Friday 27 May 2016

A Concept for Blowing - Jazz vs Classical

A Concept for Blowing - Jazz vs Classical Saxophone and More


In the shop environment, and throughout many years of teaching, I have frequently been asked to help players resolve their issues with sound and blowing in order that they may produce the type of tone, and gain the requisite control, for the style of music that they wish to play - or a multitude of styles if they are interested in many. Saxophonists are usually familiar with the dichotomy of Jazz versus Classical playing and often struggle with this. For many other wind and brass players it is matter of producing a personal sound that is appropriate for the style of playing desired.

While I certainly acknowledge that some players quite happily find a 'hybrid' personal approach that bridges the various established styles and may even build their careers from such a position, I believe that  most players are seeking to find how they can manage to separate their approaches and equipment to facilitate and to better define the differences between styles.

I suggest below a couple of concepts that I have developed and players have found helpful.

Since 'Classical' styles of playing are primarily concerned with:
  • accuracy of pitch
  • control of fine subtleties of tone
  • a variety of articulation demands
  • focus of the sound
  • blend and the ability to balance dynamics
I therefore believe that a player should look for a set-up that allows them to 'blow up to'  a resistance that offers the stability and predictability to meet these criteria. For me this implies the creation of a reliable and manageable 'platform' where if I do 'my bit' to meet the tone generation requirements of the set-up I know that everything I desire to produce is achieveable with as little additional manipulation as possible.

Since 'Jazz' styles of playing are primarily concerned with:
  • projection in loud environments
  • excitement
  • individuality of tone
  • flexibility of control
  • comfort of sound production
I therefore believe that a player should look for a set-up that allow them to 'blow through' a resistance and in doing so create the desired result. For me this implies a comfort and directness of response without unnecessary additional effort or restriction - where the mouthpiece is free to generate a sound 'propelled', as it were, by the player - while retaining maximum flexibility and ability to influence the tone.

These are concepts not just words

They imply finding the correct balance of resistance from the mouthpiece (and reed where present), the provision of a fundamentally correct and well supported air column, an understanding and application of focus in the oral cavity to the airstream itself, a well considered use of an appropriate embouchure and a choice of equipment that is designed to facilitate the achievement of the desired end result.

  • Doing everything 'right' but on the wrong equipment will surely lead to dissatisfaction.
  • Doing anything 'wrong', to varying degrees, will likely lead to disappointment with even the very best equipment.

In my opinion it is vital to view the choice of equipment and the player's readiness for physical/musical change as a whole, as ones abilities and requirements are constantly changing.
Furthermore, while there are undoubtedly many good and possibly excellent equipment suggestions to help meet the demands of a particular situation or stage of musical development there is almost never a 'magic mouthpiece' or perfect solution that will last forever.

Perhaps the best we teachers can seek to convey to our students is an understanding of the elements that go into the choice of equipment and their relationship to various playing styles. Players and pupils would do well to understand that what they 'bring to the party' (in terms of their ability to use the equipment and adapt their playing habits to suit the requirements of the desired style) is a very large part of the likely success to be found in any equipment choice - and this should be a continuing focus throughout anyone's playing career.

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The tips and comments above are the result of many years of providing help and advice, my personal interest and study, and the teaching that I have done during my career. I have many colleagues and teachers to thank for sharing their thoughts and suggestions on this and other topics. In addition I am indebted to Woodwind & Reed, Cambridge ( www.wwr.co.uk ) where, in the course of helping customers, many of these concepts have been refined and have proven helpful.


Thomas Dryer-Beers






Friday 13 May 2016

Clarinet Response and The One Handed Scale

Clarinet Response and 'The One Handed Scale'


One of more challenging early stages of clarinet learning is gaining control of the upper clarion register, specifically G3 at the top of the staff through to C3 and the first notes entering the true upper range, C# and D. I certainly remember to this day how these notes at first felt very 'wild' and later I well remember struggling with both consistent and accurate pitching and placement of this range. I wish I knew in my youth what I know now but that was not available to me!

As a teacher I feel that a great opportunity is almost always missed when introducing this register to a younger player. The mistake so often made is introducing the expectation that the upper register plays simply with the addition of the register key to the lower register fingerings. Reliance on the register key alone, while possible with reasonable effort, does not prepare the player (of any age) for the sympathetic placement and shaping that should take place in the aural cavity in order to play and tune this register most reliably. This is best accomplished by understanding that the register key is an aid to sounding these notes but it's performance is not automatic.

