By Brendan Lai-Tong
When many people think of flutes, they think of a transverse flute, which is typically used in bands and orchestras. The flute has been a part of history for thousands of years and has evolved over that time into the instrument that is often seen today. Here are ten facts you may not have known about the flute:
- A musician who plays the flute can be referred to as a flute player, a flautist, a flutist, or, less commonly, a fluter.
- There are many different sizes of flutes within the flute family: piccolo, alto, tenor, bass and contrabass flute.
- Standard concert flute is pitched in the key of C, and has a range of approximately 3 octaves.
- Alto flute is pitched in the key of G
- Flutes have been made out of lots of different materials throughout history including: bone, wood, glass, ivory, plastic, resin, brass, nickel silver, silver, gold and platinum.
- Theobald Boehm helped create the modern Western flute. He started improving flute design and the fingering system of the flute between 1831 and 1847. Most flutists had adopted Boehm’s changes to the design by the second half of the 19th century.
- George Washington, James Madison and Leonardo da Vinci all played the flute.
- Flutes are considered one of the earliest instruments and date back to Germany over 35,000 years ago.
- Many cultures have their own version of the flute. For example, one of the most popular traditional Japanese flutes is the the Shakuhachi.
- The earliest use of the word “flute” was in the 14th century
We hope that you enjoyed these facts. Please feel free to chime in if you have other interesting flute facts!
Check out our selection of flute sheet music.
Brendan Lai-Tong holds degrees in trombone performance from University of Miami and the San Francisco Conservatory of Music.
Mozart and the Tromlitz flute
© 2000 Ardal Powell
Author's note: this is an English version of 'Mozart und die Tromlitz-Flöte', as it appeared in Tibia 26.3 (2001)1
ABSTRACT: W.A. Mozart, J.J. Quantz, J.G. Tromlitz and other educated musicians of the 18th century relied on a tuning theory more complex and more accurate than today's equal temperament. This article briefly describes a flute announced by Tromlitz in 1785 that allowed strict adherence to this system in all 24 keys. Quotations from Mozart's flute music illustrate how using the intonation practice he advocated can dramatically alter the expressive effect of his music.
In 1785 the Leipzig flute virtuoso, teacher, author, and flute maker Johann George Tromlitz (1725-1805) announced the development of a new kind of flute. After a lifetime's experience of playing and making flutes, and a few years of experiment on improving the design of his instruments, he had developed a type he could rightfully claim as the most technically advanced flute of his time.
The Tromlitz flute appeared at the beginning of a period of rapid and energetic experimentation in flute design that culminated in the modern flute, and until very recently it attracted notice only as a stage in that evolution. As such it made a notable gain: Tromlitz's flute of 1785 provided the first practical model in which each of the twelve semitones of the chromatic scale was produced by a separate tonehole not shared by any other note. No more significant acoustical advance was made in flute design until, in 1832, Theobald Boehm, who with his friend Carl von Schafhäutl (1803-1890) indiscriminately called all the keyed flutes of the time 'Tromlitz' flutes, employed elaborate keywork to assign more acoustically correct positions to the toneholes than those the unaided fingers could reach.
Yet today's interest in the historical performance of classical music invites our closer attention to the musical properties of the instrument itself. Tromlitz developed his flute in pursuit of certain particular ideas about tone and intonation,2 ideas he also expressed in writing,3 as well as in performances that attracted comments from his contemporaries.4 Thus Tromlitz's flutes, publications, and playing provide a rich store of information from several different perspectives not only about how he himself played, but also about what his contemporaries heard in his playing, and about his reasons for playing the way he did.
Tone and performance style
In 1754 Tromlitz joined the Grosses Konzert, a private music club formed in Leipzig in 1743 from the Collegium Musicum that had been founded by Telemann and directed for a time by J. S. Bach. Over the next 20 years he appeared with the orchestra, as well as in solo billing with stars such as the singer Gertrud Elisabeth Schmeling and the keyboard player Johann Wilhelm Hässler, not only in Leipzig but also on tours as far afield as St Petersburg. These performances made him famous for a soloistic style of playing the flute that at that time was considered new, at least for the flute. Tromlitz's obituary in the Allgemeine Musikalische Zeitung recalled that,
As a virtuoso he was distinguished by perfection, but still more by complete purity of intonation and security of tone, as by precision in performance. He was also one of the first, and in respect of the influence he had, the first, to introduce the now usual bravura- and concerto-style way of playing the flute, and especially the strong, cutting tone best suited to it. . .
