Textbook series continued toward the present

 In the latest installment of the textbook series, I wrote:

The recently renewed series on the dominant ninth chord in treatises and textbooks began with comment on six volumes from the early 20th century: link to the first post. I am now leading us toward the present again with two items from the 1960s and 1970s. 

Those were Aldwell & Schachter Tonal Harmony and William Christ et al Materials and Structure of Music. Link to that post. I happened to have early editions as physical copies. For the more recent ones listed below, I needed a couple trips to a local university library; as of today, the second of those trips is delayed a week till the intense semester-end schedule of classes and performances is finished. 

The list is chronological and I will follow that sequence, but I will start with Vessela Stoyanova and Jeff Perry, Berklee Contemporary Music Theory (2024) because I regard it as the best exposition of current theory and pedagogy. At some point in the process, I will also write a post covering some online resources.

Leo Kraft, Gradus 2d year and after (1990)

Steven G. Laitz, Graduate Review of Tonal Theory (2010)

Miguel Roig-Francoli, Harmony in Context (2011)

Joseph Straus, Elements of Music. 3d ed. (2012)

Jennifer Snodgrass, Contemporary Musicianship (2015)

Thomas Benjamin, Techniques and Materials of Music from the Common Practice Period through the Twentieth Century.  7th ed. (2015)

Steven G. Laitz, The Complete Musician: an Integrated Approach to Theory, Analysis, and Listening. 4th ed. (2016) 

L. Poundie Burstein and Joseph Straus, Concise Introduction to Tonal Harmony (2016)

Kevin Holm-Hudson, Music Theory Remixed: A Blended Approach for the Practicing Musician (2017)

Stefan Kostka, Dorothy Payne, and Byron Almén, Tonal Harmony with an Introduction to Post-tonal Music. 8th ed. (2018)

Edward Aldwell, Carl Schachter, and Allen Cadwallader, Harmony & Voice Leading. 5th ed. (2019).  See the original post for an update: Link to that post.

Ralph Turek, Theory for Today's Musician. 3rd ed. (2019)

Jane Piper Clendinning, The Musician's Guide to Theory and Analysis. 4th ed. (2021)

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Creston saxophone sonata

 Paul Creston, Sonata for Saxophone and Piano (1945).

In the previous post I discussed two compositions in which the dominant major-ninth chord was entirely or almost entirely absent. Creston's sonata, long one of the standards for saxophone students, is quite different. The majority of the harmony would probably be called non-functional, but Creston--in contrast to Muczynski--makes much more use of familiar sonorities and occasionally clear traditional progressions, as the opening bars below demonstrate. Prominent notes in the saxophone melody are in the treble clef; left-hand chords are reduced from the piano part. It's not annotated but the first five chords are whole-tone fragments.

Unambiguous ninth chords aren't common, but they and other tall chords based on dominant sevenths do play a role, especially in quieter sections and lyrical secondary themes, as below:

The highpoint of the lyrical treatment is in the second theme of the finale, the centerpiece of an ABA form scheme. I've supplied the bass for the entire section. Note the appearance of triads (very rare earlier), M7s and M9s at the beginning, then more and more dominant 7ths and ninths later.

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Actively avoiding V9--Schuman, Muczynski

During a recent trip to a university library, I browsed the reductions under the LOC heading M35. From these I picked two: William Schuman, Chester: Variations for Piano based on William Billings' Hymn and Marching Song of the American Revolution (1957; 1989); Gustav Holst, The Planets (1914), solo piano reduction by Sam Lung, Hywie Davies, and Andrew Skirrow (2015). 

I had also planned a quick survey of well-known 20th century American compositions for woodwinds and began with Robert Muczynski's flute sonata (1965) and Paul Creston's saxophone sonata (1945). 

I'll discuss Chester and the flute sonata here and will have something to say about The Planets and Creston's sonata in subsequent posts. 

I ended my one-paragraph history of the dominant major-ninth chord with this: "Although [the Impressionist] style did persist into the 1930s, already by 1920 the dominant major-ninth sound was considered passé by younger concert composers and was often actively avoided" (link to the post).