In my own regular practice and in my teaching now I use the production of harmonics to make sure that I have correctly shaped my airstream and to play this upper register properly. With a higher, lifted placement of the tongue, and careful application of a sufficiently pressurised airstream, it should be possible to sound the entire clarion register by simply repeating the lower chalumeau register fingerings (low E through open G2) - without using employing the register key.  Admittedly this takes a bit of practice and a some patience of course but it teaches a number of very useful concepts

  • 'hearing' and anticipating the feel of upper notes before they are begun
  • correct balance between reed strength and embouchure pressure
  • increased reliance on air support
  • decreased expectancy on lip pressure as a part of the playing of 'high' notes
  • stability and predictability of pitch
  • increased resonance for all pitches as unnecessary lip pressure is discarded

If regular practice of these 'overtone' harmonics is encouraged early enough many of the problems of producing the upper register tones simply disappear.

Even if a player has long ago succeeded in understanding this register there is almost certain to be a time when, on his/her Bb clarinet, or more likely an A clarinet, there will be an entrance or a sustained quite passage on a note in the range A3 through C3 where 'something' does not feel right or the notes 'crack' downwards or simply not seem to want to behave. When this occurs it is very unnerving and I well remember how helpless I felt when I experienced this phenomenon for the first time. I sought to find answers in the regulation of the instrument, in changing the key heights venting, experimenting with reed strength and mouthpiece changes - all to only limited benefit. Years later I was introduced to learning to play overtones as above and to 'The One Handed Scale' and these approaches improved my playing greatly.

I was introduced to 'The One Handed Scale' by clarinet designer, acoustician and performer Tom Ridenour and I wish to acknowledge him and thank him for the time and interest he displayed in showing me this. The production is simple and I would encourage all clarinet players to give it a try:

Staring with long fingered middle C2, utilising the RH F/C key play the first 5 notes of a C major scale exactly as normal - including use of the register key. When ready to play the 6th note, A3, replace your fingers on the starting fingering for C2 and 'think' and shape higher, as if to 'miss' the note deliberately, and if you are fortunate, you will be able to sound an admittedly false sounding A3 as an harmonic of C2. For the next 2 notes simply finger middle register D2 and Eb2 while continuing to 'think' and 'shape' for the harmonic register. You will have played your C major scale and only have used your right hand! 'The One Handed Scale'.

If you find the A3 difficult to sound you are not alone. Acoustically it is the weakest harmonic note of this range and requires the most shaping from the player. Sometimes it is easier to access it and learn the proper feel to expect by descending from overblown fingered Eb2 (sounding C3) going to fingered D2 (sounding B3) and then working to settle into fingered C2 (sounding A3). Experiment with tongue, air and lip positions to improve the pitching and resonance of these notes. The difference when one returns to 'normal fingerings' is remarkable and can make a huge difference to how you feel about this register. If you have enjoyed this process you can, of course, expand upon the ideas expressed above and apply the principal of overblown harmonics to a number of other scales and passages where this sort of practice might help improve the results of 'normal' playing later. It can be great fun and a useful challenge for anyone. Best wishes.

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The tips and comments above are the result of many years of providing help and advice, my personal interest and study, and the teaching that I have done during my career. I have many colleagues and teachers to thank for sharing their thoughts and suggestions on this and other topics. In addition I am indebted to Woodwind & Reed, Cambridge ( www.wwr.co.uk ) where, in the course of helping customers, many of these concepts have been refined and have proven helpful.


Thomas Dryer-Beers

Friday 6 May 2016

Getting the Most from a Specialist Music Shop

Getting the Most from a Specialist Music Shop


Sometimes it pays to stop, take a deep breath, and think about what we as musicians expect from the music shops, specialist repairers and instrument manufacturers that we rely upon. Having trained as a performer on multiple woodwind instruments and as a result having to purchase and maintain many examples and various instruments over my lifetime I certainly have experience as a consumer of goods and services. Having also worked in the Music Industry in specialist shops selling and servicing instruments for nearly 3 decades to date I have also seen the 'other side' and there is much to share with those who might not have had this experience.

