Simon Sechter

Simon Sechter, organist, composer, teacher, and music theorist in Vienna (link), is best known now for his harmony treatise, Die Grundsätze der musikalischen Komposition (3 vols., 1853: link to Internet Archive copy). Earlier, he published a Praktische Generalbass-Schule, Op.49 (1830; link to copy on IMSLP).

The treatise on figured bass is very traditional. Its focus is on the inventory of figures, how to recognize and organize them in the mind, and to learn to play the associated chords. As such, the concern with ninths is with that figure, not any specific inventory of harmonies. For instance, his first example of the "Nonaccord" is for a 9-8 suspension of a simple tonic triad--circled below.

The next is for 9-8 above seventh chords of different qualities. The one circled is a minor minor seventh chord, ii7 in C major. The dominant with major ninth appears in bars 2 and 5 (not circled).

And here is a double suspension, 9-8 with 4-3, the underlying chord being a D minor triad. Notice that Sechter throws in a dominant ninth in the cadence, further evidence that he is concerned with the figure 9, not specific chord groups.

The final example shifts away from suspensions to passing tones/chords.

For the most part, the pedagogy of theory and composition throughout the nineteenth century recognized ninth chords as vertical entities but assigned them to suspension or passing chord figures. Suspensions, to be sure, were an important part of the evolution of the independent dominant ninth harmony, but so were the varieties of incomplete neighbors (especially—but not exclusively—appoggiaturas).