From the Director's Desk
Recorder Tuning and Intonation
The Bare Acoustical Facts of Life
The following editorial by ASW director David H. Green appeared in the February, 1990, issue of our customer newsmagazine Chrestologia. It is presented here for those visitors to our web site who might be curious as to exactly how and why we choose to custom-voice and custom-tune every recorder and other historical woodwind instrument sold by our workshop, as well as those who wish to improve the tuning and intonation in their own playing.
From time to time we have found it necessary to delve into the seemingly forbidding realm of musical instrument acoustics for the benefit of our readers; this would seem to be another one of those times. Please rest assured that we have no intention to provide a complete grounding in musical instrument acoustics. There are many books in print on the subject, ranging from casual sources of information for the armchair musician to ponderous scientific tomes bristling with calculus and impenetrable jargon. Our intention here is to present a few miscellaneous observations and facts of a non-technical sort obiter dicta Have no fear; we promise not to get involved with logarithms, antinodes, and other nasty things that go bump in the night.
While acoustical studies can be admittedly dull and boring to many people and downright terrifying to confirmed mathophobes, the fact remains that most musicians know very little about the physical principles which cause their instruments to function (or malfunction) as they do. There are, however, many simple facts about acoustics which can have a direct bearing on instrument selection and playing technique and yet are largely unknown or misunderstood among the great majority of amateur and professional musicians.
One of the most disheartening aspects of recorders and other historical woodwind instruments, at least from our multiple points of view as designers, dealers, and performers, is that most instruments are not very well in tune as delivered by their makers. The reasons for this phenomenon become at once obvious when one realizes that most woodwind instrument makers are craftsmen, not performing artists. They play the instruments which they make at a mediocre level at best (and in some cases very little or not at all) and are therefore not able to control the performance of their instruments at a professional level nor make fine distinctions as to whether an individual note or, for that matter, the entire instrument is exactly or only approximately in tune.
In some cases recorders are actually well-designed but, owing to production tolerances, variations due to the natural material, or lack of skill or awareness on the part of the maker, do not play as well in tune as they could or should. Such instruments can usually be improved to the point where they will play very well in tune, provided that the instrument is custom-serviced by a craftsman who is also an accomplished performer. It is, however, also an unfortunate reality that many other recorders, including some very expensive instruments produced by custom makers, are poorly designed and will never be able to play well in tune. With such instruments it is sometimes possible to improve the tuning to some degree, but it is almost always impossible to improve them to a point where they will be totally satisfactory in intonation. The quality of the woodworking is not always a reliable guide to the performance capabilities of an instrument: well-made recorders can sometimes nevertheless be poorly designed, and instruments of average quality can sometimes be improved to play rather well.
A further issue is that virtually all wooden recorders continue to change their dimensions and therefore their tuning and voicing for some period of time after they are made. The procedures used in woodworking, both by machine and by hand, tend to heat and compress the wood in certain critical areas; the wood will slowly re-expand, at least to some degree, for a period of time after the instrument has been finished. Most instruments are made to order and shipped immediately after they are finished, and no maker of my acquaintance who does maintain an inventory of finished instruments bothers to rework them again before delivery.
Then, too, changes in ambient relative humidity between the country of production and the country of use, as well as the seasonal swings in humidity and temperature that are typical of many areas of the United States, will cause the wood to swell or shrink in some areas, causing changes in tuning, voicing, and fit of the block and joints. These dimensional problems can be extremely pronounced in instruments which use wood and non-wood materials in combination, such as hybrid plastic/wood instruments, bent-neck models with metal necks, recorders with blocks made of artificial materials, and all tenor and larger instruments which have metal keywork.
As regards the perception of tuning and intonation, studies in the relatively new field of psychoacoustics have shown that human perception of pitch is heavily biased and not at all even-handed. When two instruments of different tuning are played together, it is almost always the lower of the two that sounds "wrong," whereas the higher, even if it is very sharp, sounds "correct." Furthermore, the human ear is able to tolerate surprisingly large amounts of sharpness without being even aware of it, whereas the ear is extremely sensitive and able to detect even minute amounts of flatness in pitch. These phenomena reveal the necessity of using an electronic tuner as a objective standard of reference if one is to maintain any sort of rational standard for tuning and intonation. Otherwise the law of the acoustical jungle will prevail and the loudest and sharpest instrument will set the de facto tuning level.
