The Rule of the Octave

MAIN SOURCES:

• Francesco Bianciardi, Breve Regola per imparare a sonare sopra il Basso (Siena, 1607) [link].

• Francesco Gasparini, L´Armonico Pratico al cimbalo (Venice, 1708), p.51 [link]

• François Campion, Traité d´Accompagnement et de composition selon la règle des octaves de Musique (Paris, 1716) [link].

• Jean-Philippe Rameau, Traité de l'harmonie réduite à ses principes naturels (Paris, 1722) [link]

• Johann David Heinichen, Der General-Bass in der Composition (Dresden, 1728) [link]

SELECTED SECONDARY SOURCES:

• Thomas Christensen, “The Règle de l’Octave in Thorough-Bass Theory and Practice,” Acta Musicologica 64 (1992) [link]

• Ludwig Holtmeier, “Heinichen, Rameau, and the Italian Thoroughbass Tradition: Concepts of Tonality and Chord in the Rule of the Octave,” Journal of Music Theory 51/1 (2007) [link]

FOOTNOTES:

1. [02:04] See, for example, Jean-Philippe Rameau, Traité de l'harmonie réduite à ses principes naturels (Paris: J.B.C. Ballard, 1722) [link]. Following this highly influential work, “tonique” replaced “finale” as the most common French designation for the first scale degree. Compare Jean-François Dandrieu, Principes de l’Acompagnement du Clavecin (Paris: M. Bayard, [1718]) [link], which uses “finale”; and Michel de Saint-Lambert, Nouveau Traité de l´accompagnement du clavecin[...] (Paris: Christophe Ballard, 1707) [link], which uses both terms.

2. [02:38] François Campion, Traite d’accompagnement et de composition selon la regle des octaves de musique (Paris: G. Adam, 1716) [link]. Note that in this initial publication, Campion uses the term regle des octaves (“rule of the octaves”). In his two subsequent publications on the subject, he uses règle de l’octave (“rule of the octave”), which became standard. See Campion, Lettre du Sieur Campion a un philosophe disciple de la règle de l’octave (Paris: 1729) [link]; and Campion, Addition au traité d’accompagnement et de composition par la régle de l’octave (Paris: Ribou, 1730) [link].

3. [02:55] The watershed publication was Rameau’s 1722 Traité de l'harmonie, which introduced the concepts of the basse fondamentale (“fundamental bass”) and renversement des accords (“inversion of chords”). Others have identified earlier, independent precedents for the idea of chordal inversion. See, for example, Joel Lester, “Root-Position and Inverted Triads in Theory Around 1600,” Journal of the American Musicological Society 27/1 (1974): 110-119.

4. [06:41] Interestingly, Johann David Heinichen does not use the ♯6 on the descending sixth degree in his Schemata Modorum (see below). As he explains: “We have omitted the major 6th on the sixth [degree] of the major mode because it adds a new ♯ which[...] does not belong to the mode at all, and only confuses the beginner.” (“Haben wir die 6. maj. über der 6ta modi maj. deswegen gar weggelassen, weil sie ein neuer ♯ angiebet, welches[...] gar nicht zu dem Modo gehört, und einen Anfänger nur confus machet.”) See Heinichen, Der General-Bass in der Composition (Dresden: Heinichen, 1728), p. 765 [link]. See also Ludwig Holtmeier, “Heinichen, Rameau, and the Italian Thoroughbass Tradition: Concepts of Tonality and Chord in the Rule of the Octave,” Journal of Music Theory 51/1 (2007) [link], p. 29.

5. [07:50] We described and demonstrated acciacature on our episodes “Italian Basso Continuo 1650-1700” and “Tutorial: Acciaccature & Mordenti according to Francesco Gasparini”.

6. [08:00] Heinichen (1728), for example, wrote that, “This fourth is called the quarta irregularis or la quarta irregolare because it remains without resolution. And here it takes the same freedom as that of the sustained, lying septima in transitu of the bass, in spite of the fact that both[... ordinarily] are resolving dissonances in and of themselves” (p. 151). (“Es wird diese 4te sonst 4ta irregularis oder la Quarta irregolare genennet, weil sie ohne Resolution bleibt. Und bedienet sie sich hier eben der Freyheit, wie etwan die liegenbleibende 7ma in transitu des Basses thut, ungeachtet beyde[...] an und vor sich selbst resolvirende Dissonantien seynd[...].”) Georg Muffat called this same fourth the quarta italica, the welsche Quart, and the irregular Quart; Muffat, Regulae Concentum Partiturae (ms., 1699), p. 16 [link]. Joseph Riepel disliked these contrapuntally questionable fourths, calling them türkische Quarte (“Turkish fourths”) because they reminded him of music he had once heard in Banja Luka; Riepel, Gründliche Erklärung der Tonordnung (Frankfurt: 1757), p. 39 [link]. Note additionally that because of the special contrapuntal status of the fourth, nearly all theorists and composers treated the third of the chord as a free consonance (and not as a dissonant terza syncopata). The third was therefore not required to resolve by descending step, as many modern theorists claim. See Holtmeier, pp. 36-37, 39.