Als Virtuos war er durch Fertigkeit, noch mehr aber durch vollkommene Reinheit und Sicherheit des Tones, wie durch Genauigkeit im Spiel ausgezeichnet. Er war auch einer der Ersten, und in Absicht der Einfluss der Erste, die die jetzt gewöhnliche bravour- und konzertmässige Behandlung der Flöte und vornemlich den dazu am besten geeigneten starken, scharfen Ton . . . einfuhrten . . . hat.5
A still more evocative description of Tromlitz's tone is given by an anonymous reviewer of his book of 1800 about the new keyed flute, Über die Flöten mit mehrern Klappen:
Anyone who still remembers the author's public appearances as a flute-player knows . . . that he melted the tone of the flute and the oboe into one another.
Wer sich noch daran errinert, wie der Verfasser als Flötenspieler öffentlich auftrat, der weiß . . ., daß er der Ton derl Föte und der Oboe ineinander Verschmolz.6
Tromlitz spoke for himself about tone in his pamphlet of 1786 on flute-playing, in Chapter 6 of his tutor for the two-keyed flute, published in 1791, and in an essay of 1800 in the Allgemeine Musikalische Zeitung. In the latest of these works he described his ideal flute tone as "bright, metallic, firm, well focused, strong and brilliant" [hell, von viel Metall, voll, singend, sanft und beigsam], and in the earliest wrote that:
a good flutist must have a strong low register and a weak high one. . . The high register of the flute carries much more than the low, therefore one must certainly seek to soften the high so that it does not shriek like a fife, but at the same time the tone must not be made too repressed and fearful; the low register must be more penetrating and fuller, but still so that both, high and low, stand in an equal relation.
. . . man sagt: 'ein guter Flötenist muß eine starke Tiefe und schwache Höhe haben.'. . . Die Höhe auf der Flöte sticht weit mehr durch, als die Tiefe, daheo muß man zwar die Höhe zu mildern suchen, daß sie nicht wie eine Querpfeife schreyt, aber den Ton muß auch nicht zu sehr gedrückt und ängstlich gemacht werden; die Tiefe muß schärfer und vller werden, aber doch so, daß beydes, Höhe und Tiefe, in einem gleichen Verhältnisse stehen.
In Saxony during the 1760s and 70s this style of playing may have been unusual enough to attract special notice, but by the 1790s it had become widespread, certainly among professional players and traveling soloists. In a flute tutor published in London in 1793, John Gunn wrote that by that time "every public performer" played with
The increase in the frequency and size of public performance of concertos and solos, both by traveling virtuosos and in groups of amateur musicians, seems to have been linked with this growing taste for a harder, more brilliant tone, as well as with the emergence of keyed flutes with their more penetrating and even low register. The new style stood in direct opposition to the more relaxed style of playing popular earlier in the eighteenth century, and still cultivated by amateurs, perhaps especially in England.7 Gunn describes the older manner of playing, still typical of amateurs and dilettantes ". . . the character of which . . . is softness, grace, and tender expression."
The other of Tromlitz's chief concerns was intonation. Although equal temperament had long been used in keyboard tuning and was making itself felt in the theory of melody instrument design,8 'the bases then [i.e. during Quantz's lifetime] accepted for tuning often differed fundamentally from modern views', as Edward R. Reilly noted in 1997. 9
Throughout his writings Tromlitz emphatically and repeatedly insisted that intervals, either between melodic steps in the flute part, or between the flute and its accompanying bass part, should be played 'pure', and that tempering intervals on melody instruments was both impractical and undesirable. Today pure intervals are a rarity in instrumental music except among the finest orchestral woodwind sections: the out-of-tuneness of an equal-tempered keyboard no longer strikes us as horrid, and many flutists are in thrall to the mistaken idea that playing "in tune" means matching the notes to the same pitches on the piano or harpsichord. Yet a keyboard with only 12 divisions to the octave can manage to be only approximately in tune if it is to be usable in 12 major and minor keys, and there is a world of difference between this approximation and the sound of pure intervals. Tromlitz wrote that wind instruments have the option of playing better in tune in 24 keys than any keyboard can do in half that number:
It is possible for [the flute] to be more perfectly in tune than the keyboard, on which no interval except the octave can be quite pure, so that it cannot agree in tuning all the time with a good flute-player who scrupulously observes everything that has been said above, or with a good violinist who plays in tune.
