Traité des Agréments
C.M. Sunday © 1991
In examining 18th century ornaments, a number of questions come to mind: Is the ornament diatonic, or does it require an accidental? Does it precede the main note or fall on the beat? Is it fast or slow? If slow, what proportion of the main note does the ornament require? Does the stress lie more on the ornament or the main note? Does the stress lie more on the ornament or the main note? The questions are complicated, since instructions in various treatises are often contradictory and stenographic indications are not consistent. Methods of execution were dependent upon tradition and musicians have always tended to deviate from accepted practice. In addition, writers may have put more effort into disclosing what they consider bad practice as opposed to what they accept as correct. Since up until the time of Beethoven so much was left to the discretion of the player or singer, an executant two centuries later is often left with a series of puzzles. In Tartini’s treatise, as Frederick Neuman points out several times, much of the material is unclear or ambiguous, and there are opinions stated which are given without any specific of compelling reasons.
The Apoggiatura, Trill and Mordent
Frederick Neuman categories two primary sorts of Vorsclage  in Tartini’s ornaments: (1) The long or sustained (appoggiature lunga ossia sostentatat) and (2) the short or passing type (appoggiature breve ossia di passaggio). The first type, which Tartini limits to the heavy beat and generally to pieces in slow tempo, is said to take half the value of the printed note, and 2/3 the value of the dotted note. The reason that composers do not write this material out directly is because of the difference in execution; normally, the first eight note would need a short trill to further underline it, but as an appoggiature, it should begin softly and swell and diminish before it falls on the eight note. Since dissonance "ought" to be resolved downward, Tartini dislikes a long ascending appoggiature that creates a dissonance. The second type is an anticipated gracenote, a fleeting expression with the accent on the principle note.
Tartini’s advice to singers and string players about the use of the trill is unique and sensible. The trill was the most usual and important of ornaments during this style period, and currently the most controversial, in respect to the conflict over the upper note start. Despite Neumann’s "intuitive misgivings about prevailing theories of baroque ornamentation,"  the upper note start of the trill was given with monotonous regularity from the middle of the 17th century; it is to be found in the works of Playford, d’Angelbert, Muffat, Purcell, Hottenterre, Couperin, Tosi, Rameau, Quantz, C.P.E. Bach, Marpurg, and Türk. However, Leopold Mozart mentions no rule about starting trills with an upper note, and in two long chapters on the trill, Tartini never mentions the need to start on the upper note, though patterns in the Treatise do show upper-note start and anchor. 
The trill, according to Tartini, is like salt in cooking, which must not be used too much or too little. Different speeds of trills suit different moods of music, and a good player must master all speeds. Trills may be started from above or below and there are several forms of ending trills, the bad sort being "abhorrent to nature." 
Tartini mentions two ways for a violinist to produce a trill. One is by pressing hard on the lower note and striking the trill; the other is the "ripped" not "struck" affect created not by raising the finger but by using the wrist to carry the hand in a rippling motion. This is not the same as Carl Flesch’s Bochstriller which is created with the arm in the higher positions.  In the letter to Signora Lombardini,  the composer recommends that the student learn the shake by increasing the speed by gradation, beginning first with the open string and first finger:
This exercise is also given in the Treatise with the addition of passing by gradation from piano to:
Tartini’s mordente is often a prebeat turn; in his treatise he introduces two sorts of grace notes which he calls mordente: (1) a melodic form of a turn; and (2) a genuine mordent with one to three alternations. The melodic form, consisting of scalewise notes centering on and preceding the principle note, is of two types, but the falling appoggiatura sounded better to his ears.
His instructions are that these graces are to be performed as quickly as possible, and not be heard individually but as part of a total affect which is vivacious and spirited. The accent falls on the principle note and not on the graces. In the case of the genuine mordent with the alternation, the principle note still has the accept and the ornaments are to be done piano and very quickly. The French translation of the Treatise gives an incorrect account of the two types of turns, revealing a rhythmic ambivalence not out of keeping with other difficulties the Treatise. Tartini’s mordents are anticipated turns from either above or below; they are not to be placed on notes where any accent is not appropriate. The genuine mordent is identical to our present-day mordent; at first glance it looks like a shorter trill, but falls, instead, to the note below instead of rising. It may consist of four or six notes, depending on finger speed.  The Italians have no written symbol for the mordent.
Tasteful vibrato (tremelo) was applied not continually, but as an occasional ornament.  To Tartini, this ornament was an affect produced by the imitation, on stringed instruments, of a wave motion in the air, which is naturally left behind by harpsichord strings, bells or the open string of any good bowed instrument. He disparaged its use on half-steps, but felt is sounded well on final notes of phrases, long notes in singing passages, and double steps on long notes. The modern arm vibrato was unknown in the eighteenth century, and would have been impossible to produce, given the absence of a modern chin-rest. Vibrato was produced with the left wrist, more enabling one to control the speed: fast, slow, or accelerating on one note. The hand undulated toward the bridge, rather than the scroll, and the left hand held the instrument differently than it is held today; changes in the form of the bow, and tension in the hair and string, also contribute to the difference between 18th and 20th century violin sound.
