of

Historic Musical Instruments.

MYERS, A. and CAMPBELL, D.M., 1993. Approaches to an acoustic taxonomy of brass musical instruments. Proceedings of the Institute of Acoustics 15 (3), pp.697-704.

MYERS, A. and PARKS, R., 1993. Trumpets and trombones: catalogue of the

Collection Volume 2 Part H Fascicle Hi. Edinburgh: Edinburgh University Collection of

Historic Musical Instruments.

MYERS, A., 1994. Nominal pitch. FoMRHI Quarterly, April 1994, No 75, Comm.

1247, pp.24-25.

MYERS, A. and PARKS, R., 1994. Cornets and tubas: catalogue of the collection

Volume 2 Part H Fascicle ii. Edinburgh: Edinburgh University Collection of Historic

Musical Instruments.

MYERS, A. and PARKS, R., 1995. How to measure a horn. Galpin Society Journal,

XLVH, pp. 193-199.

TOMES, F. and MYERS, A., 1995. Rudall Carte's Patent Conical Bore Brasswind and

Webster Trumpets. Historic Brass Society Journal 7 pp. 107-122.

SHARP, D.B., MYERS, A., PARKS, R. and CAMPBELL, D.M., 1995. Bore

reconstruction by pulse reflectometry and its potential for the taxonomy of brass

instruments. In NEWMAN, M. ed., Proceedings of the 15th International Congress on

Acoustics, Trondheim, Norway, 26-30 June 1995, Trondheim: ICA '95, pp.481-484.

SHARP, D.B., CAMPBELL, D.M. and MYERS, A., 1995. Input impedance

measurements on wind instruments using pulse reflectometry. In Proceedings of the

125 International Symposium on Musical Acoustics, Le Normont, Dourdan, France, 2-6 July

1995. Societe Francaise d'Acoustique, pp.74-78. ,

MYERS, A. and PARKS, R., 1996a. Small mouthpieces for brasswind: catalogue of the

Collection Volume 2 Part H Fascicle iv. Edinburgh: Edinburgh University Collection of

Historic Musical Instruments.

MYERS, A. and PARKS, R., 1996b. Large mouthpieces for brasswind: catalogue of the

Collection Volume 2 Part H Fascicle v. Edinburgh: Edinburgh University Collection of

Historic Musical Instruments, 1996.

LEWIS, P., MYERS, A. and PARKS, R., 1997. Horns and bugles: catalogue of the

Collection Volume 2 Part H Fascicle i, 2nd edition. Edinburgh: Edinburgh University

Collection of Historic Musical Instruments.

MYERS, A., 1997a. How brass instruments work. In HERBERT, T. and WALLACE, J.

eds., The Cambridge Companion to Brass Instruments. Cambridge: CUP., pp. 19-23

MYERS, A., 1997b. The Development of Technology and Manufacture since 1800. In

HERBERT, T. and WALLACE, J. eds., The Cambridge Companion to Brass

Instruments. Cambridge: CUP., pp. 115-130.

MYERS, A., 1997c. The Horn function and its application to the taxonomy of brass

instruments. In CARTER, S. ed., Perspectives in Brass Scholarship: Proceedings of the

International Brass Symposium, Amherst, 1995. New York: Pendragon, 1997,

pp.239-262.

SHARP, D.B., MYERS, A. and D. CAMPBELL, D.M., 1997. Using pulse

reflectometry to compare the evolution of the cornet and the trumpet in the nineteenth

and 20th centuries. In MYERS, A., ed., Proceedings of the International Symposium on

Musical Acoustics, Edinburgh, 19-22 August 1997: Proceedings of the Institute of

Acoustics 19 (5), pp.541-548.

126 Appendix A

Brass Instruments sold by Henry Distin, 1857

This table lists the varieties of brass instrument offered by Henry Distin, maker of and dealer in military and brass band instruments in London, in 1857. The information is extracted from an illustrated trade catalogue in the National Library of Scotland.

Alto chromatic horn in B b Alto flügel horn in C, 3 valves Alto flügel horn in C, 4 valves Alto flügel horn in B b, 3 valves Alto flügel horn in B b, 4 valves Alto slide trombone in F Alto slide trombone in E b Alto trombone in F, 3 valves Alto trombone in E b, 3 valves Alto tuba in B b Appello trumpet in F, 3 valves Baritone chromatic horn in B b Baritone tuba in C, 3 valves Baritone tuba in C, 4 valves Baritone tuba in B b, 3 valves Bass euphonion in C, 4 valves Bass euphonion in B b, 4 valves Bass piston trombone in G, 3 valves Bass slide trombone in G Bass slide trombone in F Bass trombone tuba in G, 3 valves Bass trombone tuba in F, 3 valves Bass tuba in C, 3 valves Bass tuba in C, 4 valves Bass tuba in B 3 valves , Bass tuba in B b, 4 valves Brussels model cornet in B b, 4 crooks Cavalry appello trumpet Cavalry trumpet Cologne model rotary cornet in B b, 4 crooks Contrabass in F, 4 valves Contrabass in E b, 3 valves Contrabass in E b, 4 valves Cornet, bell reversed, in B b, 4 crooks Distin's amateur cornet in Bb, 4 crooks Distin's improved portable field bugle in C Distin's military comet in Bb, 4 crooks

Distin's new cornet in Bb, 4 crooks

Distin's new model regulation bugle in C Distin's patent 6 keyed cylinder ophicleide in C

127 Distin's piccolo comet in C, 5 crooks Double-turned portable post horn in A French horn, 0 valves and 10 crooks French horn, 2 valves and 10 crooks French horn, 3 valves and 10 crooks Hunting horn (short) for the saddle Hunting horn (single turn) Mail horn in A Military french horn in G, 3 valves and 5 crooks Ophicleide in C, 13 keys Ophicleide in B b, 13 keys Ordinary valved cornet in B b, 4 crooks Perinet model cornet in B b, 4 crooks Perpendicular rotary cornet in B b, 4 crooks Piccolino soprano in A b, 4 valves Piccolo soprano in Eb Piccolo soprano cornet in Eb Portable alto chromatic horn in B b Post horn in A Soprano chromatic horn in E b Soprano chromatic tuba in E b Soprano flügel horn in E b Tenor chromatic horn in F Tenor chromatic horn in E b Tenor cylinder trombone in Bb, 3 valves Tenor flügel horn in F, 3 valves Tenor flügel horn in F, 4 valves Tenor slide trombone in C Tenor slide trombone in B b Tenor trombone tuba in C, 3 valves Tenor trombone tuba in B b, 3 valves Tenor piston tuba in B b, 3 valves Tenor tuba in F Tenor tuba in E b Trumpet in F, 3 valves Trumpet in E b, 3 valves

128 Appendix B

Instruments ranked by peak horn function value

This table lists the peak horn function values of selected instruments in several museums and private collections. The columns give data for:

Source and Specimen number

Full details of the sources of specimens are give in Appendix J.

Instrument, Nominal pitch, Maker, Place and Date

Specimens have been sought which are recognized types, typical of their place and period and

which have survived without significant modification. Further information on these instruments is

in many cases given in the catalogues of the respective museums and in other appendices to this

study.

Dpeak

These respectively are the position of the maximum horn function value relative to the distal end

of the instrument, and the diameter of the bell at the point of maximum horn function value, both

given in millimetres.

This is the maximum horn function value calculated as described in Chapter 6, given in nr2.

The principal sources of inaccuracy in arriving at these values are:

1. Errors in measurement of objects which can be deformed and damaged

2. Errors introduced by the selection of the portion of the bell flare to be modelled

3. Errors introduced by the selection of the distance Zq between the end of the bell and the

origin of co-ordinates

4. Errors arising from imperfect fit of a Bessel horn to the selected portion of the bore profile

129 The measurements of bell flares used as the basis for computations of horn function parameters are subject to some spread, especially when dealing with bells which have the deformations which are frequently found in historic instruments. The process of making a least-squares fit reduces the effect of these on the calculated values; however, it is necessary to state the expected accuracy of the resulting quantities. A further source of error is introduced by the process of selecting the portion of the flare to be modelled as a Bessel horn, so it is also necessary to calculate the variation which occurs if a different portion of the bell flare is selected (but one which also includes the peak of the horn function value). If the bore profile of the bell of an instrument were an exact Bessel horn, then selecting any portion of the flare would give the same results: the further a bell departs from a Bessel horn the more critical it becomes to model the portion of highest horn function value. For some instruments studied the value of chi-square ( x2) for the best fit of Bessel horn to eleven points exceeded a 10; no further attempt was made to compute the horn function for these instruments.

As an example of an instrument with a low maximum value of horn function, the bell flare of a

Wagner tuba in 9-ft Bb (EUCHMI 2515) can be modelled by a Bessel horn with characteristic

radius RF = 66.15mm and dimensionless 'flare parameter' a = 0.436; this Bessel horn has a

maximum horn function value of 161 nr2, equivalent to a cut-off frequency of 697 Hz (assuming

c = 345 ms1). The maximum horn function occurs at 39mm from the asymptotic plane, 21mm

from the actual end of the instrument. This is derived from a least-squares fit to eleven measured

points, the depths of insertion z of eleven rods measuring diameters ranging from 221.4mm down

to 81.45mm with the depths and diameters logarithmically transformed; the distance of the

asymptotic plane from the actual end of the instrument z0 is chosen to give a minimum value of x2,

in this case 2.515.

The depths of insertion are measured to the nearest lmm: if the depth of insertion of the first rod

(221.4mm) is taken as 3mm instead of the actual 2mm, it is found that the bell flare can be

modelled by a Bessel horn with characteristic radius RF = 65.81mm and dimensionless 'flare

parameter' a = 0.431; this Bessel horn has a maximum horn function value of 164 m~2, equivalent

to a cut-off frequency of 703 Hz. The maximum horn function occurs at 38mm from the

asymptotic plane, 21mm from the actual end of the instrument. The minimum value of x2 is now

2.521. Thus an error in the measurement of one point of lmm here increases the computed peak

value of the horn function by 1.55% and increases the computed cut-off frequency by 0.75% or

14 cents. The position of the peak relative to the end of the instrument is changed less than lmm.

If a different portion of the bell flare is modelled, using eleven rods measuring diameters ranging

130 from 200.3mm down to 73.70mm, it is found that the bell flare can be modelled by a Bessel horn with characteristic radius RF = 68.25mm and dimensionless 'flare parameter' a = 0.478; this

Bessel horn has a maximum horn function value of 147 m~2, equivalent to a cut-off frequency of

665 Hz. The maximum horn function occurs at 44mm from the asymptotic plane, 20mm from the actual end of the instrument. The minimum value of x2 is now 5.072. The portion of the bell flare modelled still includes the location of peak value of the horn function, but less of the flare immediately beyond. This change lowers the computed peak value of the horn function by 9.1% and lowers the computed cut-off frequency by 4.65% or 83 cents. The position of the peak relative to the end of the instrument is changed by very nearly lmm. For the purposes of this study, fits of Bessel horns to bell flares have been based on eleven measured points, with the greatest rod length (tube diameter) e (2.718) times the smallest length (diameter). The portion of

the flare modelled has been chosen so that the horn function value and the two ends is as far as

possible equal; in cases where the peak falls near the end of the bell this is not possible, and the

set of eleven measurements closest to the end of the bell has had to be used.

As an example of an instrument with a high maximum value of horn function, the bell flare of

"Handelian" trumpet in 41/2-ft Bb (CRB 326) can be modelled by a Bessel horn with characteristic

= has radius RF = 31.09mm and dimensionless 'flare parameter' a 0.5809; this Bessel hom a

maximum horn function value of 680 nr2, equivalent to a cut-off frequency of 1432 Hz. The

maximum horn function occurs at 24mm from the asymptotic plane, 12.5mm from the actual end

of the instrument. This is derived from a least-squares fit to eleven measured points, the depths of

insertion z of eleven rods measuring diameters ranging from 90.17mm down to 33.12mm with the

depths and diameters logarithmically transformed; The distance of the asymptotic plane from the

actual end of the instrument z0 is chosen to give a minimum value of x2, in this case 0.654.

If the depth of insertion of the third rod (73.70mm) is taken as 12.5mm instead of the actual

11.5mm, it is found that the bell flare can be modelled by a Bessel horn with characteristic radius

= maximum Rp = 31.13mm and dimensionless 'flare parameter' a 0.5840; this Bessel horn has a

horn function value of 678 nr2, equivalent to a cut-off frequency of 1430 Hz. The maximum hom

function occurs at 24.5mm from the asymptotic plane, 12.5mm from the actual end of the

instrument. The minimum value of x2 is now 1.346. Thus an error in the measurement of one

point of lmm here lowers the computed peak value of the horn function by 0.29% and lowers the

computed cut-off frequency by 0.15% or 2 cents. The position of the peak relative to the end of

the instrument is hardly changed.

If a different portion of the bell flare is modelled, using eleven rods measuring diameters ranging

131 from 99.48mm down to 81.45mm, it is found that the bell flare can be modelled by a Bessel horn with characteristic radius RF = 31.87mm and dimensionless 'flare parameter' a = 0.6112; this

Bessel horn has a maximum horn function value of 646 m~2, equivalent to a cut-off frequency of

1395 Hz. The maximum horn function occurs at 26mm from the asymptotic plane, 12mm from the actual end of the instrument. The minimum value of x2 is now 1.046. The portion of the bell flare modelled still includes the location of peak value of the horn function, but less of the flare immediately before. This change lowers the computed peak value of the horn function by 5.02% and lowers the computed cut-off frequency by 2.58% or 45 cents. The position of the peak relative to the end of the instrument is changed by less than 0.5mm.

The presence of small imprecisions in measurement thus limits the accuracy of the resulting horn

function values; however the cumulative effect of random imprecisions in measurements will tend

to be mitigated by the process of least-squares curve fitting. If (as an extreme example) the depths

of insertion of all the rods were over-estimated by lmm, then the best fit (lowest x2) would be

given by a Bessel horn with a distance of the asymptotic plane from the actual end of the

instrument z0 exactly lmm greater and there would be zero error in the horn function values

resulting from these over-estimates.

Without more detailed statistical analysis, it appears to be the case that the peak value of the horn

function can be computed to an accuracy of better than + 10% and the cut-off frequency can be

given to an accuracy 5% (in terms of pitch, better than one semitone).

The position of the peak horn function value relative to the end of the instrument (zPEAK - z0) shows

very little variation with error, and the diameter (or cross sectional area) of the bell at this point

could be considered as a candidate taxonomic parameter. In the example of the Wagner tuba

considered above, the maximum horn function occurs 21mm from the actual end of the

instrument. At this point, the cross-sectional area (computed from the best-fit Bessel horn) is

21650 mm2; since (zPEAK - z0) can be given to an accuracy better than + lmm, the cross-sectional

area of this gentle flare at this point can be given to an accuracy of better than + 2.3%.

In the example of the valved trumpet considered above, the maximum horn function occurs

12.5mm from the actual end of the instrument. At this point, the cross-sectional area (computed

from the best-fit Bessel horn) is 4000 mm2; again, since (zPEak - Zo) can be given to an accuracy

better than + lmm, the cross-sectional area of this more acute flare at this point can be given to

an accuracy of better than + 5 %.

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Instruments grouped by nominal pitch and ranked by cut-off frequency

This table lists the cut-off frequencies of selected instruments in several museums and private collections. The columns give data for:

Source and Specimen number

Full details of the sources of specimens are give in Appendix J.

Instrument, Nominal pitch, Maker, Place and Date

These are the same specimens as those in Appendix B. The nominal pitches for early instruments

may not be those that would have been used in the period of manufacture: they are ascribed to

specimens here solely to facilitate comparison with later instruments of similar tube length.

Similarly, french horns with crooks have been considered to be in 12-ft F purely for purposes of

comparison.

Cut-off frequency

This is derived directly from the peak horn function value assuming a speed of sound in free air of

345 ms'1 and is given in hertz. The accuracy of these results is treated in Appendix B.

