Mouthpieces

The basic material for constructing a reasonable air column is already secured. Now it is necessary to bring this air column to produce pressure oscillations at a definite frequency.

In clarinets this is achieved by a mouthpiece and a flexible reed. Mouthpiece and reed operate by controlling the flow into the air column as a non-linear oscillator. The flexibility of the reed allows variation of the effective inlet flow area to the instrument. Therefore, the two key parameters are pressure in the mouth's cavity and air flow. Under certain conditions these parameters enter in resonance transforming the steady supply pressure in the musician's mouth into oscillating pressure waves expanding through the air column.

The study of single reed woodwinds' mouthpieces and the effects of different geometries of the chamber, windways, baffles, facing, etc.,etc. is a complex field on its own. Since such a study is out of the scope of the project, I just bought over internet the cheapest BBb contrabass clarinet mouthpiece I could find. Studies on mouthpieces could be the subject of an advanced study in the future, but for now I do not need to reinvent the wheel. As for reeds, I happen to be very fond of Vandoren. Here is a comparison between three mouthpieces from left to right: Bb soprano Vandoren B45, Bb bass Vandoren B45 and BBb contrabass "Precision".



And below there is a comparison of reeds. All Vandoren, no exceptions.

Material procurement

As mentioned before, PVC tubing was the selected material for the project. Now it was necessary to define the proper internal diameter. The bore diameter of a Bb soprano clarinet is about 14mm and for a Bb bass clarinet is about 24mm.

In some notes "On scaling a woodwind to a new pitch" by the physicist and acoustician Arthur H. Benade, some criteria are discussed to scale a woodwind while preserving the sound color. Without entering intricate details it can be said that it is necessary to preserve the effective shape of the air column, since it will define the local characteristic impedance. It can be shown that if the ratio of pitches is phi = f new / f old, the area ratio is equal to the ratio of pitches and then the equation to scale the bore diameter is d new = d old / (phi)^2. In our case the ratio of pitches is 1/2, since the new instrument will sound an octave lower. Therefore, starting from 14mm for soprano clarinet, we get 19.8mm for bass and 28mm for contrabass. Well, we start to notice some divergence between the fundaments of physical scaling and the practical acoustic behavior. Woodwinds acoustics is, after all, a grey zone between science, craft and art.

However, after some research I discovered that Leblanc contrabass clarinets have a bore of 30mm and Selmer a bore of 34mm. On the other hand Eppelsheim claims that his instrument features "wide bore for a warm, voluminous tone".
Now we come to a remarkable advantage of USA retail shops: infinite options are available. If this supposes in many cases a real added value, is a matter of discussion, but in this case this feature proved invaluable. If you want to buy milk, there is with 1.2% fat, 1.5%, 2%, and all the way up in incredibly small steps. There is a choice of added vitamins for every alphabet letter, iron added , potasium added, you name it. In Europe options are kept within more reasonable limits.

I noticed that a PVC pipe of 1-1/4 inch schedule 40, having an inner diameter of 34mm, would be ideal for the job. Schedule 40 refers to the thicker tube wall, which for this diameter is about 4mm thick. Luckily, my brother was travelling to USA and I prepared my shopping list as follows:
- 1x PVC tubing Schedule 40/DWV 1.25 In. 10 Ft.
- 6x 1-1/4 In. PVC Schedule 40, 90 Degree Elbow Slip x Slip
- 2x 1-1/4 In. PVC Schedule 40, 45 Degree Elbow Slip x Slip
- 2x 1-1/4 In. PVC Coupling, schedule 40, slip

Here is the bill from Home Depot for a total amount of $10.99.



And here is the material, that travelled some 10'000km just for this project.

Project description

I do not recall exactly how I came to the idea of this project. Certainly it was not something that happened at a certain moment, but rather developed in the back of my mind for some time until a point when I started to give more serious thoughts to the idea. It was probably triggered by my project of Bb bass clarinet extension down to C. For that project I needed to consider different cheap materials to perform acoustical studies in order to define the tone hole placement of the three tone holes for Eb, D and Db and additionally to adjust the extension length to properly place the tone hole in the bell for the lowest tone C. Once the proper tone hole layout was derived, a second step was to build the extension in some hard grain wood like grenadilla, cocobolo or rosewood. An obvious testing material for the acoustical studies was PVC tube. A natural offspring of that idea was to use the same approach to study the acoustics of an instrument twice as long, that I had few chances of ever seeing first hand. So, here is the project description.

Goals:

• Derive the dimensions and tone hole placement of a BBb contrabass clarinet.
• Investigate acoustical effects of bends, flared bells, bore discontinuities at bends and couplings in harmonics spectrum, effects of tone hole diameters in cut-off frequencies at different registers; end corrections; etc.
• Sound spectra measurements and harmonics analysis
• Acoustic impedance measurements

Material: PVC tubing 1-1/4" schedule 40
Range: down to written C (sounding Bb0; 29,14 Hz)
Layout: Paperclip

Here is a first sketch of my original idea.