Here are the 'Bullet Points':
  • Things can go wrong and accidents do happen despite the best efforts of all concerned
  • Most mysteries can be explained when you understand the 'bigger picture'
  • A musician's needs change over time - otherwise known as 'Progress'
  • The purchase of a 'final instrument' is a myth for most players if you intend to get better and accept that products that might be attractive to you in the future are in continual development
  • Transferring your anxieties to your equipment is rarely a good strategy
  • Be Reasonable. The person with whom you might be frustrated is possibly the one who you will end up relying upon to sort out your problem
  • Sometimes genuine 'Value for Money' does cost more and is worth the expense
  • Quality products are usually better investments
  • People whose livelihood depends upon customer service really do care 
  • Hard earned reputations for good service are valuable and are based on fact
  • Music is a 'People Business', customers are important and shop staff members do care
  • Remember - The specialist advising you may actually know more than you do and in any event will likely be doing their best to help


....and the following is a bit of background that I am glad to share:

When we are learning to play a musical instrument both the beginner and parents are highly reliant on a teacher, where present, or word of mouth from colleagues and friends, when it comes to taking advice on instruments. When I was starting out so many things seemed baffling to me. I struggled to 'tongue' properly and just resolved to not use my tongue to separate notes - I just stopped blowing instead. This unfortunate habit took a lot of effort to undo. I can remember wondering for years why some of my school friends seemed to sound better than me and how it came as a great revelation that a player might upgrade a mouthpiece on their original instrument and that reeds came in different strengths and that by changing these things I too could play better! I also remember living with an unknown problem with the low notes on my saxophone not speaking until the day someone kindly explained that there the sax had adjustment screws that sometimes go out of position - a twist of a screwdriver and years of frustration were relegated to history. Perhaps needless to say I did not have a specialist shop, a knowledgeable teacher or a skilled repairer available to me in those early years.

Once I began to pursue music more seriously I became aware of a world of products, accessories, instruments, customisations and skills that were available. I began to experiment and tried many things. Practice suggestions, exercises, resource books, sheet music recommendations, etc were all of enormous interest. Items were recommended by more knowledgeable teachers, mouthpieces that friends were using and found inspiring and new reed possibilities were sampled. I sought out and spent time with repairers who offered tips and quick fixes to keep my instruments in top shape. I also read a great many articles from respected musicians who had contributed to journals and magazines. I listened to everyone who had an opinion on anything musical to discover from what further knowledge I might benefit. I did make mistakes, invested in things I only used briefly, bought poorly at times, and missed other opportunities - but I tried to learn from everything.

Then, many years later and quite unexpectedly, I found myself with the opportunity to move from full time performing and teaching into full time working in a specialist music shop. All the learning, the investment and attention that I paid over the decades of my studies, my on the job training and my previous experience helped to make my 'skill set' attractive to an employer. But it was only after entering the music industry that my real awareness began to develop. Suddenly, I had a responsibility to advise customers, to understand and grasp the intricacies of product ranges and to distil an increased awareness of a huge range of available accessories into a sensible presentation to others. I found myself regularly meeting with experienced players from many differing backgrounds and possessing a wide range of musical interests as well as many aspiring younger musicians. I was handling repair questions and requests from these customers on a daily basis, some questions were familiar to me but many also arose where I had to defer to more experienced colleagues and repairers - and those repairers were deferring back to me to test and approve their repair efforts. I found myself frequently liaising with manufacturers and distributors - learning of their challenges and obligations as suppliers. All in all this was a very significant advance on the knowledge that I had managed to accrue in my previous years of training and professional experience. The Specialist Shop environment encourages this type of learning and growth and I have been very grateful for the opportunities that came my way.

The learning curve never ends. Interesting, passionate people with greater knowledge than myself abound and I still seek them out. I try to listen more than I talk but I do look forward to the opportunity to share my knowledge with others when something I know or strongly believe in may be helpful to them. What goes around comes around. Please refer back to the bullet points above.

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The tips and comments above are the result of many years of providing help and advice, my personal interest and study, and the teaching that I have done during my career. I have many colleagues and teachers to thank for sharing their thoughts and suggestions on this and other topics. In addition I am indebted to Woodwind & Reed, Cambridge ( www.wwr.co.uk ) where, in the course of helping customers, many of these concepts have been refined and have proven helpful.


Thomas Dryer-Beers

Cracks In Wooden Instruments - Do They Matter? CASS Article

Cracks In Wooden Instruments - Do They Matter?