141 Z8 613 uopuoT AVBUS ujon ajSng SZ9 ao t-98 Z.WI Sj9qxu3iri{s[ (pqosoiQ) P§BN 3 UJoqpSBf TZ6t?I r) t>06 611 uopuoq 3jiqA\9iqqa DWt ujoiiiagiiij S9Z 3>I 80I 0t8I 3 spsstug XBS no J9UJ03 IIZ 5ia 801 098I-SS81 SUBd )ojjm?9 ou-t luoqxBs 0JJBJJU03 SU ^a 8011 06813 uopuoq OQ y ^ssooa 3 8-f ujoq p9iq SL OZU 613 S3UU9T0U3JBA juaioy 3-t 9lduiIS )9UJ[03 Z9 ao II 0^81 3 uopuoq UIISIQ 3-t moqpSny id fUl 08613 ureds XnsuoH D-t 9|3nq guixiojBi^ na

j9duiaix 6W)I 0L6I3 ÄUBUU39 ITOH a-z/i frZ. aa 9 1901 0S9T3 UOBU3A U3I19J3 puouiqjBH Z;063 pduiaix na Lin tt6I3 uopuoq U0SS9Q G-z/, Z I9SI 61 aii-Vi ujoq jsOcj tz.

ouBjdos L6U OZ-813 SIJBJ xes PV qH-y, ujoqxBS 9I9X ao OUBjdOS ZZZl 09813 uopuoq uilsiQ H qa-y> J91UO0 LW ao J9UJ00 OUBidOS oa toei 0Z.81 3 BUU3IA uuBiuiqn qa-yi Z,86I j9dumn na SZ

OUBjdOS ILZl 0S813 sued XBS PV d- 39UIO0 I

jd9lUOI} I9I SE6I3 SIIBJ UOUS3tlO3 qa WÄZ OJOOOIJ 9QLL jaduiru} na L61Z 09613 3>}UOp\[ [ qa -Vi3 oiodoij 68S3

^a 6691 00613 (/,) 9DUBJj 3 -2 J9U40D OJOOOIJ LZ f/oinj qaifd: HiOM llOlUFäJISUf 1 Uli Z.66I uossag qa u-7ifr 13UJ03 1 asN jsduiaix Hd LU Z66I3 oiiqnds^; IJ03Z3 ilEuiy qa -7ifr l isod 9Z.II 611 (L) AlBUIiSQ qg -7. fr uioq psAjBA 8861 oa jadmiux na 96II IZ6I 3 gjnqsgiMptiq ÄAiipsqDg qg w-7ifr 66 :sg 0031 OZ.8I 3 SUBJ xb§ pv qgy-7.fr moqxBS oqBJjuo3 8Z ao OZI 61 i ZUIB]AI qa -7,fr 113UJO^ Z.09X frZI 813 uopuoq upsiQ qa -7 fr ppoui jBfnojp 'PUJ03 fr 3H1 Mf frH 813 SI-IBd sioyno3 qg -7. fr J3OJ03 333 frZI 061 uopuoq 3JJB3 HBpn-a qa -7. fr ppoui g3d 'J3UJ03 619 na aw frfrH 061 3 uopuoq 3PB3 HBptl^i qa-7ifr J31UO3 93d 691 na frZI OZ'ui U3p3U3UUI^ wsiqo^j qa -y.fr ujoqpSiqj 6LLZ ujoqpitqg Mf O8H fr8I ureqSmuiiig siuoqsiQ qa -7 fr Oäü 09frZ na I6H 88I-98l SUBJ sioyno3 qa -7fr J3UJ03 3uoqdouio3 LOH 0061 3 uopuoq uosssg qa -y.fr ojtjpujoo zs na IT 981 3 uopuoq 3WB3 ^> 3scry[ 'nBPn"H qa -7 fr PUJ03 pduiaix Z,Z na 8frI 613 BD[BAOISOip9Z3 qa -y.fr suoqdojpns 01 ^g 9I 611 SUBJ sjpns J qa -7 fr J3UJ03 J3UJ03 XIAI3 Mf ! or9 SUBcf ÄuiBq-sntAnoqiqx qa -y.fr J3>J30(J na Z8I ZZ6I 3 uopuoq 03 ig Ässoog qa -7,fr }3UiO3 frOZX jaduinjj 0I 3H1 Z8I 81 3 uopuoq WBÄy^ ig qauqpuBS qa -7fr 3AJBA 'isduitux ao fr8I 61 3 uopooq 3JJB3 neptiH qa -7 fr ppoui g3d UL 'jsduIIUJ 9Z 6I 6813 uopuoq jsiqo^j qg -7fr PPOUI ,UBippUBHv 3AJBA uBadoujoo or id ZOfrl 08I 3 uopuoq SDBd qg -7fr uoiqjv 0981 na 9IfrI 0981 3 uopuoq jrajqo^I qa -7 fr PUJ03 J3UJO0 3lJSnO3B S,^3];ÄBg Z,8I 3H1 9frl 9813 uopuoq -I3mo5[ qa-7fr jsoj U91 na frfrl 0061 3 qg -7 fr ujoq "S13 Mf OZ-frl 981 3 uopuoq J311OM qg -7fr }3UJ03 pduitlll MMl Mf 99I Z6I 3 uopuoq 31IB3 IIBPnH qg-7.fr J3JSq3yVV jsduiojj 09fr na 68Z.I LZ61 3 uopuoq 3JJB3 OBpn^i qg w-y.fr isjsqsy^ pdunm era ZOZ: 8Z6I 3 uopuoq 31JB3 HBpn^l qa-7.fr J3}sq3M 88fr9

WIM raoM ZLZl 08I 3 uopuoq jgjqo^j d-9 pduimj 9pns Z.62 na 6LZI 61 ui (,;,) puBiSug d -9 auoquiojj oj{v A002 9a 6z:i 0*813 uopuoq 30BJ d -9 pduitUl 9AJEA 9L 3H1 L9l 81 oopuoq SIXIBH J -9 jgduituj 9PIIS 0/-x ao 01*1 613 d"9 3uti|iui9p gjpdmojx OLZ 5ia 2*i 0*81 3 uopuoq aoBd d"9 jadimuj 9AJBA 062 3H1 ***i Z,8I-98I irapsaiQ J -9 9j3draoflsuopu9Aui 0Z,0* 91 *0I 8813 spssrug uoijiqBj^ ä -9 pdlURIJ SpiJS PUB 9AJBA I22 na 1 091 9813 SUBJ XBS 9suoqdjv d-9 pdUItU} 9AJBA %ZL 3d 1

001 613 uoXq SToqnQ 9 -yi ao 2101 613 SUBJ mjBf 9 ~yi pduituj P9JP3 \gi ao *20I 0281 SUEJ xnoFH n li-ViC sim\nojp 3U3duioix| 192 3d 0I 08613 BIUJ0JI1B3 spiO 9 WZA9 9jSnq uBDijgrav 8 aa jgduiiuj 0801 98l raag 9 ~yi p9Ä9^f 982 3H1 2221 613 SitioqsBflS uuBiuqoszjgj^i 9 "yi 9utii|xu9p gjpduiojx 8 :sa 2621 613 pjBqomo 9UtljTUI9p 9J}9duiOJX \L ao *0l 08613 vsn ajsbuXq 9 ~yi }9duian §uiqojBjAj L aa IIl 9813 uossgg 9 '% jadratuj 3AJBA 801 M 60l 613 9 -z/i pdraan p9Ä9^ 6 3H1 I68I O613 vsn ^|BJ3X9^I 9 -z/i igduituj ppij 86 na

OIL uopuoq 03 5 A9soog qa -yi* ujoq §BSJ3g aaa Avr 068 uopuoq 03 ig Ä9soog qa -Vi* ujoq §BSJ3g laa MI 6101 261 3 nopuoq UOS 3> S9>|AVB}h[ qa -y* uJoqpSnij 22 na 6201 023/611 SIJBd uous9no3 qa -yi* ujoq 9i§ng 862 3H1 'SUOJSld B 601 0*81 3 SUBd piABQ qa -yt* 9AJBA-2 J9UJO3 2l92 na 'SUOJSld B mi 0*813 U9B3 sm pu3]Ai qa -y.* 9AJBA-3 PUJO3 WSD Mr *2II 0261 3 ppjspia piABQ qa -y* ujoq oiqn^j *6I na 8211 813 uopuoq UIJSIQ qa -y<* ppoui ipq pgujnjdn 'j9UJ03 861 3H1 8911 0Z.81 3 SUBd XBS PV qa -y* ujoqxBS 0JIBJJU03 19* ao 33Bid juoiun.ijsiij 3JBJUBJ 309 na ton 03'ui (i) ÄUBIUI3O qa w-z/i9 jaduItUJ ÄJJBABQ t9t3 na nzi 55613 uopuoq JSuqoH qa -z/i9 3AJBA-2 'ujoq ;soj f86l oa lUl 61 ui (i) ÄUBUIJ3O qa -z/i9 suoquiojj oj|v DVd Ay 0531 08813 311M / siojjnoQ qa -z/i9 pduituj iBjnjBjsi 383 na 3l 8fui uopuoq sSuijpii^ qa y-z/i9 pduitui psiiOQ 001 DHl nzi 61 qa vt-zA9 pduitu} 083 na 09L13 uopuoq J3JSBUIJOH qa -z/i9 jBjnjBM 3II3IBAB0 3p ajpdUIOJX 5601 MV 81H or' SUBd U0US9TKQ qa-y.9 suoquioij ojiv 58 DHl oet-i 611 uopuoq uossag \j qa w-z/i9 3uoquio.il ojiv L\\ 01 pni mi Sizdisq I31WBS qa -y,9 3uoquioji ojiv 0L ao 651 H81 Areuurar) qa -z/!9 jsduiiuj jBjnjBM fr83 na 1851 813 (I) puBiSug qa -z/i9 3UnBSO(J \\Y 861 waoAv 9851 5

3üii|iui3p sjpduiojx t661 oa tLOl 06U=> gjmqsSnv jaujuiq (i) d -9 JOD JOU3X UOl wv 99 83613 uopuoq 03 ^> Äasooa d-9 ujoqBipis 6L9 01 9L S613 (^) U3qDJI>pi9UJ[JB]/\[ tpiliSpUtlyW d-9 JOO I0U3X 19 na S6L 56813 J31S3l|0UBp\[ uiBqSiH d-9 ouojiuioquiifa 5I DHl 6t8 611 90U3JOJJ luoquiia d-9 J0D03JSI 05 na LS8 0t8l3 SinoqsBJJS jsppuiqos d-9 UJOqXBS JOU3X Z,88 na 306 05813 (1) SUBd (i) XBS 'PV d-9 0}]B 3uoqdoujo3 050 na 9*6 5681 3 SUBJ uossaa d-9 ojjB 3i3ng nt na OfcOl 0161 3 uopuoq uos % s^MBH d-9 moqSiU3O5[ 1801 na ZL&\__j 85813 SUBfJ sioynoo d-9 100 J0U3X 191 DHl 8Z.01 09813 uopuoq UIISIQ d-9 ujoq isoj 8lO na ton 611 Sjgquinjsi ui3|jj:ntios d-9 pduItUj DIUOHUUIO m sv 0111 61UI SIJBd sÄBqqBq d-9 sjaduiojjsuopusAui 6381 01 9131 6Ll uii-iaa 3STIB.I}} d-9 Pduitui 3A]BA 8Z,l Id 03l 58813 SUBJ SI0JJT103 d-9 moqsiSng 63 DHl 61731 OLLI SuBMlia d-9 1 ffoWD 33BM J03U1JU)SU| IZL WVSM zu 81 U3PS3JQ ujoqjn}Bfv[ spduiojx WVSM ZZ8 I8I SjsqujtiN; jszjiuqos

\L\ 3H1 066 0S8I 3 SUEJ qa ij-ViL 9uoquiojj oiiv

dn-[pq 'joo jou9x MS 889 0I6I3 uopuoq 03 ^> Ägsoog qa "z/i9 ppoui SfO na LPL 30UBJJ qa -z/i9 JO01ABJ3 0Ü9 3d 06 0T8T 3 J35jOTp3l fj qa wzä9 suoqiuofl OJJB s X'O ]3duiai) ao l0I Z.99I uopuoq qa u-Vi9 jBjn]Bj\i oiiv Z8LZ na tOI Ot-61 3 uopuoq 03 i% uoss9g qa u-Vi9 guoquroj) S88I 91 8t-0l 8i3qiun{<[ qa y-s/i9 9uoquioji ojiv ZLIZ SV 8Z.0I 068 T 3 uojsog WM TW uojsog qa -Vi9 011B ojos pitlJJ JOU3X 16 3H1 Z.60I 0S8I 3 UHSTQ X / XBS PV qa -3/i9 UJOq JOU3X S69I 3d Z.TI 0S8I 3 SUBJ XBS PV qa -s/i9 UJOqXBS uaoqpgngf joit9X on lä STI oz:3/6n ÄU9AJ33 qa -E/i9 f/otnj J3>|BM[ juaiuaijsui 856 0061 3 §Tzdi3q jsSpjqoBN pzu3d qg y-6 auoquiojj ssBqiousx 1 dÖd 1 M 596 61 3 U3IM uuBraiqß qg y-6 aunBSOd -louax|661 |pMa9M 0Z.6 0161 3 gizdpq jsddoqos "a qa-6 suoquioij J0U3X j^03 L na 886 0Z.813 SUBd XBS PV qa-6 spip 'suoquiojj J0U3X Sid M 3001 0161 3 spssiug Xsj3d qa-6 jspoui 3AJBA-9 'auoquioji lousx 163 na 101 611 uosssg qs-6 PPOUI Spip-SAJBA 'SUOqUIOfl IOU3X 0103 93 8301 lL\ 3?AV jappuqosuiBqopq qa-6 SUIlBSOd -I0U3X 553 60T 611 UEJTJAJ qjo~a qa-6 suoquioji uooipH *1 3H1 0901 61 ui SIJBJ uossag qa-6 ppoui iqSudn 'suoquiojj 3A{ba 1 3H1 9801 0881 3 SUBJ sioiino3 qa-6 3UOqUIOJl JOU3X 909 na 680T 6T613 spssnjg utugsq qa-6 SUOqUIOJ} 3AH?A 161 M 8011 0881 3 3tl§BJd IBuiBqos qa-6 SUnBSOd 33UIJV ZZ,* na pdumji na 8511 00613 ÄU3AJ33 qa-6 ssBg 8583 SZ.ll 5*81 3Jd SIJBd S3JI3JJ sio}jno3 qa-6 suoquioij J0U3X 3531 3d LtZl 03Z.13 §j3quinjs[ 9qa qa-6 suoquiojj I0U3X Z.68I 91 *931 *18l ÄUBUIJ39 qa-6 suoquiojj J0U3X ML ao 95l 96Z.1 U3qDJI5pi3U^j:BpM q3Bqu3qosa qa-6 auoquiojj lousx 6681 91

*9 0*81 3 uiniSpg uspSug UBA 3 -8 suoquioj} JOU3J 'S'X'O 1103 9a **9 05813 SUBd pjBqomr) 3 -8 J00IABJ3 83 5ia Z.9 0*813 SUBd piBqDIIU) 3 -8 I03IABJ3 903 3H1 08Z, 0581-9*81 isppuqos 3 -8 ujoqjousx esz.1 91 6 8 06813 suBd uossag 3 -8 3SSBq 3uoqdoujo3 8SZ. na 8Z.8 56813 uopuoq 03 ^> Ässoog 3 -8 uioq pBHBg 8* na 001 55813 SUBd XBS PV 3 -8 (S3AJBA UlJJSg ) aUOqUIOJJ 3A|BA *69l 3d pduitui 6301 5861 3 ZUIBp\[ 3 -8 ssBg 1 OVM *0l 61 J SUBd ÄJBJBH 3 -8 auoquiojj oajba 30Z.X ao 80l 0Z.81 3 uopuoq 3PB3 ^> 3S0H 'llBpn-a 3 -8 ujoq jbooa 98* na JO 0501 05813 uopuoq 3 -8 UJOqiJB J03IABJ3 0536 HI pdujruj 9Z.11 613 uaqounpNj jsijoqDS 3 -8 ]BjnjBis[ 361 :aa ffoinj 33B iPlld ON }lJ.llOiU)>U| 00

ujoqdjY Z,60 na 9*1 6I 3 qtuju3qosiAV Tpsqo 9 -11 ssBa 0I6I 91 909 09I Siaquitij*^ zjjoq^ojia 9 -11 suoquiojj ssBa I8 na *8 69813 SUBJ SlOJitKQ 9 -11 suoquiojj .. 3jSnq suoiuBa 08* na 268 08613 vsn SiAvpnq 9 -11 'suoquiofl ssBa tfld AVf ZL6 08813 uopuon[ 3JJB0 n^pn-a 9 -11 apqs 3|qnop ssBa 20A2 na 0001 00613 uopuoq UOS ^S S35[MBH 9 -11 suoquioji

3UtlBS0,J JOU3X 90Z. FWSAV 81* LSSl Sj3qujn^\i pqosnsN qa-6 uiniuoqdng 9LLZ na *69 08813 j3^saqDUBp\[ qa-6 J3U§BAV IZ na 0Z, 06I 3 ZUIBJAI japuBxsiv qa-6 Bqnj SUtlBSOJ J0U3X 99 FWSM *U 613 iP9ra qa-6 SUnBSOd JOU3X * PMQ9M 6LL U9I U3IAV J3Ä39 qa-6 Jouax 02 na 66/. V6LI isnEqosnH qa-6 auoqiuojj H8 'auoquiofl aousx UI wv 108 8Z.6I UUOQ qa-6 ispoui 3uoqj3dns 96 na 28 08613 vsn uoijOH qa-6 'auoquiofl Jiouax 2082 na Ll% 2613 vsn UUOQ qa-6 ppoui Hg suoquiojj J0U3X 9681 91 *8 8991 Sisquin^ aqH qa-6 ssBqiouax 6I* 91 6*8 1*81 Sizdpq iapjBS qa-6 auoquioj} jouax 8I* 91 068 1*81 Sizdreq J3IWBS qa-6 auoquiojii JOU31 S'i'O 8/. na 68 613 (l) uiniSpa jo souBJg qa-6 suoqraoij pdratu} ssBg L9Z na 906 0-626I OU03 qa-6 suoquiojj JOU3X * na 16 0I8I3 SUBJ isjjaoipsra qa-6 auoquioj) jouax OLZ na 916 261 3 uopuoq UOS ^> S3J[A1BH qa-6 suoquioj} JOU3X 28*8 9 816 281 3 ZBIO \szar& qa-6 '3uo}UBg 0I 3H1 226 611 (l) oiS§v qa-6 ppoui iBjnaip SAjBy^ U 26 00613 SUBd jsqossna qa-6 aUOquiOJJ SUOqUIOJJ 3AJBA SSBa 612 na I 6 6I6I3 spssaia utua31 qa -6 laduiai] jouox aai Mf 6 86I3 uopuoq S35JAVEH ^> ÄSSOOa qa-6 3JBJUBJ puuin-nsui ON

