Buelow, G. Thoroughbass Accompaniment according to … Heinichen, 17–18, 27–41, 75–87, 219–35, 381–84, 390–92, 398–401, 418–19. “Gradual supplanting of Baroque period actually began before J.S. Bach’s death, yet most of our current knowledge of thoroughbass realization comes from treatises written after 1750.” TP: When Buelow made this statement, none of the following treatises had been edited: • Buelow’s book (1986) • Niedt (1989) All of these treatises were published in the early 18thc. (before 1720), yet none of these had been • St. Lambert (1991) translated at the time of Buelow’s publication. • Campion (1992)
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Composers of the Baroque period constructed and organized chords on the actual bass note, NOT the root. Also, intervals related to bass notes determined the harmonic progression, whereas dissonances followed the rules of counterpoint. (18) Heinichen speaks of dissonance in terms of counterpoint in 1728. (18)
TP: As we read Heinichen, keep in mind that Rameau’s Traité was published 6 years earlier in 1722.
He recognized the M6 as an inverted triad, but he speaks of inverted intervals far more often than inverted chords. Thus, it is incorrect to assume that an inverted chord implies the priority of its root position or it existence in actual practice.
The Figures (27) • Because ideas of writers on thoroughbass differ by chronology, nationality, education, and musical background, Heinichen attempts to summarize the varieties of figures used in different countries. • He divides figures into three basic systems for writing chromatic alteration of intervals • As Lester mentions (p.58), Heinichen arranges dissonant chords in numerical order in a similar manner to that of St. Lambert. Instead of organizing by ONE, TWO, THREE figures, Heinichen organizes by figures containing the number 2, 3, 4, and so on. • Later theorists categorized dissonances according to newer harmonic theories rather than by numbers. • Buelow mentions the German method of attaching strokes or accidentals to figures (4#) • He also mentions the disagreement and inconsistencies about placing the accidental before or after the number. (27–28) • Despite the diversity of thoroughbass treatises in the early 18thc, they all (including Heinichen’s) follow a similar order. o chords and figures o rudiments of music from simple to complex o triads and first-inversion triads o dissonant intervals Triads (29) • Heinichen suggests learning to play triads on every scale degree, practicing with the 3rd, 5th, and 8ve on top. These positions are called the drey Haupt-Accorde. (29) • St. Lambert, Kellner, and Mattheson also emphasize the importance of these three positions. • Doubling the 3rd and 5th was not advocated until the mid-18thc. 1
Chords of the Sixth (30) • Heinichen fully understood 6th chords as inverted 5/3 triads. • Although doubling the 5th or “root” in 6/3 chords was more natural, Heinichen strongly urged doubling the 3rd (bass) as well. • If moving in //6ths, accompanist can omit the fourth part in order to avoid //8’s • In M6, Heinichen recommends doubling the bass (e.g., EEGC) • In m6, he says that doubling the chordal fifth is fine and NOT harsh as others have said: o e.g., in CEA, E is not considered to be a M3 above the bass; it is an inverted fifth above the root A: c4e4a4 = a3c4e4, thus doubling E is okay. • Heinichen concludes with two rules for doubling the M3 that are not joined to 6ths: o M3’s [chordal 5th of m6] natural to the key can be doubled w/o hesitation. o M3 resulting from chromatic alterations should NOT be doubled. ! e.g., in D-major, it’s okay to double the leading tone C# in C#EA ! BUT in d-minor, it is NOT okay, because C# is a chromatic alteration. (31) • Heinichen’s musical examples often contradict his instructions (31) rd th o He says it’s okay to double the 3 and 5 , but NONE of his 4vv examples do this; they all double the bass (root in 5/3’s or 3rd in 6/3’s) o He says it’s okay to double the LT in major, but NONE of his examples do this. • Heinichen wanted to remove the notion against doubling M3’s [chordal 5th in m6] on keyboards, because tuning of 3rds was no longer a problem. • He lists three doubling rules for chromatically altered 6/3 chords: (32) 1. Do NOT double chromatically altered D# in BD#G 2. Do NOT double chromatically altered G# in BDG# 3. Do NOT double chromatically altered B-natural in BDG • He concludes with a general example of three separate versions of 6th chords: (31–33) o The first version shows the octave [chordal 3rd] on top in all 6/3 chords = drey Haupt-Accorde o The second version shows the third [chordal 5th] on top in all 6/3 chords o The third version shows the fifth [chordal root] on top in all 6/3 chords • Heinichen gives these examples for developing tactile memory to coordinate the eyes, mind, and fingers. • Buelow: According to the rule of the octave, 6/4/3 is assigned to scale degrees 2 and 6; however, NO theorist limits this chord to a particular scale degree. (35) Dissonances: The Second (2, 5/2, 4/2, 5/4/2, 4+, 6/4+/2) • Seconds occur in TWO forms only: 1. SUS (requires P and R) 2. PT • Since SUS of a 3rd over a suspended bass resembles structure of chords with seconds, Heinichen discusses 6/4/3 and 6/4+/3 in his second on seconds. (36) • Heinichen again gives example w/ three versions of chords with 2 = drey-Haupt Accorde • Most theorists agree with Heinichen’s suggestions about the 2nd. • St. Lambert, however, is more conservative. For him 2= 5/2 or 5/4/2, NOT 6/4/2. (40)
