copyright © 2003 by Larry J Solomon
I. Definitions and General Properties of Nonharmonic Tones
Definitions: A nonharmonic tone (or nonharmonic note) is a tone or note that is not a part of the chord that is sounding. Step motion is linear motion by semitone or tone, but no more. A leap is anything beyond step motion.
The following is a chart of the traditional types with their definitions:
Begin each definition with "a nonharmonic tone (NHT) that":
A Revised Theory of Nonharmonic Tones
The above are the normative definitions of nonharmonic tones (NHTs) in traditional tonal theory (see Kennan: Counterpoint) and serve to legitimate them. Therefore, all NHTs are simply one of two types: 1. legitimate, or 2. illegitimate.
My purpose here is to eliminate the need to label and identify different types of NHTs, subsuming them all to one category. Since a NHT is defined as a note that is not a member of the chord sounding, the primary problems to address in this respect are the identification of recurrent chord classes (RCs) and the general nature of NHTs. It seems reasonable that once the RCs are identified and located, the NHTs occurring against them may also be easily identified. These NHTs should fall into the categories listed above. RCs are much easier to deal with in traditional tonal music because these chords have already been described and codified into their respective tertian structures. Thereby, we expect to encounter these chords in traditional tonal music: major, minor, diminished, various types of seventh, and other chords. It is therefore unnecessary to identify these RCs in tonal music. Although a procedure for identifying RCs and NHTs in nontonal music is more difficult, a preliminary exposition is presented in the analysis of Scriabin's Prelude, Op 74 No. 3.
Let us draw some generalizations from the definitions of the various types of NHTs: 1. NHTs all involve some step motion or no motion (repeating or held, as in a pedal tone). These two types together will be referred to as minimal motion or MM. MM may step into the NHT, step out, or both. Leaps may be involved in NHT but only in conjunction with MM; i.e., there is no NHT that involves both leaping into and away from the note; 2. All combinations of MM with or without leaping are represented in the above definitions. Therefore, 3. Any note is a legitimate NHT if it has some MM connected with it, but it is illegitimate if it does not, and finally, 4. any note that is surrounded by leaps must be harmonic, i.e., part of the chord.
From these generalizations we can conclude that there is no need to legitimate the various types of NHTs through labeling. A circled note should suffice to identify a NHT, which, if legitimate, must have some MM connected with it. If the note is surrounded by leaps it cannot be a NHT; i.e., it must be harmonic. Other notes involving MM may be harmonic too, but these may be readily identified after determining RCs. Fig 2 from Mozart shows the traditional way of labeling NHTs using abbreviations.
However, with the new generalized NHT definition, only the circles are necessary to legitimate them. The abbreviated labels may be omitted. MM must be involved either in the approach to the NHT or by the exit from it. If this is so, the NHT is legitimate, as they are in this example. The result is a cleaner analytical score:
We can see that all NHTs are circled, and each is either approached or left by MM; therefore, each must fall into one of the defined categories. Notice that any note in the example that is approached and left by leap is harmonic, i.e., part of a chord. These occur primarily in the bass of this example. This leaping motion, along with the verticalizations, or "simultaneities", can be used in a method to determine RCs. (See the analytical essay links at the end of this expose.)
II. Schoenberg's Denial of Nonharmonic Tones
In his book Harmonielehre (1911), or Theory of Harmony, Arnold Schoenberg makes the following statements.
"Chords are formed merely as accidents of voice leading, and they have no structural significance since responsibility for the harmony is borne by the melodic line. There you have it!" 
Since chords are "accidents of voice leading", he concludes that all notes are equally harmonic, i.e., parts of chords. He offers the following example and explains that, (in Fig 4): (a) contains all the "chords" shown in (b), and (c) shows the resulting chords with thirds moving in contrary motion.
To Schoenberg, chords are all notes that sound simultaneously. This leads him to conclude that "There are no non-harmonic tones, for harmony means tones sounding together (Zusammenklang)" [Schoenberg's italics]. "Non-harmonic tones are merely those that the theorists could not fit into their system of harmony."  These proclamations contend against hundreds of years of the history of theory and practice from the time of Zarlino. Harmonielehre contains many contradictions, not the least of which is Schoenberg's description and use of NHTs in other parts of the book. It is nevertheless interesting to speculate on the consequences of the negation of harmonic priorities. Schoenberg's "emancipation of dissonance" was put into practice in his atonal music. The denial of distinctions between harmonic and nonharmonic renders harmonic contrast impotent. It is no longer possible to distinguish between consonance and dissonance, but to Schoenberg that was "progress". The result is music that is harmonically uniform, static, and immobile, or at best, harmonically fortuitous.
On examination of an important early atonal work by Schoenberg, Pierrot Lunaire (1912), one finds a lack of harmonic consistency, which results from his emancipation of dissonance. This work has no RCs and no NHTs, i.e. no harmonic priorities, and thereby no distinction between consonance and dissonance.
Despite Schoenberg's proclamations, in most music some notes do have harmonic priority over others, and we continue to operate on this premise. It is only by recognizing harmonic priority that we can define and comprehend RCs and NHTs.
See analysis of Beethoven's C minor
Variations as a model for the identification and use of RCs and
NHTs in tonal music,
and analysis of Scriabin's Prelude, Op 74 No. 3 as a model for the identification and use of RCs and NHTs in nontonal music.
1. Schoenberg, 312
2. Ibid, 318
Schoenberg, Arnold. Theory of Harmony, (originally Harmonielehre, Third edition,1922 ), translated by Roy E. Carter, Faber & Faber Ltd, 1978, reprinted by University of California Press, 1983.