6fui SUBd XBS PV qa-i uijoj Bqrvj '9iuouiJBq,p J03 L6 SV gjiaduiojx na 8Z,8 0061 3 SUBd ddSOd qa-i 9SSBq IIZI 096 0061 3 uopuoq qa -i papip-OMj 'guoqiuojj ssBg VST 166 6rui I 90UBJJ uijoj Bqni 'aiuouiJBq^ J03 9

OK 08t 3 SinoqsBJJS d-2I ujoq puBq jBJ^sgqojo I 5 na na 2K 0t81"81 uijqna pjEiia a -2i UJOq P9AJBA tlLl na SK 698I-t98I SUBd iiossgg a -2i giuouuBq.p joq gp0 na 6 811 (1) ureaijg a -2i ujoq puBq |BJ)S9qojo 8882 na 99S 81 3 spssnjg XBS '^3 a -2i ujoq oiuojiuujo 9 na 909 08T-0I8I uopuoq qoBqpuBS a -2t ujoq puBq jBJ}S9q3J0 02 2T9 0S6T3 ZUIB]AI J9pUBX9IV a -2i ujoq gjqnoQ tO8I na 19 t^161 3 SUBd uous9no3 a -2i ujoqsjqnoQ it7j7 na na 09 09/.I 3 uopiioq J91SB1HJ0H a "2i ujoq puEq IBJiS3qoJO/.62 na K9 06813 uopuoq jo spssnjg uoniqBH a -21 ujoq {BJisgqojo tZ-81 na 099 00613 9n§BJd O"a a -2i ujoqpiBMinu9A na 899 0161 3 J9JS3qOUBp\[ ay-21 uqnjL lllZ wz na 9L9 08I 3 U9pS9Ja U3JSJ9^J a -2i ujoq |BJ^S9q3JO 1 na 9L 06I 3 (l) ÄUBUIjgr) a -2i 9U0qUI0Jl SSBqBJJUOQ 802 t%L 00Z.I3 Sjgqujnjs]; SBBH a -2i ujoH 09 ao UL tl8I ÄUBUIJ9Q a -2i auoqiuoji ssBg 2Z, ao 09 ao 008 8IUI uopuoq J9UU9g a -2i ujoH jouSem lAIMH Mf 808 0061 3 spssnjg uoijiqBpsi a -2i Eqm ao 9S8 0161 3 iiopuoq 03 ^ Ägsoog a -2i 9uoquiojj ssBg OPL* 6061 01 9L2 91 snqiiO3 Jiaaqjpo a -2i auoquioj] ssBg Mf 968 00613 s[9ssnjg a -2i auoquioji ssBqBJ)uo3 lAIAd 006 6691 uopuoq iina a -2i ujoq jBjnjBjsi L0 DHl

33BM qajM ON }u,miai3suj Z.6t- 039/611 SUBd nB3I9IIM a "83 assBqazmoo assBqo ap adiuoix lOT ^a

08 03m ZJIJSBJ9 J9SSBM0JS qg-8i auoqiuoji ssBqBijuc^ 3S3 na H8 681 o STJBd SI01IT103 qa -81 auoquiojj ssBqBfluoQ PZ 806 00613 uopuoq ÄUIJV UOIJBAjBS auoqiuoji ssEqejiuon XJ

91?t 0t8I 3 uaqounjAj SptlBS L9L\ 91

98 81UI SUBJ U. V9 ao __ _ ~aVn SSqoI-aei 6 (1)611 (i) 3DUBJJ aduiojx 109 IZLl STJBJ uaigoq a ij-n ouiqdnBp 1913 ng na 99 (I) 9061 SUBJ a ij-n Z.89 OfLI 3 uopuoq a-ti luoq iBjniBjs[ 6t3 na 00/. OKI 3 uopuoq a-ti ujoq iBJnjB|v[ Z.393 na aduiojx ZL 361 SUBd U0US3T103 a -ti 3SSBq assBqo ap 6I na

}uoiunj}su] Appendix D

Minimum shank diameter of mouthpieces in EUCHMI

This table lists the minimum shank diameters of all the mouthpieces for brasswind instruments in

EUCHMI on 1st January 1996, accession numbers in the range (1) to (3599).

The information has been extracted from the catalogue of the Collection (Myers and Parks 1996a and Myers and Parks 1996b).

Within each type, entries have been ranked by minimum shank diameter.

7.5 Mouthpiece for cornettino (1283)

7.5 Mouthpiece for cornett (1878) 8.2 Mouthpiece for cornett (3589) 8.4 Mouthpiece for cornett (3492) 8.5 Mouthpiece for cornett (3192) 8.6 Mouthpiece for cornett (626) 8.7 Mouthpiece for cornett (1147) 8.7 Mouthpiece for cornett (863) 8.8 Mouthpiece for cornett (1877) 9.9 Mouthpiece for cornett (3302)

9.2 Mouthpiece for soprano bugle (2342)

9.8 Mouthpiece for Kornett (?) (3248) 10.3 Mouthpiece for Swedish kornett (3500) 10.8 Mouthpiece for Kornett (2451)

9.7 Mouthpiece for clarion (1133) 9.9 Mouthpiece for bugle (2344) 10.2 Mouthpiece for bugle (2469) 10.2 Mouthpiece for bugle (3224) 10.3 Mouthpiece for bugle (2646) 10.6 Mouthpiece for bugle (628) 10.6 Mouthpiece for bugle (1137) 10.7 Mouthpiece for bugle (914) 10.8 Mouthpiece for bugle (904) 10.8 Mouthpiece for bugle (1730) 10.9 Mouthpiece for bugle (697) 10.9 Mouthpiece for bugle (644) 10.9 Mouthpiece for bugle (3285) 11.0 Mouthpiece for bugle (?) (3228) 11.0 Mouthpiece for bugle (3265) 11.0 Mouthpiece for bugle (993) 12.2 Mouthpiece for bugle (1086)

151 10.0 Mouthpiece for cornopean (1861) 10.2 Mouthpiece for cornopean (1298) 10.5 Mouthpiece for cornopean (1871) 10.5 Mouthpiece for keyed bugle with trumpet cup (?) (1288) 10.8 Mouthpiece for cornopean (845) 10.8 Mouthpiece for cornopean (?) (642) 10.8 Mouthpiece for keyed bugle (3238) 11.0 Mouthpiece for keyed bugle (991) 11.0 Mouthpiece for keyed bugle (1285) 11.0 Mouthpiece for keyed bugle (908) 11.1 Mouthpiece for keyed bugle (633) 11.2 Mouthpiece for keyed bugle (1284) 11.6 Mouthpiece for cornopean (3294) 11.8 Mouthpiece for keyed bugle (956) 12.0 Mouthpiece for keyed bugle (1286) 12.0 Mouthpiece for keyed bugle (3025)

8.9 Mouthpiece for flugelhorn (874) 9.1 Mouthpiece for flugelhorn (647) 9.1 Mouthpiece for flugelhorn (2817) 9.2 Mouthpiece for flugelhorn (2928) 9.3 Mouthpiece for flugelhorn (3514) 9.3 Mouthpiece for flugelhorn (3482) 9.3 Mouthpiece for flugelhorn (3513) 9.4 Mouthpiece for flugelhorn (2320) 9.5 Mouthpiece for flugelhorn (1892) 9.5 Mouthpiece for fiugeihom (1574) 9.8 Mouthpiece for flugelhorn (1672) 9.9 Mouthpiece for flugelhorn (1151) 10.0 Mouthpiece for flugelhorn (2958) 10.0 Mouthpiece for flugelhorn (2996) 10.1 Mouthpiece for flugelhorn (3088) 10.2 Mouthpiece for valved bugle (3300)

7.9 Mouthpiece for soprano comet (2810) 8.0 Mouthpiece for cornet (3364) 8.1 Mouthpiece for cornet (1886) 8.1 Mouthpiece for cornet or soprano cornet (3503) 8.2 Mouthpiece for cornet (2994) 8.3 Mouthpiece for cornet (2815) 8.3 Mouthpiece for cornet (3506) 8.3 Mouthpiece for cornet (3268) 8.3 Mouthpiece for cornet (1554) 8.3 Mouthpiece for cornet (2461) 8.3 Mouthpiece for comet (2813) 8.3 for comet . Mouthpiece (643) 8.3 Mouthpiece for comet (2811) 8.3 Mouthpiece for comet (2937) 8.3 Mouthpiece for comet (2933) 8.4 Mouthpiece for soprano comet (1880) 8.4 Mouthpiece for comet or soprano comet (1300) 8.4 Mouthpiece for comet (2816) 8.4 Mouthpiece for comet (1588)

152 8.4 Mouthpiece for cornet (1883) 8.4 Mouthpiece for cornet (1295) 8.4 Mouthpiece for cornet (3409) 8.4 Mouthpiece for cornet (651) 8.4 Mouthpiece for cornet (1879) 8.4 Mouthpiece for cornet (2812) 8.4 Mouthpiece for cornet (2936) 8.4 Mouthpiece for cornet (3504) 8.4 Mouthpiece for cornet (2372) 8.5 Mouthpiece for cornet with trumpet cup (3593) 8.5 Mouthpiece for cornet (2938) 8.5 Mouthpiece for cornet (3428) 8.5 Mouthpiece for cornet (688) 8.5 Mouthpiece for cornet (1888) 8.5 Mouthpiece for comet (1084) 8.5 Mouthpiece for cornet (1452)

* 8.5 Mouthpiece for cornet (870) 8.6 Mouthpiece for soprano cornet (3501) 8.6 Mouthpiece for soprano cornet (3502) 8.6 Mouthpiece for comet with trumpet cup (3512) 8.6 Mouthpiece for soprano comet (2814) 8.6 Mouthpiece for comet (1885) 8.6 Mouthpiece for soprano comet (2809) 8.6 Mouthpiece for comet (2956) 8.6 Mouthpiece for comet (3505) 8.6 Mouthpiece for comet (680) 8.6 Mouthpiece for comet (2995) 8.6 Mouthpiece for comet (2955) 8.6 Mouthpiece for comet (645) .8.6 Mouthpiece for comet (2318) 8.6 Mouthpiece for comet (1153) 8.6 Mouthpiece for comet de poste (669) 8.6 Mouthpiece for comet (1590) 8.6 Mouthpiece for comet (2470) 8.7 Mouthpiece for comet (2982) 8.7 Mouthpiece for comet (1884) 8.7 Mouthpiece for comet (2875) 8.7 Mouthpiece for comet with trumpet cup (3028) 8.7 Mouthpiece for comet (2437) 8.7 Mouthpiece for comet (3347) 8.7 Mouthpiece for comet (681) 8.7 Mouthpiece for comet (1887) 8.7 Mouthpiece for comet (2781) 8.7 Mouthpiece for comet (3511) 8.7 Mouthpiece for comet (3478) 8.7 Mouthpiece for posthorn (3019) 8.8 Mouthpiece for soprano comet (2954) 8.8 Mouthpiece for soprano comet (3508) 8.8 Mouthpiece for comet or soprano cornet (3055) 8.8 Mouthpiece for soprano saxhorn (3430) 8.8 Mouthpiece for comet (3276) 8.8 Mouthpiece for comet (695) 8.8 Mouthpiece (3359)

153 8.8 Mouthpiece for comet (2957) 8.8 Mouthpiece for cornet (880) 8.8 Mouthpiece for cornet (1882) 8.8 Mouthpiece for cornet (1881) 8.8 Mouthpiece for cornet (1164) 8.8 Mouthpiece for cornet (906) 8.8 Mouthpiece for cornet (641) 8.8 Mouthpiece for cornet (3507) 8.9 Mouthpiece for soprano cornet (2808) 8.9 Mouthpiece for soprano cornet (2302) 8.9 Mouthpiece for cornet (3509) 8.9 Mouthpiece for comet (3053) 8.9 Mouthpiece for comet (3226) 8.9 Mouthpiece for comet (830) 8.9 Mouthpiece for comet (3476) 8.9 Mouthpiece for comet (3510) 8.9 Mouthpiece for comet (1141) 8.9 Mouthpiece for comet (3479) 9.0 Mouthpiece for comet (1611) 9.0 Mouthpiece for comet (3316) 9.0 Mouthpiece for comet (640)

9.3 Mouthpiece for trumpet (2338) 9.3 Mouthpiece for trumpet (2820) 9.3 Mouthpiece for trumpet (1890) 9.4 Mouthpiece for trumpet (2997) 9.4 Mouthpiece for trumpet (3234) 9.5 Mouthpiece for trumpet (652) 9.5 Mouthpiece for trumpet (2322) 9.6 Mouthpiece for trumpet (878) 9.6 Mouthpiece for trumpet (3002) 9.6 Mouthpiece for trumpet (1889) 9.6 Mouthpiece for trumpet (886) 9.7 Mouthpiece for trumpet (3000) 9.7 Mouthpiece for trumpet (882) 9.7 Mouthpiece for trumpet (3516) 9.7 Mouthpiece for trumpet (2999) 9.7 Mouthpiece for trumpet (658) 9.7 Mouthpiece for trumpet (1702) 9.7 Mouthpiece for trumpet (2455) 9.8 Mouthpiece for trumpet (2819) 9.8 Mouthpiece for trumpet (3001) 9.8 Mouthpiece for trumpet (2481) 9.8 Mouthpiece for trumpet (1614) 9.8 Mouthpiece for trumpet (2998) 9.8 Mouthpiece for trumpet (2503) 9.8 Mouthpiece for trumpet (3345) 9.9 Mouthpiece for trumpet (2818) 9.9 Mouthpiece for trumpet (916) 10.0 Mouthpiece for trumpet (3211) 10.0 Mouthpiece for trumpet (3515) 10.0 Mouthpiece for trumpet (2528) 10.0 Mouthpiece for trumpet (3235)

154 10.0 Mouthpiece for trumpet (672) 10.0 Mouthpiece for trumpet (844) 10.0 Mouthpiece for trumpet or bass trumpet (653) 10.1 Mouthpiece for trumpet (2514) 10.2 Mouthpiece for trumpet (3281) 10.3 Mouthpiece for trumpet (997) 10.3 Mouthpiece for trumpet (2872) 10.3 Mouthpiece for trumpet (842) 10.3 Mouthpiece for trumpet (2495) 10.4 Mouthpiece for trumpet (3195) 10.4 Mouthpiece for trumpet (2465) 10.4 Mouthpiece for trumpet (2644) 10.4 Mouthpiece for trumpet (3159) 10.5 Mouthpiece for trumpet, formerly cornet (2978) 10.5 Mouthpiece for cavalry trumpet (1863) 10.6 Mouthpiece for trumpet (649) 10.6 Mouthpiece for trumpet (2526) 10.6 Mouthpiece for trumpet (648) 10.6 Mouthpiece for trumpet (3283) 10.6 Mouthpiece for trumpet (1720) 10.6 Mouthpiece for alto trumpet (2374) 10.7 Mouthpiece for trumpet (3291) 10.7 Mouthpiece for trumpet (650) 10.8 Mouthpiece for trumpet (3216) 10.8 Mouthpiece for trumpet (622) 11.0 Mouthpiece for trumpet (3204) 11.0 Mouthpiece for trumpet (3287) 11.0 Mouthpiece for trumpet (3289) 11.0 Mouthpiece for trumpet (679) 11.5 Mouthpiece for trumpet (995)

9.6 Mouthpiece for soprano trombone (3029) 9.9 Mouthpiece for soprano trombone (1287) 10.2 Mouthpiece for soprano trombone (639)

5.8 Mouthpiece for french horn (2628) 5.9 Mouthpiece for trompe de chasse (3493) 6.2 Mouthpiece for trompe de chasse (2162) 6.3 Mouthpiece for french horn (1891) 6.5 Mouthpiece for trompe de chasse (3495) 6.6 Mouthpiece for french horn (635) 6.7 Mouthpiece for french horn (2156) 6.7 Mouthpiece for french horn (656) 6.8 Mouthpiece for french hom (2993) 6.9 Mouthpiece for french horn (663) 6.9 Mouthpiece for french horn (3496) 6.9 Mouthpiece for french horn (1125) 7.0 Mouthpiece for french hom (848) 7.0 Mouthpiece for french horn (1868) 7.0 Mouthpiece for french horn (3161) 7.1 Mouthpiece for french horn (3118) 7.1 Mouthpiece for french horn (846) 7.2 Mouthpiece for french hom (837)

155 7.3 Mouthpiece for french horn (1875) 7.3 Mouthpiece for french horn (866) 7.3 Mouthpiece for french horn (664) 7.4 Mouthpiece for french horn (3099) 7.5 Mouthpiece for french horn (1805) 7.6 Mouthpiece for french horn (636) 7.6 Mouthpiece for french horn (3497) 7.6 Mouthpiece for Wagner tuba (1678) 7.7 Mouthpiece for French hom (3498)