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Two degrees of functional importance for dissonances in Baroque theory and practice: 1. fundamental dissonances 2. auxiliary dissonances Thoroughbass manuals give correct resolutions of fundamental dissonances. (40) No matter how many figures a treatise lists, each belongs to one of the 5 or 6 groups of fundamental dissonances. 1. 2nd 4. 7th occurs in late-Baroque works 2. 4th 5. 9th 3. 5th 6. falsae = +2, º3, º4, +5, +6, M7 Thus, the pedagogical method was actually quite practical and simple. Rameau’s principles of functional harmony caused chords to lose their independence and caused figures to be reduced to a system of symbols for harmonic analysis (40) Unaffected by Rameau, however, Heinichen continued to group 5/2, 5/4/2, 6/4/2, 6/4+/2 together as harmonic variations built on the dissonant second. (40–41) His discussion of the origin and doubling of the 6/3 chord is possibly derived from Rameau (Lester, p.55)
The Fourth (4, 4+, 6/4, 6/4+) (41) • This usually occurs as a 4–3 SUS and should resolve but does NOT have to be prepared • The fourth may also occur as an ascending PT Basic Principles of Thoroughbass Accompanying (75) • He advocates the study of thoroughbass prior to acquiring advanced keyboard techniques • Heinichen favored learning thoroughbass as a means of learning how to compose • Most 18thc theorists disagree with this idea (e.g., Couperin, Mattheson, Bach, etc.) • Most recommended achieving technical command BEFORE thoroughbass Elementary Concepts of Style (76) 1. NO //5’s or //8’s 2. Have smooth voice-leading and avoid unnecessary leaps in RH •
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Heinichen is apparently the first to allow use of the entire range on the keyboard; he does give a few rules about this, though: (79) 1. Avoid large gaps between LH and RH 2. RH alone should play the decorations Heinichen is the only Baroque theorist to systematically and exhaustively develop ideas on fullvoice realizations. (full-voice = double as many notes in RH as LH can grasp) This is good for the harpsichord, because it cannot sustain. (80) The more voices singing the fuller the accompaniment should be. D’Anglebert (1689) and Delair (1690) say that the LH can be filled in with consonances or even by doubling the second or tritone of the RH chord. (80) This is radical to conservative French, such as St. Lambert (1707), who would double notes of the triad, intervals of the 2nd, and sometimes 7th.
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Heinichen’s approach to full-voice accompaniment: (82) 1. Add top part without //5’s and //8’s to bass part 2. Fill in with as many chord tones as possible Heinichen’s approach thus frees the inner voices from contrapuntal guidelines and voiceleading guidelines. (83) Heinichen says that the organist must be more careful than the harpsichordist when making a full-voice accompaniment: e.g., EEGC sounds harsher on organ than on harpsichord. (84) ALL suspended and resolving dissonances can be doubled in full-voice accompaniment (85) RH must follow general rules of preparation and resolution of dissonances. LH has more freedom: dissonances can resolve in different octaves: LH can anticipate dissonances in the RH (87) It is important to avoid large gaps between the LH and RH, regardless of doubling (86)
Unfigured basses (219) Theorists in the 17th and 18thc HATE unfigured basses (Werkmeister, Mattheson, CPE Bach) In spite of their vehemence toward it, it led to developments in harmonic theory, such as the relationship between harmony and key. Although theorists hate unfigured basses, Heinichen says that these complications can be overcome through 1) mastery of thoroughbass, 2) a thorough acquaintance with the various chords and progressions, and 3) memorizing the ambitus modi for each scale. (220) TP: • •
In its strict sense, ambitus modi refers simply to the scale represented by each mode or key; the ambitus modi of C major is c, d, e, f, g, a, b, c. Using only these notes would constitute a piece, section, or cadence that is strictly within the ambitus modi of C major. In a broader sense, ambitus modi later applied to harmonies of subsidiary keys, whose triads were composed of notes belonging to the main key. In this broader sense, a cadence using C: V7/V ! V would still be within the ambitus modi of C major, because the cadence occurs on a triad that is diatonic to C major. Cadencing on a g minor triad or a d minor triad, however, would not be within the ambitus modi of C major, since these triads are not diatonic to C:
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Deriving Figures from a Solo Part above the Bass: (220) • Determine chords by looking at outer voices (e.g., if there is a d in the bass and c in the solo, then play a 7th chord) • Heinichen gives a musical example and shows how 32 different chords can be determined from the solo and bass lines alone. Criticisms of Heinichen’s system: (223) 1) It disregards dissonances in the harmonic texture when they fall in a part other than solo or bass 2) It fails completely when there is no solo part Heinichen defends his system: (223–24) 1) Accompanist may form harmonies freely based on ambitus modi 2) Accompanist may determine harmonies from other parts in the score when the solo stops 3) Accompanist does not have to play ALL dissonances of other parts: just don’t play conflicting chords. His third statement stresses both the importance of improvisation AND of not playing wrong notes: The accompanist does not have to play ALL the right notes: just don’t play ANY wrong notes. Deriving figures from some easy rules or notable intervals of the scale (224) Heinichen gives EIGHT rules based on the direction and interval that the bass moves: 1) If bass descends m2, ascends 3rd, or descends 6th, then next bass note has a 6-chord 2) If bass of M5/3 ascends m2, descends M3, or ascends m6, then next bass note has a 6-chord 3) If bass of m5/3 descends M2, descends M3, or ascends m6, then next bass note has 6-chord 4) If bass of m6 ascends m2, descends M3, or ascends m6, then next bass note has 5/3 triad, BUT if it ascends M2, then next bass note has a 6-chord. 