Since virtually all players, both experienced and inexperienced, are more aware of and sensitive to flatness than sharpness, most recorder makers have learned from bitter experience to err by tuning their instruments somewhat sharp in order to avoid returns and complaints of their instruments being "flat," especially from inexperienced players who underblow their instruments as a result of poor (or no) instruction in breathing and blowing a wind instrument. Plastic instruments, intended by their makers for the lowest common denominator of beginning player, are usually excruciatingly sharp in pitch unless played at artificially low breath pressures. Such playing will achieve the best intonation possible on an inherently sharp instrument, but will cause or exaggerate other problems, such as more frequent clogging and insecure high register response. And learning to play at a very low breath pressure will inevitably come back to haunt the player who eventually purchases a decent wooden recorder, finds that it is "flat" in comparison to his previous plastic one, and has to relearn how to breath and blow into a wind instrument properly.
Most wooden recorders are tuned to a'=442 or a'=444 Hz at a temperature of 20°C (=68°F.), and some are appreciably higher than that. Most American customers are not comfortable in an ambient room temperature of 68°F., but playing instruments tuned at 68° in a warmer ambient temperature will cause them to be unavoidably sharper in pitch. We feel that tuning recorders higher than the internationally agreed-upon pitch standard of a'=440 Hz is not advisable under most circumstances for most players; we therefore retune all the instruments we sell to a'=440 Hz (or a'=415 Hz for low pitch instruments) at 70° F. unless specifically requested otherwise by the customer.
In our very first editorial essay, we took an in-depth look at why so many low-pitch baroque woodwind reproductions have intonation problems. 1 The conclusions reached were that many if not most late baroque woodwind instruments were originally pitched at a'=409 or 410 Hz. and that many modern makers of replica instruments are either unaware of or choose to ignore the fact that the making of a so-called reproduction instrument at a'=415 Hz., the current if historically inauthentic standard for late baroque performance, requires a complete redesign of the instrument. A "quick and dirty" shortening and/or retuning does not do the job adequately and results in an instrument which has response and intonation problems not found in the original instrument. A mathematically correct scaling of the instrument to a new pitch will also not produce a satisfactory instrument. Acoustical formulas can certainly be a useful point of departure, but a successful "scaling" to another pitch will also involve a large amount of empirical, trial-and-error experimentation which paradoxically will produce an instrument that sounds much more like the original instrument than a literally-scaled design.
The basic principle which one can derive from all of the above observations is that a woodwind instrument, provided that it is correctly designed, tuned, and played (and that combination is in and of itself altogether a rarity), can be exactly in tune with itself only when played at the pitch at which it was originally designed to be played. Any attempt to play the instrument at even a slightly higher or lower pitch, whether by lengthening or shortening the instrument, modifying the tone holes, blowing it harder or more gently, or modifying the means of tone production (such as changing the embouchure hole on a flute, the reed on a single or double reed instrument, or revoicing the windway on a recorder), or any combination of the above, will cause the instrument to play less well in tune with itself. The further one deviates from the original pitch center, the poorer the intonation becomes.
Let us examine, by way of illustration, the function of the tuning joint on the recorder. The earliest medieval and renaissance recorders, as is generally known, were made in one piece. It was only in the third quarter of the seventeenth century that Parisian woodwind instrument makers, in the process of transforming late renaissance designs into their baroque counterparts, began making instruments of jointed construction in three or four pieces as a standard practice. The idea was clearly not new, since Praetorius a half century before had remarked on the desirability of making recorders in two pieces specifically for the purpose of flexibility in tuning:
"It is seldom that one finds recorders which are correctly in tune with one another. It has occurred to me to make a joint half way between the window and the highest tonehole, thus lengthening the upper section of the pipe by the width of two fingers. This makes the length of the tube variable and thus its pitch may be accordingly adjusted higher or lower. Although several famous instrument makers were of the opinion that this would make some of the tones of the flute false, they actually had no objection to the idea - except that some of the highest tones did not speak as well."2
As Praetorius was apparently informed by his instrument-making colleagues, the incorporation of a tuning joint in a woodwind instrument is a mixed blessing. Whatever one gains in flexibility of tuning is balanced by a loss of accuracy in both intonation and response. As we have previously observed from the vantage point of three and a half centuries later, musical instruments have not gotten better with the passage of time, just become different. Every improvement in some aspect of an instrument's performance has seemingly extracted a price in some other performance parameter. The notion of continual, cumulative progress so beloved of 18th century Enlightenment philosophers and fostered by the industrial revolution has in fact proven to be largely illusory. The limitations of modern instruments in playing music written prior to the twentieth century have become increasingly obvious as the early instrument movement has taken over performance rights to baroque, then classical, and now romantic period music as well.
In theory and in reality, a recorder performs best when it has no tuning joint or when the tuning joint is pushed all the way in. Pulling out a tuning joint even a short distance produces a disturbance (termed by acousticians a "perturbance" but called around our admittedly informal workshop a "blip") in the bore. This sudden bulge or interruption in the smoothness of the bore causes a subtle but discernible change in tone quality and also produces deterioration in response and intonation of certain notes, just as Praetorius's colleagues had warned.
Let us consider more closely what happens to tuning and intonation when the headjoint position is modified. When the tuning joint on a woodwind instrument is pulled out, it makes the entire instrument longer and therefore lower in pitch. However, it flattens individual notes by differing amounts, and therein lies the rub. Notes in the middle register just below the "break" to the overblown octave, such as f" and g"3 are those most affected by pulling out the headjoint, since the increase in distance from the window to the toneholes producing these notes is proportionally greater than to the notes produced by the lowest toneholes, such as f' and g'. 4 The basic principle to be drawn from this phenomenon is that a recorder or other wind instrument, assuming that it is in tune with itself to begin with, can be in tune only at one position of the headjoint, the position at which it was tuned. If the tuning joint is pulled more or less than this amount, it will cause the instrument to be out of tune with itself. These intonational differences are not slight, incidentally; they are substantial and palpable. The smaller and higher the instrument, the more critical the headjoint position becomes.
Why bother with a tuning joint at all, then, if it causes so many problems? Well, if every musician had a highly developed sense of pitch and played exactly at the preselected pitch du jour, whether it be a'= 415 Hz., 440 Hz., or some other agreed-upon standard, and if all other types of musical instruments were equally stable in pitch or went out of tune to the same degree, there would be no need for tuning joints. An instrument could be made for one specific pitch and would play optimally at that pitch. The reality of the situation, however, is that we live in an imperfect world of imperfect instruments and imperfect instrumentalists and are continually forced to make compromises and adjustments to our own playing for the sake of the common good.
The problems caused by tuning joint adjustment are further compounded by the fact that some notes are acoustically less stable than others and more affected by changes in breath pressure.5 In general, notes which are produced by a short tube length are less stable in pitch than notes produced by a longer tube length. This phenomenon is well-known in the field of pipe organ design, where, for example, reed pipes with full-length resonators are inherently more stable in tuning and response than pipes with half-length resonators, pipes with half-length resonators are more stable than those with quarter-length resonators, etc. In recorders, the middle register notes such as f" and g" are not only more affected by changes in overall length caused by moving the tuning joint, they are also inherently less stable in pitch and more susceptible to going sharp or flat in pitch due to changes in breath pressure. And there are even further complications: cross-fingered notes are less stable in intonation than notes of the basic scale, and notes of the second octave vary to a different degree (sometimes more and sometimes less) than the same note in the lower octave.
In addition to tuning and intonation problems inherent in the instrument itself, further difficulties can be caused by environmental conditions which are often beyond the immediate control of the player. First, there is the matter of temperature: if a recorder player and harpsichordist are performing on stage, the recorder will go sharper as it and the hall warm up; the harpsichord, however, will go flatter. The recorder player has no choice but to pull out the headjoint of his/her instrument if the accompanying instrument begins to sink in pitch, trading a deterioration in personal intonation for an improvement in ensemble tuning. In another common situation, a player with a good-quality wooden recorder correctly tuned to a'=440 Hz. must play in a group with a number of beginning recorder players using plastic recorders which are grossly sharp in pitch. That player must have the capability to raise the pitch of his or her instrument well above the nominal level for ensemble's sake.
Sometimes wind players are faced with a quintessential Hobson's choice in trying to play with other types of musical instruments: a bowed string instrument's unwound strings go flat as the wound strings go sharp. Organists know that, as a church or concert hall warms up, their flue pipes will go sharp and their reed pipes will go flat. These naturally occurring "environmental" tuning problems are frequently if unintentionally compounded by the player as psychoacoustics raises its ugly head. String players and singers in particular often play or sing on the high side of the pitch because it sounds more brilliant and "feels" better. Even the best of professional woodwind or brass players, caught up in the heat of a performance, will blow their instruments more vigorously and cause the pitch to rise, sometimes by alarming amounts.
Whereas the effect of temperature change on tuning and intonation is generally well-known, pitch changes due to ambient humidity variation are less obvious but equally important. Although tuning and pitch changes due to humidity variation occur more slowly, their effect is longer-lived, indeed sometimes permanent, and less easily compensated for. Exposure of woodwind instruments to conditions of low humidity (below 40%) for even brief periods of time can cause shrinkage of the wood in some dimensions. These changes cannot be fully corrected by rehumidifying the instrument, as the wood will not re-expand to its original dimensions. Dryness causes the toneholes to enlarge, shrinking away from their imaginary centers, and the pitch of the instrument to rise as a result. Since the toneholes are of different sizes, the relative amount of shrinkage is different for each size tonehole. Since notes in the second octave are more influenced by tone hole size than first octave notes, they will become sharper and the octaves will therefore be too wide.
The smaller tone holes are proportionally more affected by shrinkage than the larger ones. Thus the notes produced by the tiny double holes at the bottom of the instrument, namely f#', g', g#', and a' in the first octave and, most particularly, a' and e"' in the second octave become extremely sharp when an instrument has become dehydrated. When we receive an instrument which displays sharpness in these tones and an extremely wide a'-a" octave (i.e., the high a" being much sharper than the low a'), we invariably find that the instrument was allowed to dry out by its owner and the pitch problems are a direct result of wood shrinkage. This is why we provide a free case humidifier and explicit instructions for its use with every tropical hardwood recorder that we sell.
There is yet a final problem: the intonation of some notes on a wind instrument is also greatly influenced by choice of fingering. While this might seem obvious, the issue is in fact more complex than is immediately apparent. It is of course patent that the fingering of some notes will vary from one recorder to another; even standard modern recorders may require different fingerings for c#", eb"' and g"'. Renaissance recorders, even if they use so-called modern fingerings, may in fact require other than standard fingerings for b' and b", eb", f#", c#"', and d"' as well. In addition, the various alternate fingerings or trill fingerings, while intended to enhance technical facility, also frequently have a different timbre and intonation than the notes for which they are intended to substitute. Yet another source of intonational woe, however, is often overlooked: the amount of left thumb opening, frequently but erroneously referred to as a "half-hole," affects greatly the intonation of most of the notes in the upper half of the second octave, i.e., the tones from c"' upwards.
With all of this depressing information in mind, it is a wonder that any wind instrument can be played at all well in tune, Cheer up, Bunky, it can be done. There are many fine amateur and professional woodwind instrument players out there - not necessarily the ones with the famous names and world-wide reputations - who do play their instruments extremely well in tune. What do these fine players know that the general run-of-the-mill player with hit-or-miss intonation doesn't know? A well-developed playing technique and a good ear are of course essential, but that is only part of the reason for their success. The interface between the player and the instrument is really the crucial factor, and it is there that so many aspiring players come to grief.
First and foremost, the player must have an instrument which has been serviced, voiced, and tuned by a craftsperson who is also an accomplished player. Only then can the player be assured of having an instrument that is in fact exactly in tune with itself and capable of being played in tune. The instrument should be accompanied by a custom fingering chart which shows the fingerings that were used to tune the instrument and which give the best results in intonation. At the risk of belaboring the obvious, it is perhaps necessary to state that selection of a well-tuned instrument is the sine qua non for playing well in tune; with a less-than-optimum instrument that has not been custom-serviced, "you just can't get there from here".
Secondly, the player must determine the optimum headjoint position and breath pressure at which the instrument was tuned and therefore should be played. This is the step which is most frequently overlooked, even by experienced professional players and teachers. It may be done rationally, empirically, or intuitively, but it must be done correctly! Many books on playing technique or articles on recorder selection advise players to check intonation by playing octave leaps or triads. This piecemeal approach hardly ever produces satisfactory results. If the headjoint is not correctly adjusted and/or the instrument is being played at a higher or lower breath pressure than that used to tune the instrument, some notes will be in tune but others can be guaranteed to be out of tune, even though the instrument may be perfectly in tune with itself in the hands of a more circumspect player. What one needs, then, is a game plan, a procedure for trying out a new instrument which determines the correct headjoint adjustment and breath pressure for a given instrument and allows the instrument to be played with its optimum intonation.
First, one must realize that each instrument differs to a greater or lesser degree in feel and requires a different tuning joint adjustment and breath pressure: instruments of the same make, model, and wood type will be slightly different, instruments of the same make, model, but of different wood type will exhibit somewhat greater differences, instruments of the same make but a different model will be substantially different, and instruments by different makers usually exhibit very large differences, making a comparison of the proverbial "apples and oranges" very difficult for the inexperienced player. Perhaps the most common mistake that many players make in selecting or comparing instruments is to pick up an unfamiliar instrument and unconsciously expect it to play exactly like the one to which they are accustomed, except better. Players who do not have the luxury of owning several instruments of each size become accustomed to the feel of one specific instrument and have difficulty in playing and hearing a new and different instrument in an objective manner. Even when they know that their old instrument has faults and believe that they are seeking a very different instrument which does not have those faults, they are subconsciously using their old instrument as a frame of reference and standard of evaluation. It is perhaps only human to want a new pair of shoes to feel as comfortable and familiar as one's well-worn old shoes, but it is nonetheless an unrealistic expectation.
Many players check intonation by playing f' -f" and g'-g" octaves; but this procedure by itself can yield false results, causing the player to think the instrument is in tune when in fact it is not. A moment's reflection will show that, for example, if an instrument is being underblown and the headjoint is pushed in all the way to compensate for the low breath pressure, the f and g octaves may well line up but many of the other notes will be out of tune and the scale will be uneven. Before checking the above octaves, the player must first check the intonation across the break from the first to the second octave, i.e. from g" to a". Since the a" is relatively fixed and stable in pitch and the g" immediately below is highly subject to change from tuning joint adjustment and breath pressure, the combination of headjoint position and breath pressure which gives the correct intonation of g" in relation to a' and also produces well in-tune octaves from f'-f" and g'-g" is the one which will also give the best over-all intonation.
Once the optimum adjustment for tuning and breath pressure is determined, the player should proceed to adjusting the left thumb opening for optimum high register intonation. Playing the octaves c"-c"', d"-d"', e"-e"', and f"-f"' will reveal the amount of opening necessary to produce correct intonation. On a well-designed and correctly tuned instrument, the amount of thumb opening should be the same for all four upper notes and also produce the most accurate response for those notes as well. On less well-designed instruments, the optimum opening for intonation may not coincide with the optimum opening for response, requiring the player to adjust the thumb opening after the note has begun and/or use differing amounts of opening for each of these notes.
These many and varied problems of tuning and intonation are of great concern to us at Antique Sound Workshop as we prepare an instrument for delivery. Although we would prefer to tune recorders with the headjoint pushed all the way in (and did in fact tune some instruments that way for a number of years), we have come to realize that it is important for players to have the option of both lowering and raising the pitch level from the nominal tuning of the instrument to meet changing performance situations. We have also found it necessary to accommodate the wide variety of playing styles and breath pressures which exist among our recorder-playing customers. We set up most modern alto recorders, therefore, so that the tuning and intonation are optimal when the headjoint is pulled out about 3 to 4 mm. This provides sufficient leeway in pitch without creating too large a distortion of the bore. It is admittedly a compromise, but we feel that it is a reasonable and necessary one.
One last observation: different styles of recorders are designed to require different types of breath pressure. Renaissance and baroque reproduction recorders, for example, are designed to be played at relatively high breath pressures by experienced players; if they are underblown, they will not only be out of tune with themselves and flat overall, but they will not develop the rich overtones characteristic of their breed and sound dull and unfocused. Conversely, most modern recorders are designed to play at lower breath pressures and to be less dependent on the skills of the player; if they are overplayed, they will be out of tune and sharp in pitch overall and often abrasive in tone as well. Players wishing to play on a variety of historical and modern recorders must be willing and able to play on instruments with greatly differing requirements. It is unreasonable to expect all instruments to function equally well with a single inflexible playing technique.
By way of summary, it might be well to recapitulate six basic facts of life about tuning and intonation on recorders and woodwind instruments in general:
Principle #1: Recorders are capable of being exactly in tune only if they are well-designed, carefully made, and have been custom-tuned by a craftsmen who is also an experienced player.
Principle #2: Recorders are capable of being exactly in tune only at the exact pitch at which they were designed to be played.
Principle #3: Recorders are capable of being exactly in tune only at one position of the tuning joint.
Principle #4: Recorders are capable of being exactly in tune only at one breath pressure.
Principle #5: Recorders are capable of being exactly in tune only if they are maintained under controlled ambient temperature and humidity conditions.
Principle #6: Recorders are capable of being exactly in tune only if the correct fingerings and left thumb opening are being used.
While it is certainly true that many recorders and other woodwind instruments are not well in tune with themselves, either because of faulty designs or because of lack of attention or skill on the part of the maker, it is also true that many if not most players play their instruments a great deal more out of tune than the instruments themselves actually are. While players have every right to be highly critical of the instruments which they play, it would also behoove them to examine carefully their own playing habits and eliminate those which may be unintentionally causing intonation difficulties additional to those inherent in the instruments themselves.
By following a few simple precepts most players can improve substantially the intonation of their instruments and elevate the quality of their musical performances in general:
Rule #1: Purchase your instruments from a dealer who is a craftsman and performer and who will certify that each instrument has been serviced to optimal professional standards. Instruments purchased directly from makers or "off the shelf" from a commercial source are invariably not as well in voice or tune as they are capable of being and are usually a continuing source of unhappiness and dissatisfaction to their owners.
Rule #2: Play your instrument at the pitch level at which it was designed to be played. Reproduction instruments "scaled" to another pitch than the original instrument should have been completely redesigned, not simply shortened and retuned. Choose an instrument by a maker who is also an expert designer, not just a copyist of other makers' instruments.
Rule #3: Find the one correct headjoint position at which the instrument is best in tune with itself before attempting to assess the tuning, intonation, and response of that instrument. Be aware that varying from that position to change the overall tuning of the instrument will result in an unavoidable deterioration of intonation and a skewing of one's perception of its intonation. Soprano and smaller instruments are the most difficult to play in tune, because the optimum headjoint position is much more critical and difficult to achieve.
Rule #4: Find the correct breath pressure at which the instrument is designed to play and learn to play the instrument at that optimum breath pressure. If you are unwilling or unable to modify your playing technique, find an instrument that lends itself more readily to your style of playing. Some instruments can be retuned to play higher or lower more easily than others. Again, a craftsman-player-dealer who has worked on and is familiar with the capabilities of a wide variety of designs is your most reliable source of information.
Rule #5: Make certain that your recorder has adjusted to room temperature before playing and avoid performing in halls that are unusually cold or warm. Air conditioning is not harmful to instruments, but instruments should not be placed close to a stream of cold air from an air conditioner. Hardwood recorders should be maintained in an ambient humidity of about 50% year round; use the case humidifier as per the detailed instructions which we supply with every wooden recorder sold by our workshop. A case hygrometer is also highly recommended to monitor ambient humidity levels.
Rule #6: Use the fingerings which give the optimum intonation and response on your instrument and avoid using alternate or trill fingerings in place of standard fingerings when not absolutely necessary. Determine the correct amount of left thumb opening that will produce optimum intonation and response in the high register. Remember that these adjustments vary greatly from one instrument to another.
If you have an instrument which has been custom-serviced by an experienced professional player, you can assume that any intonation problems are a result of less than optimum playing techniques and/or adjustments and proceed to rectify the situation; if you have an instrument which was bought "off the shelf," you will never know whether the problem is you or the instrument or a combination of the two. Caveat emptor!
1 See "From the Director's Desk: a'=415 Hz. ±3 db.," in Antique Sound Workshop Customer Newsletter, Vol. XI, No. 1 (February 1986), pp. 13-17.
2 See Michael Praetorius,De Organographia Zweiter Teil des Syntagma Musicum (Wolfenbüttel 1619), herausgegeben von Wilibald Gurlitt (Kassel: Bärenreiter-Verlag, 1929) pp. 34-35.
3 All pitch references in this article are to the alto recorder in f'.
4 Although notes in the lower octave are lowered in increased amounts as one progresses upward from f' to g", notes in the second octave are actually lowered by irregular but generally decreasing amounts from a" through d"'. Even more oddly, several notes in the uppermost register, such as e"', f"', and g"', actually go sharp rather than flat when the headjoint is pulled out!
5 See Blowing An Ill Wind Good – Some Words of Advice on Breath Pressure.
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