For tone hole placement, the systematic approach as Theobald Boehm used for the flute in 19th century applies: to drill as many holes and as large as needed to achieve each and every note of the desired range, without wondering a priori about a keywork that would operate the resulting instrument or fingerings required.

Many would be at this point disappointed: is it going to be a real instrument on the table ever?

The answer is that I do not know yet. The project as currently planned is challenging enough and may span easily through couple of years. It is not only to produce a perforated PVC tube. The project includes acoustics measurements for which I will have to develop measurement equipment and techniques using affordable components, since I do not have access to specialized devices such as an impedance spectrometer, for example. Moreover, once a reasonably perforated tube is obtained, there is no guarantee that the resulting acoustical qualities justify the sizable effort of developing the corresponding keywork.

Why clarinets?

Let us examine next the second hypothetical question:

Why would somebody want to investigate the acoustics of clarinets, and let alone of a contrabass clarinet? Surely there are nice of-the-shelf instruments to be bought, played and enjoyed.

Just to start with, the acoustics of clarinets is unique. It is the only modern woodwind instrument that features a cylindrical bore with an air column that behaves as a cylindrical pipe closed at one end. Other than the clarinet, only its grandfather the chalumeau or a medieval instrument called rackett, feature cylindrical bore. Considering that the pressure along the tube has a node at the closed end and an antinode at the open end, a closed cylinder will produce resonance of odd harmonics (no even harmonics are produced) and the fundamental frequency is an octave lower than the one produced by an open cylinder of the same length. Another interesting feature is that the air column will overblow at a twelfth, since when opening the register hole, the fundamental frequency is cancelled and the third harmonic is produced.

Other woodwinds as the flute, for instance, behave as an open cylinder. Conical bore instruments, on the other hand, feature varying cross sectional area along the air column. The pressure wave is not plane as for a cylinder but spherical. In short, it can be said that for conical bore instruments the fundamental resonant frequency is the same as for an open cylinder of similar length. For open cylinder and conical bore, all harmonics are produced, odd and even. Instruments that behave as an open cylinder overblow at an octave, meaning that the same fingering with the addition of opening the register hole, will produce a frequency twice as high, since the second harmonic is produced.

Summarizing, the main features of the clarinet acoustics differing from all other woodwinds are the following

• produces only odd harmonics (chalumeau register). This originates the particular timbre characteristics
• overblows at a twelfth. This enables such a large range spanning over 4 octaves
  
• the same air column length produce frequencies an octave lower than open cylinder or conical air columns. This feature allows the contrabass clarinet to reach the same register as the contrabassoon (Bb0; 29.14 Hz) with half the piping (about 3 meters instead of 6)

These acoustical characteristics are valid for all clarinets. Why then a particular interest in contrabass clarinet?
The chalumeau register in the standard Bb soprano clarinet has that warm and full tone that is characteristic. Since I was specially interested in deep voices, my next step was Bb bass clarinet. The chalumeau register of this instrument is truly majestic, which such a dark tone. Bb bass clarinets usually feature a range down to written Eb (sounding Db2). Only professional instruments have a longer body (about 23 cm longer) with three additional semitones, down to Bb1. This feature is quite interesting, considering that the range of the bassoon and cello reaches Bb1. Since the solo literature for Bb bass clarinet is rather scarce, with this extended register a whole world of possibilities for playing bassoon and cello literature are opened. Of course, a professional Bb bass clarinet, say a Buffet Crampon 1193 of about 6-7 kEuro, was not fitting well within my budget, therefore I decided to develop an extension for my old and trusty Evette - Buffet Crampon. At some point in time I will be also discussing some experiences with this project. The next step in the search for deeper clarinet voices is, of course, a Bb contrabass clarinet.

Ok. It is clear why the interest in contrabass clarinet. But what about buying a nice of-the-shelf instrument? A selection of the best woodwinds acousticians of all times have been dealing with issues of tuning, intonation, flexibility, responsiveness, multiple automatic register keys, etc., etc, for contrabass clarinets for over a century: Adolphe Sax, Besson, Houvenaghel, Leon Leblanc, Robert Carre, and more recently Eppelsheim. Why should somebody bother about it? Selmer and Buffet Crampon manufacture in the traditional straight shape in wood and metal respectively. Leblanc manufactures in metal both the straight and the "paperclip" down to written C and to Eb. Eppelsheim manufactures a metal version folded in a way resembling the paperclip, yet different, down to C.

My reasons are the following,

• The motivation of the project is to learn and experiment in clarinet acoustics in a systematic way, with a project proposal that is new and was not yet explored, as far as I know. I am not just eager to play modern compositions of electronic music or contrabassoon repertoire.
  
• I do not have some spare 10 kEuro to spend in an Eppelsheim instrument
  
• Just to show it can be done
  

Questions, questions

I could very well expect already the following questions:

• What is a BBb contrabass clarinet, after all ? What kind of music can be played with it?
  