5) If bass of M6 ascends or descends M2, then next bass note has 6-chord, but if it descends m3 or ascends M6, then next bass note is 5/3 triad. 6) If bass of M6 chord descends M2, then next bass note has 5/3 triad; if it descends m3 or ascends m2, M2, or m3, then the next bass note has 6-chord. 7) If two bass notes ascend or descend 3rd and one includes accidental, then accidental is usually retained for the adjacent chord. 8) Any bass raised chromatically by # or natural foreign to key supports a 6-chord. Deriving figures by special rules or from structure (ambitus) of scale (227–29) Heinichen’s main source from which to draw thoroughbass figures was schemata modorum (harmony for each scale degree) SEVEN SPECIAL RULES: S1) Scale degree 5 uses major triad (i.e., V is always a major triad) S2) Scale degree 4 uses a minor triad in minor keys; it may also have a 6-chord or 6/5 chord S3) LT in major and minor keys uses a 6-chord S4) Scale degree 3 in major and minor keys uses a 6-chord S5) Scale degree 2 in minor keys uses a 6-chord; in major keys, it may use a triad (if the bass leaps) or a 6-chord if the bass ascends M2. S6) Scale degree 6 in minor keys uses a 6-chord; in major keys, it may use a 6-chord (if bass leaps to or from scale degree 4) or a triad. S7) When the bass is raised chromatically by # or n , then the piece modulates to the key that is a m2 above that accidental. 5
Heinichen gives reasons for each of his rules: they usually involve consideration of intervals: • e.g., LT must use 6-chord, because there is no P5 above LT • Scale degree 6 in minor uses a 6-chord, because it is a m2 from scale degree 5 Heinichen’s rules are based on natural laws of tonal harmony. His approach is systematic and more flexible than Campion’s Rule of the Octave. It is inadequate for determining and predicting harmonies in a given context, but it does NOT represent an attempt to establish harmonic or voice-leading norms within major and minor keys, nor does it attempt to explain how movement from one key to another affects harmony & voice-leading. Heinichen’s treatment of dissonances (381) Heinichen’s study of dissonances and their resolution in theatrical style is one of the most original contributions to the history of Baroque music theory. His treatise surpasses other Baroque treatises in explaining thoroughbass techniques, and it establishes specific characteristics of stylus theatricalis as it affects the art of accompanying thoroughbass. (381) (382–83) • Free dissonance treatment of theatrical style does NOT imply disorder or lack of resolutions. • Heinichen divides theatrical resolutions of dissonances into 8 major categories. • These rules ALL observe his fundamental rule yet suggest harmonic freedom far beyond that of academic counterpoint. • •
Unlike Rameau, Heinichen, who knew Rameau’s treatise, avoids evolving theoretical premises such as basse fondamentale or construction of all chords in 3rds. Heinichen attempts to codify by seeking basic principles of harmonic procedures underlying the current practice in the theatrical style of music. (383)
Variation of dissonances before resolution (383) Preparation and suspension must NEVER be omitted, though they can be varied by inserting notes between them. How to leap to and from dissonances: (390) "Heinichen suggests that ALL unprepared dissonances actually result from anticipated PT’s:
became
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"He also says that one CAN leap into any dissonance that can be prepared in another part. (391) "One can leap into ANY dissonance that occurs as a PT in another voice (393) "One can leap into ANY dissonance that occurs as a quick PT in another voice (393) His ideas suggest that voices were thought of as woven together into ONE vertical entity more so than independent horizontal lines. Inversions of harmonies before resolution (398) • Stems from the problem of unfigured bass in cantatas and operas. (399) o A sustained F in the melody against D in tb can be 3rd a d triad OR 7th of G7. • Thus, Heinichen developed a method to help accompanists with chord inversions and with recognizing inversions of dissonances before resolution (399) • His method is based on dividing the º7 chord into all possible inversions formed by the exchange of bass and upper chord tone with the remaining parts of the chord. • I think he is describing voice exchanges that allow any note of the viiº7 chord
Anticipated PT’s in the bass (418) Anticipated PT is allowed when: 1) There is a group of bass notes descending a M3 or m3 2) The second note descends M2 to form +4 with preceding chord (e.g., d3–g3–f3 # d3–f3) See example above from p.390. Many of these dissonances are created by ellipsis & are used at times to express harsh words (419) Heinichen says ellipsis is not only permissible but makes the chord more beautiful. (419)
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