The second part of the Treatise deals with natural and artificial modes, by which Tartini meant not keys (as meant in French) but the manner of placing ornamental figures, similar to the "divisions" of Elizabethan music.  Regarding natural figures; in the course of treating a bass line, certain cadential points lend themselves to figurations, whether a full stop is made or the melody is unfinished. Tartini compares these cadential points with punctuation in writing. Cadential formulae are given at length, but composite figures may occur naturally, as the primary cells are simple and few in number. In contrast, artificial figurations are very many in number and it would be necessary to treat all the possible permutations; they have to do with compositons, and good taste is the rule. One can generate ideas about these cadences by examining the possible thorough-bass progressions.
Natural cadences are those phrase endings on which the melody stops. An artificial cadence indicates a final cadence, with a fermata sign, that the signer or player may draw out as long as he or she wishes. This free cadenza was very much in the spirit of the time, though the freedom to embellish was much more limited in Tartini’s day than it later came to be. As time passed, composers increasingly gave more explicit instructions, and performers tended more and more to concentrate their improvisitory impulses on the cadenza. Initially, Tartini gives nineteen of the simplest examples of these, cautioning that one must be sure to avoid consecutive fifths and octaves. Numerous examples follow with increasing complexity. While the examples are in major, they could just as easily be used in minor, though Tartini states that they would not sound as well, due to the irregularities in the minor mode.
Giusippe Tartini is the link between the old style of Vivaldi and the "new" classicism of Viotti. His style changed gradually from baroque to style galant and was a synthesis of galant and empfindsam qualities during the mid-eighteenth century. His fame was based on a rare combination of talents; his virtuosic playing, his compositions, (consisting of over 400 works written within the space of four decades between 1720 and 1760, ), and on his scholarship and teaching. Quantz criticized Tartini’s excess of virtuosity, perhaps reflecting the prejudice against the Italian style in music, while praising his beautiful, sweet tone aimed more at expression than power, and his mastery of the great difficulties involved in trills, double trills, double stops and high positions.
Considering that he was the greatest violin master of his time, and was known all over Europe during the mid-eighteenth century, Tartini’s life was relatively sedentary and uneventful.  He was known for his well-bred and unassuming manner, warmth, sensitivity and paternal interest in his students. He was given to visionary mysticism, and wrote mottoes in secret code on many of his compositions. He was an eighteenth century genius who was not only a composer and pedagogue, but an inventor who took contemporary criticism of his scientific work quite seriously. .
Tartini’s music disappeared from active concert repertory, but continued to be used as study material. A change in musical taste is reflected in Burney’s two published opinions of the composer; the one expressed in1788 was less favorable than the first from 1770; during the interim Tartini’s ornate style had begun to seem stilted and out of fashion. Eighteenth century audiences were not historically minded; Tartini’s work was apparently not referred to in other treatises after its publication, and by the time of its publication in France, had begun to be outmoded.
Tartini’s academy for violinists, founded in 1727 or 1728, was the composer’s main source of income; he gave daily lessons, working ten hours a day. The school existed for more than forty years, and the students there comprised most of the great European violinists. . The Treatise was compiled by his students from lessons; it was unique in being the first pedagogical work exclusively to detail the reason for and applications of ornamentation, providing information continued in no other books of the period; Tartini’s Treatise takes its place among the most significant contributions during the first part of the 18th century, including those of C.P.E. Bach, Quantz, Agricola, Tosi and Leopold Mozart. . It was never published in Italy. It must have existed by 1750, since Leopold Mozart used it in 1756, but could have originated any time between 1728 (the year Tartini founded his school) and c. 1754 (when Mozart began his Violinschule).  The original manuscript, which was thought to be lost, was discovered in two independent copies, one at Berkeley and one in Venice. .
Eighteenth-century Italians were more interested in art and music than the philosophy and politics that consumed the rest of Europe and England. It was a time of growing popularity of the violin and its virtuosi, and in this Tartini’s importance is secure; he was the teacher of Pugnani who taught Viotti, and the teacher of Leclair who taught Gavinès.
Examining the master’s work today, one can only conclude that the rise of the super virtuosi in music has come full circle, and the return to the original intentions of the composers has become necessary for educated musicians. In this way the accumulated miscellany of two centuries may be removed and the purity of the originally intentioned sounds may be recreated or approximated.
In the preface to the Moeck edition, Erwin Jacobi states: