The fingering logic and performing of woodwind instruments

Inhalt

Abstract (deutsch)

Abstract (English)

Expression of Thanks

Preamble

1. Introduction and definitions
1.1 Basics of the woodwind playing
1.2 Body and instrument as a harmonious unity
1.3 Physical conditions and level of difficulty of the fingerings
1.4 Posture
1.5 Strengthening stamina
1.6 Physiology of mouth and jaw (embouchure) vs. controlled finger coordination
1.7 Instruments for children, instruments for women
1.8 Training of correct practising
1.9 Finger size, key or hole size
1.10 Level of training, age, maturity, playing at sight
1.11 Development of the body and the development of the muscles of the fingers and the hands
1.12 Relation of body height and instrument size

2. The issues of the dissertation and its relevance
2.1 Is the degree of the difficulty of fingerings and fingering combinations predictable?
2.2 The proof of the subjective difficulty rating of fingering sets
2.3 Is it possible to make a prediction of the degree of difficulty of a piece and as a result a calculation of the optimal fingering sequence?
2.4 Is it possible to generate an aesthetic prediction of the playing the clarinet?
2.5 A modelled clarinet can be a tool for composers or for instrument manufacturers

3. Preliminary studies
3.1 Preliminary study 1: Exploratory
3.1.1 Question 1: Methods of practising in the “head”. Which methods are available and which are best?
3.1.2 Question 2: How will the grade of difficulty of a piece be determined?
3.2 Preliminary study 2: Quantitative, qualitative
3.3 Hypothesis 1: Correlation between grade of difficulty and the number of used fingers
3.4 Preliminary study 3: Qualitative
3.5 Hypothesis 2: Correlation between grade of difficulty and finger position
3.6 Hypothesis 3: Correlation between the "difficulty-acceptance" and an aesthetic decision
3.7 Preliminary study 4
3.8 Preliminary study with saxophonists
3.9 Preliminary study with clarinettists
3.9.1 Test persons of the clarinettists study
3.9.2 Key index 0
3.9.3 Key index 1
3.9.4 Key index 2
3.9.5 Key index 3
3.9.6 Key index 4
3.9.7 The calculations
3.10 The saxophone-survival
3.10.1 Test persons in the saxophone survival
3.10.2 The survival of the saxophonists
3.10.3 The values of the saxophone survival
3.11 Main analysis: Quantitative study of clarinettists and saxophonists. Analysis of the obtained data

4. General investigations
4.1 Introduction
4.2 Method
4.2.1 Participants (selection, features)
4.2.2 Experimental design
4.2.3 Technical resources
4.2.4 Procedure
4.2.5 Evaluation
4.3 Results of both surveys
4.3.1 Results: Clarinet
4.3.2 Results: Saxophone
4.4 Discussion

5. Description of the model
5.1 Theory
5.2 Mathematical description
5.3 Comparison between results and predictions of the model
5.4. Discussion
5.5 Error causes

6. Conclusion
6.1 Experimental design
6.2 Methods of Evaluation (Particularly Explanation of Applied Qualitative Methods)
6.3 Methodological Results
6.4. Generalizability
6.5. Qualitative analysis of quotations, categories .

7. Summary of main results
7.1 Extension of the model
7.2 Further research: case study, analysis of pieces
7.3 Which conditions make playing a woodwind instrument difficult?
7.4 Which groups of persons have problems?
7.5 Why there are problems and why is this relevant?

8. Implications
8.1 Implication for practising
8.2 Implication for composition and publishing
8.3 Implication for music education systems

9. Literature (alphabetical listing)

10. Appendix

11 Glossary: Specific and Origin Words and their Translation

Abstract (deutsch)

Mag. phil. Peter Ninaus Bakk. art. : Die Grifflogik und die Spieltechnik von Holzblasinstrumenten. Eine psychologische Untersuchung und ein Modell.

Da es keine empirischen Untersuchungen des Holzblasinstrumentenspiels gibt, zeigt diese Arbeit einen Weg wie man z.B. „Angststellen“ berechnen und umgehen kann oder wie man optimale ästhetische Grifffolgen suchen kann.

Die Auswertung explorativer Tests zeigt einen Zusammenhang zwischen subjektiver Schwierigkeit und der Anzahl der in Verwendung befindlichen Finger bzw. der Veränderung und der daraus resultierenden Anzahl von Fingerbewegungen. Um diesen Umstand zu erklären, verwende ich eine Grifftabelle, die ich in 0-en für offen oder nicht gedrückt und in 1-en für geschlossen oder gedrückt umforme (Konjunktoren). Mit dieser Tabelle war es mir möglich die Griffbilder als Vektoren darzustellen und diese miteinander in ihrer Veränderung zu vergleichen. Über Vektor-Summen hatte ich die Möglichkeit die subjektiven Ergebnisse mit den errechneten Werten zu vergleichen. Der Zusammenhang zwischen subjektiver Wahrnehmung und errechnetem Schwierigkeitsgrad war gegeben. Dieses Ergebnis ermöglicht es nun ein Vorhersage-Modell über optimale Grifffolgen für Musiker, Lehrer und Komponisten zu erstellen, ohne sich mit der Spielweise der Klarinette zu beschäftigen.

Die Zahlen ermöglichen es aber auch ästhetische Analysen von Stücken zu machen, wenn die Grifftabelle um klangliche Kriterien erweitert wird. Es können Notenpassagen auf anderen Instrumenten übertragen und auf deren Spielbarkeit überprüft werden, wenn eine klangliche Situation dies erfordert.