8.7 Mouthpiece for neocor (3351) 8.8 Mouthpiece for tenor cor (3425) 8.8 Mouthpiece for tenor cor (3427) 8.9 Mouthpiece for ballad horn (3349) 9.2 Mouthpiece for tenor horn (3047) 9.2 Mouthpiece for tenor hom (1893) 9.4 Mouthpiece for tenor horn (876) 9.4 Mouthpiece for tenor horn (668) 9.5 Mouthpiece for tenor horn (2960) 9.5 Mouthpiece for tenor horn (693) 9.8 Mouthpiece for mellohorn (?) (3517) 9.7 Mouthpiece for tenor horn (2303) 9.7 Mouthpiece for tenor horn (2821) 9.8 Mouthpiece for tenor horn (2976) 9.9 Mouthpiece for tenor tuba (3546) 10.0 Mouthpiece for tenor horn (1557) 10.0 Mouthpiece for tenor horn (674) 10.1 Mouthpiece for tenor horn (2959) 10.1 Mouthpiece for tenor hom (673) 10.1 Mouthpiece for tenor hom (629) 10.1 Mouthpiece for tenor hom (2737) 10.2 Mouthpiece for tenor hom (3518) 10.2 Mouthpiece for alto trumpet (3258) 10.2 Mouthpiece for tenor hom (2775) 10.3 Mouthpiece for tenor hom (3046) 10.3 Mouthpiece for tenor hom (2972) 10.3 Mouthpiece for tenor hom (683) 10.4 Mouthpiece for vocal hom (890) 10.5 Mouthpiece for tenor hom (3485) 11.3 Mouthpiece for tenor saxhorn (2657)

11.8 Mouthpiece for alphom (3098) 12.2 Mouthpiece for alphom (1828)

10.2 Mouthpiece for quinticlave (3240)

9.5 Mouthpiece for tenor trombone, suitable for alto trombone (661) 9.9 Mouthpiece for tenor trombone (3523) 9.7 Mouthpiece for tenor trombone (1895) 9.9 Mouthpiece for tenor trombone (1896) 10.0 Mouthpiece for trompette basse or tenor trombone (3218) 10.2 Mouthpiece for tenor trombone (3100) 10.3 Mouthpiece for tenor trombone (675)

156 10.3 Mouthpiece for tenor trombone (3006) 10.3 Mouthpiece for tenor trombone (827) 10.4 Mouthpiece for tenor trombone (1131) 10.4 Mouthpiece for tenor trombone (685) 10.4 Mouthpiece for baritone (3003) 10.5 Mouthpiece for tenor trombone (3008) 10.5 Mouthpiece for tenor trombone (3007) 10.6 Mouthpiece for tenor trombone or baritone (3594) 10.6 Mouthpiece for tenor tuba (3547) 10.6 Mouthpiece for tenor trombone (2828) 10.6 Mouthpiece for tenor trombone (2963) 10.6 Mouthpiece for tenor trombone or baritone saxhorn (2826) 10.6 Mouthpiece for tenor trombone (840) 10.6 Mouthpiece for tenor trombone (2983) 10.6 Mouthpiece for tenor trombone (2656) 10.6 Mouthpiece for baritone (805) 10.6 Mouthpiece for baritone (2304) 10.6 Mouthpiece for tenor trombone (2729) 10.6 Mouthpiece for tenor trombone (838) 10.7 Mouthpiece for alto trombone (2825) 10.7 Mouthpiece for tenor trombone (2962) 10.7 Mouthpiece for tenor trombone (1771) 10.7 Mouthpiece for tenor trombone (3005) 10.7 Mouthpiece for baritone (2961) 10.7 Mouthpiece for tenor trombone (637) 10.7 Mouthpiece for tenor trombone (2803) 10.7 Mouthpiece for tenor trombone (3009) 10.7 Mouthpiece for clairon basse (bass bugle) (3163) 10.7 Mouthpiece for tenor trombone (1289) 10.7 Mouthpiece for tenor trombone (701) 10.8 Mouthpiece for tenor trombone (665) 10.8 Mouthpiece for tenor trombone (2829) 10.9 Mouthpiece for tenor trombone (2696) 10.9 Mouthpiece for baritone (2822) 10.9 Mouthpiece for tenor trombone (2497) 10.9 Mouthpiece for tenor trombone (657) 10.9 Mouthpiece for baritone (2824) 10.9 Mouthpiece for baritone (2823) 10.9 Mouthpiece for tenor trombone (3526) 10.9 Mouthpiece for tenor trombone (2501) 10.9 Mouthpiece for baritone (1894) 11.0 Mouthpiece for tenor trombone (1123) 11.0 Mouthpiece for tenor trombone (2498) 11.0 Mouthpiece for tenor trombone (?) (3591) 11.0 Mouthpiece for tenor trombone (3597) 11.0 Mouthpiece for tenor trombone (1696) 11.0 Mouthpiece for tenor trombone (2964) 11.0 Mouthpiece for tenor trombone (666) 11.1 Mouthpiece for tenor trombone (3206) 11.1 Mouthpiece for baritone (2482) 11.1 Mouthpiece for tenor trombone (3595) 11.1 Mouthpiece for baritone (2827) 11.1 Mouthpiece for tenor trombone (2984)

157 11.1 Mouthpiece for baritone saxhorn (3353) 11.2 Mouthpiece for trompette basse (3522) 11.2 Mouthpiece for tenor trombone (2305) 11.2 Mouthpiece for tenor trombone (3413) 11.2 Mouthpiece for tenor trombone (2830) 11.3 Mouthpiece for baritone (3004) 11.3 Mouthpiece for tenor trombone (3525) 11.3 Mouthpiece for tenor trombone (3524) 11.3 Mouthpiece for tenor trombone (654) 11.3 Mouthpiece for bass trumpet (1290) 11.4 Mouthpiece for tenor trombone or Tenorhorn (1586)

10.6 Mouthpiece for euphonium (3014) 10.6 Mouthpiece for bass trombone (3011) 10.7 Mouthpiece for euphonium (3012) 10.8 Mouthpiece for ophicleide (3244) 10.8 ^Mouthpiece for euphonium (2832) 10.8 Mouthpiece for bass trombone (2985) 10.9 Mouthpiece for euphonium (3488) 10.9 Mouthpiece for bass trombone (2831) 10.9 Mouthpiece for euphonium (3490) 10.9 Mouthpiece for euphonium (3013) 10.9 Mouthpiece for bass trombone (677) 11.0 Mouthpiece for ophicleide (3314) 11.2 Mouthpiece for euphonium (2109)

11.2 Mouthpiece for ophicleide or bass trombone (1296) 11.1 Mouthpiece for trompe de chasse basse (3520) 11.1 Mouthpiece for ophicleide (3368) 11.3 Mouthpiece for bass trombone (824) 11.3 Mouthpiece for bass trombone (676) 11.4 Mouthpiece for bass trombone (2788) 11.5 Mouthpiece for euphonium (2326) 11.5 Mouthpiece for euphonium (3527) 11.5 Mouthpiece for ophicleide (2158) 11.6 Mouthpiece for bass saxhorn or trompe de chasse basse (?) (3473) 11.7 Mouthpiece (623) 11.7 Mouthpiece for bass trombone (3340) 11.7 Mouthpiece for bass trombone (2966) 11.7 Mouthpiece for bass trombone (638) 11.8 Mouthpiece for euphonium (2306) 11.8 Mouthpiece for bass trombone (3010) 11.8 Mouthpiece for bass trombone (2965) 11.8 Mouthpiece for bass trombone (3256) 11.8 Mouthpiece for euphonium (1899) 11.8 Mouthpiece for bass trombone (3095) 11.9 Mouthpiece for bass saxhorn (3529) 12.0 Mouthpiece for bass trombone (1291) 12.1 Mouthpiece for bass trombone (1577) 12.2 Mouthpiece for euphonium (3528) 12.5 Mouthpiece for bass trombone (3027) 13.2 Mouthpiece for bass trombone (2707)

11.1 Mouthpiece for bass horn (3306)

158 11.2 Mouthpiece for Russian bassoon (2981) 11.2 Mouthpiece for serpent or bass horn (3311) 11.4 Mouthpiece for serpent or ophicleide (1897) 11.8 Mouthpiece for Russian bassoon (3308) 11.9 Mouthpiece for serpent (3373) 12.0 Mouthpiece for serpent (999) 12.2 Mouthpiece for serpent (1007) 12.4 Mouthpiece for serpent (1726) 12.6 Mouthpiece for bass horn (627) 12.7 Mouthpiece for serpent (1898) 12.3 Mouthpiece for serpent (884) 13.2 Mouthpiece for serpent (624) 13.5 Mouthpiece for serpent (3304)

12.9 Mouthpiece for contrabass serpent (2930)

11.0 Mouthpiece for Eb bass (872) 11.3 Mouthpiece for Eb bass (655) 11.7 Mouthpiece for Eb bass (1159) 11.8 Mouthpiece for Eb bass (2836) 11.8 Mouthpiece for tuba (686) 11.9 Mouthpiece for bombardon (2967) 12.1 Mouthpiece for tuba (2132) 12.3 Mouthpiece for contrabass (3531) 12.5 Mouthpiece for Eb bass (2834)

12.4 Mouthpiece for bombardon or Eb bass (2588) 12.4 Mouthpiece for bombardon (1161)

12.5 Mouthpiece for bombardon or Eb bass (631) 12.5 Mouthpiece for Bb tuba (825) 12.5 Mouthpiece for Bb tuba (801) 12.5 Mouthpiece for Bb tuba (634) 12.6 Mouthpiece for Bb tuba (1794) 12.6 Mouthpiece for Bb tuba (2710) 12.6 Mouthpiece for Eb bass (1873) 12.6 Mouthpiece for Bb tuba (632) 12.7 Mouthpiece for Eb bass (2835) 12.8 Mouthpiece for Eb bass (3530) 12.8 Mouthpiece for Bb tuba (2837) 13.1 Mouthpiece for contrabass saxhorn (3230) 13.2 Mouthpiece for contrabass (2483) 13.4 Mouthpiece for contrabass (3532) 14.0 Mouthpiece for contrabass (2499) 14.3 Mouthpiece for contrabass (2340)

159 Appendix E

Mouthpieces ranked by cup volume

This table lists the cup volumes of selected mouthpieces in several museums and private collections. The columns give data for:

Source and Specimen number

Full details of the sources of specimens are give in Appendix J.

Instrument, Maker, Place and Date

Specimens have been sought which are closely associated with particular instruments typical of their and place period. There is nearly always a considerable degree of uncertainty as to whether a historic mouthpiece was supplied with an instrument when new, used by a former player with an

'thrown instrument, or in with' an instrument when it was last sold. In many cases curators and collectors do not know the nature of the association. Consequently, there will be some degree of scatter in the instrument names given to these specimens, especially where mouthpieces have in the been past numerous and readily interchangeable as with keyed bugles and cornopeans, bass trombones and ophicleides respectively.

Volume

This is the cup volume calculated as defined in Equation 7.2, given in cubic millimetres.

The calculation of mouthpiece cup volumes depends on measurements of depth and diameter using plug gauges. Since most mouthpieces are lathe turned to close tolerances, the gauges give measurements to of a high degree accuracy. An error in a single gauge depth of lmm leads to an

in the volume of error an average mouthpiece of only 1.5%; the plug gauges can in fact be confidently used to an accuracy of better than 0.1mm and a mistaken depth measurement of much less than lmm would be noticed in the drawing of the profile. The least precise measurement is that of the bite radius of which is curvature, given to the nearest 0.25mm but is necessarily an

since in the curvature of between approximation general the cup and the rim is not a quadrant of a

Calculations data for circle. on typical small, medium and large mouthpieces, a cornett

160 (EUCHMI 3492), a trompe (EUCHMI 3493) and a trombone (EUCHMI 665) respectively, show that an error of 0.25mm in the bite radius of curvature leads to an error in the computed volume of between 1 % and 3 %.

Thus for comparative purposes, these mouthpiece volumes can be considered accurate to + 3%.

There must be a higher degree of uncertainty in the degree to which volumes calculated in this way correspond to the acoustically effective volumes. There is necessarily a degree of uncertainty as to where the cup ends and the grain or backbore begins, though the contribution to total volume of a short distance of narrow diameter tubing is small. There is an even greater degree of uncertainty as to how much of the cup volume is occupied by the lips of the player since this is dynamically changing as a tone is produced and statically varied by the player as part of performance technique.

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6161 61-ui uopuoq i jajqox 3j§nq psXs^i 83 na 161 611 suBj1 sioyno3 [spoui s,J3/I J3UJO3 ao 061 61 (6) uiBjug jsduimx 183 na 3881 01781 3 uopuoq (6) J3>[Bg UB3d0lU03 q/,61 id 9Z.81 0061 3 J3JS3qOUBJAi iUBq§(H J3UJOO 906 na 5981 09-55813 subj sioynoo J3UJO3 9LP na 058 t 0061 3 VSn ,i3poiuÄA3qv 'UU03 J31UO3 a ao 6^81 61'3 (l) UIBJIjg 1 (l) i3jZ}3JAJ 3jSnq p3^3^ L 1 8t>8l 61'ui uopuoq J3jqo]j| [pooM] jsdiunjj opus ISl A\f ' 3 Jsrao^si 58l SS8I uopuoq i (;,) 19Ü1OJ KI Id 38I 0681 3 uopuoq uosssg 'd jsduinjj 3pi[S V161 ^la 6I8I 06813 uopuoq uosssg 'd jaduituj 3pi[S ai6i' >ia ' Z,l8l 0Z.81 3 SUBd SlOJJtlOQ X31U0J 8z.i/e na 9181 6 I'm (6) uiBjug (i) W^M. V qsBqpires }3duinjx 051 Dm 1081 0t?8l 3 UOpUOq (l) 30B(] jsduitux /.83 na P2H 61'* uopuoq [j[3A[is] pdumj} 3pi[s )IS1 AVf ( 35/, I 611 3[§ng, 66 na ZZLI 6I'3 uopuoq (l) ii!qu33J) 3j§nq paXs^ t78 dO

UI i 61'ui uopuoq Jsiqo^ pduirux na [_ 913, r 50LI 61-1 ei tu _T siouno^ [apoui JB[n§3j 'J31UO3 B91/0 id 17691 61'3 UOpUOq H3XIBQ 3[§nq paXs-x A38 dO 9891 05813 uopuoq (6) Ä3^ pduirux 059 na 891 0^81 3 uopuoq (i^,) 3DBJ i^ua y-yt ui ai§nq ps^^i III id PL9\ 0^813 uopuoq (6) IS^BQ UB3dOUJO3 VL61 Id Z,59I 6 I'm uopuoq >iSBd J31UO3 339 ao 59I LY\ (1) uiBjug (6) ling luoH L0 DHl 6391 6Vm (1) uiBjug (6) S31I0H 3(3nq p3Ä3^ 511 DHl LZ9\ 613 (i) uq^f pdiumj JB[noi|3 5L ao 9391 031 >in ai7 ^3!Av J3UJ00 auinjo/ |i!3Uin.l)SU| 3JJB0 iiBptra luoq (Boo/j, SHD Mf 813 I 611 uopuoT 03 031 ÄUBUU39 jnq>(3Bs! 9693: na ' (I) ^a^ luoq pBjiBg 9l id L9\ i 06813 uopuoq I9l 08t a uapsajQ i uajsja-^ aioq qou9Jj S9 na 631 i 611 SIJBd [ 3jI!W / sioyno3 j y9 UT luoq Xpopj^1 owl! Mf 8W) 1 (i) 991 (l) uopuoq (I) 3le9a jaduitux 8Z.X 90

