The Gesangleiter in Joseph Riepel ’ s Baßschlüssel ( 1786 )

Joseph Riepel’s Anfangsgründe zur musikalischen Setzkunst (Fundamentals of Musical Composition) is an important source for our understanding of eighteenth-century compositional theory and pedagogy. One of the most noticeable aspects of the Anfangsgründe is the fact that the treatise is written in dialogue form. Only the chapter published posthumously in 1786, the Baßschlüssel (Bass clef), which focuses on how to write a bass against an existing melody, does not, except for the last four pages, follow the dialogue format. Because of this, the Baßschlüssel seems to present a different theoretical approach to composition. Most noteworthy is the absence of other theoretical positions that result from the typical back and forth between teacher and student. While the original manuscript upon which the edited version is based does not seem to have survived, a manuscript copy held in the British Library (GB-Lbl Add. 31034) contains at least twelve pages in dialogue form that are related to the Baßschlüssel, but that are not part of the published chapter. These twelve pages relate to Riepel’s Gesangleiter, his instruction on how to harmonize ascending and descending scale steps in the upper voice, which follows his discussion of the Baßleiter, the harmonization of scale steps in the lowest voice, or bass. The following essay, provides an overview of the Gesangleiter in Riepel’s Baßschlüssel, followed by a discussion of the manuscript pages as compared to the published version and a transcription of the manuscript pages. Joseph Riepel’s Anfangsgründe zur musikalischen Setzkunst ist eine der zentralen Quellen für unser Verständnis der Kompositionstheorie und pädgogik im achtzehnten Jahrhundert. Ein auffallendes Merkmal der Anfangsgründe ist das das Traktat in der Form eines Dialoges verfasst ist. Nur der nach Riepels Tod veröffentlichete Baßschlüssel, das Kapitel das darauf fokusiert wie man einen Baß zu einer bestehenden Melodie setzt, ist, abgesehen von den letzten vier Seiten, nicht in Dialogformat. Deshalb scheint der Baßschlüssel einen ganz anderen theoretischen Ansatz zur Komposition darzulegen. Am auffallensten ist die Abwesenheit von unterschiedlichen theoretischen Positionen die ein Resultat des typischen hin under her zwischen Lehrer und Schüler sind. Obwohl das orginale Manusript auf dem die herausgegebene Version basiert nicht überliefert ist, eine Kopie der British Library (GB-Lbl Add. 31034) enthält wenigsten zwölf Seiten in Dialogform die mit dem Baßschlüssel zusammenhängen aber nicht Teil des publizierten Kapitels sind. Diese zwölf Seiten beziehen sich auf Riepels Gesangleiter, seine Anleitung wie man aufund absteigende Tonstufen in der Oberstimme harmonisiert, die auf die Baßleiter, der Anleitung wie man Tonstufen in der Unterstimme, dem Baß, harmonisiert, folgt. Der folgende Beitrag liefert eine Überblick über die Gesangleiter in Riepels Baßschlüssel gefolgt von einer Besprechung der Manuskriptseiten im Vergleich mit dem publizierten Kapitel und einer Abschrift der Manuskriptseiten.

The Gesangleiter in Joseph Riepel's  Baßschlüssel (1786)   Stefan Eckert ABSTRACT: Joseph Riepel's Anfangsgründe zur musikalischen Setzkunst (Fundamentals of Musical Composition) is an important source for our understanding of eighteenth-century compositional theory and pedagogy.One of the most noticeable aspects of the Anfangsgründe is the fact that the treatise is written in dialogue form.Only the chapter published posthumously in 1786, the Baßschlüssel (Bass clef), which focuses on how to write a bass against an existing melody, does not, except for the last four pages, follow the dialogue format.Because of this, the Baßschlüssel seems to present a different theoretical approach to composition.Most noteworthy is the absence of other theoretical positions that result from the typical back and forth between teacher and student.While the original manuscript upon which the edited version is based does not seem to have survived, a manuscript copy held in the British Library (GB-Lbl Add.31034) contains at least twelve pages in dialogue form that are related to the Baßschlüssel, but that are not part of the published chapter.These twelve pages relate to Riepel's Gesangleiter, his instruction on how to harmonize ascending and descending scale steps in the upper voice, which follows his discussion of the Baßleiter, the harmonization of scale steps in the lowest voice, or bass.The following essay, provides an overview of the Gesangleiter in Riepel's Baßschlüssel, followed by a discussion of the manuscript pages as compared to the published version and a transcription of the manuscript pages.Joseph Riepel's Anfangsgründe zur musikalischen Setzkunst ist eine der zentralen Quellen für unser Verständnis der Kompositionstheorie und pädgogik im achtzehnten Jahrhundert.Ein auffallendes Merkmal der Anfangsgründe ist das das Traktat in der Form eines Dialoges verfasst ist.Nur der nach Riepels Tod veröffentlichete Baßschlüssel, das Kapitel das darauf fokusiert wie man einen Baß zu einer bestehenden Melodie setzt, ist, abgesehen von den letzten vier Seiten, nicht in Dialogformat.Deshalb scheint der Baßschlüssel einen ganz anderen theoretischen Ansatz zur Komposition darzulegen.Am auffallensten ist die Abwesenheit von unterschiedlichen theoretischen Positionen die ein Resultat des typischen hin under her zwischen Lehrer und Schüler sind.Obwohl das orginale Manusript auf dem die herausgegebene Version basiert nicht überliefert ist, eine Kopie der British Library (GB-Lbl Add.31034) enthält wenigsten zwölf Seiten in Dialogform die mit dem Baßschlüssel zusammenhängen aber nicht Teil des publizierten Kapitels sind.Diese zwölf Seiten beziehen sich auf Riepels Gesangleiter, seine Anleitung wie man aufund absteigende Tonstufen in der Oberstimme harmonisiert, die auf die Baßleiter, der Anleitung wie man Tonstufen in der Unterstimme, dem Baß, harmonisiert, folgt.Der folgende Beitrag liefert eine Überblick über die Gesangleiter in Riepels Baßschlüssel gefolgt von einer Besprechung der Manuskriptseiten im Vergleich mit dem publizierten Kapitel und einer Abschrift der Manuskriptseiten.Joseph Riepel's Anfangsgründe zur musikalischen Setzkunst (Fundamentals of Musical Composition) was among the first treatises to discuss composition on the basis of combining measures and to address musical form on the phrase level. 