Dieses Werkzeug is ein Rohinstrument und sollte um akustisch-physikalische und ästhetische Parameter erweitert werden, um die Weiterentwicklung der Klarinetten (Wiener Klarinette und Französische Klarinette) zu forcieren. Ziel einer Weiterentwicklung von Blasinstrumenten sollte es sein, klangliche und Griff-technische Erscheinungen zu optimieren und zu erweitern. Griffvorteile der einzelnen Klarinettensysteme sollten auf dem anderen Instrument verfügbar sein und abgesehen von der Bohrung der Systeme universal einsetzbar gemacht werden.

Abstract (English)

Mag. phil. Peter Ninaus Bakk. art.: The fingering logic and performing of woodwind instruments. A psychological study and model.

Since there is no empirical research about woodwind-playing, this work shows a way, for example, to calculate "Fear Parts", and how you can circumvent them, or how you can find the best aesthetic fingering sequences.
The analysis of explorative tests showed a correlation between subjective difficulty and the number of fingers in use or the change and the resulting number of finger movements. In order to explain this situation, I use a fingering table, where “0” represents open or keys not pressed, and in “1” closed or pressed keys (Conjunctors). With this table, it was possible for me to handle images as vectors and represent them together with their transformations to make a comparison. With the vector sum, I had the opportunity to compare the subjective results with the calculated values. The relationship between subjective perception and calculated level of difficulty was given. These results make it possible to create a forecast model of optimal fingering sequences for musicians, teachers and composers, without knowing about the playing of a clarinet. These calculations also enable the Aesthetic Analysis of pieces, if the fingering table is expanded with aural criteria. Passages of pieces could be transcribed to other instruments, and be reviewed on their playability, when a sound situation requires this.
This is a crude tool and should be extended to acoustically-physical and aesthetic parameters, to make further developments of the clarinets (Vienna clarinet and French clarinet). The aim of further development of wind instruments should be: Optimizing and expanding sound and fingering techniques appearances. Advantages of the fingering of each clarinet system should be usable on other instruments and, apart from the bore of the systems, universal.

Expression of Thanks

Einen Dank möchte ich allen aussprechen, die mich ideell oder materiell unterstützt haben. Besonderen Dank verdienen, die bei mir das Interesse an der systematisch- musikwissenschaftlichen Arbeit geweckt hat und mir dadurch ermöglicht hat zwischen und hinter Musik zu sehen.

Einen großen Dank gebühren Herrn Dr. Richard Parncutt, der mich seit meiner Diplomarbeit immer wieder unterstützt und Frau Dr. Adina Mornell, die sich sehr viel Zeit genommen hat, wenn ich mit Fragen zu dieser Arbeit gekommen bin.

In diesem Zusammenhang soll auch alle interdisziplinären Denkern gedankt werden, die ich auf meinem bisherigen Weg getroffen habe: Meinen Klarinettenprofessoren und -Lehrer: Mag. franz Schöllauf, Mag. Hildegard Monsberger, Prof. Johann Königshofer, Prof. Eugen Brixel, Prof. Robert Fischer, Prof. Bertram Egger und Prof. Anton Fritz. Meinen Professoren an den Universitäten: stellvertretend: Prof. Werner Jauk, Prof. Gerhard Wanker, Prof. Reinhard Kamitz.

Einen weiteren Dank möchte ich meiner Frau Alice Ninaus aussprechen, die mich immer wieder ermutigt hat, meine Ideen weiter zu verfolgen.

Preamble

This doctoral thesis is an attempt to write a systematic musicological work about playing woodwind instruments, especially the clarinet and the saxophone. Even though I have tried to work with empirical and music psychological methods, this work also includes systematic approaches and methods of other musicological disciplines. A complete separation from historical musicology, in the treatment of this issue, is not possible. The research on this question represents a first attempt to work through this type of questioning, and is to be understood as a pilot investigation. The trials and exploratory studies are developed over several years. The basic ideas originated from my bachelor thesis, which I wrote at the University of Music and Dramatic Arts in Graz. This work was the basis for further research. With more empirical questioning, I expanded it to a master’s thesis at the University of Graz. I was aware from the outset that this issue would not be easy, and that all sorts of related topics may result in a number of other works. From this work many interesting mathematical, technical and educational data could be derived and explored in greater depth. The investigations of the model and its subjective verifiability could be explored in more detail.
All names in this work were used as gender neutral.

1. Introduction and definitions

"You just have to close with the next finger the next hole, then the next lower tone will come." This is a sentence, which is often said to clarinet students. Behind this seemingly simple exercise is a hidden process that requires a lot of interdisciplinary thought. This logic is actually applicable to very few notes. The idea behind this development and the resulting linking of fingerings is, for a growing woodwind-instrumentalists, the decisive issue in the selection of practice strategies. The possibility of free choice of fingering combinations is not always guaranteed, because of sound or ideological reasons, or the ignorance of further combinations.

Fingering and tone generation can be well illustrated with physical models (Wolte 2006). The resulting fingering charts can be schematically illustrated with the aid of the methods of the logic, and with mathematics they will be converted. The resulting vectors enable one to rate the fingering images and make them comparable. The control of the fingering can be explained anatomically using medical methods, and its movements can be described with the help of sport science. The remaining questions about woodwind playing can be explained and clarified by using the techniques of brain research, and the fingering-combinations can be psychologically modelled.

The clarinet is the most difficult woodwind instrument to play, because it is the only instrument in its family, which does not overblow in the octave, but it overblows in the duodecimo. The advantage of this circumstance is that the B-flat clarinet has, with a relatively handy tube length, the range from the D3 to the C7. The disadvantage resulting from this fact is that there is little similarity of the fingerings, and so every note must be learned as a (almost) new fingering. Another problem of clarinet playing is, that some combinations of sounds are considered "unplayable" and therefore the trained clarinettist should cheat "inaudibly". This is known by the term "sliding". These and other circumstances may, for the sight reading musician, lead to a technical dead end which is difficult for good musicians as well.