1 8O I 6l"i (i) 30UBJJ 3ABpi}Uin^) 0i73! na LZO 031 30UBJJ SU3HI!W assBqo 3p aduioax 6t7 na fr30 f 58813 uopuoq syBo nepn^i ujoq JBOOA 068 na 1 8663 1 6813 uopuoq 00 ^> Ä9SOOQ luoq pB[[Bg 6Ki na 5363 luoq ajSna: 63i DHl S6Z,3 61 uaoq qousjj q9| ao fr8Z.3 611 uopuoq uioq [BOO/\ Mf 89Z/3 0981 3 uopuoq upsia Bqnj J0U3JLJ 9^5 na ZZLZ OPLl o uopuoq uaoq qouajj 8393! na 1 ' L99Z 0Z.8I3 SUBJ sioynoQ j y;9 ui ttioq Siu3O>[| d>111 Mf frO93 61 (L) SUBd (I) stopnoo [/CiOAi] aioq qousij S91 ao 1 - - 33 61'9 (i) 90UBJJ 9AB[DlJUinö vöej Mf \_ H5Z 61-ui piuo3i 861 i SPZ 03'3 SUEJ gduioax I 951 >fa LtPZ 611 >[JOA Malst qoBg luoq q3U9Jj L6P\ na 83 I 611 SUBJ uossag gduiojj / ujoq qougaj P9\ ao I3 611 Sjnqsu3§9"a (6) q3}Ipi3M pdunu} oj[v PLZ\ na 603 uopuoq UllSlQ lUoqxBS ouBados 36 J DHl SLIZ 08I 3 SIJBJ UB[BH Xjqissoj 9[§nqpaX3^ 80ö! na 1503 03'3/6H (i) ÄUBUU39 aioq qou9Jj 998 na LPOZ 61'3 (I) uoXq (6) PJBqei 9[3nq paXs^ j 9| ao 1303 017813, uopuoq (i) -raw UB9d0lU03 3/.61 Id Z.66I 981 SUBd siopnoQ 9[§nq jo ujoq jsoj ^39; ao j 1861 0581 3 uopuoq J9UJ03 533 J id 961 0/.813 SUBd siounoo ;9iuo3 6LV\ na 36I 6 rut uopuoq J9iqo>i 9[§nq p9Ä9^[ >!>!e Mf auinjoA 33BId }U3uin.qsuj 1 /.85 5981 = J3JS3qOUBJAJ ureqgiH suoquiojj JOU3X 1/6 XJ 9985 (l) seen ujoq qou3Jj 509 ao 88Z.5 0861 3 a"ubuu3) 889 lAJV 1 90/.5 02'3/6F uosssa suoquiojx 862 na SSS 0^81 3 (i) uiBipa uoossBq UBissn"y 80 na 805 03'3/6H SUBJ sioynoQ 3uoquiox( jouax 00I na 6835 61'3 (l) uiBjijg luoq ssBq jo jusdiss ll na 6935 0581 3 (1) SOUBJg J03IABJ3 82 ^a [ 1815 (^,) 3DUBJJ [ajoai] 3pi3|oououi|qdo 22 Ma Z-505 0981 3 uopuoq UJJSIQ Bqnj JOU3X LPS na 8t?6t7 orm uopuoq S9>|A\BH 5> Ä3S00Q suoquiojx 211 na IZLP 02'3 eijjsnv luoqjousx / uiojj JOU3X 9851 na 61917 61 (l) BUjsny auoqmojj aousx 902 na 1917 or1 uopuoq i3UIj3S suoquiojx 599 na 0I9fr orui ÄUBUU39 BULI3M suoqiuojx 0Z,9 na 58t- 611 uopuoq suoquioji ojjy HVd AVf 2fr 51/81 3 JOOIABQ 902 DHl OWfr 61'3 (6) uiejijg ujoq qauajj 9^8 na t>21^ 9581 uopuoq luoq qDU3Jj 959 na 0i7 03'3/611 (6) urejua suoquiojj ojjy 5382 na 32017 6T3 3SSEq JOQ 18 ao 90017 uoossBq uBissiry 91/2 M6 611 30UBJJ UOSS3Q 3SSEq suoqdoiuoQ 65A na LL% lUOqXBS J0U3X 16 06L 6I"wi (6) Raid JOO JOU3X 191 3H1 , 8Z.Z. ! 611 SIJBd 311! lAJ / sio^noo auoquioj} ojjy 3Vd A\r LLL 0Z.813 uopuoq 3JJE3 [[Bpn-y1 lUOq (B3OA 6U Na SLL 611 uopuoq suos ^> JB3-M -H 3[|13AJOI JU3CÜ3S 'AVE 905 ao , 09L 00/.1 3 (6) H3UU3a aioq qou3Jj 09 ao , LPL 03'11" uojnq Xiaiy uoijEAjBg suoquiojj JOU3X 2962 na 1 595 6i'3/8n ujoq qousjj B9 ao 8S2 (6) WW auoqiuojx W 3H1 33B,a vo 3888 0061 3 SUBJ sioyno3 suoquiojj ssBg LL9 na 088 6TUJ lajsaqouBj^ i uiBqSfH spispiqdo 8i3 na 31/.8 88l 3 uopuo^ [[B}3Ui] }U3dl3S WI Id 8998 1813 MOSSBJO (6) iOJÄBX }U3dl3S 1/39 na 9/,8 1613 uopuoq S3^A\Bj~i g> Xssoog suoquiojj ssBg q 93 na i 9LZ2 6f9 (1) uiBjug uioi) -q jo spiapiqdo 9631 na 108 81 3 suoquiojj ssBg LZOZ na I _ 66/, Z./.6I 3 vsn suoquiojx 361 wv \ ' f 066/. 09LI 3 (6) 30UBJJ JU3dl3§ wee na 96/, 61'3 (6) SIJtJd (6) UII[03 apispiqdo Doa AVf j ' IP6L (i) uiBjijg (6) uojjig JU3CÜ3S 393 1 1 106/, 08l 3 (i) uiEjug spjspiqdo Pl na 1 1 69Z, 61 "tu 33UBJJ (6) lOflnBO apispiqdo 901 ' 9L9L 38 fo uopuoq (1) J3IZPIAI ez.ee na

~~ _ f _ IPL 6l'9 }U3dj3§ /.OOl na 06L 61'3 (i) u[Bj[jg [Ajoai] jusdras 30x ao 933/, juadaas 8198 dO 69 61'3 luoq ssBg \>Z\ Dm W69 /,66l uopuoq S3UIOX IV id 1789 jusdjas 33 169 03'9/6n assBq assBqo ap adujojx 03 na 99 03'3/6FI uopuoq uosssg auoquiojj Jouax 083 na 09 9L61 3 vsn lVr/i9 H3Bg auoquiojx 681 wv LPP9 81 3 SIJBd sioyno3 luoqxBS auojiJBg na I99 03'1" vsn 81 MDBO auoqiuoj} Jouax 6831 na 3639 03'3 uopuoq uosssg auoquioix 6 na LLZ9 0981 3 qSjnquipa (6) "SID "I apia[oiqdo 89 na LL\9 6l'3 (l) [OOdj3AjT (6) SO' juadjas 6/. JLd 96 03'3/6n 30UBJJ auoquiojj Jouax na l6 6I'3 (i) uiBjiag ujoq ssBg 0 ao t?36 auoquioix \L\ DHl 6I6 luoq ssBg 90 na amnio/ 33BIJ J3>JBW )U3iun.)jsii| 3/.56I 0fr81 3 PPiJS-iappnH sjsqjojq poo^v jiradras ss^qBajuoo 063 na 58991 QZ'V UBdBf UB5PKM ssBqt3J}U03 35 na 1 85331 uioq ssBg LZ9 na 08601 j 6l-uf, uopuoq URSiQl uopaBquiog 191! na I WO I 0061 souBjj (i) ÄiuEq-9[[iAnoqiqxs auoqiuojj ssBqBajuo3 Olfr a*J3 33Z.01 5681 (l) 33UBJJ (i^ sjojjnoQ auoqiuojj ssBqBJjuoQ PZ >ia LZPOl 8681 na , 1 Z,IOI z' DHl 1 i 036 08I 3 (i) 93UBIJ 31JI9AJOj }U3dj3S OP "Ma 1806 ] 6I'l| sPBd 9JIJJAJ / siojjnoQ luniuoqdng 38 ao 9906 61'ui J3}S9qOUB^ lUBqSiH 9pi9[3iqdo 1105 do aiuniOA 33BW J3>Jt!J4I JlI3UnS.l)SH| Appendix F

Mouthpieces ranked by Shape Quotient

This table lists the Shape Quotients of selected mouthpieces in several museums and private collections. The columns give data for:

Source and Specimen number

Full details of the sources of specimens are give in Appendix J.

Instrument, Maker, Place and Date

These are the same specimens as those in Appendix E.

Shape

This is the dimensionless Shape Quotient calculated as defined in Equation 7.3.

The considerations of accuracy are as for Appendix E.

168 ON 390"! 6l"l uopuoq syB3 UBpn"a ujoq [booa ^190 Mf O 1 390"! ujoqjsoj PL 3H1 T OSO"! 0S81 3 (timwuQ spispiqdo p\ na 8W! qSanquipg 8179 na I PPO'l 0Z"3/6I1 (l) XUBUUSQ ' uaoq qou3Jj 998 na ZWl ! 61 'l SUBjJ (^) }OJ}nB) moqxBS ouBjdos 0i7 na 80'l 611 uopuoq (l) Xssoog aioq psiq SL Z,0"! 0Z'3/6l"l 93UBJJ1 suoquiojj JOU3X SS na "iZO'l 0L81 3 SUBJ siopno^' j y9 ui uaoq §iU3O">| 000" l QZ, *V6l l SIJBji siouno3 auoquiojj aousx 00l na 000" l 611 SUBJ 9IIlIAI / siojjno3 auoquioaj oj|v DVd i 000" l UOpUOH[ 9JJB3 HBpiry uioq [BOOA 068 na 000"! OPLl 3 uopuoq luoq qousjj 8Z9Z na 000" l OZ"3 SUBd, y,0 }9uii9j uaoq [BOOA 6/.1 M8 1 IWO 6! "9/811 uaoq qousaj B9 90 l_ ( OWO Zn (i) Iln9 uaoH L0 DH1 SPL'O | 6l1 uaoq qougaj 19 ao LOL'O I 6l"3 (l) uiBjug uaoq qousajf 9178 na 099"0 I 08l 3i irapssjaf U31SJ9^ uaoq qougaj 9 na adBqs 33BIJ J3>JB^ )iI31iUlJJSU| 1911 0061 3 J3}S3qOUBJAI uiBqSiH J3UJ03 906 na 6S11 61 luoq ssBg 90 na ^ 9S11 61-3 (l) 30UBJJ SABjoijumo voa Mr ssn SS813 SUB,} sioynoQ luoqxBS 3uojjJBg S na osn 0061 a vsn jspoui ÄA3qv'UU03t^ J31UO3 a ao 6Wl 61 (l) 30UBJJ oi73 na nvi 6l uopuoq J3mo^i 3[§nq paÄ3"X 83 na Kll 981 SUBrf sioynoo 3|Snq jo luoq }soj 1739 ao ll 031 sn 3 >P!A\ jsduirux 3MQ MH Oll 611 uopuoq 3UB0 oBPn"a JEUH ty'Vi ul UJ01! Jsod 139 ao 1 8311 6l SUBJ sioynoQ 131UOQ 893 na 9311 611 s]oyno3 jspoui s,a3/(B|dujoq 'jaiuoo q9frO Id S311 031 :m 5[UO]AI W3UJO0 3}tlJAI Dm dra 17311 0981 a qgjnquipg (i) U9IO '1 89C na 311 0S81 a (^,) 30UBJJ aoo[AB[o 6111 6l'3 (;) uiBjug uuoq ssBg Eos' ao 8111 611 uopuoq SUOS ^> JB3^ "J-I 3Jl}3AJ0J JU3dl3S 'AVE 90s' ao i LlVl 61 uopuoq J31UOQ 339 ao LlVl 6l'3 3OUBJJ (,i) UUBUiqDSpj^J SldUIIS J31UOQ 103, DHl LlVl 6l (1) urejug U) S30OH 3[§nq p3Ä3->i SI I DHl Olli 6I-UI uopuoq UIJSIQ luoqxBS ouBjdos 36 DHl 6011 S361 SIJBJ (i^,) uousano3 suoquiojj ouBjdos Z.831 na SBinjSQ JJ3UJ03 3d MH son , 031 33UBJJ son 61 (i) URSIQ 861, DHl oon 61-ui uopuoq J3[qo>[ UB3d0lU03 3179 na t>601 03-3/611 3DUBJJ 3ssBq sssBqo sp sduiojx 03S na 6801 611 SliBJ 3[H!AI / sioynoQ j y9 ui luoq Äpo[3[Aj DiAji A\r Z.801 0/.81 3 SUBJ sioynoo J31UOQ 2LPZ na Z.80'1 611 J3}S3qOUBIAJ[ uiBqSiH J31UO0 ouBjdos 30S na 3801 611 ^JOy^ A\3f4 qoBg luoq qou3Jj L6PZ na 8Z.01 611 30UBJJ uossag assBq suoqdouiOQ 6S/.E na ZLO'l dno jsduinj} qjiM jaujoo 6S na

- adeqs nZ 30 By 3331 0*813 uopuoi (6)-i3^a 1 uBsdoiuoo BZ.6l Id r 6131 6T3 (<<,) SUBJ (l) UIJJO3 apisjorqdo DOB /M 8131 S8l 3 uopuoq (<<,) J3iqo>i J31U00 *I Id LIZ'I 03'3 Biflsnv luoqjousx / uiojj JOU3X 9851 na 5131 6l'3 uopuoq (i) [[iqussjr) aiSnq psXs^ *8 dO 131 06l 3 uopuoq 3JJB3 llBpn^i jsdturux 3*3 Id 3131 08I 3 uopuoq upsiQ J31U00 33 Id 8031 S*8l 3 iO0lAB[O 903 3H1 1 LOZ'l uopuoq uossag suoqiuoxj JOU3X 083 na 6611 O3'ui yiOX M3M1 q3B8 jsdumax i na 8611 vsn ivzA9 i[3Ba suoqurcux 68i nv 8611 03"l vsn Di ipsa jaduirux OiaA A\H Z.611 6Vm uopuoq (i) i3[qo>i J3OI03 *89 ao 611 *161 3 XuBUUar) 3j3ng *06 na

0611 i 0*813 uopuoq (i) -is^a UBadoujoo 3Z.61 Id 6811 r 031 vsn Biwz pduiTux 9i na [ 1 6811 f03'3/6H U3P3AVS uossjqo ^y S-iaqiqv U31UO>{ qSip9M§ oo na 6811 (6) tpo^I suoquiojx *l 3H1 8811 0981 3 uopuoq UIJSIQ Bqm -IOU3X 9* na 1 8811 6l3 (6) uiBiiaa7 uiojj "q xo 3pi3[oiqdo 9631 na *8H 0*81 3 uopuoq (i) J3)[Bg UBsdouaoo qz.61 id 6Z.ll 031 vsn DZ. H3Bg DZ.aA AVH SLVl 0881 3 uopuoV -is^ng piuoo 18Z.3 na z,n uopuoq oo 3> Äesoog luoq pBjjBg 6* na ZLVl 6T3 uopuoq W3-UB9 9[§nq p3X3)j Z,38 dO 6911 611 SUBJ sio^inoo [SpOlU JE[nS3J 'J31UOO B9*0 Id 691 I 03 3/611 jsdiutijx 3Z.9 na 8911 611 3[Sng 66 na Z.911 0Z.8I 3 SUBJ sio^noo J9UJ00 6Z,* na 911 03-UI uojnq Xuuy aoijBAjBS 3U0qUI0JJ iOU3X 3963 na 1911 uoossBq uBisstry 9*3 DHl 1911 6I-UI 30UBJJ 9pi3[0iqdo 901 DHl aaBltä 1 9631 06813 uopuoq uosssg j pduiruj spiis fll6l 38 r 3631 03'3 uopuoq uossag suoquiojx 565 na 5831 031 ÄUBUU39 pqong jnq>jDBS 9693 na 1831 61 (1) umiuQ *~(6) wbXav g> qoBqpuBS jsduirux 051 DHl f 8Z.31 (6) 33UBJi (I) uuBUiqoszprs }3duitux 58 33 ' LLZl t>861 uredg 31§ng ^3 na 5 LZI JU3CÜ3S S3 DHl

931 61'iu uopuoq J3RO>[ 1 3[§nq paX3>{ 33a A\r ^ 9931 09-5581 3 SUBJ sioynoo 1 J3UJ03 9LP na P9ZI 59813 JSJSSqOUBJAJ uiBqSiH suoquioxi JOU3X Pß ij 4 1931 lU3dl3S 33 3H1 8531 JU3cLl3S 8198 dO Z.S31 61 (I) uiBjpg jsdiurux i83 na 3531 03-3/611 uosssg suoquiojx 863 na LPZl 5861 uiBds XnsuoH 3[§ng 69^3 na SPZl 031 H31UOQ 3 A\H h ppzi uopuoq S35JMBH ig Xssoog suoquiojx 3U na ZPZl 00613 SliBJ sioynoo auoquioa; ssBg LL9 na T 01/31 O3'I >in at? w>]M J3UJ0Q at^Ava MH 0^31 611 SUBJ 31I!W / siojjno3 uiniuoqdng 3H OO I 31 0061 3 30UBJJ () XuiBq-3ii}Anoqiqx 3UOqUlOJl SSBqBXJUOQ oit a>10 8331 031 UBdBf UB>pjIJ^ SSBqBXJUOQ 35 na 8331 UiOqXBS JOU3X 16 3H1 8331 61'3 (l) urejijg (i) J3[Z}3]^ 3[§nq p3Ä3^ L DHl LZZl 6Vm UBsdoujoo 1763 na 9331 031 "Mn J13UJ03 D MH 5331 00/. I 3 gjaqiuBM (1) SBBH jsdumjx Z.66 na 5331 0fr8I 3 uopuoq (6) 33BJ jBjjg y-yr ui 3j§nq psXs^ \L\ Id PZZl 8581 3 uopuoq (6) IFpn-a '^33 [[BJ3UI] }U3dj3§; PZZl on >in W31UO3 36t na 331 61-ui (^,) UpSIQ iOO JOU3X 191 DHl 331 ÄUBUU3Q suoquiojx o/.9 na %ZY I 6I-U1 uopuoq 9iz; ng LZVl 1 08613 XUBUU3{) r upqx 889 nv 3ri 61'9 }U3dl3S 8681 ng f 66"l 61'3 luoq ssBg VZ\ DHl 86'l 0W13 uopuoq jsduiTux L2Z ng 86n 1 auoquioax Ul 3H1 96'I (6)/.99l (1) uopuoq (/,) 3[B3g jsduinax 8Z.XI ao fr6" I 61'ui uopuoq jajqo^ fpooAv] jaduiruj spijS ISX A\f T" 36e"i r Z.661 uopuoq S31UOX 1 }nqj[3BS IV Xd r we" i OWl 3 (1) uiBjug uoossBq uBissn-y 80 na " 6L'l i 03-UI uopuoq jsuips 3uoquiojx 599 na