The vexed question of cracks in wooden clarinets and oboes arises frequently and can be the cause of much anxiety for players or potential purchasers of instruments. A bit of background may help to bridge a gap in the perception of cracking, its reason for occurrence and its relevance to performance. I wish to state that this blog entry is a sharing of information and a relation of my experience over many years - it is not a scientific treatise and should not be interpreted as such.

The African blackwood Grenadilla, latin name Dalbergia melanoxylon, or mpingo in Swahili, which is chosen for most wooden instruments is among the densest wood available for instrument manufacture. It has been the wood of choice for centuries, prized for its stability, workability and resonance for the purpose. It is still a piece of wood. The wood has a grain and the grain is a natural occurrence.  Blackwood grows very slowly (hence its density) and with a very close grain that helps to resist motion and absorption of moisture. The best wood is quite rare and supplies are diminishing worldwide so manufacturers take great care of their wood stocks and use them very efficiently.

Once the wood is harvested, billets are cut from which the joints, barrels and bells will eventually be manufactured. Since the late 1970's until the present day the billets are subjected to a heat and pressure treatment by the manufacturers to stabilise them and further reduce the likelihood of cracks occurring. For instruments manufactured before this technology came into use oil soaking was employed to the same end.

FYI - This is why oiling is not often recommended for modern instruments as it tends to be ineffectual and is more likely to cause damage to pads than real protection to the wood. For older instruments oiling with almond or linseed oil can be very helpful but the caveat of taking great care not to oil in excess must be observed. Oil will shorten the life of any pad with which it comes into contact. If you do wish to oil an instrument use a dedicated swab, chamois leather if available, and only apply a small quantity of oil at a time. Oil the inside of the instrument, as this is where the oil has a preventative role stopping moisture absorption. If the outside of the instrument has a 'tired' or dry look about it some oil may be applied to 'liven up' the appearance but do exercise caution.

Should the wood grain on the surface of an instrument 'open up', either following use or due to climate changes, it is a sign of the wood releasing tension and if this is sorted out by a skilled repairer, usually by the application of modern 'super glue(s)', the wood will actually be more stable than previously and the repaired 'crack' will be made invisible. If the crack opens up to a greater extent and goes through the wood entirely it may require more extensive attention including the possibility of 'pinning' to stabilise it - this is the more serious insertion of a screw mechanism into the wood which is used to draw together the walls of the crack. Prior to the advent of super glue technology this was the common practice to address cracks. If the crack goes through to the edge of a tone hole sealing with glue may work and should be tried initially but it may be necessary for an experienced repairer to insert a liner, usually made of plastic, and remake the tone hole itself. Once this is done the instrument should perform 'as good as new' and will be even less likely to have a similar problem in the same are in the future.

I have played on clarinets and oboes that have had cracks both sealed and pinned for many years with no loss of performance or my confidence in them. When a crack happens on a new instrument despite the best efforts of the manufacturer, if it still under warranty (typically a 1 year warranty is standard with exceptional manufacturers offering a 2 year warranty against cracking) in most cases the instrument will be received back by the manufacturer to have the crack assessed for either repair or  joint replacement. If an instrument is out of warranty an experienced repairer should be able to offer the same attention and the same likelihood of a successful repair to the instrument.

Players can dramatically reduce the occurrence of cracking by observing some very simple care suggestions:

  • Use the swab frequently during practice sessions and performances
  • Pull it through slowly to allow for absorption of moisture - do not 'whip it though'
  • Blow across opened upper joint tone and trill key holes to dislodge moisture
  • Clean the inside of joint recesses to remove accumulated moisture
  • Use cork grease regularly as this helps both assembly and to seal joint tenons
  • Avoid moisture extremes wherever possible
  • Avoid 'stressing' cold instruments with warm air, always bring to room temperature before use
  • Never store instruments in cold conditions
  • Avoid direct sunlight or any heat source that could damage the wood
  • Examine your instrument regularly but without anxiety - just get to know it's natural condition
  • If a grain is noticed to be opening up have it seen to straight away and you will likely have no further trouble
In my experience it is extremely rare that a grain 'crack' has not been able to be successfully and cosmetically satisfactorily corrected. I have taken more than a little solace in the knowledge that should a crack happen and been sorted out my (an) instrument is actually better off and more stable than it was previously when the 'crack' was waiting to happen. It is a bit like the adage 'Whatever does not kill you makes you stronger' and but another example for the musician to heed.

