Textbooks, update, part 5 (Persichetti)

 I have added Vincent Persichetti's classic Twentieth Century Harmony: Creative Aspects and Practice to this series of posts, first, because it is in a traditional textbook format and uses a traditional sequence, despite the very different material being discussed, and, second, because it is a good representative (still cited today) of mid-20th century attitudes toward harmony and harmony pedagogy among then-practicing North American and European composers. 

Like other texts that tackled complex harmony beginning already in the early 20th century, Twentieth Century Harmony also stands in the awkward position of prescribing harmonic solutions at a time when harmonic function was quickly losing its hegemonic force. Persichetti's claim isn't small: The book is "a detailed study of the essential harmonic technique of the twentieth century,  presented according to the practice of contemporary composers. This text aims to define this harmonic activity and make it available to the student and young composer."

The magnitude of the problem--and of Persichetti's optimism--is apparent in the opening of chapter 1:

Any tone can succeed any other tone, any tone can sound simultaneously with any other tone or tones, and any group of tones can be followed by any other group of tones, just as any degree of tension or nuance can occur in any medium under any kind of stress or duration. Successful projection will depend upon the contextual and formal conditions that prevail, and upon the skill and the soul of the composer.

It's hard to know what to expect of ninth chords, given those assertions. But under the circumstances, the general statement seems straightforward enough, though it certainly requires the information and examples that follow to be saved from vagueness and to offer any kind of practical instruction:

The seventh and ninth members of chords are traditionally dissonant tones but they have been freed of some of their former restrictions. These chords have become stable entities in themselves with their dissonant tones not necessarily prepared or resolved. Seventh and ninth chords, like triads, may progress within or outside any scale formation, original or traditional. Under certain formal conditions the seventh and ninth are treated as dissonant tones needing resolution; but as independent seventh and ninth chords they have the facility of triads.

A problem common to related literature is the definition of chords. Ninth chords have five members and can be considered complex. As we saw with Sessions, inversions can introduce considerable ambiguity about chordal identity. Persichetti says fourth inversions are used freely, and one example offers an opening chord of A2-G3-F4-B4 as G9. I have trouble hearing this as anything other than Am9, despite the "extraneous" F4. (Hindemith, btw, would agree with Persichetti, as the strongest interval by his calculation is the third G-B.) 

Much the same with non-harmonic notes. Here is the beginning of one example with my annotations:

It is almost impossible to avoid the "reduction to simpler sonorities" priority in cases like these, even if as here those are seventh chords rather than triads.

Finally, after all this, there isn't much to say that connects to the topic of this blog, because--as the example above hints--Persichetti greatly favors other seventh and ninth chord types over the major dominant 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.

Textbooks, update, part 4

Ratner

Chapter 11 of Harmony: Structure and Style is on dominant sevenths and the tonic 6/4. Chapter 12 is titled "VII7 and V9--The Major Sixth in Dominant Harmony"; it ends with a helpful summary. Here that is, with further quotes and my comments:

1. The major sixth in dominant harmony appears in two chords, the V9 and the VII7.  [Note that Ratner uses the non-distinctive capital letters of scale-step theory. Since he is writing only about the major key at this point in the book, we know that VII7 is the same as viiø7.]

2. The sixth degree adds a strong characteristic element of color to dominant harmony.  [He is referring mainly to later 18th century music, where the supporting harmony is viiø7: his first two examples are from Mozart and Beethoven. But a brief excerpt from Brahms, Symphony no. 1, II, has a V9 in first inversion--see below--though in typical Brahmsian fashion it sounds as much like an accented neighbor chord as an independent ninth chord.]

 

3. Usually, the sixth degree appears in the uppermost voice, since it possesses marked melodic value.  [In the main text he says ^6 is best in the top voice "where its melodic tendency will be realized in a salient manner."]

4. The sixth will tend to resolve downward to the fifth degree, before the dominant harmony moves to tonic or at the change of harmony. [This "tending to resolve downward" comes from the idea of ^6 as a neighbor to ^5. His options cover my internal and direct resolution categories, respectively.]

5. The sixth may leap downward to another tone of the dominant harmony in a chordal melodic figure, relieving the sixth of the need to be resolved directly.  [His point about this in main text, though, is that ^6 makes a very effective "melodic apex," after which comes a fall to the cadence or other resolution.]

6. In a 6-7-8 pattern the sixth moves upward to the leading tone, and the V9 is first struck without a leading tone.  ["Occasionally, when one voice moves 6-7-8, the harmony momentarily becomes V9 with 6 supplanting the leading tone at first. The musical effect of this can be quite poised and elegant, as shown below."]