3 ZL'l 58I , 3uoqiuozi ssBg LZO ng un (L) JSJti j ttioq 3j§ng 6Z: OHl un ori vsn suoquiojj JOU3X 6831, na L9-\ 61 (1) Bujsny auoquioaj Jousx 903 na 1 61>UI uopuoq J3jqo5[ [j3A[is] jsdiutuj spijs ylkjjj /111 99'l , /.sn 1 I56I3 uopuoq suoquioj} ssBg o 9S3 na 05813 oopuoq (6) ^3^ jsdumjx 059 na 6I-UI (6) uojiig JU3CÜ3S 393 3H1 8"l ors/6n (l) uiBjjjg 3uoquioj( 0}[V 53831 na 9'l 03'3/6l'l ÄUBUU3O uioq-jsoj 6io ng S'I 6I"l SinqsusSs^ jsduiruj oj|v PLz na

_ ^ JU3dj3S na 3"l j 6f9 z.00^ i er i 0681 3 uopuoq uosssg -j jsduiiu} 3p[|S V161 >ia 93fl 6l""i ureqSjH 3pi3[3iqdo 8513 na 33"I 1 LL6\ 3 vsnj uo}§uiura>i auoqiuojx 361 MY 6l"l I 6FIJ uopuoq S3>[MBH auoquiojj ojjv HVd, AVf 9in 56813 (6) 33UBJj (6) sjoynoo auoquioj; ssBqBojuoo Vz >ia ein 09813 uopuoq upsja Bqru JOU3X Lps na oin 1 61*01 uopuoq UIJSIQ uopjBquiog 1911 na /.on 61'9 (1) ufBjug [AJOAl] JU3CÜ3S 305X ao OO'I 61-ui uopuoq uosssg asx AVf adBqs 33BJJ J3>JBM JU3UIIU*SUI t r-

uaoq ssBgj LZ9\ na 09LI 58l o (i) uimsjg SSBq JO JU3CÜ3SI na t^891 61'3 (i) uiBjug lUOlJ llj 3[|l3AJOj JU3CÜ3S 0f\ ZW\ 08l a juadias W9 na 86"l 181 3 MO§SB[r) JU3CÜ3S j na 69S'l 09L\ 3 (1) aouBaj j3duitujoB|noji3i 9L\ ao 8'l 61-9 (i) uqBf [ajoai] 3pi3i3ouoiniqdo Z3 L09'\ 61'9 (i) 30UBJJ JU3CÜ3S SSBqBJJUO3 062 na 9~LY\ 01/81 3 ppij&rapptiH sasipcuq pooyW ' apigpiqdo IlOj dO WVl 61-ui J3JS3qOUBJ/\[ uiBqSfH }U3dj3§ J 6/J Id \W\ 61-3 (1) [oodi3Aiq JU3dj3S 1 na ~L9V\ 381 3 uopuoq (i) J3IZ13JAI Aj adBqs juaiHtijjsuj Appendix G

Mouthpieces ranked by Resonance Factor

This table lists the Resonance Factors of selected mouthpieces in several museums and private

collections. The columns give data for:

Source and Specimen number

Full details of the sources of specimens are give in Appendix J.

Instrument, Maker, Place and Date

These are the same specimens as those in Appendix E.

R factor

This is the Resonance Factor calculated as defined in Equation 7.4, given in nr1.

The considerations of accuracy are as for Appendix E.

175 Z.6*8 031 >[uojA] I W9U4O3 91 MH Z,6'8 /(6)Z.99I (l) uopuoq (i) 3iB3g }9duinjx 8/x ao 868 61 I uopuoq 3UB3 iiBpn>i jBjjg y-y, ui aioq jsoj 139 ao 006 S86I ureds 3jSng 69^3 na 1 ^ 81'6 6l'3 uopuoq W3JJB9 3jSnq p3^3->i A38 dO VI'6 611 3j§ng 66 na vre 031 Nn W3uao3 3 MH

63'6 611 SIJBd siounoo I jgpoui iBjtiSsj 'jsuao^ B9^o XJ LV6 (i) ure;ug (i) HB^M ^ qoBqpuBs jsduirux OSl DHl 69"6 O3'a dno jsduinj} qjiM jsiuoq 6S na 9L'6 0211 30UBJJ SBIUJ9Q H91UOQ aa MH ~9L'6 ~~6nu uopuoq uosssg }3duiru| 9P!is HSl1 Mf 986 [ 03*1 >fUO{/\[ U3UJ03 3 MH 986 S361 3 SUBJ (l) uous9no3 9uoquioaj ooBjdos Z.831 na L2'6 6I'9 30UBJJ (l) uuBuiqosj9X5j gjduiis J3UJ03 103 3H1 90'0t 0t?8l 3 uopuoq (1) J3?iBg UB9d0Ui03 B/.61 Id 90"0I 031 JJ91UO3 36K na LVOl 03'3/6H U9p3Mg uossjqo ^y §J9q|qv H9iuo>i qsipsMS oos na r ZS'Ol 031 ÄUBUL13O pqong jnq>[3BS 9693 na 39*01 61-ui uopuoq [pooM] J3duimj 3pi[s ISI Mf Z.8'01 61'3 (6) 3DUBJJ ((,) UUBUiqOSZ}3J>I pduitijx 8 >ia SO'It 61-ui uopuoq isiqo-x jgduinjx 9i3 na 63'It 61'UJ SIJEJ siojjnoo J91U03 893 na 8f 11 0^813 uopuoq (i) 90Bd 13duinjx A83 na W'll luoqjsoj PL Dm 99'11 611 jajssqouB]/^ uiBqSiH }3UJO3 OUBjdoS 30S na 80X1 00/. I 3 SasqiunjsL (i.) SBBH pduunjx z,66 na 3IXI 0581 a uopuoq (i) ^3^[ jsdumax 0S9 na PYZl 031 ^sn isduitux 3MQ MH O3'l 03-ui qoBg jsduirux si na 8fr*Sl 61-ui uopuoq J9|qo>i [j3A[is] jaduitui 9pns >!SX Mf I'3 031 >in JJ3UJO0 3jn|^[ DiAi ay J0J3BJ y 3?BQ 33|d J3>IBW }0,isur3.ijsii| 99'L ' 0Z.813 SIJBJ siojjnoQ j y9 ui aioq 3iuao^ Dm, AVf L9'L 0061 a vsn japoiu XA3qv 'uuo3 J3UJ03 ej ao w/2 J ors/6ri pdujtux ZL91 na /.//Z. S881 3 uopuoq aWBO OBpn^i Uioq [B3OA 068 j na * 08'Z, 0881 3 uopuoq J3UJ00 mz] na 88'Z. Z.I1 (i) urejiig (I) IPe luoH Z,0 DH1 Z-6'Z, [O9-5S813 SIJBJ sioynoo J31UOQ 9LPZI na 00'8 01781 3 uopuoq JBUa 'z/i u! 3l3riq pa^9^[ UIj Id 1 W8 i 61'3 uopuoq 3[§nq p9/(3^[ K8| dO T 018 0681 3 uopuoq uossag -j pdiuruj apiis ei6ii ^a 01*8 6T"tu (i,) urejug (6) S3II0H 9|Snq p9/(9^ 511 i DHl 3F8 0i/8l a uopuoq r (6) J3^a UBadoiuoQ 3/,6i: Id ^ T8 611 uopuoq (i) Xssooa ujoij paiq Sl\ DHl

I a 31§na Z.l'8 H6I ^ W6i na 6T8 ! 61 oioq qouajj q9l ao ?8 ! 0Z.813 SUBd siojjno3 J91U03 8z,fre! na T 9'8 981 sioyno3 9[§nq jo luoq isoj raj ao

9'8 1 61'"* uopuoq 9[3nq paÄa-^ 8; na 617-8 OZ'3/6 PI XuBuuao uioq-jsoJ 'H 3j[i3Ajoj juadjss ^b 90s ao 8S'8 0981 a uopuoq Bqnj JOU3X 9PS\ na t?9'8 0fr8I 3 uopuoq (i) j9>|Ba UB3d0Ui03 q/,6i| ij , S9'8 61'ui uopuoq UB3d0lU03 SW na 99'8 Oil vsn jsdmrujL 9i5 na 89'8 on HI/ >|3}M J3UJ03 awwal A\H 69'8 on vsn oz. q3BQ jsduinax MH , DLOAj PL'S 581 3 uopuoi (6) JSRO- J3UJ03 PZ\ M 8Z/8 O613 uopuoq pduinax 3t73 Id 8'8 61-ui uopuoq J3[qo~x 3|Snq p3Ä3>j ^[^a A\f I6'8 611 uopuoi 3PB3 IIBpiTfl luoq JBOOA 168 t-861 XnsuoH 3j§ng i7t73j na W8 03'ui uojnq ÄUUV UOIJBAJBS suoquicuj JOU3X 96Zj na JOPBJ a 33BJd )O3UI!iJ)SU| Z.0'9 02'3/6n (^,) ÄUBUU3JT) moq qouajj 998 na Z.0'9 09813 uopüoq UIJSIQ Bqm JOU3X Z,K na ^ Z.0'9 (1) loodisAiq (6) 90^1 JU3dj3S 6Z, XJ

809 1 6l'3 (i) uqBf pduiru} JBjnojiQ SL ao 1'9 L 611 gjnqsu3§3-a jsduiiu} ojiv PLZ na PV9 6l'ai UBSdOttlOQ PbZ na 1'9 0Z.81 3 SIJBd siojjnoQ paioo 6/,t7 na Sl'9 r 6n uopuoq S3>[MBH suoquiojj ojiv HVd T 91'9 6813 uopuoq OQ ^> Xssooa luoq pB[jBg 6t na 61'9 8l 3 SUBd siojjno3 UIOqXBS 3lIO}lJBa S na 12'9 611 j[aoA. A\3M qOBQ aioq qDusjj L6f na Z.2'9 00Z.I 3 (l) }}3UU3a luoq qoirajj 09 ao LZ'9 0861 3 1 ÄUBUU39 U!3HX }nqj|Des ssBg 889 Wi 82'9 0581 3 uopuoq J3UJO3 szz M 8-9 6l (I,) SUBd (1) sioynoQ [/CioAi] uuoq qou3ij 9 ao 1- 017-9 611 3Il!IAI / siojjnoo j y9 ui luoq Xpoj3p\[ DM A\r lfr'9 61-ui (,?,) 30UBJJ 3AB[0IJUinö 01/2 na 5<7'9 61-3 (;) uoÄq (i,) pJBqBx ajinq paXa>j 9 ao 8S"9 9S81 uopuoq (l) JSiqo^i Txioq qou3Jj 9S9 na 9Z/9 6l"3 (6) 30UBJJ sABjoijuino vöa AM LL9 08l U3pS3Ja U3}SJ3^[ uioq qou3Jj 59 na 16'9 6rm uopuoq (1) J3]qo^ J31U00 1789 ao JOOIABI3 902 DHl 86'9 I WZ, 6l'I SUBd [spoiju s,i9XBiduaoq 'jaiuoQ Xd PVL 6I'9 (6) urejpe (6) J3IZJ3JAJ 3[§nq paXa^ Li DHl i 61L 0^81 3 (i) urejpa 80 na i srz, 61 jaduiaix 182 na or/, 6ruj uopuoq }[SBd J3UJ00 229 ao 6rz. 0681 3 oopuoq uosssa "J isduiruj apfis VI61 >ia es'z. 0061 3 J3}S3qDUBJAJ uiBq§|H POIOQ 906 na 9'Z. on vsn 31 ipBg isduiiux DIHA 9'Z. (1)5521 qgjnquipH (6) U91O pduitux 8^9 na JOPBJ H 3jBa aoBItl J3ilBp\i )U3iiin.i)suj Os 88'fr suoquiojx Pit DHl 06> 017813 piaysjapptiH sjgqjojq poo^V }U9di3S sseqBfluoQ 062 na \6'P 02'3/6l1 3DUBJJ suoquiojj JOU3X na lO- 02'3 Bijjsny aioqjousx / uiojj jotox 98l na r PI'S 08I 3 (l,) uiBiug 3DI9T9ludo Pl na 6V9 08I 3 (i) 33UBJJ JO0IAB[3 82 >ia 22' SL61 3 vsn lVz/i9 R3Ba 9uoquioax 681 lAlV 62' 61-3/811 aioq qou9Jj B9 ao ' 0061 3 90UBJJ (6) AuiBq-3i[iAnoqiqx 9uoquiojj ssBqBJ}U03 Olfr a'HD /,' O813 SUBjJ 3[§nq p3Ä9"x 806 na 1 lt?' 611 SIJBd 3ll!W / siounoQ 9uoquiojj ojiv DVcJ Mf , T V9 6t'3 (6) uiBiug uaoq qou3Jj 9^8 na ' 02 m uopuoq s3>jMBj-[ g> /(ssoog suoqujojx 211 na

' ' 02'1" uopuoq J3UIJ9S suoquiojx 99 na ' 6l'3 uaoq ssBg t^21 DHl P9'9 02'9/6H SIJBJ sioynoo 9U0qUI0i} iOU3X 001 na 29' 09813 qijnquipg (6) U31D "1 3pi9[0iqdo 89 na 29' 61'3 (/,) SUBd (6) moo 9pi9piqdo Doa Mf WS 0Z.813 r uopuoq 9JJB3 l[Bptl"y aioq iBOOyv 6Z.I }IQ 69' aioqxBS JOU9X 16 DHl I8' 06813 uopuoq aioq pBjjBg 9l Id 28' 6VW to) uijsia aoD JOU9X 191 DHl WS 6I'3 (6) uiBjug uioq ssBg 0 ao h 98 öl'1 (i) uiBjug (i) uojjig JU3CÜ9S 292 DHl I6' 02'3/6l1 ((,) UIBJTjg suoquiojj OMv 282 na 26' OKI 3 uopuoq (i) sSui3fUI/^ aioq qousjy 8292 na 6' uoossBq UBissn^i 9i?2 DHl 1?6' 02'9/6l1 uopuoq uossgg 9UOqUIOJJ JOU3X 082 na 1 009 02'3/6I'I uossgg suoquioax 862 na 009 of"* uopuoq upsja aioqxBs ouBjdos 26 DHl 09 SO uopuoq aioq IBOOA. S3D Mf W9 611 SJJtBd (i) joflnBO aioqxBs ouBjdos 0t7 na J0P8J a 3JBQ 33KIJ J3JJBM juaiurujsuj o 0V O3'I UBdBf SSBqBJJUOQ z5 na oo SV 6I'3 JU3CÜ9S 8681 na LS' 61'ui j9js9qouBiA[ uiEqSjH 9pi9[oiqdo 851 z na 6S' 6 J 'UI J9}S9q9UB]^[ uiBqSijj 3pi9[Diqdo I (OS dO 09- LL61 a vsn uo}§urui9^i 3uoquiojx 361 WV S9' S8l [ 9uoquiox( ssBg Lzo na 9Z.' 981 | JrajsgqDUBiAl uiBqgfH 3UOqiUOJl JOU9X Pß Id 8Z/ 0061 3 s!JBd ST0JJT103 9uoquiojj ssBg LL9 na 8// JU9CÜ9S 8198 dO 18' 6l-ui) uopuoq UpSIQ uopjBquiog i9ii na Z,8' 9uoquioax \L\ DHl gduiojj 88 Ö L I oiJ-OQ uosssg / luoq qsu3Jj w ao S6' 51813 MOSSBJO (l) jojXbx }U3dJ3S t^39 na

_ 56' 6i'3 (i)u\nuQ [ÄJOAI] JU3dJ9S 30 sx ao Z,6 ' 03'111 vsn 81 qoBg guoqiuoj} Joirax 6831 na 31> 611 SUBJ 3JIJPV / siounoQ uiniuoqdng 3a ao 9l> /,66l uopuoi S3UIOX jnq>[OBS IV Id 8l> er1" ujoq ssBg 90 na 33> 61 (6)Bujsnv suoquioj} JOU9X 903 na 9> lU9dJ9§ S3 DHl 9> 156! uopuoq S9JJMBH ^> Xgsoog suoquiojj ssBg q 9S3 na L P 5681 (i) aouB-iJ (l) siopno3 guoquiojj ssBqBijuoQ ^3 ^a IVP 09LI O (6)33UBJj JU9CÜ9S PQ na VP uossgg 9SSBq 9uoqdouJO3 6s/, na 9t?> 61-3, 9SSBq 10J la ao LPP OF10 30UBJJ (1) joajnBQ 9pi9[oiqdo 901 3H1 Wfr 03 3/6 I'! 33UBJJ 9SSBq 9SSBqo 9p gduioix 03S na w> 61 'a i ((,) uiBjug luoq ssBq ao }U3di9S ii na w> 03'9 uopuoq uosssg 9uoquioix 6S na 99> (i) SBBH uaoq qousaj 509 ao

~~ SZ-> 61'ui (L) ilsiQ ;91UOQ 861 3H1 oz,9 na oo

95'I 61'3 (i) 30UBiJ [ÄaoAi] 3p[3[3ououiiqdo 32( >ia L6'l 81 (1) urejug luoq ssBg LZ9\ na ZZZ jusdiss 3H1 r Vi'Z on' 3DUBJJ su3ij[i]/\i sssBqo ap aduicux na 1 \5'Z y,0 isuusd 'j aduioax QC j >!a jsjn 3i§ng DHl SL'Z I () j ujoq 6 Z wz 8S8I a uopuoq (i) lIBPn>I l^A [[B}3Ui] lusdaas frOl Id \%'z 6F3 [ 1U3CÜ3S Z.001 na LWZ S281 3 uopiioq (l) J3[zj3p\[ jusdaas /. na 86X 08I a' (l) 33UBJJ 3[[19AJIOJ }U3dj3S Ot7 >ia 80' 6F3( (6) UIBJIJg uioaj "q io spppiqdo 9631 na JOJ3BJ y 3|BQ asBId J3?|B|AI ;u3iunjjsuf Appendix H

Instruments ranked by value of parameter K

This table lists the values of parameter j<: for selected instruments in several museums and private collections. The columns give data for:

Source and Specimen number

Full details of the sources of specimens are give in Appendix J.