7. [10:12] In addition, the descending sixth degree often includes the fourth, which in this case is augmented. Like other dissonant forths we have looked at, this augmented fourth cannot be explained according to traditional rules of counterpoint, but may be rationalized in other ways, for example as an acciaccatura.

8. [10:17] In Renaissance terms, the distinction between the half cadence of the descending sixth degree in major VS minor is the same as the distinction between a “hard cadence” - where the tenorizans descends a whole step and cantizans ascends a half step, and a “soft/mi cadence” - where the tenorizans descends a half step and the cantizans ascends a whole step. See our episode “Cadences in the 16th and 17th centuries” [link].

9. [14:44] Campion (1716), p. 7. “There is a very particular way of making these octaves on the Theorbo & on the Guitar, which is the invention of the late M. de Maltot, my Predecessor in the Royal Academy of Musique. I received it from him as the greatest proof of his friendship. He made this instrument very practical in a short time[...] and I do not know that he shared this secret with others than me, who are able to teach it.” (“Il y a une manière toute particulière de faire ces octaves sur le Théorbe & sur la Guitare, qui est de l'invention de seu M. de Maltot mon Predecesseur en l'Academie Royale de Musique. Je l’ay receu de lui comme le plus grand témoignage de son amitié. Il a rendu cet instrument très praticable en peu de temps[...] & je ne sçache pas qu'il ait fait part de ce secret a d'autres qu'a moi, en état de l’ensieigner.”) On the Maltot story, see also Thomas Christensen, “The Règle de l’Octave in Thorough-Bass Theory and Practice,” Acta Musicologica 64 (1992) [link]: p. 96; and Holtmeier, p. 14.

10. [16:43] Agostino Agazzari, Del Sonare sopra'l basso con tutti li stromenti (Siana, 1607), p. 4: “But to consider the heart of the matter, I conclude that one cannot give a fixed rule for playing pieces without any signs.” (“Ma per venir'all'atto, conchiudo che non si può dar determinata regola di suonar l'opere, dove non sono segni alcuni.”) For more on Bianciardi and Agazzari, see Elam Rotem, ‘Early Basso Continuo Practice: Implicit Evidence in the Music of Emilio de' Cavalieri’ (Würzburg University), pp. 40-56 [link].

11. [16:52] See for example: Anonymous (ca. 1670-90), Regole di canto figurato, contrappunto, d'accompagnare (MS Bologna E25) [link]. See also the episode that we dedicated to this treatise [link]. Mention must also be made of Antonio Filippo Bruschi’s Regole per il contrapunto, e per l’accompagnatura del Basso Continuo (Luca: Venturini, 1711) [link], pp. 36-37. Bruschi presents “Consonanze per le 8. Corde del Tuono” and “Regolamento Per il Tuono Minore”, which resemble the rule of the octave. For discussion, see Johannes Menke, Kontrapunkt II: Die Musik des Barock (Laaber: Laaber-Verlag, 2017), pp. 99-105.

12. [17:58] ”[...]mi nasce nell' Idea un ripiego, che senza tante confusioni potrà il mio ingegnoso Suonatore venir in chiaro di ciò, che appartiene al ben modulare ogno Tono con i suoi giusti accompagnamento.” Francesco Gasparini, L´Armonico Pratico al cimbalo (Venice, 1708), p.51 [link].

13. [18:24] Not having a term for the “leading tone”, Gasparini describes it as the note that is the "major accidental which is used at cadences": the major 3rd over the fifth degree, and the major 6th over the second degree. Gasparini, p.52.

14. [19:20] Jean-Philippe Rameau (1722), pp. 212, 384-387.

15. [19:37] Mercure de France (June 1730), p. 1337. Rameau says that he was introduced to the rule of the octave in 1702 by a certain Monsieur Lacroix. See Christensen, p. 100.