• Why would somebody want to investigate the acoustics of clarinets, and let alone of a contrabass clarinet? Surely there are nice of-the-shelf instruments to be bought, played and enjoyed.
  
• What is this project about? It was already announced many times, but never discussed in detail.
  
• What is the final goal of this project, if any? Is it going to be a real instrument on the table ever?

Well, let's start with the first question, at least.

A contrabass clarinet is the largest and lowest member of the clarinet family. The common instrument that comes to mind under the concept clarinet is the soprano Bb clarinet, measuring about 66 cm. The Bb bass clarinet is twice as long and reaches a full further octave down and the BBb contrabass clarinet is four times as long and reaches two octaves lower. Under "family" it is understood a series of instruments that share common characteristics, such as sound emission by means of single reed and mouthpiece, cylindrical bore, similar tone hole design and placement, similar keywork. Here it is essential to underline that for woodwinds a different air column length means a different instrument, even if belonging to the same family. There is not such a concept as for stringed instruments like violin or cello, where a 1/2 or 1/4 scaled instrument can be made for children or young people with small hands, being essentially the same instrument. There are bassoons for children, in fact, as the fagottino by Guntram Wolf, but it is actually a different instrument of the bassoon family. Technically, it is a tenoroon (or quart bassoon), an instrument used in medieval times, of course with a much more primitive keywork .
This means that we can not scale up a soprano clarinet by a factor of 4 and expect to get the same acoustic behaviour as for the original instrument, but for a lower voice. Even if the length will be roughly 4 times as large, this does not hold true for bore diameter, tone hole diameters, tone hole placement and register hole (instead of one, even three may prove necessary. Bah, .. as for a standard oboe!)
And here is where the "BBb" issue plays a role. The family of instruments share a similar pattern of tone holes that are closed by means of keywork. A certain specific fingering will not produce the same tone or frequency in different instruments of the family, of course, due to different air column lengths. However, for the musician it is very practical to call the fingering a name, rather than calling the tone a name. Therefore, when the C fingering is played in a Bb soprano clarinet, the pitch of the resulting sound is Bb (if you are in tune), a whole interval lower. On the other hand, if you use the same C fingering in a Eb alto clarinet, what sounds is a frequency commonly known in western conventional 12-tone equal temperament tuning system as Eb, one and a half steps higher. Of course, ethnomusicologists would probably frown upon the western temperament system. So many microtones that nature created for us, are just being wasted! Well, to be fair, in western music and specially among players of stringed instruments without frets in the neck as the violin, enharmonic pair of pitches could be distinguished (as F# and Gb, for example). On the other hand, there were many western composers experimenting and composing with microintervals, notably Karlheinz Stockhausen. Additionally, musicians in Middle East and Far East have been giving these microtones good use, for centuries.
Ok, I am back from the digression. The bottom line is that using this trick called transposition, instruments of the same family can be switched easily without the need to learn new fingerings. This brings us to the lovely feature of the BBb contrabass clarinet, that the lowest note Bb0, corresponding to a frequency of 29,14 Hz is written in G-clef, a clef used for soprano register. Consider that the lowest note in a piano is A0, 27.5 Hz and only half a step lower. Here you can hear some scales in a Eppelsheim Bb contrabass clarinet. For testing the lower notes being in tune, better than an electronic tuner a seismograph would be required.

As regards to the second part of the first question, it has to be borne in mind that the contrabass clarinet is a rather recent instrument in history of music. Adolphe Sax developed a rudimentary contrabass clarinet in mid 19th century, which did not see much success. Only in late 19th century and early 20th century some instruments with reasonable flexibility and intonation were developed. Therefore, most compositions for contrabass clarinet are from the 20th century and contemporary.
Here is a list of literature and composers for contrabass clarinet.
Here is Marco Mazzini playing some contemporary and electronic music.

Introduction

Call me Jaromír Hladík, there are good reasons for it. I am an engineer and an amateur musician. I would like to think of myself as an all-terrain woodwinds multi-instrumentalist. However, my achievements as woodwinds player are probably not as impressive as I would dream. Therefore, I am pursuing on the side of my player career some other music related activities, mainly in the field of musical acoustics and physics of musical instruments. There, I can put to good use my professional skills as an engineer to research, calculate, experiment, plan, develop, manufacture, test and validate; creating papers, prototypes, reports and patents along the way. All this, of course, in my free time, which is not boundless.

At this point it is evident that English is not my native language. Neither is Czech. However, I believe that sacrificing some subtleties in my writing will be compensated by the extended access of these notes to the international community of BBb contrabass clarinet acoustics enthusiasts.

Thus, this blog is mainly intended as a logbook to document the development of a very specific project in clarinet acoustics. Eventually, I could put forward some comments, ideas and impressions on different topics that may call my attention along the way. Typically, other than music and axial compressor aerodynamics, these topics include history, literature, classic cinema, travelling.