The following system was developed to try to calculate fingering problems and propose solutions for difficult fingerings. Furthermore, this system can be applied to other wind instruments to compare them with each other.

1.1 Basics of the woodwind playing

The playing of an instrument cannot be reduced to just contact with the instrument. An interest in the ergonomics of playing instruments is a basic requirement for good playing and learning of wind instruments. In addition to these conditions, practice endurance and mental conditions are criteria for good development with the instrument. For the non-musician, the playing of a wind instrument looks as if the musicians just make sure that there is enough "air" carried through the instrument and make their fingers move as quickly as possible on the instrument. Those who have ever tried to play a wind instrument discover that blowing the wind instrument is a combination of embouchure and breathing. Only when one studies such an instrument does one find that whole-body use is necessary for making music. Making music is comparable to high-performance-sport. In addition, optimal fingering, endurance, strength, disposition, optimal breathing, posture and mental strength, affect logical operations in the development of a musician.

Without educational intervention, only those so-called "talents" can become professional musicians. The talented have the problem that they do not necessarily have to learn to optimize their fingers. This will cause little problems to not be prevented, and a comprehensive knowledge of the different fingerings will not be developed. This can cause overuse syndrome, other ailments and problems with anxiety and cause failure at anxiety passages.

Nemoto and Arino (2007) found that clarinet players as well as flute and oboe players often have more hand and upper extremities problems, than other wind players in Japanese military bands. Most players have problems with the digit and the wrist. Women have more risk for problems with the upper extremities than men.

Lahme (2000) recommends that, first of all, to avoid illness playing an instrument, a beginner should be checked orthopedically and physiologically by a specialist. The suitability for a particular instrument depends on the individual constitution and the body proportions. Therefore, such an analysis of the suitability should contain the following aspects:

-Constitutional factors,
-length ratios of the spine
-length and length ratios of the upper arm to the forearm and hand, the position of the shoulder and pelvic girdle, muscle conditions
-hand span
-proportional relationships of the fingers
-length and proportion of the lower extremities (legs).

These physiological aspects are responsible for third variables (see chapter about sources of errors) and influence the evaluation whether something is “difficult” or is felt to be “easy”, because even the so-called "long fingering set^[1] " won't make concessions for a clarinettist. This is especially difficult for untrained musicians or beginners. "Long fingering sets" are often played with keys, which are, because of lack of space, mostly peripherally mounted.

1.2 Body and instrument as a harmonious unity

To be good at an instrument means to feel comfortable playing the instrument, and to handle the instrument like a game. The playing of an instrument should be a harmonious sequence of movements.

Playing an instrument should be accomplished without physical concessions (such as bringing forward of the shoulder, etc.) if possible, but it is possible to reach a lot of physical results through the right training. To play the clarinet it is necessary to lower the right shoulder slightly and set the fingers in a non-natural position, but too much adaptation of the body to the instrument should be prevented with ergonomic tools. In other cases, it is helpful to do hand exercises. It is also good to imagine that the movements of the fingers on the instrument are mechanical to get exact movements. The musician's posture with the instrument should be as close to posture without an instrument as possible. Only then is a physiological breathing possible within the musical phrase (Lahme 2000). The fingers should find “their” place with mechanical exercises.

1.3 Physical conditions and level of difficulty of the fingerings

The problem of fingerings is not only dependent on the motor function of simple fingers, but also many other variables. This third variable can be of a musical type (tempo, rhythm, ...) or of a physical type.

An important question is, what are the conditions which make playing an instrument like the clarinet “difficult”? Some of these conditions are: Inexperience, difficult surrounding, physical condition of the player, handicaps, problems with the construction of the instrument, position changes, light conditions, nervousness, genre or heaviness of the instrument.

As previously mentioned, physical and psychological conditions play an important role in what is perceived in music-making as "difficult". To play the clarinet there are some important factors: 1. the length and proportion of the length of the upper arm to forearm and hand, 2. the position of the shoulder and pelvic girdle, 3. muscle conditions, 4. hand span and proportional relationships of the fingers and 5. a basic training of motor skills.

From my experience, I can report that there are many opportunities to learn playing the clarinet. Missing teeth, false tooth positions, size of fingers or respiratory illnesses are no obstacles in learning woodwind instruments. The awareness of exercises and their sense require that a teacher take extra effort and time, teaching with a creative teaching method. Here are the factors: power, patience, imagination and continuance of the teachers in demand.

Prevention of illness and optimizing of practising have the same aims. General measures for health promotion and health maintenance are the basis of good physical conditions and good playing. Calm, deliberate, focused practising prevents stress, which causes cramps and lack of concentration. A physiologically correct posture guarantees an optimal physical performance. Relaxation exercises and breaks are needed to optimize the duration of high level performance and prevent cramps. Body awareness and body-experience is important for knowing the personal limits. Shorter, but more practice sessions help practising with a higher level of efficiency. The ergonomics of the instrument and of the fingering technique are the physical part of optimal playing.

With all these factors it is possible to reduce the grade of difficulty of playing. These factors also cause third variables which sometimes make easy parts more difficult.

1.4 Posture

The solution to the problem of the right posture can be found in the placement of the feet while standing.