1 Recognized by contemporaries for offering hands-on instructions and practical suggestions for budding composers, Riepel's treatise continues to be an important source for our understanding of eighteenth-century compositional theory and pedagogy. 2The Anfangsgründe consists of ten chapters, five of which were published by Riepel during his lifetime between 1752 and 1768.Two chapters were edited and published posthumously in 1786 in one volume by Johann Caspar Schubarth (who was one of Riepel's former students); another three chapters have survived in manuscript form. 3One of the most noticeable aspects of the Anfangsgründe is the fact that the treatise is written in dialogue form.According to Riepel, the different chapters resemble actual lessons in composition, unfolding as lively discussions between a teacher, the Praeceptor, and his student, the Discantista.Only the chapter published posthumously in 1786, the Baßschlüssel (Bass clef) does not, except for the last four pages, follow the dialogue format.Because of this, the Baßschlüssel seems to present a different theoretical approach to composition.This change in structure is most profound when noting the absence of other theoretical positions that result from the typical back and forth between teacher and student.Because Riepel usually does not present compositional issues as codified theory, but instead uses the dialogue to convey the multifarious aspects of mid-eighteenth-century musical practice, this difference is highly significant. 4hile the original manuscript upon which the edited version is based does not seem to have survived, a manuscript copy held in the British Library (GB-Lbl Add.31034) contains at least twelve pages in dialogue form that are related to the Baßschlüssel, but that are not part of the published chapter. 5Since no copy of the original manuscript seems to exist, it is impossible to know which aspects of the treatise were changed by the editor, Johann Kaspar Schubarth, and which can be traced back to Riepel.In his listing of Riepel's works, Thomas Emmerig stated that "[a]fter the [manuscript] copy of the Baßschlüssel in GB-Lbl.[the British Library] follow 22 pages (fol.71a-92b), 'which do not appear in the published edition' (Hughes-Hughes III, 326).These pages are without any doubt fragments of earlier manuscript versions, among others of the Baßschlüssel-in its original dialogue form!-and of the Harmonisches Sylbenmaß III; some parts could not be identified.Whether these constitute autograph pages or copies cannot be ascertained, because proven autographs from Riepel's earlier years for comparison are missing.Literature: Mettenleiter, 52 -Twittenhoff, 38 f. and 107 ff." 6 Emmerig refined his assessment of ZGMTH 11/2 (2014) | 233 the forty-four single pages in the appendix to the complete edition, stating that 12 pages related to the Baßschlüssel still remain unidentified in their content. 7 have transcribed these twelve pages and identified that their content relates to Riepel's Gesangleiter, his instruction on how to harmonize ascending and descending scale steps in the upper voice, which follows his discussion of the Baßleiter, the harmonization of scale steps in the lowest voice, or bass.While the manuscript pages approach the Gesangleiter from different perspectives, several passages seem fragmented and slightly cryptic, almost as if they were taken from another context or constituted only a preliminary stage of the material.However, the employment of different perspectives compares well with the overall approach in the rest of the Anfangsgründe and complements the opening sections of the Baßschlüseel which seems to offer a somewhat categorical approach to the material.It is also noteworthy that the first five pages of the Baßschlüssel, which contain the Baßleiter, restate material already presented in the previous chapter on Counterpoint, a situation that is unique within the Anfangsgründe. 8In the following essay, I provide an overview of the Gesangleiter in Riepel's Baßschlüssel, followed by a discussion of the manuscript pages as compared to the published version.My transcription of the manuscript pages follows in a separate article.While the content of the manuscript pages, due to their limited size and the topics addressed, do not reveal any extraordinary new insight into Riepel's ideas, it is interesting how there is a distinct reorganization of the material.In addition, despite its scholarly neglect, Riepel's Gesangleiter does offer interesting insights into his conception of the interaction between melody, harmony, and counterpoint and thus deserves our attention.

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The Baßschlüssel, das ist, Anleitung für Anfänger und Liebhaber der Setzkunst, die schöne Gedanken haben und zu Papier bringen, aber nur klagen, daß sie keinen Baß recht dazu zu setzen wissen (Bass clef, that is, instruction for beginners and music lovers, who have beautiful ideas and can notate them, but who complain that they do not know how to set a proper bass against them), is intended to teach students how to write a bass against an existing melody and consists largely of two parts.Figure 1 provides an overview of the topics and demonstrates that the Baßleiter and the Gesangleiter make up the largest sections of the treatise.The Baßleiter, which is also known as the Rule of the Octave, builds the foundation for the Gesangleiter, which constitutes Riepel's idiosyncratic appropriation of the octave rule to the highest voice. 9While the Baßleiter and the Gesangleiter create an overarching structure for the Baßschlüssel, there exist significant portions, especially pages 33-63, that do not explicitly relate to either of the two topics.Also, while the Gesangleiter in major is treated in great detail, the minor and chromatic versions are only mentioned briefly, without additional examples for their applications.I begin with a summary of Riepel's Baßleiter and provide a more detailed discussion of Riepel's ascending and descending Gesangleiter in major, which consists of twenty-six rules, and end with an overview of the extension of the Gesangleiter in minor and a brief account of the final, rather loosely connected rules around Gesangleiter and Baßleiter, including some chromatic issues, with which Riepel ends the Baßschlüssel.