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The tips and comments above are the result of many years of providing help and advice, my personal interest and study, and the teaching that I have done during my career. I have many colleagues and teachers to thank for sharing their thoughts and suggestions on this and other topics. In addition I am indebted to Woodwind & Reed, Cambridge ( www.wwr.co.uk ) where, in the course of helping customers, many of these concepts have been refined and have proven helpful.
Thomas Dryer-Beers 





Double Reed Resistance and Adjustment Tips

Double Reed Performance and Adjustment Tips - What To Do and When

This is a big subject. Knowing what to do to make the most of a double reed becomes important to most players after only a few months of learning. Even with the available guidance of a knowledgeable teacher (and this is not always available) there will certainly come a time when a reed one is reliant upon just 'does not play' as it used to and something must be done in order to get through a performance. There are many textbooks and articles that can help with illustrations and advice though the best contact probably remains a successful player with experience of adjusting and if possible the making of their own reeds. This is a quick reference summary from my experience and advice I have given to pupils over many years -



Best practice starts with care in soaking the reed for about 60 seconds in water up to but not over the level of the thread - every time before you play. Bassoon reeds can be placed entirely in the water. Some players always soak their reeds by placing them in their mouth. I feel that this exposes the cane to an unnecessary degree to sugars and acids from saliva - eventually shortening the playing live. Water is cleaner, warm water is best as this relaxes the reed fibres more quickly. Not wetting at all prior to playing is a sure route to disappointment and shorter reed life.

Once wetted the reed blades may require subtle adjustment to achieve a good-looking aperture.

  • If the opening is too great the blades may be pressed together with a light touch of the fingers taking care to not press so hard that the cane splits. If the reed is wired (oboe or bassoon) adjusting at the wire by hand or using a small pair of pliers may be required. For bassoon reeds adjusting at the second  (middle wire) 'opposite' to what initially seems logical will often be what is required as the first wire will act as a fulcrum.
  • If the opening is too small the blades may require the opposite correction with a gentle squeeze to increase the aperture on the oboe reed and once again the 'opposite' correction for a bassoon reed.
Test the aperture and the readiness of the reed to play by blowing a 'crow' on the reed - accomplished by playing more of the reed in the mouth than usual and blowing a sustained and forceful air stream with a minimum of lip support. This is a simultaneously high and low rackety noise that is an indication of a reasonable 'balance' to the reed. If after practice you cannot obtain a crow then that reed is likely to need further adjustment to get into a proper balance and a reed knife may be called upon to remove cane. Always use a plaque when working to remove cane from a reed. I prefer a 'bellied' plaque, as these tend to provide the reed blades more support during scraping. Always work slowly and carefully with a wetted reed and test frequently.

  • If the upper noise is absent in the crow cane may need to be scraped from the tip area using the knife and a plaque. It is often said that the secret to a good reed is a thin tip.
  •  If the lower noise is hesitant or resistant in the crow the tip area may need to be 'integrated' into the heart and back profile of the reed. Check against a strong light source to see the location of darkened areas on the reed. Compare the 'look' of the problem reed to the appearance of a good reed and see what areas might need to be scraped.
  • If all looks good but the reed is still resistant then try scraping cane from the rear of the cut away profile at the 'back' of the reed vamp. Do this slowly and keep testing, as you do not want to take away the resilience of the reed and leave it incapable of supporting pitch.
  •  If the crow is satisfactory but the pitch has gone flat the usual correction on an oboe reed is to carefully 'clip the tip' removing a fraction of a millimetre of cane. To do this you will need a very sharp straight knife and a cutting block. Test the result after clipping and be prepared to rebalance the reed if necessary to ensure the proper relationship between tip, heart and back of the reed. On a bassoon reed this may also be the appropriate correction before cutting the tip try arching the reed at the second wire to see what effect this has upon pitch. Bear in mind you may have to rebalance at the first wire also to maintain a proper aperture opening.
  • If the crow is satisfactory but the pitch has gone sharp the cane may be 'clogging up' and might benefit from a light general scraping overall to remove the build up of skin cells, saliva and dirt that may have come over time. If no response is gained from the approach one can take 'pitch' out of a reed by scraping the tip, the heart region and or the back to give the reed back its flexibility. Try this systematically and in very small stages and test frequently. It is very easy to go too far!