There should be a dynamic standing during the playing of an instrument. There are a few exercises to find balance between standing and moving while playing. The breathing and moving of the fingers will be better if there is a use of more floor space. Long fingering sets need to activate the body, because great movements e.g. of the extremities help to compensate for problems with small fingers and work against cramps in the hand. But good training would minimize the “great” movements, so that the fingers will move fast and precise.

A lot of clarinet teachers know about right positions for the thumb. Lehr (2000) e.g. says the thumb is at an angle on the thumb hole, not straight up and down. Wrong thumb positions often are signs of an incorrect posture, because the thumb is only the last element of the hand as well as of the arm.

A prerequisite for the optimal fine motor skills is a good posture. If it is not good, it will block muscles and tendons. Lahme (2000) says concerning posture, that a balanced spread of the total load (weight) on the ligaments and muscles (principle of the ship mast) forms the basis of a physiological posture. The upright posture requires continuous muscle activity, especially the “autochthonous back muscles”^[2]. Without muscle power the spinal column and ligaments, despite the double-spring design, are not able to guarantee an erect posture.

Thus the asymmetrical handling of the woodwind instruments makes playing difficult for young beginners. The weight of the instrument and the fingering coordination lower the concentration and the physical condition. But this doesn’t have to be the case.

1.5 Strengthening stamina

For the posture of the body the rule is: Not power is important, but endurance. An analogy to that is: not force and velocity of the fingers, but the endurance and fine motor coordination are important. This endurance is also necessary, because the clarinet keys themselves have some important similarities and differences from keys on other instruments that may influence the sensory feedback available to performers. Similar to piano keys, clarinet keys have springs that provide resistance to fingers when they are depressed from their resting position (Palmer et al. 2009).

So the mechanical training, which every time starts with slow coordinated movements, is the basis for playing fast passages.

Factors which causes additional problems are age, sex, psychological problems, physiological problems, surroundings and climate, pressure for higher performance or lack of concentration.

The main task of the ligaments and intervertebral discs is acting against excessive movement rashes. Gravity loads on the ligaments of the spine cause irritation: band structures, which are not meant for posture are used incorrectly. This also applies to the hand and arm. Force and excessive demands lead to problems and with physiological problems, the fine motor skills become slow.

The starting position of the hand should be relaxed while playing.

Each handling of an instrument is contrary to a certain degree to natural posture. This applies to the hand and the rest of the body. Anxiety, stress, low temperature or uncomfortable clothes handicap fine motor skills. The posture is of course also determined by a hereditary component, and by environmental influences and therefore individual and highly variable. The posture and the hand use and hand position is the expression of the inner life of a musician.

1.6 Physiology of mouth and jaw (embouchure) vs. controlled finger coordination

Lehr (2000) suggests a special training because of the finger problems to 'cover the holes' while playing clarinet of beginners.

The conditions for "the beautiful sound" or the right tone for reed instruments are subject to a complex interplay between:

-psychosomatic aspects
-posture of the body and the handling of the instrument
-breathing
-embouchure
-the correct timed finger coordination

There are many influences that have an impact in favourable and unfavourable manner to the tone generation and beyond, to the artistic interpretation. If there is a problem in the instrumental lessons it should be solved. Therefore sometimes so-called "dry runs" without the instrument are necessary. Especially when it comes to improvements in posture, breath control and grasping consciously. The experience gained should be reviewed on the instrument slowly. This will be for advanced instrumentalists even harder, the more solidified the resulting errors have already been, or if they have never dealt with the problems, or if they don't know any alternatives. Repairing often solves problems (Lehr 2000). But repairing instruments and playing on defective instruments costs a lot of energy which is needed to optimize playing.

1.7 Instruments for children, instruments for women

The development of musical instruments for children is a must for any musical instrument manufacturer. Selling and manufacturing of these instruments is necessary, because the consumer group represents an important market. Larger companies advertise with instruments for children for their future.

Here mostly old doctrines and opinions will be presented, but not with experts who could help with their experience and research.

This leads further in the problem of the individual building of the hand and the search of the correct size for an ergonomic instrument. The size of the fingers and the distance between the tone holes is a matter of the correct ergonomic building of an instrument. Anatomically there are differences between a female hand and a male hand and between a hand of a child and a hand of an adult. These variables create a complex range when building “the right size” woodwind instrument. So the decision to construct a woodwind instrument is followed with thoughts about the persons who will play this instrument. Probably it is too expensive to construct instruments especially for young adults or female woodwind players, but the research on the correct fingerings is connected with this problems.

Starting with the question, what physical conditions should be present to learn an instrument, the response must include concessions. These concessions relate to the instrument and the body of the child.

When concessions are awarded to the instrument, they are termed "children's instruments”. Children's instruments are usually smaller constructed instruments that have a higher tuning, but this does not address the nature of fingering for children.

“Child-oriented instruments” are instruments that look like a toy and orient themselves in their construction of historical instruments.

If there were concessions made to the child, I describe these instruments as “Child-oriented constructed instruments”. These are adapted to the physical characteristics of the child.

1.8 Training of correct practising

The sense of responsibility is very important for learning an instrument. Learning an instrument at an early stage is for a child playing with a very special toy, which needs care and protection. The playing with this toy is a "game", which must be played every day. This playing should be enjoyable and not a burden. Here the importance on regular and daily practice is given. Thus playing an instrument will be more enjoyable, because correct practising prevents mistakes, which don't make playing enjoyable. To hear mistakes means to feel playing an instrument as hard work. But in an early stage of learning an instrument, the playing should be as easy like any other game.