Riepel's Baßleiter
Riepel begins the Baßschlüssel with a discussion of the common (allgemeine) Baßleiter, that is, the rules on how to harmonize the different pitches within a scale, assuming mostly stepwise motion.For the ascending scale, Riepel sets root position chords above scale degrees ➀, ➃, and ➄, and first inversion triads on scale degrees ➁, ➂, ➅, and ➆. 10 However, he points out that composers often harmonize scale degrees ➃ and ➆ with a 6/5 and scale degree ➁ with a 6/4/3; the latter he shows in both ascending and descending motion: ➀-➁-➂ and ➂-➁-➀ (Figure 2): For the descending scale, he keeps root position chords on scale degrees ➀ and ➄, but harmonizes ➃ with a 4/2.In addition, he harmonizes scale degree ➅ with # 6, a major sixth (Figure 3): In addition, he highlights further context-specific harmonization of scale degrees ➅, ➃, and ➁ (Figure 4).While ➅-➄ be harmonized with a major sixth ( # 6), if scale degree ➄ 10 Following Gjerdingen 2007, I will identify the scale degree of notes in the bass using ➀, ➁, ➂, etc.
based on the major scale.That is, regardless of mode, ➆ will always identify the leading tone, the major seventh above the tonic.I use accidentals to identify any alterations or to clarify ambiguous moments; for example, b ➆n ➆-➀ identifies a motion from the minor to the major seventh to the tonic.Similarly, I use ➊, ➋, ➌, etc. to identify scale degrees of notes in the soprano.
does not follow scale degree ➅, then it should be harmonized with just a minor sixth (6).
In addition, if scale degree ➅ is approached by step from either direction without a stepwise continuation, it should be harmonized with a 5/3.Scale degree ➃ should be harmonized with a 4/2 when moving ➄-➃-➂; however, if scale degree ➃ moves to ➂ without the context of a Dominant chord, it should be harmonized with a 5/3.Similarly, while scale degree ➁ is usually harmonized with a 6 or 6/4/3, if it does not move stepwise within a Tonic chord, that is scale degrees ➀ and ➂, it should be harmonized with a 5/3.I have summarized these context-specific harmonizations of ➅, ➃, and ➁ in Figure 4 below: The fixed harmonizations result in root position chords for scale degrees ➀ and ➄ and first inversion triads on scale degrees ➂ and ➆; with the possibility of the latter taking a 6/5, that is, a chordal seventh.Scale degree ➁ may be harmonized with a root position chord if ➁ does not move to tonic harmony (that is, to either scale degrees ➀ or ➂) as seen in mm. 12 and 19; scale degrees ➃ and ➅ may be harmonized with root position chords, if ➃ and ➅ do not move to a dominant chord (that is, ➄ or ➆) as it happens for ➃ in mm.11 and 22 and for ➅ in m. 17.In addition, ➅ takes a major sixth ( # 6) moving to ➄ as in mm.6-7, but a minor sixth (6) when it does not moves to ➄ as in m. 10.For the ascending minor scale (Figure 5), all changes are due to the mode change, otherwise the same rules as in the ascending major scale apply.In contrast, the descending minor scale (Figure 6   Finally, Riepel ends his presentation of the octave rule with two unfigured basses in both major and minor as examples for applying the octave rule to a bass that moves to all closely related keys.The bass lines appear first without figures but with annotations identifying the different keys followed by a figured version that provides the answer key on how the bass lines should be harmonized.
What is unique about the presentation of the octave rule in the opening five pages of the Baßschlüssel, is that this constitutes the second complete presentation of the octave rule within the Anfangsgründe.Indeed, halfway through Chapter Six "On Counterpoint," at a moment when Riepel rewrites counterpoint examples by J. J. Fux from a harmonic perspective, the teacher already introduces the octave rule to the student. 11While the content of the two presentations is essentially the same, that is, the information concerning how specific scale degrees should be harmonized, the differences between the two presentations are significant.Most importantly, the presentation of the octave rule at the beginning of the Baßschlüssel is not in dialogue form and proposes root position chords above scale degrees ➀, ➃, and ➄, as a matter of nature.
Since the fourth F and the fifth G demand by nature a complete chord [The Baßschlüssel defines a complete chord as consisting of a third and fifth, either of which may be omitted in practice 12 ], yet their immediate progression easily leads to forbidden fifths or octaves, even the oldest masters have used the six-five chord as a good emergency assistance.Although it sounds somewhat drudging, it is often used for [above] the seventh as well as the fourth [scale degree]. 13el Lester has suggested that such emphasis on scale degrees ➀, ➃, and ➄ demonstrates that Riepel embraces "aspects of Rameauian harmony."14Yet, the introduction to the octave rule in the counterpoint chapter does not contain this reference to nature, and the student-teacher discussion does not sound as categorical as the opening in the Baßschlüssel.Moreover, throughout the Anfangsgründe, Riepel either ignores or comments negatively on Rameau's mathematically grounded principles of music, which he considers to stand in contrast with his hands-on approach.For example, he compares the ideas contained in one of Rameau's treatises, Démonstration du Principe de l'Harmonie, to a satire by Ludvig Holberg, stating, "I was just as eager to read [Rameau's] treatise as I was to know how Nicolaus Klim finally found a fifth monarchy in the center of the earth." 15epel's Gesangleiter I would first like to note that the ancient bass, which accompanies a melody [Gesang]  has been explained by some to be systematical (perhaps only in this century).According to this explanation, the whole octave scale has only three Grundbaßnoten [fundamental-bass notes], the remainder are neighboring or passing tones, which I in appreciation of their good service call at least Mittelbaßnoten [middle-bass notes] (6). 16is opening statement, with which the author of the Baßschlüssel begins the presentation of the Gesangleiter seem foreign to Riepel's ideas.Most importantly the claim that ZGMTH 11/2 (2014) | 239 the bass derives from a system, which reduces it to three fundamental bass notes, seems reminiscent of Rameau's ideas.However, as mentioned in the context of Riepel's discussion of the octave rule, there does not really exist enough evidence to substantiate a specific relationship.The Gesangleiter with its various and usual bass notes [mit ihren verschiedenen und üblichen Baßnoten] directly and indirectly takes up the majority of the Baßschlüssel.Since the Baßschlüssel is not in dialogue form, there exists no back and forth between the teacher and student, no questions are raised, and no contradictions appear.On the other hand, the single authorial voice allows for an uninterrupted presentation of the topics at hand.Even though we are unable to prove or disprove Riepel's authorship of the printed version of the Baßschlüssel, I continue to identify him as the author in the following discussion.
