The German theorist and composer Johann Philipp Kirnberger (1721–1783) was the first musician to make a distinction between two specific types of dissonances, between what he has called essential dissonances (wesentliche Dißonanzen) and non-essential —or incidental— dissonances (zufällige Dißonanzen).
According to him, an essential dissonance comes in only one form: a chordal seventh that “does not replace the sixth or the octave, but has its own place” (Kirnberger (1771), p. 31; English translation in Beach-Thym (1982), p. 45; see also Demeyere (2013), p. 59–62 and p. 66).
In other words, the seventh is essential to the identity of the chord, its presence/inclusion determining the type of chord. Indeed, if you omit the seventh from the chord, you get a different chord, namely a triad.
As for a non-essential dissonance, it delays a consonance, temporarily replacing it with a non-chord note.
Joel Lester formulates the difference between these two types of dissonances in the following way:
“those in which the suspended interval can resolve over the same chord root and those that require a new chord to resolve. If a suspension can resolve into a chord with no other voice motion, it is an incidental [non-essential] dissonance; if other voices must move and a new harmony appears along with the resolution, the suspended tone is an essential dissonance.” (Lester (1996), p. 242)
This implies that an essential dissonance in the form of a prepared seventh, although very similar to a suspension, is strictly speaking not one.
A supporter of Rameau’s theory of chord inversion, unlike his teacher Bach, Kirnberger sees the 6/5, 6/4/3 and 6/4/2 chords as inversions of the seventh chord, defining the dissonance in all as essential.
Select Bibliography
Demeyere, Ewald. Johann Sebastian Bach’s Art of Fugue — Performance Practice Based on German Eighteenth-Century Theory (Leuven: Leuven University Press, 2013).
Kirnberger, Johann Philipp. Die Kunst des reinen Satzes in der Musik (vol. 1) (Berlin and Königsberg: 1771). English translation in: The Art of Strict Musical Composition — Johann Philipp Kirnberger, ed. David Beach and Jurgen Thym (New Haven and London: Yale University Press, 1982).
Lester, Joel. Compositional Theory in the Eighteenth Century (Cambridge, Massachusetts: Harvard University Press, 1996).