Eine dergleichen Stimung is weit schwerer, als die auf dem Claviere, und dennoch ist es möglich, daß dieses instrument . . . reiner gestimmet werden kann, als das Clavier, auf welchem kein Intervall, als die Octaven, ganz rein seyn kann, dahero kann es auch nicht überall zu einem guten Flötenspieler, der alles Vorhergesagte genau beobachtet, oder zu einem guten Geiger, der rein spielet, passen.10
He advised the student, in his 1791 tutor for the two-keyed flute, to train his ear to hear the intervals correctly, and although he mentions 5ths and 3rds, he most frequently reminds us how important it is to learn the "semitones and whole tones in particular", "and how they are supposed to sound".
J.J. Quantz had explained the proportions of the semitones in 1752:
The motive which induced me to add yet another key, not previously used, to the flute, stems from the difference between large and small semitones. When a note on the same line or space as another note is raised with a sharp, or lowered with a flat, the difference between the altered note and the principal note consists of a small semitone. When, on the other hand, one note stands on the line while the other stands a step higher, and is lowered with a flat; or if one note stands on the line, and is raised with a sharp, while the other stnads on the space a step higher, and remains natural, the difference amounts to a large semitone. The large semitone has five commas, the small one only four.
Die Ursache, welche mich veranlasset hat, der Flöte noch eine Klappe, welche vorhin nicht gewesen ist, hinzufügen, rühet von dem Unterschiede der großen und kleinen halben Ton her. Wenn eine Note auf eben derselben Linie, order auf eben demselben Zwischenraume durch ein Kreuz erhöhet . . . oder durch ein b erniedriget wird . . . so bestehet der Unterschied zwischen dieser und dem Haupttone, aus einem kleinen halben Tone. Wenn hingegen eine Note auf der Linie, die andere aber eine Stufe höher steht, und durch ein b erniedriget wird . . . oder wenn eine Note auf der Linie steht, und durch ein Kreuz erhöhet wird; die andere aber auf dem Zwischenraume, eine Stufe höher ist, und natürlich belibt . . . : so beträgt der Unterschied zwischen diesen beyden Noten, einen großen halben Ton. Der große halbe Ton hat fünf Kommata, der kleine aber hat deren vier.11
Thus in Quantz's tuning system, whichTromlitz, like other educated musicians of his period, espoused, the octave contained not twelve but twenty-four notes, with distinct fingerings for every enharmonic pair.12 The disappearance of these major and minor semitones is perhaps the most notable of many shifts to have occured over the past 200 years in the way music sounds.13
The Tromlitz flute
Three views of Tromllitz's flute of 1796, showing (left)keys for G#, long and short F, and D#; (middle) keys for C, long and short B flat, G#, long and short F, D# and E flat; (right) keys for C, long and short B flat, the short F touchpiece just visible, E flat and D#.
In the late 18th century, this shift had not yet taken place. During the period when Tromlitz was making his reputation as a performer, in the 1760s and 70s, he, like Quantz, was playing on a two-keyed flute of his own design. Despite the extreme limitations of this type of flute for realizing his precise notions of intonation, but perhaps in deference to Quantz's example, it was the two-keyed flute he recommended in his tutor of 1791. He looked back on this unsatisfactory situation in 1800:
However by the early 1780s, a decade before he published his tutor for the two-keyed flute, Tromlitz had begun adding keys to his flutes, as London flutemakers had already been doing for about 30 years.15 His quest for a "superlative instrument" led him after only a few years of experiment to the design of 1785, in which for the first time all 24 notes in an octave could be played with accurate intonation and equal tone. For Tromlitz, this was an achievement literally twice as important as the one he is credited with by later writers.
By 1796, his most advanced instruments were being made with keys for D#, Eb, double F, G#, double Bb and C, and four years later Tromlitz published a tutor for this instrument. He wrote that, though the maker could tune the notes produced by the keys so as to be usable as both sharps and flats, they could more usefully be tuned as flats and a different fingering used for the lower-sounding sharps. The detailed fingering tables in the 1800 work listed all the large and small semitones, as well as exhaustive examples of how to play—perfectly in tune, with pure intervals—in all keys. In his Foreword he noted that by no means all flutists were in a position to appreciate the importance of this development:
In general people think that anyone who from much practice has acquired a certain facility in the usual keys and commonplace passage-work is a Virtuoso. But, dear reader, he is not; he is only someone who makes a living from this instrument, not a Virtuoso; since for this is required a thorough knowledge of music, which he must possess and be able to apply, so that he does not just parrot other people's conventional ideas, but can produce new and artful idioms even in the remotest keys. This has a marvellous and exquisite effect, especially on the flute. However it is seldom if ever to be heard on this instrument, because on a one-keyed flute it cannot be done.
