Showing posts with label textbook. Show all posts
Showing posts with label textbook. Show all posts

Monday, March 2, 2026

New publication on Texas ScholarWorks

Over the past few years, I have made quite a few posts on the history of the dominant major-ninth chord in treatises and textbooks. I have now gathered those posts into a single PDF essay and have provided a small amount of additional material. You can find the PDF here: link.

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I have published an updated index to this blog and to essays about scale degree ^6 and the dominant ninth chord on the Texas ScholarWorks platform. Here is the linkThe date for this was November 5, 2024. I have made several posts since then; please see individual blog entries for those.

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.

Saturday, December 6, 2025

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 postI happened to have early editions as physical copies. 

For the more recent and current ones listed below, I needed a couple trips to a local university library; the second of those was delayed a week till the intense semester-end schedule of classes and performances finished. 

The list is chronological.

Miguel Roig-Francoli, Harmony in Context (2011)

This is a comprehensive--nearly 700 page!!--harmony text. It is in two parts, with 31 chapters. The repertoire breadth and theoretical breadth are greater than other textbooks of its type (Laitz, Kostka & Payne, and so on), and I could see students benefiting from the encyclopedic scope in the eBook version, which, unfortunately, is only available as rental, according to the publisher's website.

Ninth chords are stuck in the usual "extra stuff" chapter near the end of the book. Chapter 29 of the 31 (pp. 667-697) is “Expanding Functional Tonality: Extended Tertian Chords; Linear Chromaticism II.” Ninth chords are on 668-670, 11ths & 13ths on 670-673, non-dominant extended tertian chords on 673-75. Linear chromaticism takes up the rest of the chapter. All three types of extended chords are discussed in the one-page introduction and good, if conservative, lists of rules for use are offered. The familiar Franck sonata opening--which after all is an excellent example--shows up, but the only other one for V9 (as Vb9) is a Wolf song in Cb major. A rewrite in B or even transposition to C would have been desirable. Dominant 11ths and 13ths have good examples from Chopin, Alma Mahler, and Hart & Rodgers.

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

As the title suggests, this is an introductory or "foundations" text. The glossary doesn't mention ninths or dominant ninth chords.

Jennifer Snodgrass, Contemporary Musicianship (2015)

As its initial adjective implies, this takes a radically different approach from the traditional harmony texts such as Laitz, Roig-Francoli, Clendenning, and Kostka. It still covers the ground of elementary harmony (chapters are laid out accordingly), but the priorities in repertoire are flipped. As an example, one page of the examples index, "Elgar" to "Loesser," has 38 musicians listed, of which 8 are pre-1900: the majority either recently have been or are now active. And, as "artist" in the subtitle suggests, attention is by no means stuck on the printed scripts of musical scores. I can applaud the latter, but I am not able to make any comments on how effective this pedagogy might be. My guess is that it works best in a specialized curriculum.

My goal here is simply to assess the presence and significance of the dominant ninth in ch 11 "we will learn about them later." [I will add more to this entry after a library visit scheduled for 12/17/25.

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

I discussed the 2d edition (2008) in these posts: link 1link 2.

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

Traditional organization: 5 parts, 39 chapters total.  Ninth chords are in the usual late-chapter position (32 of 39): “Other chords: Altered, Common-tone Chromatic, and Ninth Chords”. They offer an excuse in the subtitle: "Chords can be altered with chromatic or added dissonant tones." All in all, this ghettoization makes little sense unless one is stuck with a focus on 200-year-old repertoire, but even that doesn't excuse the appearance--after 300 pages--of simple diatonic extensions and some chromatic chords that were already a part of musical practice in the 17th century (+6 and Neapolitans). 

Ninth chords are given a page and a half. Only the major and minor V9s are mentioned, no non-dominant ninths. Two examples are from early Schubert waltzes. They do not include inversions but they do make very concise generalizations about voice-leading and voicing: "The ninth of the V7 is a chordal dissonance that leads down by step (though this resolution is often implied); the chordal ninth should not form a harmonic second or seventh with the root" (305).

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

My blog post with comment on the 4th & 8th editions: link. There are no changes to the section on extended chords in the 8th edition

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

See this post: link.

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

Another traditional harmony textbook, this is in 9 parts, with a total of 34 chapters and about 700 pages. Part 7 of the 9 has four chapters: (21) CHECK Advanced chromatic harmony — mixing modes, altered predominants, other [?], (22) modulation II, and (24) harmonic extensions and chromatic techniques. This last is 15 pages--at the far back corner of the pedagogy again, in other words.