Instrument, Nominal pitch, Maker, Place and Date

Specimens have been sought which are typical of their place and period and have survived without

significant modification. Further information on these instruments is in many cases given in the

catalogues of the respective museums and in other appendices to this study.

Mid bore

This is the bore diameter in millimetres at a point mid-way between the two ends of the

instrument, (no slides extended, keys opened or valves operated) excluding any mouthpiece and

ignoring local irregularities.

K

This is dimensionless parameter K calculated as defined in Equation 8.2, being the ratio of the

cross-sectional area at the midway point of the windway to the minimum cross-sectional area (near

the mouthpiece receiver).

The measurement of the overall length of the instrument by flexible measuring tools and rulers has

inherent inaccuracies; instruments with long straight sections such as trombones can be measured

to an accuracy of 10mm (better than + 1%) but for instruments with many coils such as french

horns measurement of L is hardly possible to obtain better than + 25mm. The use of pulse

reflectometry increases accuracy for these instruments, but since the bore reconstruction technique

breaks down for acutely flaring sections of tube, it is always necessary to graft physically

182 measured bell section data onto the bore reconstruction, again with an accuracy of + 10mm

(better than 1%). The identification of the midway point of the windway will be on average determined with half the error of the measurement of L.

The accuracy of the bore measurements and thus of K depend veiy much on the configuration of the instrument. With many instruments the minimum bore can be measured using expanding bore gauges inserted into the mouthpipe to + 0.2mm, (approximately 2%); using pulse reflectometry any local irregularities can be recognised and avoided and an accuracy of + 0.1mm for bore

diameter achieved (better than + 1%) (Sharp 1996).

The accuracy of the mid bore measurement of slide trombones can be as good as 2% since the

bore is cylindrical and there is ready access to the foot of the ascending main slide for an

expanding bore gauge. Even for rapidly-expanding instruments such as flugelhorns the

identification of the midway point is not a significant source of error, since the expansion over a

distance of 10mm (about 0.2mm) is not as large as the error in estimating the diameter. If the

midway point is on a curved section it may be necessary to measure the external diameter and

estimate the wall thickness, reducing the accuracy to + 0.5mm. Thus the value of the mid bore

diameter in the worst cases can only be given to + 5 %, which will translate into an error of

+ 10% in K.

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UZ 5ia 00Z 96I 0fr8T3 spsstua xBs qo PUJ03 auojuBg Z99 ao 661 0891 S98T3 SUBJ XBS 'PV qa-6 uioqxBS na 861 OO'Zl U-Z981 SUBJ siopno3 qa i&-zA\? PUJ03 01 L T asN Z.61 0811 Z.66T ^n uossag qa u-y.i7 J9UI03 8Z sa 61 00I 0S8T3 SUEJ pjBqoin9 D-8 JO0XABJ3 pdunuj sssa L9Z QH 061 ozzi 0e-6Z6T UU03 qa-6 ^13 Mf 881 61I S981O uopuoq iaiqo^i qa-z/it PUI03 01 pgipid 'uojXiBa Z9 na 981 08l SS8I3 sioynoQ §ny qa-6 qa 9pi]s UOJÄIBa Z9 na 981 08I SS8T3 SIJBJ sioyno3 Sny 3 -8 J9UJO0 9pi|S 81 id 81 0911 033 UU03 qgw-yit ujoqxBS ouBJdos 919* ao ni OL'il 0Z.8T0 SUBd XBS PV qa-yi a3d 'PU103 886Z na 81 0911 L06I uopuoq 9]JB3 HBpn-y qa s-z/it- yapoui __ sajba iou9x 181 V9l 088T3 j9jsaqouB]A[ xuBqSiH qa-6 guoquioi} PUJ03 9LZ na 081 0811 S6I3 VOA qa H-Vit' auoquioi} ssFqBJjuo3 01t a^3 6/.1 06ZI 00613 SIJBJ ÄuiBq-aiiiAtioqiqx 3 -91 PÜJ03 698Z na 9Z/I OtHI L68T3 uopuoq uossag qa-z/it' gjoq-jBDiuoo 'POJO3 t69 na /.! Z61I 0Z6I3 vsn J9iinjno3 qa -Vti7 pduitu} jgisqgyv^ 09t na L'\ t>811 Z,Z6I3 uopuoq 3JJB3 ilBpn-g qa -y.i7 9SSBq U0JIBJ3 HIT wv ZLl 0991 SA6T3 SUBjJ U0US3T103 qa-6 ijbuis) umiuoqdng jpq-gjqnoQ L%n na L9'l ort-T Or" UBq^iH UU03 qa-6 (ipq pduituj ssßa 8S8Z na 91 06tI 00613 ZJBlSSlUO^ ÄU9AJ93 qa-6 PUJ03 fOLZ na 091 09'11 ZZ6I3 oopuoq 03 ig Ägsoog qa -%* pdman sseg 6ZZ na 091 ovn 0061 3 (l) XuBiuiag qa -6 ujoq iBOOyv 688 na 1 oi ei 881 3 uopuoq 3^B3 HBpn^i D-8 uioq isoj ZSO na Z91 90T 08I3 SjnoqsBjJS miBiuqoszpi^ 3-t7 Bqnj i9u8s^ WAR IST 8rn 006 T 3 spsstug uoiiiqBjAi J-ZI auoquiojj J0U9x OLLI na ZYl 6813 uopuoq 33Bd H'9 qa-6 aunBsod 99UUV ZLV na 0\ ozti 08813 anSBjj IBuiBqos qa-6 jusuin.sjsui 3joq pij\[ J3J1BMI qajij moN 00 fS'L OLIZ 06l 3 ZUIBp\[ J3PUBX3JV qa-6 Bqnj jsuSb/W gigs na \5'L oo'oz 0681 3 SUBd uosssg 3 -8 3SSBq 3uoqdoujo3 8SL na 6ZL 0L6Z 03'iu UU03 qa-6 (ipq 3§JB{) uiniuoqdns ipq-siqnoQ L%f na '9 OL'Zi 09813 SUBd S10U1103 qa -i 3SSBq3J}UO0 UJOqXBS LOlZ na 65'S 00'93 0881 3 isjssqouBjM uiBqSiH qa-6 uimuoqdng 9LLZ na 90S ozsz 00613 uiyjg 3dSRI^[ qa-6 ujoqjousx IZL na L9'f S8"9T (i) 3 qZ.T (l) &W11 O "G~ZAZ })3UJO3 68l na 95't 08'Sl O813 SjnoqsBJJS xiuBuiqaszj3j[-)j qa-6 ^oojo qg 'ujoq puBq [Bjijs31[Djo I 5 na 5't O9'tZ Z.98I XBS PV 3 -8 3sseq tiBSAtiou ujoqxBS ll na OZ't 08TZ 08I3 SUBd UBIBH 3"t? 3[§nq p3Ä3^j Z,06 na 8Z't OO'H 0t8I 3 aouBij ÄjqBqojd 3 -8 spppiqdo psAjBA 60 3d oot qyzz 09813 SUBd jsqosij 3 -8 3SSBq luoqxBS II nv 9 0003 09813 SUBd SIOUHO3 3 '81 luoq 3iu3O^} out na 0 08"6I 068T 3 J3JS3qDUB]AI raBqSiH qa-6 3U0}UBg IILZ na 8l 5vzz OZ UEIM IUBZZB3 qa-8i ossBqrai3 Did AVf 96T 09"6I 611 gjsqujiJN ipara 3 -8 luoqpSnjj JOU3X tS na t6Z 00'8l 09813 SUBd uoöuBssg qa-6 ujoqxBS suojuBg L69 na OLZ 6S'9l 00613 uopuoq 03 g> uosssg qa wvif luoqpSnjj Z6S na WZ 00l H6I3 SUBd U0US3Ü03 3 -8 3 01 psAiBA 'uioq 3iqnoQ na 00Z,I 006T3 zjbj8§iuo^[ ÄU3AJ33 uioqpSnjj f99 na %5'Z 9091 0Z,8I3 SUBd XBS 'PV jBjnjBu g Q-z/it jsduian Bpi.v tt na 9SZ LS'Ll OZ'ra SUBd U0US9I103 aii-n 3ssBq sdxuoax mi wv 9YZ S"SI 61 I uopuoq 31iqAV3iqqg D9-V luoqpSnjj S9Z 3 VZ /.8'tl 08813 SUBd 9IIM / sxouno3 J -9 ujoq ÄpopjAi 3X1 AVf 6Z 0611 0S61 3 ZUIBJAI J3pUBX3JY qg n-6 3pis qg 'luoq siqnoQ W)8I na 'Z orn H613 SUBd uous3no3 qa-6 spis qg 'luoq siqnoa W na orz S8813 SUBd sioutio3 d-9 oijB 3i§ng $9 ffH3 6ZZ 0S'9I 0/.813 SUBd XBS PV qa wzAt ujoqxBS 011BJJU03 S19X ao Ll'Z 08'9l CQQ T 0 uopuoq J3JZ}3p\J qa-6 suoqdojouos t-OZ-I na 603 6911 rAQT jj iiopuoq isjqo^j qa wvif PUJOD OIJSllODB S,Ä3|ÄBg LL na WZ OL'91 00613 (l) ÄUBUU3Q qa-6 suoiiJBg I60 na X ajoq p!W 3*BO 33B|d 00 00

D-8 apppiildo 0911 nn t8I Ot>813 lUBqguiuuia 3 -8 3SlJ§3,p )U3dl9S 909 na T'l ooet1 0Z813 SUBJ UITlOptlBa j ujoqdjY Z.60 nn 00'Li S6T3 ljnUU31|0STAVZ qa-8i assBqajjuoo ujoijxbs (XZS. 0I OOSt> ______A98lj SUBd XBS PV d-ZT Bqnx \i\Z QH 986 00'8 016TO qajjd uioN JT 3joq pjn[ 33BJJ Appendix I

Instruments ranked by value of parameter C

This table lists the values of parameter C for selected instruments in several museums and private

collections. The columns give data for:

Source and Specimen number

Full details of the sources of specimens are give in Appendix J.

Instrument, Nominal pitch, Maker, Place and Date

Specimens have been sought which are typical of their place and period and have survived without

significant modification. Further information on these instruments is in many cases given in the

catalogues of the respective museums and in other appendices to this study.

This is the overall length of the windway between the two ends of the instrument, (no slides

extended, valves operated or keys opened) excluding any mouthpiece and ignoring local irregularities.

This is the dimensionless parameter C calculated as defined inscribed in Section 8.5, being the

proportion of the overall tube length of the windway up to the point in the air column where the

cross-sectional area is double that at the mid-point. C is necessarily between 0.5 and 1.0.

The considerations of accuracy in Appendix H apply to the measurement of the overall tube length

and the bore at the midway point of the windway. The critical measurements here are determining

the point where the bore diameter is V2 times the diameter at the midway point, and measuring

the length along the windway to it from the midway point.

However, any errors in finding the absolute position of the midway point are not critical, only

189 errors in measuring the length along the windway between two points. Again, the accuracy varies from one configuration to another. With slide trombones, the point at distance CL from the proximal end of the windway is usually in the bell section and can be found to the nearest 5mm by

direct measurement as described in Chapter 6. The use of pulse reflectometry allows accurate

measurement and permits local irregularities to be recognised and avoided. In the case of less

amenable instruments, any errors introduced by estimating the wall thickness at the mid-point tend

to be cancelled out in measuring the wall thickness at the point at distance CL from the proximal

end of the windway.

As with the parameter K, therefore, the determination of C is least accurate for instruments which

are most 'conical' and most accurate or instruments which are most 'cylindrical'. The value of the

C in the worst cases can only be give to + 10%.

190 lZ/0 8Z 06T 3 ZUIBJAT J3PUBX9IY qa-6 apis qg 'luoq ajqtioa PQ%\ na OZ/0 96tZ f 161 3 SUBd U0US9I103 3 -8 3 Ul P9AJBA 'UJOq 9[qnOQ \WL na OZ/0 OZZT (\ 1 OT r SUBd XBS PV jBjnjBu g y-y,t7 }9duiai} Bpiy tt na OZ/0 nn 006T3 uopuoq 3 ^ uossgg qa ij-zAP moqpSnjj Z6 na 690 LPLI 088T3 SlJBd 3IIM / siounoo J -9 moq Apoj9]Ai 3X1 MI 690 6T 6T 3 qnpiraqpsiAiz ipgqO O-IT ujoqdjy Z.60 na 890 8ZT 0Z.8T3 uojsog Äqurnf) Tg i\m qa y-E/it pujOD iBflsgqojo ZOZ na 890 ZZ.Z 068T3 J3JS3qOUB]A[ xuBqSiH 9TI0JUBg TTZ.Z na 890 OZT 08T 3 SUBd IIBPH 91§nq P9Ä93 Z-06 na Z,90 OtT 006T3 z^Bjggrap5[ ÄU3AI93 qa wzAP ujoqpStqj fr99 na Z,90 9ZT 0Z,8T 3 SUBd XB§ -pv qa -z/it ujoqxBS o^Bj;uo3 T9X ao 990 06 0Z.8T3 SUBd XBS 'PV qa-Vi ujoqxBS ouBjdos 9I9X ao 990 LZLZ OZ'ui WBq5(lH UU03 qa-6 (ipq 9§JBj) uitiiuoqdng |pq-9jqnoQ na 990 9WZ 098T3 SUBd uoduBsgg qa-6 moqxBS auojuBg I69~~~ na 90 OZ.ZS Z,98T SUBd XBS 'PV qa-8i 9SSBq9flU03 ujoqxBS 6ZZ na 90 fr6 006T3 spsstug d-ZT Bqtl] J9u8ßyW lAIAVH AVf 90 8Z.Z 06T3 ZUTBp\J J9pUBX9IV qa-6 Bqnj J9U§BA\ TZ na WO V\f9Z 98T 3 uopuoq J9JZJ9JAJ qa-6 guoqdojouos tOLT na WO 09Z 088T3 jajsaqauBpv lUBqSiH qg y-6 uinraoqdng 9LLZ na WO TZ Z.98I SUBd XBS PV 3 -8 9SSBq riB9Anou raoqxBS IT na 90 ILPZ 068T3 SUBd uoss9g 3 -8 assBq 90oqdoujo3 8Z, na 90 L\Pi 0T6T 3 uiBqSiH Bqtix IIZ na Z90 66 098T3 SUBd siopno3 qa -T 9SSBq9IJU0D UIOqXBS Z.OIZ na Z90 t?9Z 098T3 SUBd jgqosifii 3 -8 9SSBq ujoqxBS ZT8 na Z90 OZ,Z 006T3 (l) ÄUBUU39 qa-6 9UOJUBg T60 na T90 90tZ 0178 T 3 30UBJJ Ä|qBqojd 3 -8 spppiqdo psAjBA 60 3d T90 Z,9Z 006T3 unjjg 9dstu^{ qa-6 uioqjouax TZZ. na 090 Z8Z 08T3 SUBd pjBqDinr) 3 -8 JO0IAB13 8Z :xa 80 Z-Z 8T 3 SUBd S10UT103 §ny qa-6 qg o\ pgjjnd 9pijs 'uojXjBg Z na 90 ZZ,T 08T3 (I) SUBd (l) XVS 'PV d-9 UJOqXBS J0U9X Z.88 na WO 06frZ 8T3 SUBd sioyno3 -3ny 3 -8 uojiiBg Z na