Überhaupt glaubt man, daß der, der sich durch vieles Üben einige Fertigkeit in den gewöhnlichen Tonarten und alltäglichen Passagen erworben hat, eine Virtuose sey. Allein, mein Lieber, das ist er nicht, er is nur einer, der Profession von diesem Instrumente macht, aber kein Virtuos; denn dazu gehöret eine weitläufige Kenntniß in der Music, die er besitzen und anwenden können muß, damit er nicht nur andern ihre alltägliche Gedanken nachbeten darf, sondern neue und kïnstliche Wendungen auch in den entfernsten Tonarten hervorbringen könne. Dieß macht vorzüglich auf der Flöte eine herrliche und vorterffliche Wirkung. Allein man höret es auf diesem Instrumente selten oder gar nicht, weil es auf einer Flöte mit einer Klappe nicht möglich zu machen ist.
Mozart and intonation
At the same time as Tromlitz was developing a flute that made Quantz's tuning system so much more practically achievable, Wolfgang Amadeus Mozart (1756-1791) was teaching the same theoretical framework to an English composition pupil in Vienna. Thomas Attwood's lessons in theory and thorough-bass took place from 1785 to about the beginning of 1787. Among the details in Attwood's notes that are written in Mozart's hand are chromatic scales with enharmonic equivalents showing large and small semitones, and the sizes of intervals as the sum of whole tones and differently-sized semitones. Mozart himself made corrections to other material that appears in Attwood's hand, which John Hind Chesnut discussed in an important article in 1977.16 Chesnut concluded that Mozart taught Attwood the same rules of tonality and intonation as the ones in practical manuals for performance by Tosi, Quantz, Leopold Mozart, Tromlitz, and others. He concluded: "Modern intonation practice is not appropriate if our goal is to play Mozart's music as he himself wanted it played."
With the Tromlitz flute in hand, we can put Chesnut's conclusion to the test. A chromatic scale played with Tromlitz's fingerings sounds very different from the smooth, homogenized sequence of intervals we are accustomed to hearing. And passages containing the kind of chromaticism Mozart uses to paint melodies and enhance their features seems much stronger and more challenging when interpreted as Mozart imagined them compared to the comparitively bland effect when played with equal-sized semitones. In ensemble music the contrast between concords that sound perfectly in tune and discords that sound jarring greatly increases the tonal pull of the music as well as its dramatic power. W.A. Mathieu wrote that even when listening to Mozart on a good day, the ear gets tired and restless in twelve-tone equal temperament. Indeed, playing Mozart's music according to his own specifications as to intonation practice can have a dramatic result on its expressive quality.
Mozart's flute music provides abundant examples of his expressive use of these intonation features, but only four brief excerpts must suffice here. In the first subject of the Andante ma non troppo of Mozart's D major concerto K. 314 (see example 1 above), chromatic appogiaturas play a structural role. On the first beat of bars 12, 13, and 14, the G#s and A# should sound a large semitone below their upper neighbors. All the notes marked with an asterisk, in fact, sound much lower than they would in equal temperament, in direct opposition to the tendency of conservatoire-trained musicians since the mid-nineteenth century to sharpen leading notes.
The Adagio of Mozart's Quartett in D KV 285 for flute and strings (example 2 above) employs appogiaturas in a similar manner. For a one- or two-keyed flutist to execute the E#s in bars 2, 3 and 5 of the example so that they sound low enough is already difficult, owing to the fact that a separate fingering for E# does not exist, and that for F (a comma sharper than E#) already has a tendency to be sharp on most flutes. Tromlitz's flute provides an appropriately low fingering for this note, as well as for the D# in bar 7.
Another of Mozart's flute quartets, KV 298 in A major, appears to have been composed a year or so after Tromlitz announced his new flute in 1785. The key of A major fits well on most German keyed flutes of the period, which tend to have D# and G# tuned lower than their equal-tempered pitches. The Tromlitz flute, however, provides the added advantage of correct fingerings for A# and E#. On a one-keyed flute the Rondeau of KV 298 (example 3 above) comes across with far less success, especially in a large room.