Before making tones with a wind instrument, it is important to activate the breathing. This will be practised by learning a wind instrument from the first hour. A good breathing technique is the basis for having success in making a good tone. With correct breathing technique, it is also possible to compensate for an instrument’s weaknesses, such as leaking keys, cracks in wood or broken reeds, or to circumvent them. I have had this experience as an instrumental teacher. Often students can compensate for obvious defects on the instrument with a natural, untrained technique, or, if I was testing a used instrument, I often didn't find the fault the first time, because I was compensating for the problem. Another example of correct breathing technique is the fact, that if I e.g. play a Eb-clarinet after a long period of non-playing, I do not succeed at playing all the notes for this instrument because I do not have the proper breathing or playing technique, and I search for defects on the instrument, rather than correct warm-ups. So the right practising is the way to have success playing an instrument.

1.9 Finger size, key or hole size

Fingers that are too small or too short have problems closing the tone holes. The length of the 5th finger (small finger) is also essential to the perception of “long-fingerings”. If the 5th fingers are too short, a long-fingering will be perceived as much more difficult than if the 5th finger is well developed. Ergonomically-built instruments do not have these fingering problems. So-called instruments for professionals often give up the ergonomics of an instrument to have more and better keys. Keys which aren't really necessary. The result is a difficult to play instrument that is heavier due to the higher number of keys, or has key construction, which makes little sense to use of these keys. A problem often occurs with the ab/g#-lifter-key and the bb/a#-lifter-key, because they are usually positioned with more than one centimetre distance under the e- and f-key. For a teacher it is often impossible to convince a student of the usefulness of these keys, although these keys would be useful.

In this context, studies of musical instruments would be useful because measuring instruments to the measurement of the fingers of practising musicians certainly would not result in a correlation. A construction of hand-models which are optimised for such instruments would be very interesting and informative for instrument builders and instrumental teachers. The positioning of other roles on e.g. the a4-key, the overblow-key or the f3-key, which are standard on other woodwinds, could improve the fingering and make the playing easier or could eliminate "fingering conflicts" such as "slipping".

1.10 Level of training, age, maturity, playing at sight

The knowledge and skill of all or at least most fingerings and fingering combinations also are important for the objective ability to distinguish between difficult and easy playing on a woodwind instrument. In the main study it was a criterion that the subjects were well-trained musicians with a lot of experience.

I assume, that musicians who do not like playing at sight or are not good at playing at sight, do not see problems with fingering combinations or misinterpret them. I found this problem during the first investigations. Because of this problem, I tested musicians with the instrument in their hands, to be able to check the grade of difficulty by trying out. So the fingerings and fingering combinations were scored with the instrument in the hand. The checking of the difficulty was actively tested by the subject. It is more objective with this method than with musicians trying to imagine the fingerings and fingering combinations.

1.11 Development of the body and the development of the muscles of the fingers and the hands

The factor "physical development" is significant for playing and learning an instrument. Weak muscles lead to problems with the fingerings of the right hand, because the right hand is holding the instrument and works against the weight of the instrument. The tension of the palm of the right-hand cannot be perpetuated if the muscles do not allow it. The result is that musicians have problems with the 4th fingers (ring fingers). The ability to hold the instrument and the ability to shut the tone holes without cramps is elementary for playing tones of more than three fingers. Beginners can detect problems with fingerings, which are not really "long fingerings”. This could be a problem in general, because there are a lot of causes for weak muscles or untrained hands.

Arm length and body proportions were mentioned here as examples. But with training the seemingly impossible can become possible.

1.12 Relation of body height and instrument size

The relation between body size and the instrument size plays a minor role. But it is a fact that instruments, like the bass clarinet or baritone saxophone, with the same fingering technique, like smaller forms of the same instrument family, are more difficult to play with the same technique. The body proportions and strength factors (muscle power) certainly play a role here.

For this reason the investigation was made with the standard instruments. like Bb-clarinet and Alto- and Tenor-Saxophone.

2. The issues of the dissertation and its relevance

2.1 Is the degree of the difficulty of fingerings and fingering combinations predictable?

For the practical performance of music, it is always important to know whether a piece is playable for a beginner or a professional musician. Experts classify a piece with levels, which should show if a piece is playable for a clarinettist who has played three years without a lot of practice. A teacher finds a piece in a catalogue and has to trust the indicated level of difficulty. Not many teachers are able to afford to buy every new piece just to try it out. Pieces that are often too difficult end up in a box or shelf, and the next time the teacher doesn't buy pieces from this publisher.

The estimates, which are found in several publishing catalogues, would therefore be interesting to investigate because they can show a picture of the measurement with what level the pieces were classified.

There are too many parameters to calculate, with a simple investigation, the difficulty of a piece. Pitch, construction of the instrument, reed, environmental conditions, etc. could also be used as parameters when you want to rate the difficulty of pieces or passages.

An important parameter for determining the grade of the piece is to determine the difficulty of the fingerings. The grade of a piece can be calculated effectively by beginners using an analysis of finger actions, because overblowing for the beginner is not possible or relevant. For all other clarinettists the simple overblowing, that means, that tone range can be adopted from the E3 to the C6, is not a problem at all. For professional clarinettists, the range up to the C7 is no difficulty with well trained blowing technique. Because of this I made the premise of my studies that the number of finger action is the most important criterion to calculate the grade of difficulty playing a woodwind instrument.

For octaving woodwind instruments the register change is not so relevant, but can be considered.

The fingering problems for young students is that the the 4th and 5th fingers are not well trained enough or do not have the muscle power which is necessary for playing long fingering sets.

For this reason, tones that must be played with these fingers are perceived as unpleasant and difficult. This issue is repeated in the upper register, which is also known as “clarion-register”. This is aggravating by the fact that the reeds used by beginners are too soft for a stable way of playing.