The Gesangleiter begins quite simply.Declaring C, F, and G Grundbaßnoten and the remaining pitches Nebenklänge or Mittelbaßnoten that arise from the triads above C, F, and G (Example 3), Riepel first demonstrates that this approach results in a complete scale (Example 4) and then goes on to harmonize this ascending scale in treble clef using only the Grundbaßnoten C, F, and G (Example 5).gests that if composers would use only Grundbaß-and no Mittelbaßnoten, compositions would seem desolate and barren.Thus he suggests that the root of the chords could be replaced with by its third, which "the old have called Nota median (mediating note)." 18xample 6: Ascending Gesangleiter §. 4, p. 7 Example 6 reproduces the harmonization of the ascending Gesangleiter, which, except for the final C, replaces the chordal roots with the thirds where possible.That is scale degree ➌, E, and ➏, A, which are the chordal thirds of the triads on C and F respectively, continue to be harmonized with their roots.However, scale degree ➐, B, is not harmonized by its root G, but D, which in this context is 'mediating.'Indeed, Riepel's chordal harmonization of the ascending Gesangleiter §. 4 (Example 7), demonstrates that the scale degree ➐, B, is harmonized by its third, D. Riepel thus expands the repertoire of chords adding a B diminished chord.It is noteworthy that he does so without making an attempt to explain the origin of the diminished chord.Riepel, however, points out that even though scale degree ➊, C, is harmonized by scale degree ➂, its third E, in the bass, that this is meant as a continuation in the middle of a melody, "otherwise, there should not be the note E at the beginning but the Grundbaßnote C." 19 Example 7: Harmonization of the Ascending Gesangleiter §. 4, p. 8 18 "… von den alten Nota medians (vermittelnde Note" genannt" (Riepel, Baßschlüssel, 7).
19 "[…], sonst müßte es (wie bekannt) zum Anfange nicht di Note e, sondern die Grundbaßnote C seyn" (Riepel, Baßschlüssel, 7).The next two harmonizations of the ascending Gesangleiter (Examples 8 and 9) use only consonant thirds and sixths."I also imagine," Riepel writes, "that, except at the beginning and the end, there can always be thirds between the melody and the bass, may they be mediating or not mediating, Mittelbaß-or Grundbaß-like, for example:" 20 Example 8: Ascending Gesangleiter §. 5, p. 8 Example 9: Ascending Gesangleiter §. 6, p. 8 In addition to using thirds and sixths, Riepel suggests that scale degrees ➌, E, and ➏, A, could also be harmonized with fifths (Example 10) and octaves (Example 12) between the outer voices: Example 12: Ascending Gesangleiter §. 8, p. 9 Example 13: Two Harmonizations of the Ascending Gesangleiter §. 8, p. 9 The two harmonizations in Example 13 share the bass of Example 12; however, Riepel interprets E and A first as chordal roots resulting in E minor and A minor chords and then as the chordal thirds of the C major and F major chords respectively.Figure 7 schematizes the two different harmonizations of the octaves in comparison: Ascending Gesangleiter §. 9-11 (Examples 14-17) introduces the use of the chordal seventh.Example 14 harmonizes scale degree ➍ in the soprano with ➄ in the bass, resulting in a minor seventh.In his brief discussion before the example, Riepel acknowledges that the minor seventh, while a dissonance, now constitutes a common sonority, especially in a chord containing also a third and fifth.Example 21 uses first inversion chords where possible, but includes also a cadential 6/4 chord at the half cadence in m. 8.That is, when chordal thirds appear in the melody, the bass always takes the root of the chord, as seen on the last beat in mm. 1 and 3 where E and A are harmonized with C and F respectively.Example 23: Application of the Ascending Gesangleiter according to §. 6, p. 12 Example 23 contains two extensive passages in parallel sixths (last beat of m. 1 -last beat of m. 3 and last beat of m. 5 -last beat of m. 7).However, Riepel notes that the bass starting at † seems more like an inner voice and he rewrites mm.5-6 by placing the bass as the melody harmonized in parallel 3rds.
Example 24: Application of the Ascending Gesangleiter according to §. 7, p. 13 Example 24 presents the 5ths below ➌ and ➏, resulting in the Am (m. 2 beat 1) and Dm (m. 5 beat 1).Interestingly, Riepel comments how the passage at (O), in mm.4-5, while acceptable, sounds better when fully voiced.However, Riepel's harmonizations concern only the motion from ➃-➂ in the bass, harmonizing them with first inversion chords d6-C6 respectively, which contradicts the B in the melody.
Example 25: Application of the Ascending Gesangleiter according to §. 8, p. 13 Example 25 contains the 8ves below ➌ and ➏, resulting in Em and Am chords on the downbeats of mm. 2 and 3 respectively.
Example 26: Application of the Ascending Gesangleiter according to §. 9, pp.13-14 Example 26 includes chordal sevenths.Unlike §. 9 which only focused on the resolution of the minor seventh in the context of the dominant, (Q) presents a half-diminished seventh chord above ➆, while (P) and (R) treat the V7 in root position and inversions.
