Recently I was able to visit a university music library, where I looked at the presentation of ninth chords in the following textbooks. They are not current editions (those are on reserve for students in pedagogy courses), but I have good reason to suspect that these are representative, in other words that little has changed in the pertinent chapters.
Allen Forte, Tonal Harmony in Concept and Practice, 2d ed.
Robert Gauldin, Harmonic Practice in Tonal Music
Paul Harder/Greg Steinke, Harmonic Materials in Tonal Music, Pt. II, 6th ed.
Paul Hindemith, Traditional Harmony, vol. 1
Steven Laitz, The Complete Musician, 2d ed.
William Mitchell, Elementary Harmony, 3rd ed.
Robert Ottman, Advanced Harmony: Theory and Practice, 4th ed.
Walter Piston/Revised and Expanded by Mark Devoto, Harmony, 5th ed.
Leonard Ratner, Harmony: Structure and StyleRoger Sessions, Harmonic Practice
In earlier posts, I wrote about historical textbooks, mostly 19th century, beginning in January 2019: link. The only post-1950 textbook I looked at was the 8th edition of a music score anthology by Benjamin, Horwitz, Koozin, and Nelson: link.
Of the ten books discussed here, five put the ninth chord in the usual, relatively brief chapter late in the volume: Gauldin, ch. 31; Harder/Steinke, ch. 11 (final); Mitchell, ch. 16 out of 18; Ottman, ch. 11 in book 2 of the sequence; Piston/Devoto, ch. 24 out of 31. Forte doesn't mention it at all, not surprising given his Schenkerian loyalties. Laitz doesn't, either. Hindemith, on the other hand, puts the ninth and the thirteenth in chapter 6 (out of 16 total), immediately after inversions of the dominant seventh. Ratner has the same placement, in ch. 12 out of 27, as does Sessions: 9th chords are in §5 of ch. 7 "Accessory Tones"--ch. 6 introduced seventh chords.
Here are repertoire lists for the eight volumes (excluding Forte and Laitz). As a reminder, only items with the major dominant ninth are included.
Gauldin
Kuhlau, Sonatina, op. 20, no. 1, II
Franck, Violin Sonata, I
Wagner, Götterdämmerung, Prologue to Act I
Wagner, Götterdämmerung, Act I
Harder/Steinke
Fauré, "Après un Rêve"
Debussy, Pelléas et Mélisande, Act II, scene 1
Hindemith: only his newly written exercises
Mitchell
Schubert, waltz, op. 50, no. 18
Schubert, waltz, op. 9, no. 34
Beethoven, Quartet, op. 18, no. 6, IV
Schumann, op. 99, no. 11, trio
Schubert, waltz, op. 9, no. 30
Ottman
Verdi, Il Trovatore, Act IV, no. 19
Grieg, In der Heimat
Tchaikovsky, The Nutcracker, Overture
Chopin, Nocturne, op. 72, no. 1
Wagner, Götterdämmerung, Act III
Dvorak, Quartet, op. 105, III
Piston/Devoto
J. S. Bach, WTC II, Fugue in D major
Schubert, Mass no. 6 in Eb, Kyrie
Wagner, Rheingold, scene 2
Haydn, [Piano] Sonata no. 7, II
Chopin, Nocturne, op. 72, no. 1
Mussorgsky, Songs and Dances of Death, no. 3
Franck, Symphony, I
Verdi, Requiem, Requiem
Schumann, Symphony, no. 2, III
Franck, Piano Quintet, I
Ratner
Mozart, Sonata, K. 576, I
Schubert, Fantasia, op. 78
Chopin, Preludes, op. 28, no. 21
Sessions: only reference examples, no repertoire
In the next post, I will begin description and commentary for each book in turn.