In article 55 I mentioned the pedal as a way of writing in the modal system, but a French AFanziner who has been following this series form the beginning, and whom I salute, commented in the French forum that the definition I gave for the pedal, as well as the nomenclature I used in the chord examples weren't entirely appropriate. I publicly thank him for his comment and will try to explain better the concept of the pedal in this article, to complement the information in articles 55 and 29.
The main point raised by him was that, according to the definition I gave for the pedal, the pedal note had to be a chord tone of the chords forming part of the pedal in question, even though it can be a non-chord tone of the chords. If you don't remember what chord and non-chord tones are, refer to article 8. This comment obviously demanded some clarifications from my part, so here I go...
The pedal in jazz
This remark is all the more interesting because it points out the main differences that exist between jazz and classical music. I'm well aware of the extremely simplifying aspect of these denominations and the diversity and richness of the realities they represent, so please excuse me in advance.
You could say that jazz incorporates much more easily dissonance as an intrinsic characteristic of the genre, which doesn't require resolution but is justified in and by itself, whereas in classical (often tonal) harmony dissonance is usually associated to the need for resolution. Consequently, the concept of chord and non-chord tones is not as significant in jazz as it is in classical music.
Hence, when you harmonize a jazz song, non-chord tones are often considered an enrichment which give way to new types of chords. Pedal notes are considered chord tones of these new types of chords, rather than non-chord tones of the more "classical" chords. This makes chord inversions a central element in the use of pedal notes for this type of harmonization. This is what I intended to convey in the example of article 55.
The pedal in classical harmony
In classical harmony things look somewhat different. In this case, the pedal note must be a chord tone of the first and last chords, but not necessarily the transition chords, where it can be a non-chord tone as long as it isn't so for more than two consecutive chords.
Finally, the pedal is considered one of the typical expressions of the oblique motion we discussed in article 22.