A further note - Playing the oboe and the bassoon should require a strong, well-supported air stream. I should not require a great deal of 'biting' at the lips or cause fatigue in your embouchure within a few minutes of blowing. The most attractive double reed sounds are lyrical, exciting and characteristic over the entire range of the instrument without any sense of hesitation or 'dropping out' due to problems with basic tone production. Strive for this always and try to make sure that, as much as possible, you have your reed on your side!

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The tips and comments above are the result of many years of providing help and advice, my personal interest and study, and the teaching that I have done during my career. I have many colleagues and teachers to thank for sharing their thoughts and suggestions on this and other topics. In addition I am indebted to Woodwind & Reed, Cambridge ( www.wwr.co.uk ) where, in the course of helping customers, many of these concepts have been refined and have proven helpful.
Thomas Dryer-Beers



Thursday 5 May 2016

A Guide to Current Vandoren Single Reed Products 2016

A Guide to Current Vandoren Single Reed Products 2016

Vandoren make a truly remarkable range of top quality products for the clarinettist and saxophonist. So much so that perhaps a little additional background might be useful when considering which choices might be right for your set-up and style.

For the manufacturer's explanation I recommend a visit to the main Vandoren website where their many products and much additional specification information, artists, news and images may be found.

www.vandoren-en.com

For UK and European ordering of Vandoren reeds I am pleased to be able to recommend visiting:

www.reeds-direct.co.uk for their unrivaled stock and service.

For information and ordering any of the wide range of Vandoren accessories I would like to recommend visiting:

www.vanbleu.com

For my summary and opinions - stay right here!

For each of the reed products the Vandoren website offer their intentions and design details. I find that these are sometimes difficult to decipher and I have developed my own, deliberately short, and hopefully memorable, characteristic tone and performance descriptions. I hope they might help and I encourage all players to try the logical options for them - as I have - and see what these fine reeds can offer.

For clarinet reeds the range now extends to 5 products:

Traditional - Brilliant, with great attack
V12 - Flexible, woody and warm
56 Rue Lepic - Dark, centred and stable
V21 - Response with warmth
and the quality student reed by Vandoren, the Juno - Reliable, easy play

For saxophone reeds the range extends to 8 products:

Traditional - Brilliant, with great attack
Java - Flexible and round
Red Java - Responsive, flexible and bright
V12 - Flexible, woody and warm
V16 - Punchy with edge and projection
ZZ - Flexible, responsive and characterful
V21 - Response with warmth
and the quality student reed Juno, by Vandoren - Reliable, easy play

All the above reed designs are manufactured using the same top quality cane - their different performance is due to the variety of profile used in the cut, the thickness of the tube of the cane used, the thinness of the reed tip, the taper of the blank and the amount of cane left in the heart and spine.

All the above reeds are, of course, available in different strengths, and the effectiveness of the match to the mouthpiece being used and the playing approach of the player are critical factors in the performance and successful use of any reed. An incorrect reed  cut or strength match will compromise the intended performance without any doubt. While it is true to say that a successful match is an individual choice there are some generalizations, based upon likely use and type of mouthpiece match that may help. I am attempting to place these on a spectrum of likely successful use - bearing in mind that narrower tip openings demand stronger strength reeds where as larger tip openings will generally require softer strength reeds - medium tip openings can match most strengths and cuts. The characteristic use (C) - Classical, (J) Jazz is shown at the far left of each line.

Use      Narrow Tip Opening          Medium Tip Opening       Wide Tip Opening 

(C)/(J)       Traditional --------------------------------------------------------------------                     
(C)      V12 --------------------------------------------                                                                 
(C)               V56 ------------------------------------------
(J)                                       Java --------------------------------------------------------- 
(J)                                       Red Java----------------------------------------------------                 
(J)                       V16 ----------------------------------------------------------                             
(J)                                       ZZ -------------------------------------------------------       
(C)            V21 --------------------------------------------------------                             
(C)                                           Juno ----------------------------------------                                     


I hope the short summaries above will prove useful. It certainly helps me to keep all these products clearer in my mind when I am advising pupils or customers.

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The comments above are the result of many years of providing help and advice, my personal interest and study, and the teaching that I have done during my career. I have many colleagues and teachers to thank for sharing their thoughts and suggestions on this and other topics. In addition I am indebted to Woodwind & Reed, Cambridge ( www.wwr.co.uk ) where, in the course of helping customers, many of these concepts have been refined and have proven helpful.
Thomas Dryer-Beers