Here are two examples showing how long this reticence persisted. They are drawn from repertoire quite different from what I had in mind when I wrote that generalization but they certainly fit "actively avoided."

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William Schuman, Chester: Variations for Piano. I am using a piano solo version created by Schuman for the Eighth Van Cliburn Competition in 1989. After the theme in a diatonic triadic setting, a sudden shift--subito Allegro--introduces sharply delineated chords (accented 8th notes shown here in whole-note form) over which the theme sounds (represented here by its prominent note D6). A single B9 chord (not shown) strikes with the opening of the final phrase.

The second variation is entirely in parallel thirds. The third variation offers the melody at the top of soft staccato triads in each hand. Note that the hexachords thus formed are all M9s or, in one case, M13. These are repeated in various forms and transpositions throughout--they even return twice later in the piece.

At the mid-point of the fourth variation is the second "verifiable" dominant ninth in the piece.

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Robert Muczynski, Sonata for Flute, op. 14 (1965), is an important post-mid-century piece in the flute repertoire. In general with sonatas from perhaps 1920 through this time, you'll see that affects/topics/style/general design are all pretty traditional--and that includes a strong focus on melodic/motivic development--but rhythms and harmonies are more complex. 

Much of the harmony would probably be called non-functional: in a subsequent post, we will see Creston's a little more conservative that way, whereas Muczynski is quite consistent with his particular dissonant vocabulary, and dominant ninth chords have no place in it. See the samples at (a) & (b) below. Nevertheless, the first movement ends, a bit abruptly, with a very clearly defined Fm(add6)--at (c) below.

In the third movement, a few tall chords are built on a V9 base. At (a) the first chord is reduced to a stack of thirds; (b) pulls out the #9 and compares it to a "split third"; at (b2) is the source F(#11); at (c) is the final chord in the example as thirds stacked.

This is the meager tally of dominant ninths.

Blog update November 2025

 For a one-paragraph historical narrative of the dominant ninth chord in European and European-influenced music, see this post: link.

I have published an updated index to this blog and essays about scale degree ^6 and the dominant ninth chord on the Texas ScholarWorks platform. Here is the link. The date for this was November 5, 2024. I have made six posts since then, as part of a series on the dominant ninth in textbooks.

For a list of all the essays I've posted to Texas ScholarWorks, go to the front page of the UT Faculty/Researcher Works section: link. If you click on Filters/Author, my name will come up as one of the most frequent contributors.

On 18 December 2024, I published the fourth and last part in my most recent series: Dominant Ninth Harmonies in Music from 1900 to 1925, Part 4. Here is the link.

Aldwell and Schachter, Christ et al

The recently renewed series on the dominant ninth chord in treatises and textbooks began with comment on six volumes from the early 20th century: link to the first post. I am now leading us toward the present again with two items from the 1960s and 1970s. These pick up from the 2023 series that included Forte, Gauldin, and others from roughly the same period: link to the first post. I am using editions for which I have physical copies; I collate with more recent editions when I can.

Edward Aldwell and Carl Schachter, Harmony and Voice Leading, 2d ed. (1989). The first edition was 1978. The fifth edition is 2019; I see no changes.

Chapter 27 (of 32) [in 5th ed it's 28 of 33] is titled "Sevenths with Added Dissonances," which says most of what we need to know--with the important exception that they begrudgingly acknowledge the dominant ninth chord as an independent sonority: "Except, perhaps, for V9 in root position, ninth chords are best understood as seventh chords that support an additional dissonant tone of figuration" (454; 522 in 5th ed). 

Their origin explanation is clumsy: "Adding ^6 to V7 produces the dominant ninth chord" (441). The example is the second strain of Schubert, D734n5.

It's hard to imagine Schubert improvising for his friends' dancing and thinking "What if I add ^6?" Here, extension by stacked thirds is far more likely, and it's practical: it's easy to do, in this instance it fits the pianist's hand, and it enriches the sound. The phenomenon of third pairs is hardly rare in the early dance repertoire; here are several more from D734 (the title for the set, "Wiener-Damen Ländler" is the publisher's, not Schubert's, btw).