A passage from the Allegro of quartet in D KV 285 (example 4 above) illustrates the unsettling effect of chromaticism in the Mozartian tuning system. Rather than slipping gently from one key to another, the listener feels the tonal ground shifting beneath his feet at such moments. The 'harmonic experience', to use W.A. Mathieu's expression, of the key of D major when it reappears, feels like the solid footing of the dock after a trip on a sailing vessel. 17
Performing Mozart's music today
Though our picture of Tromlitz's manner of playing and of the instrument he developed to facilitate it is clear enough to reveal much about 18th-century musical taste and practice, it would be a mistake to conclude that that everybody played the same way as he did—the contemporary reports of his excellence are testimony to that, and after all he produced his exceptional instruments one at a time in his one-man workshop, not in a factory that sold to the trade. Indeed it is tempting to speculate that when Mozart referred to the flute as "an instrument I cannot bear" it was because few of his contemporaries observed the distinctions in intonation Tromlitz was so careful to make. That Mozart shared Tromlitz's concern for correct intonation is clear from his words of praise for his friend the Mannheim flutist Johann Baptist Wendling:
It's another thing with your brother, you know. In the first place he's not just a tootler, and then you don;t have to worry in his case when you know there's such and such a note coming up that he'll be much too flat or too sharp--see, it's always right and he has his heart and ears and the tip of his tongue in the right place and doesn't think his job is done just by blowing and fingering, and then he also knows what Adagio means.
Ja wissens das ist was anders beim Herrn Bruder. Der ist erstens kein so Dudler, und dann braucht man bei ihm nicht jedesmal Angst zu haben, wenn man weiss, jetzt soll der eine Ton kommen, ist er wohl so viel zu tief oder zu hoch—schauens, da ists immer recht, er hat's Herz und die Ohren und das Zungenzpitzl am rechten Ort und glaubt nicht, dass mit dem blossen Blasen und Gabelmachen schon was ausgerichtet sei, und dann weiss er auch, was Adagio heisst.18
Although Tromlitz's executive skill, likeWendling's, was surely exceptional, his ideas on intonation were clearly in the mainstream of educated musical practice in the 18th century. And even the brief examples here should indicate that their effect in the performance of Mozart's music amounts to more than a minor quibble.
Yet it must be noted that while most of today's historical-instrument flutists have cultivated the 'soft and tender' style Gunn referred to, only one or two notable exceptions have made any attempt to play classical music in a style that resembles that of the period's professional players. Still less have today's interpreters of the classical repertoire on 'original' flutes absorbed the intonation practice spelled out by Mozart, Tromlitz, Quantz, and others, though interestingly oboists and even clarinetists tend to play with more attention and sensitivity to such matters. Of course, how to apply what we learn of contemporary ideas and performance practice in our own interpretations of late 18th-century music is a difficult question: clearly, our conditions are quite different from those of 200 years ago. But the parallels between Tromlitz's ideas of intonation and those of Mozart, and the dramatic expressive effect of putting them into practice in place of an unthinking adherence to modern convention, makes experiencing these ideas an indispensable study for anyone who wishes to understand the true nature of Mozart's musical feeling and bring it alive today.
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1. Parts of this essay were read at the 1995 meeting of the American Musical Instrument Society, and published in 'The Tromlitz Flute', Journal of the Americal Musical Instrument Society XXII (1996), 89-109. Other material is taken from Ardal Powell, trans. and ed., The Keyed Flute by Johann George Tromlitz (Oxford: Clarendon Press, 1996) (hereafter The Keyed Flute), in which further detail and documentation on the points covered in this article may be found. 'Powerful tone and perfect intonation: Tromlitz and his "superlative instrument"', a paper read at the Convention of the National Flute Association, Phoenix AZ, 13 August 1999, gave a practical demonstration of the effects of using appropriate intonation practices in Mozart's music. Research on the Tromlitz flute was funded by a 1993-94 Fellowship from the National Endowment for the Humanities' program for College Teachers and Independent Scholars.
2. Tromlitz described his motivation as a flute maker in the pamphlet An das musikalische Publikum, Leipzig;[Author], 1796; R/1982; translated in The Keyed Flute, Appendix II.