3 7 3|BQ 33BId qajij hon ;u3oiaijsui OS 6L0 6L9Z SL61 3 SIIBJ U0US3I103 qgy-6 9SSBq UOJIBO 3111 6L0 HLZ 0I6T3 jaddoqos E qfl-6 auoqoiojj iOU9X A03 na 8Z/0 6LLZ 8Z-6I UU03 qs-6 ppoui Hg 'guoquiojj JOU9x UI wv 8Z/0 33 0*813 uopuoq 93BJ qa -z/i/. J00IABI3 331 id 8Z.0 8931 0*813 qgjtiquipg U3IO qa y-z/it UB3dOUJO3 13 na 8Z.0 0193 619 ipara qa-6 gutiBsoj JOU3X 99 MVSM 8Z/0 63! Z.66I W\ uossag qa M-VxV J3UJ0Q I asM 8Z/0 911? 03'ui SUBJ U0US9T103 aii-n 9SSBq sduiojx TITl wv 8Z/0 ZLZ\ U-3981 SUBJ siojjnoQ qa v-Vif J9UJ03 0U na LLO 9831 l6T3 uopuoq S95[AiBH ^> Äasoog qa y-y.t- }9duiaii 3I3 na LLO 8993 00613 Sizdpq laSpjqoBN; pzuaj qa-6 9uoqiuofl ssBqiou9x dÖd Mr LLO 3tI 613 uB§iqoij/\[ >poA qa v-zAP J9UJ03 Z-3 na LLO 60I 5S613 uojsog B§3A qa -y.fr pduiaix I0Z,I na LLO ULZ 08T3 iinoqsBJJS UUBUiqDSZpj^j qa-6 Jioojo qg 'ujoq pireq jBiissqDJO I na 9L0 LL9Z 0061 3 spsstug UO|IIl[Bp\[ d-n auoquiofl ssBqBJjuo3 INAd AVf UBSdOlUOQ 9L0 0831 fr8I3 puBiSuH qa -z/ifr 813 na 9L0 893 S613 ÄUBUU9) iö{snBX{Dsiv SuiqosjipM qa-6 suoqiuoj} JOU9X /. na Z/0 0Z,0 068T3 uopuoq uosssg D-I1 9uoquioij ssBg 6I na na L0 LOZZ 03813 SUBd üinopnBg 3 -8 3SI{§3,p JU3dl9S 909 PL'O 09T 317813 uopuoq J3JZPj/\I qa wviv sdidqjnoui mojibu 'uBsdoujOQ ! na fL'O 61*3 8813 uopuoq 3UBO IIBpn^ 3 -8 moq jBOOA 688 na §IU3O^J ZLO 03 09813 SIJBJ sioijno3 O-8 UJOq OUI na L0 3393 9813 SUBd XBS PV qa-6 luoqxBS 3uo^uBg 399 ao ZLO 6 00613 (i) 3DUBjy D-3 ptijoo opaoici Z,3 ^a ZLO 09LI 8813 SIJBJ sioptio3 d-9 ojiB gjSng fr ffa3 pduitux na ZLO 8T3I I36T3 §jmqs§iAipiiT[ ÄAvipaqos qa y-yit 66 pduiiui ZLO t393 00613 (i) ÄUBUU99 qa-6 ssBg 633 na ZLO 9*3 0fr8I3 ureqSmumg qjiuis 03O 3 -8 gpppiqdo 0911 na pduituj na ZLO 00Z,3 00613 zjBjSSrag^j ÄU9AJ9Q qa-6 ssBg 883 ZLO 08/.3 t^1613 SIJBJ U0US9T103 qa-6 apis qg 'ujoq 9iqnoQ IH> na \L0 8t?ll 0*813 spsstug XBS qo 3-fr PUJOQ 113 ^a J 7 H3|ij ion ,)m;hulujsui Os 80 OtLZ mi Sizdraq J3JWBS qa-6 suoquioj} ssBqjousx 6It 80 (>19Z 6813 uopuoq 33Bd H'9 qa-6 suoquiojj JOU3X OLLI na 80 tO9Z IL91 J9Ä90 qa-6 3UTIBSOJ J0U3X t MQ9M 380 SLSZ OZLl 3 3qa qg-6 suoquioij JOU3X L68I 91 Z80 S6LZ OZ"i UBqj[t3 OU03 qa-6 (ipq IIBuis) umiuoqdns ipq-siqnoQ Z.817 na Z80 0Z 61 ui 3Jj3iq U3[3§Ug UBA qa -J/i9 suoquioij oiiv 086 3d Z80 KZ 8613 ZUlB]/\[ japuBxsjv D-8 pduinjj ssBg I 9VM Z80 8061 0691 §J3qUJTl|4 qa-y.9 auoqraoij o\\y J788I 91 Z80 t96I 98-88T uopuoq 03 ^> Ässoog qa -z/i9 3uoquioj| ojiv 9I na 180 0831 LZ6\3 uopuoq 3JJB3 nBpn^[ qa v-Vip pdUItU) J3}Sq3yW 09t- na 180 OILZ Z.98T 3 SUBd XBS PV qa-6 3AIBA-9 'SUOqUIOfl 3AJBA lOZ ^a 180 0Z 0t8T 3 raniSpg U3|3§Ug UBA 3 -8 suoquiojjJOU3} SIO TIOZ 9a 180 96ZI 6813 uopuoq qa 9-Vif ppoui ,UBippuBHv 'pduiruj saiba 9Z arao 180 teei 029 UBMia UU03 qa v-Vit pujoo spiis 81 M 180 Z9Z 0613 SIJBJ sio]jno3 qa-6 auoquiofl ssBq/iouax 8017 3H3 180 1882 08813 anSBjj puiBqos qa-6 SUnBSOJ 33UUV ZLn na 180 8Z t>6I Siaqiutif^ .I3z}nnps qa-6 suoquioj} JOU3X 69Z na 080 IZ 0881 3 uopuoq 3UB3 nBPn>I O-II 3pijs 3{qnop 'suoquiofl ssBg Jlld Avr 08 0 z,9zi 981 3 uopuoq J3iqo^[ qa %-ViP PUJ03 HID Avr 080 Z.0H ZZ6I3 uopuoq 03 3> Ässoog qa wzAv PUJ03 fOLZ na 08 0 6I 9813 uopuoq jsiqox qa -E/ifr J3UJO0 OpsnOOB S,/C3JÄBg LL na 080 8Z.ZI 08I3 SinoqsBJis uuBuiqoszpj^ 3-t ujoq jsoj Z0 na 080 99H 3JS3UX BU§EJUO]/\[-[ODIIAI qa wvif pduiaix 8i7Z; na 080 L9ZZ ZLSl Jsod SUBJ sioimo3 9 -11 suoquioji ssBg 09 3d 080 0I U6l WBqJiia UU03 qa -J/it PUJ03 Z,Z na 6Z/0 tl 0Z6I3 vsn J3unjno3 qa -z/ifr SJOq-JBDIUOO 'J3UJO3 t69 na 6Z/0 8 9T snqnoQ jfosqipo d-ZI suoquion ssBg 6061 91 6Z/0 OOH 0t"8I3 90UBJJ qa-y.fr sdidqjnoui spiM 'suojsid b PUJ03 69Z na 6Z/0 0I 8Z6T 3 uopuoq 3yB3 iiBptva qa -y.t' jsduiTUj j3jsqsA\ 88^9 era 6Z/0 an 6813 SUBd sioiino3 qa-8i suoquiojj ssBqBJiuo3 fZ "sa 6Z/0 t6Zl 661 3 oi[qnd3^[ qo3ZQ IJBUIV qa -3/it' pduitux I Hd

J 1 JU3UMJJS! 98 0 0091 61' SjnoqsBJis uuBuiqoszjaj^j 0 -z/iS 9UtllIUI9p 9}}9dUIOJX 92 5ta 980 KOZ in Sizdpq jgpxBS qn -s/i9 guoquiojj ojiv Lilt 91 980 66LZ 0L21 SUBJ XB§ PV qa-6 gpifis '9uoquiojj JOU9x Sid Mr 980 t6l 9L9 Sj3qujnfs[ jpiuiqos qa -z/i9 aunBsod JiV 86T WQ9AV 980 2LZ Sizdiaq J3IWBS qa-6 9UOqUIOJJ JOU9X seit- 91 920 LL9Z 9ni aid SUBJ S9J3JJ SIOpnOQ qa-6 9UOquiOJJ J0U9X Z9ZI 3d 920 969Z t6Ll BUU3IA jatiBtpsiiH qa-6 9U0qui0JJ J0U9X 90Z na 920 009Z ZL\ U9IAY japraunostiiBqopi qa-6 9UnBSOd J0U3X 99Z PWSAV 920 9Z0Z 01813 SUBd jsJfOipaiH qa -s/i9 9uoquioj} ojiB S'lO 0Z9 3d 920 9Z9Z 613 U3?M uuBuiiqfi qa-6 9UTlBSOd -I0U9X 661 lAia9A\ 920 lOLZ 0881 3 SIJEJ sioynoQ qa-6 guoquiojj jouax 909 na 920 929Z 61 a (^) umiSpg jo aouBJj qa-6 JB3J oi ipq 'OToqraojj jou9j SXO 8Z- na 920 8992 981 SUBd sioynoQ qa-6 9UOquiOJJ JOU9X LtLi na 920 t99Z 619 (^) uiniSpg jo 30UBJj qa-6 juojj oi ipq '9uoqraoJi J0U9i Sl'O 8L na 920 069Z L2l SUBd Ajbjbh qa-6 suoquioji J0U3X UZZ 3d 920 ZI9Z 613 uopuoq UOS y S3J[MBH qa-6 auoquioji jou9x OLZ na no tttz tI8I &!BUIJ3) dWZl auoquioji ssBg ZL ao no OZLZ 0T8IO SUBd J9J[D0|p9ra qa-6 9UOquiOJl J0U9X t9 na no 009Z L991 Sjsqujnjsj pqOStl3|s[ qa-6 9UtlBS0d J0U9X 90L PMVSAV no 629Z 00613 uopuoq uossag qa-6 9UOquiOJl JOU9X I66Z na t8U 96Z SS8I3 SUBd XBS PV 3 -8 (S3A]BA UT|J9g ) 9UOquiOJl 9A|BA t^691 3d no 90Z; 9813 J3}S3ipirep\[ raBifSiH 3 -8 9UOqUIOJl 3A|BA J0U9X t6 M no 6tl 08I3 (I) puBjSuH O-II 9uoquioji ssBg T06 na 80 8t6T 08813 SUBd 3IIM / sxowno3 qa -Vi9 auoquioji oiiv 3Vd Air 80 0V9Z 8991 Sjaqujtijsj qa-6 9UOquiOJl JOU9X 9681 91 80 ZtZ 09I SjaqujtiM zjioq^ojig O-II 9uoquioji ssBg 0T6T 91 80 H8Z 0S8T3 SUBd XBS PV qa-6 3AJBA-9 'guoquioji 9ajba UL 3d 80 929Z 96LI uaqojp[n3U5[jBi^[ qoBquaqosg qa-6 9UOquiOJl J0U3X 668T 91 80 99l 813 uopuoq IE53J9 9-IT 9uoquioji ssBg 9Z0 na 80 9Z6Z 0-6Z6t jJBqjlia UU03 qa-6 pduitui ssBg L9Z na 80 8821 9Z613 uopuoq 3WE3 HBptl^ qa -c/it ppoui god 'pduitux UL ao 3 7 31VQ qajij aiOM lUOlUllJJSUj oz IUBZZB3 qa-8i ossBquiD Old MI ujoqpSnij fSS na 060 Lin 611 3-8 IOU3X in pduiaij na 680 Z69Z 8I8I lanBg qa-6 qa P35[ooj:o iBiniBM\oLL Id 680 1191 08813 J3JS3ipiIB]/\[ uiBqSiH qa-6 auoquiofl sajba jouax SSI 68T na 680 9LS (I) D qii (i) Ae O -z/i3 jadiutujL /.frZ na 880 oeiz; ULI O3IAV j9nBi|osnH S88T Dl 880 JBI^ Appendix J

Sources of specimens

The following are the source collections of instruments investigated.

AM Arnold Myers, Edinburgh AS Ann Arbor: Stearns Collection, University of Michigan BG Boston Museum of Fine Arts, Leslie Lindsay Mason (Galpin) Collection BK Bruno Kampmann, Paris CEB City of Edinburgh Band CRB Christopher Baines, Burford DB Dave Butcher, Edinburgh DMC Murray Campbell, Edinburgh EU Edinburgh University Collection of Historic Musical Instruments FT Frank Tomes, Merton Park G Graz: Steierisches Landesmuseum GBC Glasgow: Burrell Collection GS Gerhard Stradner, Wien HC Holton Co., Elkhorn, Wisonsin JC John Creed JK Jonathan Korzun, U.S.A. JM Jeremy Montagu, Oxford JW John Webb, Padbrook LC Leblanc Corporation, Kenosha, Wisconsin LG Leipzig: Grassi Museum, Univerität Leipzig LSA London: Salvation Army Heritage Centre LH London: Horniman Museum LHC London: Horniman Museum, Carse Collection MB Mole Benn, per Frank Tomes NSB Newtongrange Silver Band OB Oxford: Bate Collection, University of Oxford PC Paris: Musee de la Musique (formerly the Paris Conservatoire collection) PH University of Edinburgh Department of Physics and Astronomy RC Royal College of Music, London RD John R.T. Davies, per Frank Tomes SR Steve Reed, per Frank Tomes SSC Simon Carlyle, Edinburgh TRM Trondheim: Ringve Museum WAG William Giles, Rosyth

WGDM Kunsthistorisches Museum, Vienna: instruments on loan from the Gesellschaft der Freunde Musik WSAM Kunsthistorisches Museum, Vienna: Sammlung Alter Instrument

The acquisition numbers of museums and other collections have been used where they exist.

However in some cases the numbers have been abbreviated since they have been incorporated in

computer file names of limited length in the course of this study.

196 Appendix K

Table of tube lengths

Note that the actual tube lengths given in Appendix I are significantly shorter than the length given here for instruments of the same nominal pitch. This is partly because L was measured without the mouthpiece and partly because end-corrections need to be applied. Nevertheless, this table, in

with conjunction Appendix I and knowledge about prevailing pitch standards, can be used to estimate the nominal pitch of instruments which cannot be sounded for any reason.

Nominal size Fundamental Equivalent cone length (mm)

6-inC c6 1047 Hz 165.2 6V4-in B B5 987.8 Hz 175.1 7-in Bb Bb5 932.3 Hz 185.6 7V4-in A A5 880.0 Hz 196.6 8-in Ab Ab5 830.6 Hz 208.4 8%-in G G5 784.0 Hz 220.7 9-inGb Gb5 740.0 Hz 233.8 9'/2-in F F5 698.5 Hz 247.7 10-in E E5 659.3 Hz 262.4 lOVi-inEb Eb5 622.3 Hz 278.0 11-inD D5 587.3 Hz 301.9 ll'A-inDb Db5 555.4 Hz 311.5 12-in C c5 523.2 Hz 330.7 13-in B B4 493.9 Hz 350.3 14-inBb Bb4 466.2 Hz 371.1 15-in A A4 440.0 Hz 393.2 16-in Ab Ab4 415.3 Hz 416.6 17-in G G4 392.0 Hz 441.3 18-inGb Gb4 370.0 Hz 467.6 19-in F F4 349.2 Hz 495.4 20-in E E4 329.6 Hz 524.9 21-inEb Eb4 311.3 Hz 555.7 22-in D D4 293.7 Hz 589.0 23-inDb Db4 277.2 Hz 624.1 2-ftC c4 261.6 Hz 661.3 2>4-ft B B3 246.9 Hz 700.7 2!4-ft Bb Bb3 233.1 Hz 742.2 2'/2-ft A A3 220.0 Hz 786.4 21/2-ft Ab Ab3 207.7 Hz 833.3 2%-ft G G3 196.0 Hz 882.7 2%-ftGb Gb3 185.0 Hz 935.1 3-ftF F3 174.6 Hz 990.6 3%-ft E E3 164.8 Hz 1050 3M-ft Eb Eb3 155.6 Hz 1112 3V2-ft D D3 146.8 Hz 1178

197 3%-ft Db Db3 138.6 Hz 1248 4-ftC c3 130.8 Hz 1323 4'/4-ft b' B2 123.5 Hz 1401 4'/2-ftBb Bb2 116.5 Hz 1485 5-ft A A2 110.0 Hz 1573 5-ft Ab Ab2 103.8 Hz 1666 5V2-ft G G2 98.00 Hz 1765 5>/2-ft Gb Gb2 92.50 Hz 1870 6-ftF F2 87.31 Hz 1981 6V4-ft E E2 82.41 Hz 2099 6'/2-ftEb Eb2 77.78 Hz 2224 7-ftD D2 73.42 Hz 2356 7'/2-ft Db Db2 69.30 Hz 2496 8-ftC C2 65.41 Hz 2645 8'/2-ft B B, 61.74 Hz 2802 9-ftBb Bb, 58.27 Hz 2969 9/2-ft A A, 55.00 Hz 3145 10-ft Ab Ab, 51.91 Hz 3333 11-ftG G, 49.00 Hz 3531 11-ftGb Gb! 46.25 Hz 3741 12-ftF F, 43.65 Hz 3963 13-ft E E, 41.20 Hz 4199 13-ft Eb Eb, 38.89 Hz 4448 14-ftD D, 36.71 Hz 4713 15-ft Db Db, 34.65 Hz 4993 16-ftC c, 32.70 Hz 5291 17-ft B Bo 30.87 Hz 5604 18-ftBb Bb0 29.14 Hz 5945 19-ft A Ao 27.50 Hz 6291 20-ft Ab Ab0 25.96 Hz 6664 21-ft G Go 24.50 Hz 7061 23-ftGb Gb0 23.12 Hz 7483 24-ftF Fo 21.83 Hz 7925 25-ft E Eo 20.60 Hz 8398 27-ft Eb Eb0 19.45 Hz 8895 28-ft D Do 18.35 Hz 9428 30-ft Db Db0 17.32 Hz 9988 32-ftC Co 16.35 Hz 10581

Lengths calculated for equal-temperament at A4 = 440 Hz, speed of sound in free air

c = 346ms'.

198 Shelf Mark