And here are three more; these are from keyboard reductions of an orchestral dance set by Hummel (1808). All clearly show the Ländler's link to the 18th-century pastoral topic.

The authors indulge in a lengthy comparison of the V7 and V9 chords (443), which comes down to this: the seventh influences harmonic direction whereas the ninth just resolves to a note already in the chord. They don't mention that this note is most often in the bass, or that the 9-8 suspension was recognized as legitimate long before 1800, nor do they seem to realize that 4 of their 5 examples of progressions with V9--their Ex. 27-4--involve definite chord changes. All of this amounts to a very wordy, unconvincing defense of conservative views we've seen before. Consistent with that, they ignore other diatonic ninth chords. 

Finally, I should mention that, as in many other texts, both dominant major ninths and dominant minor ninths are given attention. Examples list (these are all brief excerpts): 

for the dominant major ninth, from Schubert, Ländler D734n5, D365n2; Beethoven, Sonata, op. 10n1, I; op. 24n1, II; Chopin, Barcarolle, op. 60; Mazurka, op. 63n2; Schumann, Liederkreis, op. 39 "Mondnacht." 

for the dominant minor ninth, Beethoven, Sonata, op. 31n1, I; Chopin, Barcarolle, op. 60; Mazurka, op. 63n2; Dvorak, Symphony op. 88, IV; Schumann, Symphony op. 38, I; Dichterliebe "Das ist ein Flöten und Geigen." 

for "elevenths" and "thirteenths," Bruckner, Symphony no. 8, III; Chopin, Ballade, op. 38; Ravel, Valses nobles et sentimentales, I; Schumann, Fantasy, op. 17, I; Novellettes, op. 21, no. 8.

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William Christ, Richard DeLone, Vernon Kliewer, Lewis Rowell, and William Thomson, Materials and Structure of Music, 2 vols., 2d ed. (1972).

Ninth chords appear in chapter 4 (of 17) in volume 2. Elevenths and thirteenths are in chapter 13, which is titled "enriched tonal resources"; it has a number of sensible observations about chordal ambiguity to recommend it. Chapter 15, "Harmony in Twentieth-Century Music," opens with a section on atypical 11th and 13th chord constructions.

The curriculum for which Materials and Structure of Music was designed (in Indiana University's School of Music) was a limited version of a popular but not long-lived program called "comprehensive musicianship"; that is, it combined literature (repertoire), harmony, counterpoint, and form analysis. One obvious result is a heavy emphasis on examples from repertoire in a wider range of historical periods of European and European-influenced music.

Perhaps in alignment with that priority, chapter 4 is distinctive in that it opens with explanation of diatonic ninth chords in general, not just the dominant ninth, which first appears on page 3 in a brief excerpt from Tristan und Isolde. Starting a page later, it is given 6 1/2 pages, and non-dominant ninths follow with another 3 pages. The prescriptions and recommendations for notes omitted, resolution, progression contexts, and voicings are all familiar. Despite the claim of repertoire breadth, the seven examples for the dominant ninth are from Bach, Beethoven, Brahms, Schumann, and Wagner. Examples for the non-dominant ninths are also seven; they do include Mahler, Ravel, and Wolf.

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Terminology update

 I have decided to make a change in terminology, which I will use from this point forward. I will also try to update previous posts as quickly as I can.

I have recently been using the term "major dominant ninth chord," but I admit that's caused confusion and so I am reverting to "dominant major-ninth chord," which fits better with the common label "dominant ninth chord." Here that is in Mark DeVoto's chapter on Debussy: "The dominant major ninth sonority D♭–F–A♭–C♭–E♭."  ("The Debussy sound: color, texture, gesture," in The Cambridge Companion to Debussy, 189.)

No matter what labels and terms one uses, there is some kind of awkwardness and one has to rely on whatever convention is being observed. Under (a) below is C7, but note that it is not diatonic in C major--that's G7--but it can be called a "dominant seventh chord" anyway. Likewise with C9 under (b). Thus, "dominant ninth chord" becomes a general category, regardless of how the chord is actually used in any musical context. The even more general "ninth chord" is used by some authors, especially more traditional ones, to apply only to the dominant ninth chord; many others use it for any construction of stacked thirds encompassing the interval of a ninth.

