Regarding the history of the term “improvisation,” and the unfortunate negative attachments that have come to be associated with it, Jeremy Begbie writes,
At first it [improvisation] carried the relatively neutral sense of extemporization, […] By the 1850’s it appears to have acquired pejorative connotations-off-hand, lacking sufficient preparation (as in ‘improvised shelter’, ‘improvised solution’). Many musicians and musicologists continue to view it with considerable suspicion, if not disdain. For some it is synonymous with the absence of rigour. There are educationalists who see it as a distraction from authentic music-making.
Contra this pessimistic and mistaken construal of improvisation, I suggest that jazz improvisation requires just as much skill, creative genius, and intellectual stamina as written orchestral compositions, and that the latter in fact are not without improvisatory elements. To begin with, it is important not to gloss over the pervasiveness of improvisation in music in general. Before going further, I should pause, however, to acknowledge the well-known difficulty among music specialists in arriving at a satisfactory definition of improvisation. Given this difficulty, we shall move through a number of possibilities, noting various aspects of improvisation broadly construed with the hope of finally obtaining a working definition of improvisation as related to our present purposes.
If improvisation is understood as a simultaneous occurrence of composing and performance, then improvisation cannot be limited to jazz. In fact, what we find is that improvisation characterized in this manner has been prevalent in a wide variety of cultures and musical genres-from Gregorian chant, to Baroque music, as well as the majority of non-Western expressions of music which are by and large not notated. However, even subsequent to the development of music notation, we find composers such as J.S. Bach, Handel, and Mozart highly skilled in the art of improvisation and expecting those who performed their pieces to possess this skill as well. Nonetheless, as concerts in the 18th and 19th centuries gained in notoriety, the growing sophistication of musical notation seems to have played some role toward a more diminished view of improvisation. Although the increase in notation severely limited opportunities for improvising in classical music, the improvisatory elements even in meticulously notated music cannot be totally removed so long as human beings are the performers. Avid music listeners can attest that whether speaking of an individual soloist or an orchestral unit, the personalities, stylistic particularities, and interpretative nuances manifest in the actual performance of a musical work all contribute a degree of creative liberty that falls within the sphere of improvisation broadly construed. For example, how do we explain why we prefer one well-known cellist playing Bach’s solo concertos over another renowned and equally proficient cellist? The notes on the page are exactly the same; yet, we are aware of differences in the ways in which one performer interprets the piece or articulates a musical passage. In addition, it is common for a soloist to engage in what is called “ornamentation.” That is, rather than simply play the melodic line as written, one adds neighboring tones and trills that dress up or “ornament” the melody line.
A second consideration possibly fueling a negative view of improvisation as somehow intellectually substandard is perhaps due to an overly rigid distinction that we in the Western musical tradition tend to make between improvisation and composition. As I have indicated, improvisation is often understood as non-calculated, free-flowing and as lacking in intellectual rigor. Composition, in contrast, is thought to be more or less inflexible, rule-governed and by nature, given its high degree of musical notation, purposely without spontaneity. However, as we shall see, both views are misleading and set up sharp distinctions that do not correspond to what takes place in actual music making and performance.
 Jeremy Begbie, Theology, Music and Time (Cambridge: Cambridge University Press, 2005), p. 180.  I am using the word “classical” in this essay in the colloquial, generic sense. I am not referring to the specific style of music that falls historically between the Baroque and Romantic periods.  A “trill” typically consists in the rapid alteration between two musical notes adjacent on the musical scale; however, there is no fixed or single way of executing a trill. Whether or not one has “correctly” executed a trill is largely dependent upon the context in which it is found, and the musical genre in which one is performing.