The change in the upper register requires playing with harder reeds and a change of the mouthpiece so that this new register has a good sound as well. This beginner’s problem is caused by the teacher. The beginning with the instrument should succeed quickly and easily, so for starting open mouthpiece side rails and soft reeds were used for playing the instrument. With this configuration it is possible to “play” the woodwind instrument from the first lesson without difficulties. There is no need for having a professional tone, but the sound is acceptable. Often there is no consideration that in this case, it will be more difficult to exclude fingering problems and prepare for the register change.

The imprecise fingering sets of beginners are usually not audible, because a softer reed is able to compensate in this situation. An experienced teacher is able to hear these imprecise fingering sets by recognizing the incorrectly intoned deep tones. The age of the instrument or the cheapness of the instrument is often accused of causing this problem by inexperienced clarinet teachers. But right here the experienced musician should emerge from the teacher and should test the instrument itself with his professionalism and knowledge.

An important factor in the occurrence of fingering set problems is the condition that practising the new register is not as much "fun" as the deep register. So the practice of the new register will diminish and the success won't come. Preparative fingering exercises, analysis of the finger motor and sound examples would be appropriate to make the register change more successful.

2.2 The proof of the subjective difficulty rating of fingering sets

During my initial investigations I came to the idea, how a clarinet player imagines playing the clarinet, how he is able to identify difficult passages in parts of music, and if having audition training or not could be a criterion for the subject being able to identify such passages without an instrument in his hand. A test of this ability without an instrument in the hand leads to a high error rate, especially for beginners. This trial shows that investigating the smallest elements, e.g. single fingering sets and fingering combinations, could be easily detected with the instrument in the subject’s hands. They were able to identify difficulties and fingering problems. A psychological investigation by questionnaire or card, which examined only the finger action, showed the subjective rating of the difficulty of a fingering set. These finger actions can be mathematically converted into vectors. The investigation of the correlation of the mathematical data with the subjective perception of the grade of difficulty made a model possible, from which further calculations could be derived.

The investigation of all possible parameters is beyond the scope of this work. So only the basic model is examined in this study. In another part of this work, it is shown that, when all factors are taken into account, that it will make a data flood. All preliminary investigations have an explanatory nature. They should show why certain measurements were not made and why these simplifications of the analysis still reflect the nature of the premises and provides useful first results.

2.3 Is it possible to make a prediction of the degree of difficulty of a piece and as a result a calculation of the optimal fingering sequence?

The transformation of the data to vectors can be explained by a system of a machine control. The conjunction logic provides the basic idea. The data obtained can be transformed in numbers, like the switch logic and presented in vectors. This very simple model is able to be empirically investigated. Vectors describe the directions and movements. The smallest difference between two vectors is the easier way of fingering. These calculations are the mathematical expression of practical knowledge. Lehr (2000) describes such thoughts with the practical experience of a 'right-hand down-technique'. Lehr knows as a practical teacher, that it is easier to avoid unnecessary finger movements than to practice finger coordination of two hands.

2.4 Is it possible to generate an aesthetic prediction of the playing the clarinet?

Not all tones on the clarinet sound as well as others. Their tuning can be illustrated by calculation of their impedance or using an impedance measurement. It is possible to link the data with each other and make aesthetic investigations. If only by using calculations, a musician avoid so-called "fear passages", a piece will sound "better", because the piece can be interpreted more freely. A composer also could use this principle of "difficulty" as an effect.

2.5 A modelled clarinet can be a tool for composers or for instrument manufacturers.

The combination of fingering calculation with a calculation of the acoustics of the clarinet could make, as a computer program, the clarinet and other woodwinds more interesting for composers. To write for clarinet without understanding it, is difficult for a non-woodwind composer. A model would facilitate this. A model of the clarinet also can help in the development of manufacturing the clarinet, because optimal routes, fingering holes or key distances can be calculated.

3. Preliminary studies

The preliminary studies were made to develop a questioning with a wide relevance and connection point to other disciplines for further research.

3.1 Preliminary study 1: Exploratory

The first survey was made with guided interviews. The demographic data show that the subjects were between 10 and 36 years old and had different levels of qualifications. This is a typical picture of a private clarinet-saxophone class. The survey was summarized in tabular form so that individual statements are clearly broken down into keywords. The names of the subjects were coded for anonymity. The table was divided into several individual tables, because the data would be too large for a good overview.

The first table shows the demographic data, age, sex, educational level, plays instruments, what kind of instrumental education, how long and which instruments were learned, and what other resources the students have for collecting musical experience.

TABLE 1

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The second table shows the time for playing and practising the instruments. As is shown in the table, only 2 students reach an approximate practice time of one hour per week.

TABLE 2

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The third table shows the practising strategies of students. Answers with just “yes” were described with the number “1” and “no” with the number “0”.

TABLE 3

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Table 4 shows statements about imagination while practising. This showed that there could be cognitive playing that allows for the perception of fingerings and fingering set combinations like a scheme.

TABLE 4

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Table 5 shows the answers about imagination during playing the instrument. I tried to preserve these schematic answers in the next investigations.

All answers here are mechanical observations of the subjects. A lot of these answers include a finger-coordinated playing of wood wind instruments. Fingers and finger positions are described as „servos“.

The question about the imagination during the register-change showed a picture of the clarinet with its register-characters. Students perceived the clarinet as non-uniformed, the individual registers are perceived as separate instruments. This is a hurdle for beginners when they learn the first register-change. This mechanical difficulty (strain) is connected with the problem of the register-change. Advanced students later learn, that this change should be well-balanced with all fingering-techniques and auxiliary fingering sets.

TABLE 5

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In table 6 there are interesting answers by the subject MA-KB, because for the answers to what is „difficult“, terms were used like „register change“, „low tones“ (long fingering sets) or „a lot of jumps“. The question of knowing the note examples should show the possibility of imagination of pieces. The pieces are like passages of concert pieces, but fictitious and should seem to be well known or unknown.

TABLE 6

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Table 7 shows the results of the questions about practising „without the instrument in the hand“and if there is „mental practising“. Mental practising means that there will only be the imagining of fingering on the instrument.

TABLE 7

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Table 8 shows the results of the survival to the note examples.

This examples were the second part of the this investigations and should be studied by the participants without their instrument. The participants should mark fingering sets and difficult passages. The first column shows the number of marks made. The examples allowed many marks, because there were more than 30 combinations hidden. “Wrong” signs are marks which are an incorrect fingering or fingering sign or if there was a sign of being difficult which wasn't difficult. Because of the marking of “wrong” and “right”, it is easy to divide into beginners and advanced students. The error rate of beginners is higher than of advanced students. This rate manipulates the results.

TABLE 8

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The collected commentaries of table 9 were the motivation for further investigations in the field of “investigation of difficulty of playing woodwind instruments”. I tried to mathematically explain the sentence: “... if a tone combination goes up, you have to lift fingers ...”.

TABLE 9

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3.1.1 Question 1: Methods of practising in the “head”. Which methods are available and which are best?

The preoccupation with Edwin Gordon and his "Audiation" had reason to set me apart with the idea of musical performance during music performance. During my job as a woodwind teacher I was always confronted with the question: "Why do students always have the same problems at similar passages, although these passages seem easy for me?"

Instead of answers, I found in these observations, only more questions. There must be a connection between difficulty and the fingers of a musician.

The following findings are related to the learning of the clarinet and the "difficulty-perception" and always visible: sounds and fingerings that are played only with the upper hand (left hand) are not a problem for beginners. The additional use of the index finger of the right hand makes a small but solvable problems for some students. This use of the index finger of the right hand refers first to the B3 and the F4. Depending on the method of teaching, beginners also play with the index finger of the right hand the Eb4. The middle finger of the right hand is easily used, because the responsible of this finger is only for the A3 in the Shawn register. Starting from the ring finger of the right hand (known by clarinet players as the 4th finger) for most students, the first problems begin. Indeed, if this finger is still too weak or too thin, it is not always possible to close the tone hole and instead of the G3, a terrible squeaking sounds

Here the main problem is often not the width of a finger, but a cramp in the right hand. The thumb of the right hand has the job to prop up the weight of the clarinet. The weight of the clarinet lies only on this finger. This problem is complicated by the fact that most clarinettists try to compensate for the lack of power of this finger by using a wrong position. To prop up the clarinet with the thumb, instead in the nail bed area the clarinet will be held in the area of the thumb knuckle. The effect of this posture is that the position of the right hand instead of 90 ° to the clarinet is slipping down more and more, which will be matched with the raising of the wrist. The following additional tension and cramping make it impossible for the beginner playing the clarinet more than 15 minutes.

This problem can only be solved with specific, controlled exercises that are made with relaxation exercises while standing, because the muscles will be better trained in a standing position. The deliberate, slow, relaxed movement of the fingers, the memorizing of fingering sets and finding the tone holes by touching are giving safety for precise playing on the instrument. These are the basic requirements for fast and fluid playing on the instrument.

3.1.2 Question 2: How will the grade of difficulty of a piece be determined?

Clarinet students are often not able to see fingering set problems of pieces when they get primavista exercises. The playing or practising of a piece usually leads to the finding "... able to play ..." or "... unable to play ...". Only students who are really regularly practising see the problems in the piece.

Is the ability to detect difficult parts connected with the level of training?

My observations suggest that beginners mostly practice difficult passages or simply do not practice, because they come to the conclusion "... I cannot anyway ...". Advanced students play down difficult parts with the opinion that they had simply exercised too little.

What is perceived as "difficult"?

High notes and long fingering sets are very unpopular with clarinettists. Difficult Fingering sets in the default location will be underrated until such parts of a piece are explained by the teacher. The duty of the teacher is not to make simple pieces difficult, but without the explanation of the “why” and the “what”, students do not improve their ability of primavista playing. Playing a woodwind instrument is not only moving one finger after the other while blowing in a black tube.

3.2 Preliminary study 2: Quantitative, qualitative

This study used a questionnaire which collected data about age, sex, education level, school type, type of instrumental education and musical practise. With this questionnaire, “difficult passages” should be found by the Test persons. There also was a question, how well known are these passages by the Test persons. This was answered, the passages were discussed with the investigator and played with the instrument.

The results showed a connection between educational level and the ability to find difficult passages. The observation that difficult fingering sets were almost identical with the long fingering sets, leads to further investigations, because the answer of this finding was missing. The first results were systematized and were the basics for further investigations.

3.3 Hypothesis 1: Correlation between grade of difficulty and the number of used fingers

The results showed, that there is a correlation between “difficult” and the number of finger which were used for the tested fingering set on the clarinet. The translation of a fingering table for a clarinet into a logical system (comparable with a switch logic system or a conjuncture logic system) makes the fingering sets used visible as vectors. Because of the presentation of vectors of these fingering sets and fingering combinations, it is possible that: 1. Each fingering set could be shown as a mathematical value 2. Each fingering combination could be shown by vector-subtraction as a mathematical value 3. Subjective perception of difficulty (collected with a rating scale) could be correlated with these values 4. Predictions about optimal finger movements for specific passages of a piece could be made 5. Woodwind instruments could be compared by their difficulty 6. Physical-acoustic calculations on woodwind instruments (impedance calculations) could be used for performance research or empirical aesthetic researches.

3.4 Preliminary study 3: Qualitative

Survey: Cards with the tone (note) and the symbol of the fingering set were mixed. The subject now should rate this fingering set. The subject makes the rating by testing the fingering set with the instrument in the hands. This method should be a test that the subject is testing the right fingering set or the right tone. The investigator is able to interfere if the subject misinterprets the symbol or uses a wrong fingering set. The investigator make notes of the rating. Because of this series it is possible to test more tones or fingering sets. The spontaneity of the subjects during the rating is better, because the reflection phase will be shorter. This investigation will be more successful with the instrument in the hands. To make this investigation without a investigator, e.g. by online-testing, pictures of the fingering sets have to be delivered with the questioning. The results could also be uncertain or invalid when the subjects test the fingering sets with the instrument, because the control mechanisms were missing. Above all, by testing students there is the danger that they would mistake fingering sets or would not able to find the difficulty of the fingering set.

Instead of Cards the tones and fingering sets could be shown by screen and mixed by random generator.

3.5 Hypothesis 2: Correlation between grade of difficulty and finger position

There are fingering set combinations that are hardly used or not used at all. These will be assessed as much more difficult as they are calculated on a simple model. This is related to the keys. The fingers, which are in the basic position, or move in this area, can be represented using these simple 1-0 calculations. But if you leave that position, the results shift, leading to uncertainty. This leaving may be compared to a change of position on a key or string instruments, or if a passage played on a keyboard instrument would have to be played with many black keys. This "leaving" can be represented as a position change with algorithms (1-10-100-1000-10000). The calculations were sharper and the factor of "difficulty" is better illustrated.

3.6 Hypothesis 3: Correlation between the "difficulty-acceptance" and an aesthetic decision

"Main fingering sets on the clarinet sound better, auxiliary fingering sets may be used only when there is no alternative.", is the rule for each clarinettist, although there often exist playable alternatives. The "leaving of fingers on the tone holes" changes the sound of a tone, and usually also the tuning. Nevertheless, it is desirable, to use this fingering help for "technical" passages. These two rules were deliberately excluded from the previous study.

3.7 Preliminary study 4

This preliminary study has a similar design as the final investigation, but does not include all factors. To understand the results better, the vectors are added to the first two fingering sets. The fingering set combinations with all calculations are shown in table form.

The fingering set „ fis “ has the vector value of „ 3 “ and an algorithmic value of „ 10.39 “. The divergence of the difficulty to the calculated value lies at 5. The square value of the vector is „ 9“. The algorithmic divergence is „ 3.449“. Test person 1 gives this fingering set a value of „ 7 “, Test person 2 gives this fingering set a value of „ 6 “ and Test person 3 gives this fingering set a value of „ 2 “.

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The fingering set „ g1 “ has the vector value of „ 0 “ and an algorithmic value of „ 0 “. The divergence of the difficulty to the calculated value lies at „ 0“. The square value of the vector is „ 0“. The algorithmic divergence is „ 0“. Test person 1 gives this fingering set a value of „ 0 “, Test person 2 gives this fingering set a value of „ 0 “ and Test person 3 gives this fingering set a value of „ 0 “.

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The fingering set „ b° “ has the vector value of „ 2.45" and an algorithmic value of „ 2.45". The divergence of the difficulty to the calculated value lies at „ 4.70“. The square value of the vector is „ 6.002". The algorithmic divergence is „ 0“. Test person 1 gives this fingering set a value of „ 1 “, Test person 2 gives this fingering set a value of „ 4 “ and Test person 3 gives this fingering set a value of „ 1 “ .

The fingering set „ g2 “ has the vector value of „ 2.24" and an algorithmic value of „ 3.74". The divergence of the difficulty to the calculated value lies at „ 4.20“. The square value of the vector is „ 5.02". The algorithmic divergence is „ 0.7". Test person 1 gives this fingering set a value of „ 1 “, Test person 2 gives this fingering set a value of „ 3 “ and Test person 3 gives this fingering set a value of „ 1 “ .

The fingering set „ d2 “ has the vector value of „ 3 “ and an algorithmic value of „ 5.2". The divergence of the difficulty to the calculated value lies at 6. The square value of the vector is „ 9“. The algorithmic divergence is „ 1.04". Test person 1 gives this fingering set a value of „ 2 “, Test person 2 gives this fingering set a value of „ 2 “ and Test person 3 gives this fingering set a value of „ 1 “ .

The fingering set „ gis1 “ has the vector value of „ 1 “ and an algorithmic value of „ 3.16 “. The divergence of the difficulty to the calculated value lies at 1.3. The square value of the vector is „ 1“. The algorithmic divergence is „ 1.008". Test person 1 gives this fingering set a value of „ 0 “, Test person 2 gives this fingering set a value of „ 1 “ and Test person 3 gives this fingering set a value of „ 1 “ .

The fingering set „ h “ has the vector value of „ 2.24" and an algorithmic value of „ 2.24". The divergence of the difficulty to the calculated value lies at „ 2.20“. The square value of the vector is „ 5.02". The algorithmic divergence is „ 0“. Test person 1 gives this fingering set a value of „ 7 “, Test person 2 gives this fingering set a value of „ 7 “ and Test person 3 gives this fingering set a value of „ 3 “ .

[...]

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^[1] The term „long fingering set“ describes fingerings, which are played with the little finger (5th finger).

^[2] Muscles for stabilization of the spinal column