Under (b) & (c) are the traditional "dominant major-ninth chord" and "dominant minor-ninth chord." I agree that these labels are preferable as they put the focus on the quality of the interval of the ninth: C4-D5 or C4-Db5. The diatonic seventh chord, with a major seventh C4-B4, is CM7 (some write Cmaj7) or "C major seventh chord": (d) and reinforced with a natural sign at (d*). The CM9 is under (e), and the corresponding minor chords are under (f) & (g).

NB: Unfortunately, I can't make changes to essay files previously published on the Texas ScholarWorks platform.

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Seeger, Parkhurst

Charles L. Seeger, jr., and Edward G. Stricklen, [Outline of a Course in] Harmonic Structure and Elementary Composition (Berkeley, CA: [self-published], 1916). A copy sent by Seeger to the Harvard College Library is available through the Internet Archive.

Seeger was the spouse of Ruth Crawford Seeger. He is well-known for strong musicological and ethno-musicological interests. He was born in 1886, graduated from Harvard in 1908, and after study in Germany took up a position at the University of California at Berkeley; he was dismissed in 1916 for his public opposition to U.S. entry into World War I. (Information from Wikipedia.) Stricklen was a long-time instructor at the University, beginning as a Reader under Seeger but then becoming chair of the music department after Seeger left. He was skilled as a pianist and composer but never attended college. (Information from University of California In Memoriam [1957]: link.)

The title page makes clear what was obvious anyway, that these are course materials--the subtitle is "An outline of a course in practical musical invention"--and that Stricklen did the editorial work and revision. Seeger's grandiloquent introduction has little to do with the actual content; it ends with modern ideas going "upward and onward in true Hegelian fashion, to higher, more complete and more comprehensive forms, not forsaking the old, but reaffirming transcending and embellishing it as each new fragment of dissonant chaos is conquered and found beautiful to the eyes of a more universal consciousness" [4]. This is interesting with respect to extended  and other complex chords but the real work of the book is mostly traditional diatonic writing in four voices. The theory is dualist but that has little impact on instruction. Chord symbols are inconsistent but generally are figures or scale-degree-theory capital letters with figures added where needed.

There are two parts: diatonic consonances and diatonic dissonances. Each has 15 chapters. Stricklen's preface [5] announces a "Chromatic Harmony" but that was apparently never written. In Part 2, chapters 16-27 are on seventh chords, beginning with the dominant seventh but also giving considerable attention to other diatonic seventh chords. Chapters 28 & 29 are on ninth chords, and chapter 30 presents 11th & 13ths.

The dualist theory relies on overtones and undertones, and so the dominant ninth-chord is derived from the harmonic series (46). "On account of its natural origin, it is the only primary ninth chord in the diatonic key scheme" (47). Seeger and Stricklen require the seventh to be present in all positions, and like most others they reject the fourth inversion. The major-key vii°7 is the dominant ninth without root (a very old idea but consistent with derivation from the harmonic series). The chapter is 4 pages; other ninth chords get 2 pages (50-51), and elevenths and thirteenths another 4 pages (52-55). The other ninths are accepted--see an example below. There are no repertoire examples but "the student is recommended to the study of the works of Grieg in which may be found fine examples of the treatment of these chords" (51).

The dominant eleventh is "extremely artificial" and yet is available for use. Pragmatically, the third is always deleted--see examples below.

In the end, the dualist superstructure gives way to traditional instruction, but it is to be noted that the extended chords are accepted as usable. 

In the volume's final paragraph, they prepare for the projected Volume 2 by observing that a few chords to be found "in modern music. . . . may be also analyzed as incomplete chords of the ninth, eleventh, or thirteenth, [or] passing formations arising from suspension, but the majority are due to methods of chord construction which represent the result of studies much further advanced than those covered by the limitations of diatonic harmony" (55). I don't know if this is the volume written by Stricklen and used in courses under the title [Outline of a Course in] "Chromatic Harmony and Free Counterpoint," Parts I and II, in 30 assignments (Edward Stricklen Collection, Music Library, UC Berkeley, folders 6 & 7); I have no current access to it.