Example 27: Application of the Ascending Gesangleiter according to §. 10, p. 14 Example 27 includes 4/2 below ➋ and ➍ (ii4/2), both using the repeated note paradigm (➀-➀-➆-➀), harmonized with 5/3-4/2-6/3-5/3.However, at †, the bass moves not to ➀, but using ➂-➀ in order to avoid moving into the fifth C-G (downbeat of m. 3) in the outer voices.Example 30 contains a chromatically ascending bass segment.Unlike §. 13, where its harmonic interpretation was ambiguous because the segment ended the example, Example 30 clearly remains in the key of C because of the phrase ending on the dominant.
The descending Gesangleiter, taking up §. 14-26 (pp.17-26), includes a tonicization of the dominant, an extensive discussion of cross-relation, and several schemata (Romanesca ( §. 18), Prinner ( §. 22), and Quiescenza ( §. 24)).Examples 31-33 ( §. 14-15a and 15b) harmonize the descending scale degrees ➐-➏-➎ with ➄-➁-➄ or ➄-# ➃-➄, that is with G-D-G and G-D6-G respectively (Figure 8) with the comment "We have seen this hasty departure from the main key into the fifth in the Generalbaßleiter above."Aligning both, Gesangleiter and Baßleiter, Riepel further conflates Baßleiter and Generalbaß into Generalbaßleiter, which up to this moment in the Baßschlüssel appeared separately.The term Generalbaßleiter highlights the close relationship between thoroughbass and the octave rule and may indicate how futile it is to keep these two concepts separated because they overlap in so many ways.While Riepel highlights the Grundbaßnoten C, F, and G in his harmonization of the ascending scale, the harmonization of the descending scale adds D, which he describes as a "swift deviation from the main key to the fifth." 21ligning both, Gesangleiter and Baßleiter, Riepel further conflates Baßleiter and Generalbaß into Generalbaßleiter, which up to this moment in the Baßschlüssel appeared separately.The term Generalbaßleiter highlights the close relationship between Thoroughbass and the octave rule and may indicate how futile it is to keep these two concepts separated because they overlap in so many ways. 22While Riepel highlights the Grundbaßnoten C, F, and G in his harmonization of the ascending scale, the harmonization of the descending scale adds D, which he describes as a "swift deviation from the main key to the fifth." 23ample 31: Descending Gesangleiter §. 14, p. 17 neralbaßleiter gesehen" (Riepel Baßschlüssel, 17).
22 Giorgo Sanguinetti begins his 2007 article by discussing the close relationship between thoroughbass and partimento, of which the octave rule is an important aspect.Sanguinetti's most pronounced difference between thoroughbass and partimento, speaks to the independence of the partimenti, because thoroughbass is usually meant to accompany something, thus is in service to some other musical force.
23 "[…] eilfertige Abweichung von der Haupttonart in die Quinte."I am taking the liberty to translate "eilfertig" as "swift" despite that it literally translates into "rash," because I detect no negative connotations in the German text.
ZGMTH 11/2 (2014) | 249 Harmonizing ➐-➏ in the soprano with ➄-➃ in the bass, which results in a G major to F major progression in mm.2-3 of Example 34 ( §. 16), Riepel identifies the Mi contra Fa (➐-➃), or cross-relation (Querstand), in the outer voices, that is, the presence of scale degree ➐ in the soprano followed one note later by scale degree ➃ in the bass, with an extended front slash.
Example 34: Descending Gesangleiter §. 16 Stating that the "old [masters] condemned such two major thirds in a descending Gesangleiter," Riepel explains in a footnote that this concerns "especially [two major thirds] between the highest voice and the bass; yet, only in certain positions and turn of phrases." 25 24 "Man könnte dagegen durchaus in der Haupttonart bleiben, wenn ein fridlicher Querstand zu dulden wäre" (Riepel Baßschlüssel, 17).
Marking the example containing the cross-relation with " §. 16" (Example 34), Riepel seems to indicate that he considers the example part of the Gesangleiter, despite the fact that he explicitly points out in most of the following examples ( §. 17 Examples 42-43, §. 24-25, show both a stepwise ascending and descending soprano above a tonic-pedal bass.In the case of the stepwise ascending soprano, the last four notes, ➎-➏-➐-➊, create a Quiescenza with 5/3, 6/4, 7/4/2, and 5/3 above the pedal which can appear both with and without chromatic alterations. 29ample 42: Ascending Gesangleiter §. 24, p. 21 Except for the five-page distance between §. 25 (Example 43) and §. 26 (Example 44), which makes §. 26 appear almost like an afterthought, the thirteen rules for harmonizing an ascending Gesangleiter ( §. 1-13) are followed by thirteen rules for harmonizing a descending Gesangleiter ( §. 14-26).Similar to the treatment of the ascending Gesangleiter, which was first introduced and then exemplified, pp.21-25 also present examples for how to apply the rules of the descending Gesangleiter.Most of the examples demonstrating the application of the Gesangleiter are in three or more parts, which is helpful for clarifying some of the harmonically ambiguous rules.Except for Example 46, which consists only of four measures, all examples create a complete harmonic and melodic context.That is, all begin on and end with a cadence in the tonic C major.
Example 45 combines both rules §. 14 & 15.That is, D is harmonizing scale degree ➏ as a secondary dominant to G as a detour to the fifth of the key, (Abweichung in die Quinte), and ➎-➍ are harmonized by ➄-➅ (V-IV6), which avoid the parallel octave that would result from successive root position chords of ➄-➃ (V-IV).