3. Tromlitz's didactic writings are:
Johann George Tromlitz, Kurze Abhandlung vom Flötenspielen, Leipzig: Breitkopf, 1786
-----Ausführlicher und Gründlicher Unterricht die Flöte zu Spielen Leipzig: Böhme, 1791, trans. and ed. Ardal Powell, The Virtuoso Flute-player by Johann George Tromlitz (Cambridge and New York: Cambridge University Press, 1991)
-----Über die Flöten mit mehrern Klappen, Leipzig: Böhme, 1800, trans. and ed. Ardal Powell, The Keyed Flute by Johann George Tromlitz (Oxford: Clarendon Press, 1996)
-----"Abhandlung über den Schönen Ton auf der Flöte", Allgemeine Musikalische Zeitung 2 (January 1800), 301-04 and 316-20.
He wrote about his flute making activities in a series of articles and pamphlets:
Johann George Tromlitz, "Nachricht von Tromlitz Flöten", in Johann Georg Meusel, ed., Miscellaneen artistischen Inhaltes 8 (1781), 115-21
-----"Nachricht von Tromlitz'schen Flöten",in C. F. Cramer ed., Magazin der Muzik, 1. 2 (Hamburg, 1783), 1013-21, trans. Ardal Powell, "Information on Tromlitz flutes", Traverso 6. 1 (January 1994), 1-2
-----"Neuerfundene Vortheile zur bessern Einrichtung der Flöte", in Johann Georg Meusel, ed., Miscellaneen artistischen Inhaltes 26 (1785), 104-09
-----"An das musikalische Publikum", Musikalische Korrespondenz der teutschen filarmonischen Gesellschaft, 32-4 (10-24 Aug. 1791) 252-69
-----An das musikalische Publikum Leipzig, 1796 R/1982
-----`Replik auf die Anfrage,"Sollten nicht undere Flöten durch die vielen Klappen sehr verloren haben; und hat jemand beweisen, daß die nöthig waren"', Kaiserlich-privilegierter Reichszanzeiger, Gotha, 1800, No. 98, 1271-72.
4. Most of the relevant reviews of Tromlitz's playing are quoted in Fritz Demmler, Johann George Tromlitz (1725-1805): Ein Beitrag zur Entwicklung der Flöte und des Flötenspiels, Ph. D. dissertation, Freie Universität, Berlin, 1961; R/1985.
5. 'Nachricht über das Ableben von Tromlitz', Allgemeine Musikalische Zeitung 7 (1805), 337-38.
6. Allgemeine Musikalische Zeitung II (1800), 600 ff., quoted in Demmler.
7. On ideals of flute tone in the late eighteenth century, see section 2 of the Introduction to The Keyed Flute.
8. The first to actually suggest that wind instruments should be tuned with equal-sized semitones sems to have been Anon. [H. W. T. Pottgiesser], 'Über die Fehler der bisherigen Flöten, besonders der Klappenflöten, nebst einem Vorschlage zur Besseren Einrichtung derselben', Allgemeine Musikalische Zeitung 5, (1803), 609-16, 625-38, 644-54, 673-83.
9. Edward R. Reilly, 'Quantz and the transverse flute: Some aspects of his practice and thought regarding the instrument', Early Music 25 (1997), 429-38
10. Unterricht, 3.22
11. Versuch 3.8
12. For further discussion of vocal and instrumental intonation practice, see Bruce Haynes, 'Beyond Temperament: Non-Keyboard Intonation in the 17th and 18th Centuries', Early Music 19 (August 1991), 357-81
13. Mary Oleskiewicz makes a strong argument for the importance of intonation in Bach's flute music in "The Trio Sonate in Bach's Musical Offering: A Salute to Frederick's Tastes and Quantz's Flutes?" in Bach Perspectives, vol. 4: The Music of J.S. Bach, Analysis and Interpretation (Lincoln: University of Nebraska Press, 1999), 79-110.
14. Über die Flöten mit mehrern Klappen, 1.1
15. For details of Tromlitz's work on his flute, and a comparison with the activities of other instrument makers in Germany, France, Austria, Italy, and England, see the Introduction to The Keyed Flute, and 'The Tromlitz Flute'.
16. John Hind Chesnut, 'Mozart's Teaching of Intonation', Journal of the American Musicological Society 30 (1977), 254-71
17. W.A. Mathieu, Harmonic Experience (Rochester VT: Inner Traditions International, 1997)
18. Jane Bowers, 'Mozart and the Flute', Early Music 20.1 (Feb 1992), 32, citing H. Abert, W.A. Mozart: Neubearbeitete und erweiterte Ausgabe von Otto Jahns Mozart, 2 Vols, (Leipzig, 7/1955-6), i, 473, who in turn cites Wolzogen, Recensionen 1865, No. 6, 82.