Most of the traditional textbooks now make an effort to include a wider variety of repertoire and styles than "Bach-to-Brahms"--or for the 20th century, only concert repertoires--and this seems to me to be the most determined. (Roig-Francoli is close; the others lag far behind.) Standard chord symbols are even provided for some pieces--though the implementation is very inconsistent. Here are the chapter's subheadings:

Triadic Extensions
The Rise of the Ninth
    The Dominant Ninth Chord
        Common Voicings (3 pp)
        Inverted Ninth Chords  (0.2 pp)
    Secondary Dominant Ninth Chords  (2 pp)
    Other Ninth Chords  (2 pp)
        Eleventh Chords  (2 pp)
        Thirteenth Chords  (2 pp)

The extended chords are explained with an historical narrative of "climbing up the overtone ladder" (428).

Three traditional harmony textbooks I intended to look at but left off the list due to time constraints:  Steven G. Laitz, Graduate Review of Tonal Theory (2010); Thomas Benjamin, Techniques and Materials of Music from the Common Practice Period through the Twentieth Century.  7th ed. (2015); Jane Piper Clendinning, The Musician's Guide to Theory and Analysis. 4th ed. (2021). 

Vessela Stoyanova and Jeff Perry, Berklee Contemporary Music Theory (2024)

This volume was made for a five-week summer workshop and, if it therefore lacks a lot in elaboration, it is admirably concise and its pedagogy is exceptionally clear. Given its student audience, the applicable range of musical styles is large, but the presentation is conservative jazz theory. Thus, the core or ground chords are triads and sevenths (the latter appear in chapter 9 of 28) and ninths, elevenths, and thirteenths are extensions or "tensions" (chapter 10). All the diatonic seventh chords are presented together (48), but the V7 and ø7 are given a paragraph to themselves (49). Cadences are introduced in this chapter; all five types use 7th chords, including what they call a "dominant cadence"--see (a) below. The jazz cadence--at (b)--is the one example for added tensions--see (c) below). (In examples (a) & (b) I have added the bass. I have not included the chord labels from the original.)

 

NB: In the curriculum standard Berklee Book of Jazz Harmony (Joe Mulholland & Tom Hojnacki, 2013), the presentation is compressed so that all diatonic harmonies, including extensions and related chord scales, appear in chapter 1 (of 11). 

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To gain some level of control over online material, I focused on a few open access resources from academic institutions and scholar/teachers. Here are comments on three of them:

Open Music Theory. Subtitle: Version 2 by Mark Gotham; Kyle Gullings; Chelsey Hamm; Bryn Hughes; Brian Jarvis; Megan Lavengood; and John Peterson. Edited by Erin K. Maher. Accessed on 24 November 2025, again on 9 December 2025.

Harmony and Musicianship with Solfège: interactive textbook by Laszlo Cser and Daniel Wanner, edited by Jonathan deRoche. Los Angeles City College (LACC). Link. Accessed on 24 November 2025, again on 9 December 2025.

Music Theory for the 21st-Century Classroom. Accessed on 24 November 2025, again on 9 December 2025.

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Open Music Theory. Subtitle: Version 2 by Mark Gotham; Kyle Gullings; Chelsey Hamm; Bryn Hughes; Brian Jarvis; Megan Lavengood; and John Peterson. Edited by Erin K. Maher. Accessed on 24 November 2025, again on 9 December 2025.

This is presented as "a natively-online open educational resource intended to serve as the primary text and workbook for undergraduate music theory curricula." It looks more like an encyclopedia to me; I suppose the idea is that an instructor would choose the elements they want to create their own textbook. That's certainly possible as the organization is very clear, the index of materials well presented. Along with that comes a level of segregation matching traditional priorities; there are 11 sections plus some appendices: jazz appears in section 6, popular music in section 7, but at least we may note that atonal and 12-tone music, now largely irrelevant to contemporary practice, follow after them.

Extended chords are discussed in section 5, under a heading similar to the one in the large traditional textbooks that lumps together chromatic and extended chords; here is it "altered and extended chords." The chapter on extended chords contains only one altered chord as an example that gets less than a sentence. It might be two if a V(b9) in a major key is included. It's never made much sense to me, and in any case here the examples for the ninth are the usual Schubert waltzes and the inevitable Fauré violin sonata opening.

All this aside, the presentation of the dominant ninth is concise and effective. The term "extensions" is adopted but not exploited.

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Harmony and Musicianship with Solfège: interactive textbook by Laszlo Cser and Daniel Wanner, edited by Jonathan deRoche. Los Angeles City College (LACC).   Link. Accessed on 24 November 2025.

The "blurb" on the main page (table of contents) describes the book's goals and design succinctly: "The textbook adheres to the harmony and musicianship course requirements of college music programs, presenting comprehensive harmony studies and assignments of the Common Practice Period (1600-1900), sight singing and ear training materials, and chapters introducing 20th century music techniques including jazz."

The online format encourages "comprehensive" character: there are nine sections with nearly 100 subheads or chapters ("n"):

Introduction
I. Review: Fundamentals of Music    n = 9
II. Diatonic Harmony    n = 16
III. Diatonic Musicianship    n = 18
IV. Chromatic Harmony   n = 14
V. Chromatic Musicianship    n = 11
VI. Rhythmic Exercises  n = 3
VII. Introduction to 20th Century Music  n = 7
VIII. The Harmonic Structure and Forms of Jazz Standards     n = 12
IX. Appendix     n = 14

Music Theory for the 21st-Century Classroom. Accessed on 24 November 2025, again on 9 December 2025.

Very concise online source that is an expanded glossary, not a course textbook. 35 chapters. The progression of topics is traditional, and chapter 31 "Introduction to Jazz Harmony," where ninths first appear, is well-placed historically. (But note the anomalous intro to strict counterpoint and fugue!)

 


The dominant ninth is not separated out from others.

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One-paragraph historical narrative: link.  ----  Updated index to this blog and essays on Texas ScholarWorks. Here is the link.   ----  List of all my essays on Texas ScholarWorks: link, then click on Filters/Author.

Wednesday, November 19, 2025

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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One-paragraph historical narrative: link.  ----  Updated index to this blog and essays on Texas ScholarWorks. Here is the link.   ----  List of all my essays on Texas ScholarWorks: link, then click on Filters/Author.

Tuesday, November 18, 2025

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 a 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 assume 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. According to Malik Sharif (Speech about music: Charles Seeger's meta-musicology, 2019, p36n35), the first volume was made by Seeger and Stricklen in 1913 as "Outline. . . ," revised by Stricklen as "Harmonic Structure. . ." in 1916, who and it was Stricklen who wrote the "Chromatic Harmony. . ." the same year.

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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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One-paragraph historical narrative: link.  ----  Updated index to this blog and essays on Texas ScholarWorks. Here is the link.   ----  List of all my essays on Texas ScholarWorks: link, then click on Filters/Author.

Monday, November 17, 2025

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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Sunday, November 16, 2025

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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One-paragraph historical narrative: link.  ----  Updated index to this blog and essays on Texas ScholarWorks. Here is the link.   ----  List of all my essays on Texas ScholarWorks: link, then click on Filters/Author.

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 (linkand 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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One-paragraph historical narrative: link.  ----  Updated index to this blog and essays on Texas ScholarWorks. Here is the link.   ----  List of all my essays on Texas ScholarWorks: link, then click on Filters/Author.

Tuesday, June 6, 2023

Textbooks, update, part 6

My last post added to the series on traditional harmony textbooks (link to first post) discussion of a modern harmony text from the 1950s. Vincent Persichetti doesn't have anything negative to say specifically about the dominant major-ninth chord, but as I wrote, he "greatly favors other seventh and ninth chord types over the dominant major-ninth, which does appear in a reference example of the same kind of sequential progression that we saw in Mitchell and Ottman, but only once in the chapter's nine composed examples."

Just a few years earlier, Paul Hindemith indirectly offered an explanation: the dominant major-ninth harmony (like its close cousin the half-diminished seventh) was too strongly associated with 19th century music. Hindemith was a student in the years before WWI, and matured as a musician and composer in the years immediately following, when the aesthetics and practices of the earlier era, especially anything Wagnerian, were soundly rejected. Thus there is a definite sarcasm in his proposing composition exercises for the harmonium, that "primitive wheezebox": "Is not treasuring such a pitiful instrument like preaching the virtue of poverty and the moral value of asceticism to one living in luxury? The counter-question might be: Why not, if that will further the development of the individual and the general welfare?" (Traditional Harmony, vol. 2, 31, 32) In other words, the argument is a bit like that for writing species counterpoint. . . .

In his conclusion, it's obvious that Hindemith is referring to the dominant major-ninth, the ø7, and various altered dominants: 

In respect to harmony and tonality, our pieces will inevitably sound like so many hundreds of the sentimental genre pieces of the post-Tristan style. . . . What was originally felt to be so 'modern' and to promise so much, turns out to be a technical device that is useful only for the creation of all too limited effects. Nevertheless, it is advisable once, for practice, to wallow thoroughly in this style of writing if only to learn through exaggeration what in the end one wants to avoid.

Like Persichetti's harmony, Leon Dallin's Techniques of Twentieth Century Composition was a very influential text in the 1960s and 1970s (edition I looked at: Techniques of Twentieth Century Composition: A Guide to the Material of Modern Music, 3rd ed., 1974). Dallin makes the same point as Hindemith but very explicitly and with prejudice against "popular" music styles:
Major and minor ninths can be added to all of the seventh chord structures, both diatonic and altered. The dominant ninth was the first to be incorporated into the harmonic vocabulary, but its value to serious composers is impaired by popular connotations and triteness. The sounds of other less hackneyed ninth chord forms are still capable of pungent expressiveness, even to jaded twentieth-century ears, when used with imagination.

Ouch. Still, for the era, and for professional concert and college-based composers, Dallin was undoubtedly right. In a recent essay, I wrote that musicians working in the popular styles he denigrates were equally reticent: the statistics show that the dominant major-ninth harmony appears surprisingly infrequently in songs from the 1920s through the 1980s (at least in the songs' published form; performances and arrangements may well differ). Link to Dominant Ninth Harmonies in Music from 1900 to 1925, Part 4.

Tuesday, March 8, 2022

Harmony at the Ninth: The repertoire problem

 In a previous post, I outlined a harmony pedagogy that would place the ninth chord near the beginning of the curriculum, not—as is typically the case (if it's taught at all)—somewhere near the end. I also noted that my plan got into trouble at the point of choosing repertoire. I'll discuss the three main reasons here: (1) repertoire bias in the traditional theory core curriculum; (2) conflict between 18th/19th century and 20th/21st century theoretical models; (3) difficulty in finding entirely diatonic examples suitable for first-year theory classroom use.

To begin, I have assembled and posted to my Google Drive a list of all the musical examples for the five essays on the dominant ninth chord that I have published on the Texas ScholarWorks platform to date: 

The essays are named at the beginning of the file, and abstracts and links are provided.

(1) repertoire bias in the traditional theory core curriculum

The historical narrative for classical music that prevailed through much of the 20th century was progressive, that is, it began from one point (usually medieval chant) and led by more or less regular steps forward into contemporary music. So, we have the first inklings of counterpoint around 1000 AD, eventually a perfected polyphony in the 16th century, an organized major/minor tonal system thanks to continuo practice and pedagogy in the later 17th and early 18th centuries, and a gradual expansion or break-down of that system through more complex harmonic relations and increased chromaticism in the 19th century, till we reached a fully chromatic model epitomized by twelve-tone and serial music. Despite this scheme, the heart of the story remained with the High Classical period (sometimes called the First Viennese School) with Haydn, Mozart, and Beethoven.

This is the narrative I learned as a young student. We had only just begun to acknowledge some of its problems even by the time I started college in 1968. For my purposes here, though, and beyond noting that these repertoire biases have barely changed in mainstream college introductory theory textbooks, the one point that is immediately relevant can be easily understood by a quick comparison of the repertoire list linked above with two textbook-based lists. The smaller of the two is derived from Kostka & Payne, 3rd ed. (even earlier than my 4th ed. copy!): David Temperley corpus study: see the bottom of that web page. The larger is the table of contents for the score anthology by Benjamin, Horvit, Koozin, and Nelson, Music for Analysis, 8th edition (2018).

Temperley extracts the 46 longest examples from the Kostka & Payne workbook. Of these, 29 are by Haydn, Mozart, Beethoven, and Schubert. For these 29, 11 are from piano sonatas, 3 from other pieces for piano, 9 from chamber music, 2 from concertos, 3 songs, and 1 opera.

Benjamin, Horvit, Koozin, and Nelson has 477 examples ranging from the 17th century to the present. Of these, 378 are prior to 1900, with 175 by Haydn, Mozart, Beethoven, and Schubert. For the 378, 49 are from piano sonatas, 12 from other pieces for piano, 32 from chamber music, 2 from concertos, 15 songs and vocal ensemble music, and 5 operas. In addition, 24 are dances in keyboard format, and 37 are from orchestral ensemble music (symphonies and overtures).

For reference, in Benjamin, Horvit, Koozin, and Nelson there are two examples from Johann Strauss, jr., while in Temperley's extracts from Kostka & Payne there are none—which points up the problem: there is very little intersection between their lists and mine, in which Johann Strauss, jr. and sr. dominate. Some important caveats: Apart from the Strausses, my study of the major dominant ninth chord is skewed toward the decades surrounding 1900. As I have noted in essays, I have generally looked at shorter compositions; for longer works, I use keyboard reductions rather than full scores but I haven't focused on large instrumental ensemble music and have done even less with chamber music. I have studied dances—especially polkas and waltzes—throughout the 19th century, not just Schubert dances. The historical circumstance that ascending cadence gestures, upper-register cadences, and clear treatment of the major dominant ninth all seem to have arisen in music for dance led me to the larger repertoires that incorporated them, beginning with opéra comique in the 1830s, then blossoming in operetta in the 1850s and later. In general, composers—including Schubert himself—would be more conservative when writing in the larger instrumental forms than in the popular forms of dance music and music for the stage. In another post I will report on my look at the Allegretto grazioso quasi Andantino in Brahms's Symphony no. 2 and at his Waltzes, op. 39. Even in the midst of the Schubert craze of the 1860s—to which he also contributed—Brahms was a genius at suggesting but avoiding the two characteristic chords of scale degree ^6: the dominant ninth and the add6.

(2) conflict between 18th/19th century and 20th century theoretical models

Textbooks still lump the “extended chords” together, in a model of progressive stacked thirds, even if, as Kostka & Payne remark in their 4th ed.: "Just as superimposed 3rds produce triads and seventh chords, continuation of that process yields ninth, eleventh, and thirteenth chords (which is not to say that this is the manner in which these sonorities evolved historically)." (!!) Jazz theory, on the other hand, doesn't bother with that, because the harmonic vocabulary is based on the dominant seventh with a variety of sounds, "tensions," and alterations built on it. In Mark Levine's Jazz Theory Book (1995), for example, "extensions" (9th, 11th, 13th) are listed in the glossary, but the ninth chord is never explicitly introduced in the text. Instead, it simply appears in the first example for the II-V-I progression:


This version of the opening of "Stella by Starlight" is a concise catalogue of the three main 9th chord types, but note that none of Levine's chord labels (above the score; mine are below in blue) indicates a 9.

Here are some additional examples drawn from different places in The Jazz Theory Book. My labels are below the score. The 9 is included in the fourth chord only because it is altered (G-nat = Fx).


(* I am grateful to UT-Austin doctoral alum and friend Joel Love for telling me about Levine's book. Link: His web page.)

(3) difficulty in finding entirely diatonic examples suitable for first-year theory classroom use

My first examples would, of course, come from Schubert waltzes, but it turned out to be difficult to find simple examples of V9 without also including chromatic chords. Here is the second strain of Valses nobles, D. 969, n11 (1828), with its "textbook perfect" V9 with a direct resolution. Bars 5-6 would require some discussion, however.


In their section on the dominant ninth, Benjamin, Horvit, Koozin, and Nelson include Strauss's Künstlerleben, one of the best known of his mid-period waltzes. I don't know what they say about it, as I don't have a copy of the anthology, but I can say that I find the choice of no. 3 particularly good because the ninth appears several times in different roles, and the only chromatic consideration is a relatively simple cadence to V at the halfway point. At (a) and (c) are internal resolutions (9 resolves within V). At (b) and (d) are "almost direct" resolutions (9 is held over the first part of I); the example below the score shows what a direct resolution would have been in (b). At (e) is the upward resolution of 9 that facilitates an ascending cadence. And at (f1) & (f2) is a very common device that flips the functional status of scale degrees ^7 & ^6: at (f1) ^7 is a simple chord tone and ^6 forms the ninth, but at (f2) ^7 is an appoggiatura and ^6 is a simple chord tone.


Simplified, correct, but not as expressive version of bars 6-8:


The question of repertoire choices appropriate for different levels can be explored through the repertoire list mentioned and linked to at the top of this post. I can add here that I have studied but have not yet reported on stage works from opéras comiques of the 1830s (mainly Adam, Auber) to operetta (Offenbach, Lecocq, Strauss), Savoy opera (Sullivan), and American operetta (Herbert) and musical (Kern). And of course there is something still to be said about that "genius of avoidance," Brahms.