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Howard E. Parkhurst, A Complete System of Harmony (New York: Carl Fischer, 2d ed. 1908)

Parkhurst was born in Ashland, Massachusetts in 1848. I don't have information about his training but I assume it was in Boston. He spent his entire career as an organist in New York; he died in 1916. Parkhurst composed a number of religious pieces. A Complete System is his only book on music theory.

The most conservative of the volumes examined in this new series, it uses figured bass and has no Roman numeral labels. Parkhurst does not recognize the dominant ninth chord (in fact, never mentions it). 

Because of the focus on figured bass, the figure "9" does occur fairly often. Under "suspension of the ninth" an internal resolution appears.

Under "passing chords" a decidedly unconvincing reading makes a V11-V9 neighbor pair subordinate to an unaccented triad.

An equally plausible reading gives even more prominence to V9 in a direct resolution:

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Strube, Maryott, Andersen

Gustave Strube, The Theory and Use of Chords: A Text-Book of Harmony (Boston: Ditson, 1928)

Like Lehmann (see previous post), Strube's story is typically American for the later 19th and early 20th century, but in the opposite direction. He was born in Germany in 1867, studied in the Leipzig Conservatory with Reinicke and Jadassohn, was professor of violin in the Mannheim Conservatory, but then moved to Boston in 1891 to join the Boston Symphony; in 1913 he went to Baltimore to lead the music theory department at the Peabody Conservatory and two years later was also appointed conductor of the newly founded Baltimore Symphony Orchestra. (Information from Baker's Biographical Dictionary of Musicians, 4th edition [1940], p. 1069.)

The dominant ninth chord appears relatively early--chapter 10 of 32--and is safely isolated from elevenths and thirteenths (chapter 31). Strube treats the chord as an independent harmony, but many of his examples have internal resolutions or show the ninth in an appoggiatura construction--see the first example below. The book has no repertoire examples and all of his own are in SATB. Like many others, he rejects the fourth inversion and comments that, if inversions are encountered, the first and third are more likely than the second.

His explanation for an ascending figure is unusual--see the second example above. By "elliptical progression" he means a leap to a chord tone (A4-C5 in this instance) where a step (here inclusion of B4) was expected. In other words, this is a leap, not a rising line.

Strube does say that "any chord may be extended to [the ninth], or farther to

chords of the eleventh and thirteenth. These added tones [are] readily explained as suspensions, elliptical progressions, or vicarious tones" (173). He never explains this last, charming term, but he does assert pragmatically that "the addition of tones, such as the seventh, ninth, eleventh, and thirteenth does not . . . change the function of a chord."

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Harold B. Maryott, The Essentials of Harmony (Chicago: Gamble Hinged Music, 1923).

I have a physical copy of the book obtained from a local non-profit's book sale. Maryott is identified on the title page as "Teacher of harmony . . . and public school music methods in Chicago Musical College." I am not certain which he was known for, as he is described as a "well-known specialist in public school music" in the Music Supervisor's Journal but is only listed as a member of the theory and composition department in the College's faculty listings (1928). 

Ninth chords appear in chapter 8 (of 18), after seventh chords. Text is minimal; the whole chapter with exercises is only 2.5 pages. Here are a couple quotes. He acknowledges a ninth chord other than V9: "The ninth chord is used most frequently on the dominant, sometimes on the super-tonic." In this note the "usually": "After singing the ninth of the chord, the voice usually descends one degree." On preparation: "The tone that is to become the ninth of the chord is very frequently held  over from the same voice in the previous chord." His example is Schumann's "Träumerei" (79). Of the inversions, the third is "used frequently."

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Arthur Olaf Andersen, The First Forty Lessons in Harmony (Boston: C. C. Birchard, 1923).

Andersen was born in Rhode Island in 1880, studied in Boston, Paris, Berlin, and Rome, was at the American Conservatory of Music in Chicago when this book was published, and later became a dean in the University of Arizona. (Information from Wikipedia: link.)