7. V° and VII' are usually used within a phrase, except in cases described in summary points 5 and 6.

Sessions

Of all the books surveyed in this series of posts, Session's Harmonic Practice shows the most obvious evidence of an experienced and practically- minded composer. "Frozen" accessory tones are of two types: "Ninth, Eleventh, and Thirteenth Chords" and "Substitute Functions." He offers no method of derivation, just says the ninth chord is "generally classified as a basic chord type," later adds "so-called" to first mention of elevenths and thirteenths, and ends the section with the statement that "in the overwhelming majority of cases, these chords are used on the dominant degree, but use on other degrees is also possible."

The ninth can be resolved internally because the root is already present (he shows both V9 and I9) and thus the ninth can be left by leap internally, but the same cannot be said of the seventh.

As to inversions, they "are extremely varied in harmonic effect, even in the case of different positions of the same inversion, which . . . if they are played in alternation seem to denote a genuine change in harmony." Here is the second inversion of C: V9.

Sessions closes with "For these reasons, it seems better to consider the ninth as an accessory note which habitual usage has 'frozen' onto the chord." Quite sensible from an historical perspective, though he omits to say the same is true of the dominant seventh chord and the add6.

Textbooks, update, part 3

Harder/Steinke

In Harmonic Materials in Tonal Music, Pt. II, 6th ed., the three extended chords are grouped together, and the model of superimposed thirds is assumed. The historical summary I might have written myself: "Used sparingly by earlier composers, ninth, eleventh, and thirteenth chords occur more frequently toward the end of the 19th century. They are especially characteristic of Impressionistic music." The chords may be built on any scale degree, "but the majority are dominant chords."

The chords are definitely regarded as harmonies, but the authors acknowledge that "since these tones often appear as non-harmonic devices, it is sometimes difficult to decide whether they should be interpreted as members of the harmony or as incidental melodic occurrences." Given this quite reasonable statement it seems odd that they do not offer more repertoire examples--there is none with a direct resolution.

Hindemith

The laconic style of Traditional Harmony, vol. 1, was quite deliberate: the volume is really a set of exercises with notes for reference, not a narrative or expository presentation. Hindemith ignores third-stacking except for the dominant ninth chord. He does not mention 11ths, and the 13th originates from substitution; he says "dominant seventh chord with sixth"--which replaces the fifth--but figures the 6 as 13. He allows first and third inversions of the ninth chord, not the second or fourth (implicitly--he just doesn't mention them). Finally, he says that "in progressions, the two derivations [9th and 13th] and their inversions are treated like V7 and its corresponding inversions." The exercises maximize spelling opportunities and as such don't really reflect characteristic practices in existing compositional genres.

Ottman

In Advanced Harmony: Theory and Practice, 4th ed., ch. 10 is divided into three topical units: (1) "chords of the ninth," (2) "eleventh and thirteenth chords," and (3) exercises in "writing ninth chords" plus "the ninth chord in the harmonic sequence."

After an introduction, the sub-sections in the first unit are (1) "ninth chords in which the ninth resolves before a change of root," (2) "ninth chords in which the ninth resolves simultaneously with the chord change," (3) "ninth chords in which the ninth and seventh are arpeggiated," (4) "irregular resolution of the ninth," (5) "ninth chords in sequence." Third stacking is used, and non-dominant ninth chords are accepted but are only "occasionally seen."

Of the ten textbooks discussed in this series, Advanced Harmony has the best arrangement of well-defined sections coordinated with multiple repertoire examples.

Sub-sections 1 and 2 align with my "internal resolution" and "direct resolution" of the major dominant ninth chord. After noting that most internal resolutions can be regarded as melodic figures over V7, Ottman does observe that "When the ninth is held or repeated, a stronger feeling for an independent ninth chord may result. . . . As emphasis on the ninth increases, analysis as a ninth chord becomes more likely, but in any case, the decision is a subjective one at best." This aligns with my emphasis on a melodic-to-harmonic continuum in my "seven types" (link).

Sub-section 3: Here is the reference example with my annotations.

The one example in sub-section 4 is an upward resolution of the ninth, which should be very familiar to readers of this blog and my essays published on Texas ScholarWorks (see the index here: link). Sub-section 5 consists of a reference example showing alternating seventh and ninth chords in a sequential passage--the same progression from Mitchell's Elementary Harmony that I reproduced in the previous post.

Piston/Devoto

In Harmony, 5th ed., chs. 22 & 23 are on seventh chords other than the dominant seventh. Ch. 22 is short, more of a footnote to the preceding: it's on the "incomplete major ninth"--that is, to say the half-diminished seventh or viiø7. The idea that this chord may be added to below--"subtended"--goes back to Rameau and appears in many 19th century texts and treatises. 

Ch. 24, then, takes up the ninth chord proper, which of course is called the "complete dominant ninth."

The author(s) isolate "three important aspects" of the chord:

1. "The ninth may appear as a non-harmonic tone, resolving downward into the fifth degree [my internal resolution], or sometimes, if it is the major ninth, up to the seventh degree [my ascending figure], before the chord itself resolves. It is often an appoggiatura, in which case the harmonic color is very pronounced." 

2. "The ninth may be used in a true harmonic sense as a chord tone but it may be absent from the chord at the moment of change. This is an important aspect of harmonic treatment of the ninth in common practice. It actually consists of the resolution by arpeggiation of a dissonant factor, a principle applied to no other dissonant chord (it is also called dissolution by some theorists). . . ." Ottman's 9-to-7 arpeggiation--see the musical example earlier in this post--is one instance of this.

3. "Finally, the ninth may act as a normal dissonant chord tone resolving to a tone of the following chord."  This is my external or direct resolution.

The major dominant ninth has further limitations; it represents a harmonic color characteristic of the end of the common-practice period rather than the eighteenth century. Employed as in the third of the aspects just described, it is rarely encountered until the latter part of the nineteenth century. We will meet the dominant major ninth again in Part Two of this book in connection with impressionistic harmony, in which it is of great importance both as an independent, quasi-consonant sonority and as an adjunct to the triad in modal harmony.

Here is their particularly clear presentation of inversions, with my annotations. The fourth inversion (with ninth in the bass) is rejected.

Textbooks, update, part 2

Forte (none); Laitz (none)

Of the ten textbooks I browsed during a recent visit to a college library, two don't mention ninth chords. These are Allen Forte, Tonal Harmony in Concept and Practice, 2d ed.; Steven Laitz, The Complete Musician, 2d ed. In Forte's case, the reason is clear: his pedagogy is based closely on Schenkerian theory, a conservative (in 2023, one might better say reactionary) model of harmony in which everything is reducible to triads and their linear elaborations. I don't know Laitz's reason--I am relying only on the table of contents and the index, where extended chords including ninths don't appear. It's possible he may say something in the preface or elsewhere.

Gauldin

Ch. 31 of Harmonic Practice in Tonal Music is 11 pages, of which 4 are given to the dominant ninth and just a half page to non-dominant ninths. He does give some space at the end of the chapter to added 6ths and 9ths, which is a positive point.

Gauldin uses a simple "extended tertian harmonies" model. The 9th in the dominant chord, whether major or minor, "became a bona fide member of the V chord" in the later 18th century, which is fair if we mean V(b9) but overstates the case if we mean V9 as an independent chord. The same is true of the claim that "by the middle of the 19th century, composers were using prolonged dominant ninths quite frequently" -- he then quotes the inevitable Franck Violin Sonata (1886) as well as the Prologue to Act I of Götterdämmerung (prod. 1876). European and European-influenced musicians working in all styles were indeed using dominant ninths by this time, but "quite frequently" misrepresents the statistics if by "frequently" one means "commonly" or "often." And "prolonged dominant ninths quite frequently. . ." is simply not the case: "expressive" and "prominent," perhaps, but "not often" if we take the repertoire as a whole before the 1880s. Finally, we note that he doesn't mention inversions.

Early on, Gauldin asserts that "we will regard [the] added thirds as dissonances and treat them as suspension or neighboring figures, much like the chordal 7th in seventh chords." Later examples do have chord labels for V9 but show voice leading figures above. I would read these as direct resolutions: V9 goes to I. Saying that these independent V9s "have their [historical] source in suspension or neighboring figures" would be adequate to clarify the situation.

Mitchell

In Elementary Harmony, 3rd ed., ch. 15 is 30 pages long, the topic being seventh chords, after which 10 pages are given to ninth chords in ch. 16. Eleventh and thirteenth chords are not mentioned. The final chapters are on applied/secondary dominants (17) and modulation (18).

Mitchell distinguishes between "simple" and "manipulated," which correspond to my "internal resolution" and "direct resolution." (For definition and examples, see my early post on the 7 types of the major dominant ninth: link.) Despite the seemingly derogatory "manipulated," Mitchell regards the V9 in direct resolution as a distinct harmonic entity. Later he strengthens the point by calling internal resolutions "pseudo ninth chords." He does, however, return to a "descending natural succession" to describe the origin of the major dominant ninth chord.

He rejects all non-dominant ninth chords out of hand: "they remain details of horizontal motion"--a bit extreme perhaps but still a reasonable description of most music before the 1890s. He says of inversions, "chances are that [they are] the result of simple figuration," but in a later paragraph he rejects them as "fiction" and "alleged." 

Mitchell was also under Schenkerian influence, and we can be thankful that he did recognize the independent ninth chord, even if it still suffers the stigma of being "manipulated."

Ninth chords in harmony textbooks: an update

 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 Style

Roger 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.