Example 45: Application of the Descending Gesangleiter according §. 14 & 15, p.21  Examples 46 highlight again the Mi contra Fa (➐-➃), or cross-relation (Querstand), in the outer voices.Riepel argues that the second example with its rest on the last beat of m. 2 moderates the cross-relation at (✝).Following this example, Riepel demonstrates other harmonic means to avoid the cross-relation.Most important is the use of a minor seventh, that is scale degree ➆ below scale degree ➏, resulting in half-diminished seventh chord, which resolves to the tonic (➏-➎ harmonized by ➆-➀).Following the ascending and descending Gesangleiter in major, Riepel also provides brief examples for the Gesangleiter in minor §. 27-36, which reiterates many of the rules for the Gesangleiter in major.Figures 9 and 10 summarize rules §. 27-28 and 29 respectively, which provide guidelines for harmonizing ascending melodic minor scales.Similar to Example 5 ( §. 3), the bass for §. 27 uses exclusively the Grundbaßnoten C, F, and G; similar to Examples 8 and 9 ( §. 5 and 6) the bass for §. 28 and 29 move in parallel thirds and sixth respectively.In Figure 10 ( §. 29), Riepel separates the last four notes from the first five in order to diminish the effect of the Fa contra Mi, that is scale degree ➍ in the soprano followed by scale degree ➆ in the bass.30 "Bis zum ab (also fa) inclusive ist diese Leiter ganz natürlich; wenn mir das h als ein hierzu ungehöriges mi nicht darauf folgte.Es läßt sich aber die Leiter mit einer dazwischen gesetzten Note durchaus natürlich machen, z.Ex." (Riepel Baßschlüssel, 30).
Concerning the descending minor scale, Riepel provides rules for the descending natural minor ( §. 32 and 33, Figure 12) followed by four additional example basses (Figure 13) and rules for the harmonic minor scale ( §. 34-36, Figure 14).In §. 32, Riepel expands the Grundbaßnoten C, F, G to include E-flat, that is, the major triad above b ➂; in §. 33, he also includes a first inversion chord above ➃ and harmonizes ➍ in the soprano with either ➃ or ➄ (V7).The four basses in Figure 14 demonstrate a range of chromaticism, including tonicizations the subdominant below b ➐ and bº6 chords below scale degree ➍ in basses 3 and 4. Noteworthy is the harmonic ambiguity of scale degree ➎: the "3" in basses 1 and 2 potentially allows both a root position E-flat major or a first inversion c minor chord (Riepel usually uses "5" to indicate root position chords, yet in rare cases also "3").All of these issues are more or less relevant to the overall goal of the Baßschlüssel and often demonstrated with more than one example (Figure 15).Similar to the Baßleiter, the Gesangleiter (Figure 16) is based on some shared principles without actually creating a strict method.While the Gesangleiter starts out with a claim for a unified theory, §. 1-2 argue that everything derives from the Grundbaßnoten C, F, and G and §. 3-4, §. 14-15, 31-32, and 27 use mostly the I, IV, and V chords first in root position then in first inversion-the remainder of the Gesangleiter cannot be described as a logical outcome of this opening.§. 5-8, §. 19-21, 28-29, and 34 incorporate intervals (first 3rds and 6ths, then 5ths and 8ves), §. 9-11 and 33 introduce chordal sevenths and §. 12-13 chromaticism and §. 17-18, 22-26, and 35-36 focus on various local solutions and schemata (Romanesca, Prinner and Quiesenza) to address problematic harmonic issues such as the cross-relation and augmented seconds.Riepel's approach to the Gesangleiter is thus not unlike his approach to harmony in general, that is rather than theorizing harmony as a system, Riepel appropriates aspects of harmony and counterpoint and applies them to specific moments without a concern for an overarching method or system (Figure 16).In summary, I believe that Riepel's Gesangleiter succeeds in outlining a method for writing a bass against a melody that goes extensively beyond the simplistic method suggested in the opening where all harmonic content is reduced to C, F, and G, that is, the tonic, subdominant, and dominant harmonies.While this opening suggests an approach linked to or based on Daube's General=Bass in drey Accorden (Figured Bass in Three Chords) published in 1756, Riepel neither generates all bass notes strictly harmonically, nor does he agree with Daube's 6/5 chord above scale degree ➃. 32 Instead, Riepel's thirty-six rules for the Gesangleiter also borrows principles from the Baßleiter and in many instances combines harmonic and contrapuntal procedures for the purpose of writing a bass that both supports the melody and results in an recognizable musical line.The fact that there exist no traces of the Gesangleiter in the wake of the Baßschlüssel may be due to a combination of issues, most significantly, because counterpoint-in its close affiliation with partimento and solfeggio practice-already provides the tools for writing such bass lines, and it would seem that only amateurs without much formal training might be interested in Riepel's approach.However, the Baßschlüssel documents Riepel's wrestling with issues of melody, harmony, and counterpoint and provides us with an eighteenth-century insight into issues that are still relevant for the training of musicians today.
32 Diergarten 2008 provides an insightful summary of Daube's compositional approach.  .37-41, 42, 43, 44, and  45 (pp.53-54, 56, 61, 62, and 71)   Opposite page: the section ends with a dismissal of the monochord.However, the assertion that there exists only a major mode can be found throughout the manuscript pages and within the printed Baßschlüssel. 36In addition, both the manuscript pages and the printed version acknowledge that this position fails to derive the minor mode.While this slant towards the major mode helps to explain why both the Baß-and the Gesangleiter pays significantly less attention to the minor mode, it is interesting that both texts repeatedly invoke, dismiss and acknowledge the limits of the monochord.The resulting uncertainty about the status of acoustic principles for compositional practice is not unusual for Riepel's Anfangsgründe.Indeed, I believe that such moments serve to inform readers about the existence of multiple perspectives and eventually challenge readers to make up their own minds.
The first introduction to the Gesangleiter (pp.43-49) begins with a reference to the Capellmeister from Monsberg, who either plays or knows of the Maultrommel (Jew's Harp), which supposedly is able to produce all intervals.In this version, the Discantista reports that Hansmichel and the two musicians from Vallenthal and Urbstadt utilize only three pitches, C, F, and G in order to explain the Baßleiter.The Praeceptor continues this thread and derives the bass scale similar to §. 1 and of the Gesangleiter.Instead of Mittelnoten, both designate D, E, A, and B as "abstammende" (derived) pitches that complete the scale together with the Grundnoten C, F, and G.In contrast to the discussion of the Gesangleiter in the Baßschlüssel, the student, the Discantista, proposes a different system for deriving all pitches.He suggests that the C, the third below E-G in the C-E-G chord, is replaced by B, the third above, thus relating C-E-G and E-G-B, similarly F-A-C and A-C-E and G-B-D and B-D-F # ."This invention", says the Praeceptor, "is as casual as useless," yet he acknowledges that one needs to try to explain all the many sounds in music. 37Again such a statement is reminiscent of the teacher in the Anfangsgründe, who both draws on and critiques systems.The remainder of the discussion does not directly concern the Gesangleiter, but the student reports of a composer in Opolisburg, who claims that he can teach his system of composition within a week's time using simple bass motions harmonized in parallel thirds and sixths, which the teacher judges as old and formal.
The second introduction to the Gesangleiter (pp.49-52) begins with a reference to the Baßleiter.Unlike the Baßschlüssel and the first introduction, this discussion does not derive the scale from the triads above C, F, and G. Instead, the Praeceptor simply states, "in this key, the note C is the Grundnote [fundamental note] because the melody begins and ends with it.It [C] is hereby interrupted by G, because it is necessary for creating a complete cadence.The note F takes care of the Amen cadence as can be seen in the five different cadences in Chapter Five page 56." 38 Thus instead deriving the scale from harmonic principles, the argument here is focused on observations and examples taken from practice, an approach that is not uncommon in the Anfangsgründe.Declaring uni-36 See Riepel, Baßschlüssel, pp.6-7.37 "Diese Einbildung ist so lässig als Vergeblich" (Riepel, Baßschlüssel Ms, 46.)   38 "Praec.In dieser Tonart ist die Note C folglich eine Grundnote, weil der Gesang insgemein damit angefangen und geendigt wird.Hierauf unterbricht sie die Note G, weil sie zu einer vollkommenen Cadenz notwendig ist.Die Note F besorgt die Amen-Cadenz so wie im 5ten Cap: S: 56 die fünferley Cadenzen zu sehen sind" (Riepel, Baßschlüssel Ms, 50).
son, octave, fifth, third, and sixth consonances, the Praeceptor, then "every essential note in the melody must be accompanied by at least one of these five consonances."39Thus, even though the basic harmonization of the scale is based on C, F, and G, the studentteacher discussion solely focuses on consonances and dissonances, and highlights counterpoint, as the cause for harmonizing the scale.While I have described the twelve manuscript pages as structured in roughly three sections, because of visual breaks and apparent beginnings in the text, it is also possible to all pages a continuous introduction to the Gesangleiter.Such a view would be supported by the fact that there exist several references to earlier moments in the text.For example, the discussion of the Maultrommel (see page 43), seems to respond to the limits of the monochord, the emphasis on C, G, and F (pages 44 and 50) could be considered related.However, due to the limited material, the status and function of these pages remains unclear and any conclusions seem preliminary.Having spent a significant amount of time with this material, I do recognize that they should be best addressed in the larger context of the Anfangsgründe, because Riepel's teachings on harmonic and contrapuntal issues, while fragmented, seem to be part of a larger thread that appears throughout his writings.

Figure 1 :
Figure 1: Contents of Riepel's Baßschlüssel (84 pages) 9 See Christensen 1992 and Jans 2007 for an extensive discussion and historical context of the octave rule.

Figure 4 :
Figure 4: Context-Specific Harmonization of ➅, ➃ and ➁ ) with its flattened scale degrees b ➅ and b ➆ usually does not ZGMTH 11/2 (2014) | 237 include the major sixth ( # 6) in its stepwise descend to ➄.With the exception of the major sixth ( # 6) and the necessary alteration due to the lowered third and sixth scale degrees ( b ➂ and b ➅), the other context-specific harmonization of scale degrees ➁, ➃, and ➅ as outlined in Figure 4 above apply also in minor.

Figure 5 :
Figure 5: Ascending scale with minor third

Example 3 :
Gesangleiter §. 1, p. 6 Example 4: Gesangleiter §. 2, p. 6 Example 5: Ascending Gesangleiter §. 3, p. 7While it seems implied that the pitches in the top voice are harmonized by the triad to which each pitch belongs, two pitches, G and C, which both are part of the triads on C and G and C and F respectively, are harmonized in the ascending scale with C without explanation. 17Commenting on the resulting leaping root motion in the bass, Riepel sug-17 Since C appears only at the beginning and the end of the scale, it makes sense to harmonize it with C, and a possible reason for not harmonizing G with G would be that since G is preceded by F, which is harmonized by F, harmonizing G with a G would create parallel octaves.
Example 10: Ascending Gesangleiter §. 7, p. 9Example 11: Right Hand Chords for the Ascending Gesangleiter §. 7, p. 9 20 "Auch stelle ich mir vor, daß Terzen außer Anfang und Ende zwischen Gesang und Baß durchaus statt finden, sie seyen zum Gebrauche meinethalben vermittelnd oder unvermittelnd, mittelbaßoder grundbaßmäßig, z.Ex."(Riepel, Baßschlüssel, 8).The fifth below E results in an A minor, the fifth below A in a D minor triad as shown in Example 11.In addition, since the D remains stationary in bass through the ascent from scale degree ➏-➐, the outer voices create a 5-6 motion.While the fifths below scale degrees ➌ and ➏ resulted in root position chords, Riepel harmonizes the octaves below ➌ and ➏ (Example 12) in two different as shown in Example 13:

Example 14 :
Ascending Gesangleiter §. 9, p. 10 However, the unusual resolution of the chordal seventh, ➍ moving stepwise up to ➎, is far from ideal and Riepel presents six resolutions reproduced in Example 15.Example 15: Ascending Gesangleiter §. 9, p. 10 -Resolution of Chordal Seventh Discarding No. 1 and No. 4 because of the outer voices moving into a fifth, Riepel accepts No. 2 where ➍-➎ in the soprano is countered by ➄-➂ in bass; however, he prefers Nos. 3, 5, and 6 where the seventh resolves stepwise down.Examples 16 and 17 demonstrate how ➋ and ➍ and ➌ and ➐ can be harmonized with a 4/2: Example 16: Ascending Gesangleiter §. 10, p. 10 Example 17: Ascending Gesangleiter §. 11, p. 10 Finally, Examples 18 and 19 demonstrate the inclusion of chromaticism: Example 18: Ascending Gesangleiter §. 12, p. 10 Example 19: Ascending Gesangleiter Example §. 13, p. 11 Example 18 consists of two chromatic segments, each having three descending half steps: ➀-➆b ➆-➅ and ➄-# ➃-➃-➂ ending on an F6 and C6 chord respectively.The chromatic ascent in Example 19 clearly moves towards scale degree ➅, but as the progression ends with the arrival of scale degree ➊, C, in the soprano, the harmonic orientation of the chromatic motion leaves a certain ambiguity, as it can be heard as both: ➃-# ➃-➄-# ➄-➅ or b ➅n ➅b ➆n ➆-➇.Examples 20-30 reproduce the examples with which Riepel demonstrates the application of the eleven rules ( §. 3-13) for writing a bass below the ascending Gesangleiter in major.What is striking is that all eleven examples could serve as the first part of a minuet.Consisting of eight measures, which are divided into two four-measure phrases, the first phrase ends on the tonic, and the second on the dominant.While most examples end with a half cadence, two examples, Examples 20 and 26, modulate to the dominant and end with an authentic cadence in the key of the dominant.Example 20: Application of the Ascending Gesangleiter according to §. 3, p. 11 Example 20 uses only root motion to harmonize the melody, mm.5-8 modulate to G, which shifts the root motion from C, F, and G to G, C, and D. ZGMTH 11/2 (2014) | 245 Example 21: Application of the Ascending Gesangleiter according to §. 4, p. 12

Example 22 :
Application of the Ascending Gesangleiter according to §. 5, p. 12 Example 22 contains two extended passages harmonized in parallel thirds (from the last beat of m. 1 to the downbeat of m. 3 and last beat of m. 5 to the last beat of m. 7).

Figure 8 :
Figure 8: Simple Harmonizations of the Descending Gesangleiter, §. 14 and 15a&b -22) how they avoid the Mi contra Fa (➐-➃).Example 35 introduces the Romanesca bass with its characteristic bass motion of a descending fourth followed by an ascending second (➀-➄-➅-➂-➃-➀), provides an effective harmonization of the stepwise descending soprano with root position chords. 26Though unusual, Examples 36 ( §. 18), harmonize the descending scale with a Romanesca starting on A, or scale degree ➅.Riepel argues that the cross-(➐-➃) between mm.2-3 in Example 36 matter less because of the two-measure units created by the sequential bass motion.Example 35: Descending Gesangleiter §. 17, p. 18 Example 36: Descending Gesangleiter §. 18, p. 19 Similar to §. 5 and 6, which focused on harmonizing the ascending scale using thirds and sixth respectively, Examples 37-39 ( §. 19-21), focus on intervallic relationships.Example 37 ( §. 19) moves in parallel 3rds, 38 ( §. 20) in parallel 6ths, and 39 ( §. 21) combines sixths and thirds.Throughout his discussion of intervallic relationships, Riepel highlights how the respective examples address the cross-relation.While the sixth below scale degree ➏ prevents the cross-relation in Examples 38 and 39, Riepel argues that the cross-relation in Example 37 are mitigated by the opening minor third and the two-measure unit.In support of this, he rewrites several of the examples to demonstrate that they can be conceptualized in two-measure groups.Example 41: Descending Gesangleiter §. 23, p. 21 Example 43: Descending Gesangleiter §. 25, p. 21 Finally, Example 44 ( §. 26) appears in the context of examples that demonstrate an application of the descending Gesangleiter.Unlike the other illustrations of the rules for the descending Gesangleiter, Riepel presents Example 44 in an open three-part score (violin, viola, and bass).While Examples 42 and 43 demonstrate ascending and descending scale harmonizations above a tonic pedal, this final example harmonizes a sustained tonic in the soprano.ZGMTH 11/2 (2014) | 253 Example 44: Descending Gesangleiter §. 26, p. 26 Example 46: Application of the Descending Gesangleiter according §. 16, pp.21-22 Examples 47 and 48 both make use of the Romanesca schema, which consists of a descending fourth and ascending second sequence harmonized by root position chords.While the Romanesca usually starts on scale degree ➊, moving ➊-➎-➏-➌-➍-➊, Example 48 begins the pattern on scale degree ➏, moving ➏-➌-➍-➊-➋-➏.In contrast to Example 36 which seemed harmonically ambiguous because it started on A and ended on C, Example 48, both begins and ends with a cadence in the tonic harmony C (with the bass motion ➊-[➏-…-➏]-➍-➎-➊), thus ensuring that the Romanesca does not move out of the key of C. Example 47: Application of the Descending Gesangleiter according §. 17, p. 22 Example 51: Application of the Descending Gesangleiter according §. 22, p. 24 Examples 52 and 53 finally, provide four-part harmonizations of the "good diatonic turn of phrase" (ascending fifth sequences leading into a harmonization of ➏-➎-➍-➌), and of the tonic pedal below an ascending and descending scale.The examples also contain a Prinner and Quiescenza respectively.Example 52: Application of the Descending Gesangleiter according §. 23, p. 25 Example 53: Application of the Descending Gesangleiter according §. 24 & 25, p. 25