After a compact review of fundamentals and introduction of triads, Andersen begins a very thorough inventory of triads and seventh chords in major and minor. The last lesson (n40 of 40) is on the dominant ninth; it is 5 pages long with exercises.

His explanation for the chord is unusual: "We recognize [the dominant ninth chord] as a . . . combination of the V and II triads. It is, therefore, both dominant and subdominant in character, richly so, and consequently is one of the most beautiful and romantic chords in music. Its dominant quality is most apparent, perhaps, when it progresses to chords of tonic quality; its subdominant richness, when it substitutes for this formation when preceding the chords of V character" (120-121). His positive view continues with omission of notes: "Since the chord contains so many tones of value, it will not lose greatly of its strength if [even the seventh or third] is omitted, especially if the fifth happens to be the melody-tone" (121).

Another point of interest is in the section on irregular progressions, where the V9 "may move to the V, V[superscript I], III', VI, VI, and VI +3. The 9th of the chord should tie over into next formation or move down to the next degree" (124).

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Lehmann

See the previous post for information on this continuation of a historical survey of treatises and textbooks.

Friedrich Johann Lehmann, Harmonic Analysis (Oberlin, OH: A. G. Coming, 1910)

Lehmann's experience was quite common for an American musician in the latter half of the 19th century. He was born in Cleveland in 1866, enrolled in the Oberlin College Conservatory where he studied piano and voice, went to Leipzig for further studies that included theory under a pupil of Jadassohn, and then returned to Oberlin, where he taught for 30 years (1902-1932); he died in 1940. (Information from Baker's Biographical Dictionary of Musicians, 4th edition (1940), p. 647.)

Harmonic Analysis was published locally but achieved some circulation--this copy comes the library of the University of California. The volume's practical focus, inclusion of contemporary repertoire, and simple reduction techniques clearly show its author's connection to the Leipzig Conservatory tradition of Jadassohn and E. F. R. Richter. (A closely related method can be found in a book of the same title by Benjamin Cutter, who taught in the New England Conservatory.)

Basic instruction in harmony is assumed, and it is for that reason that Lehmann introduces the ninth chord very early.

Each lesson in the book is dominated by musical examples; text is adequate but minimal. Lehmann says the only ninth chord to be analyzed as an independent harmony is the dominant ninth; his examples include both the dominant major ninth and the dominant minor ninth. The latter is in examples from Schumann, Beethoven, and Brahms. The major ninth is in Korestchenko, op. 1n1 (internal resolution), Bargiel Nocturne (direct), and Czerny op. 335 (indirect). See these below.

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Textbook survey continued

I began a survey of the dominant ninth chord in treatises and textbooks in 2019 with a post on a figured-bass manual by Simon Sechter (link) and another discussing the repertoire list for a score anthology (link). The work got underway seriously a couple months later, however, with a series of posts in August and September covering Catel through Schoenberg (link to the first post). After a considerable hiatus and following a library visit, I began again in May 2023 and discussed 12 books published in the United States from 1944 to 2008 but focused on the 1960s to 1980s (link to the first post). 

Here I continue with six more books; these were picked up online through the Internet Archive or Google Books.

Howard E. Parkhurst, A Complete System of Harmony (New York: Carl Fischer, 2d ed. 1908)

Friedrich Johann Lehmann, Harmonic Analysis (Oberlin, OH: A. G. Coming, 1910) 

Charles L. Seeger, jr., and Edward G. Stricklen, Harmonic Structure and Elementary Composition (Berkeley, CA: [self-published], 1916)

Arthur Olaf Andersen, The First Forty Lessons in Harmony (Boston: C. C. Birchard, 1923)

Harold B. Maryott, The Essentials of Harmony (Chicago: Gamble Hinged Music, 1923)

Gustave Strube, The Theory and Use of Chords: A Text-Book of Harmony (Boston: Ditson, 1928)

As you can see, these revert to the first half of the 20th century. I am now planning another library visit that will focus on post-1990, and I hope to report on those documents in due time. Admittedly, bringing the work into the present will be more difficult: changes in pedagogical priorities and the now-abundant online resources will pose a challenge, but I hope to draw the thread of dominant-ninth pedagogy forward nevertheless.

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