16. [19:47] Heinichen (1728), pp. 746ff. According to Heinichen, the somewhat simpler harmonizations of his Schemata Modorum make it “much more universal and applicable” (“viel mehr universaler und applicabler”) than Rameau and Gasparini’s models, especially to basses that do not always move by step: “On the other hand, the schemes of both other authors indicate many special signatures that are only valid as long as the notes march nicely along in the order in which they were written.” (“Da hingegen di Schemata beyder Autorum viel speciale Signaturen angeben, die nicht länger gelten, als die Noten sein in der Ordnung marchiren, wie sie hingeschrieben worden.”) Heinichen (1728), p. 746. See Holtmeier, p. 30.

17. [19:58] Heinichen (1728), p. 763. Heinichen wrote that he developed his Schemata in 1710 and is presented in his earlier treatise Neu erfundene und Gründliche Anweisung zu vollkommener Erlernung des General-Basses (Hamburg: Benjamin Schillers, 1711), pp. 201-204. However, it should be noted that Heinichen’s earlier model differs somewhat from his 1728 Schemata, the older version being more distant still from “the rule of the octave” per se. See Holtmeier, p. 27.

18. [20:07] Heinichen (1728), pp. 765-766. “Let us ask, therefore, how it comes to pass that three subjects of different nations (who knows, whether there may be more still) could fall on the same principle on this matter. So follows the well-grounded answer that it comes from the fact that the thing is so natural, so well-founded, and so practicable that no author could ever arrive at another principle if he wants to teach an accompanist or a beginning composer the natural Ambitum Modorum, or wants to give rules for Generalbass without figures.” (“Fragen wir also, woher es komme, das drei Subjecta von unterschiedlichen Nationen (wer weiß, finden sich derer noch merer) in dieser Materie auff so gar gleiche principia fallen. So solget die wohlgegründete Antwort, das es eben daher komme, weil die Sache so naturmäsig, so gegründet, und von sich selbst so gangbar ist, dass nimmermehr kein Autor auf andere Principia fallen kan, wer einen Accompagnisten oder anfangenden Componisten den natürlichen Ambitum Modorum beybringen, oder Regeln vom Generalbass ohne signaturen geben will.”)

19. [21:14] Other names of the rule of the octave include “Ambitus Modi”, “Sitze der Accorden”, “harmonical scale”, “canone armonico”, “modulazione dell'ottava”, “regola per la scala”, “scala di ottava”, and simply “scala”. The term “regola dell’ottava” does not appear in Italian sources until around the beginning of the nineteenth century. See Giorgio Sanguinetti, The Art of Partimento (Oxford: Oxford University Press: 2012), pp. 113, 365; and Christensen, p. 91.

20. [21:16] See Christensen, 100-101.

21. [21:23] Four conservatories established in Naples in the sixteenth century—Santa Maria di Loreto, I Poveri di Gesù Cristo, Sant’Onofrio a Capuana, and Santa Maria della Pietà dei Turchini—became renowned in the eighteenth-century for producing many celebrated composers. A central element of instruction at these institutions were partimenti: figured or unfigured musical exercises written on a single staff, using predominately the bass clef (but also commonly changing clefs). The many surviving partimento collections are stylistically diverse, and could be realized at the keyboard as basso continuo exercises, as florid galant-style movements, and as elaborate fugues (additionally, they could serve as written counterpoint exercises known as disposizione). See especially Sanguinetti, The Art of Partimento. The four sources shown are: Giovanni Paisiello, Regole per bene accompagnare il partimento[...] (ms., I-Nc 18-3-3/18); Carlo Cotumacci, Partimenti Del M.^o Carlo Cotumacci (ms., I-Nc 34-2-2); Fedele Fenaroli, Partimenti ossia basso numerato (Milan: Forni [c.1850?]); Giacomo Tritto, Partimenti e Regole generali (Milan: Artaria, [1816?]).

22. [21:50] Denis Delair, Nouveau traite' d 'accompagnement pour le théorbe, et le clavessin (Paris: 1723) [note that this comment is found in the revised 1723 (1724?) edition and not the original of 1690]. See Christensen, p. 105.

23. [22:06] Francesco Geminiani, The art of accompaniment, or a new and well digested method to learn to perform the thorough bass on the harpsichord (London: 1756), preface.

24. [22:45] Joseph Riepel, Sechstes Capitel: Vom Contrapunkt (ms., Regensburg, 1786); in Joseph Riepel: Sämtliche Schriften zur Musiktheorie, ed. Thomas Emmerig, Vienna: Böhlau, 1996, p. 580). “Mir deucht, es sey diese harmonische Leiter unserm Gehör von Anbeginn der Welt eingepflanzt.” See Holtmeier, p. 14.

25. François Campion (1729), i.

Credits:

Created by Elam Rotem & Sean Curtice, April 2021.

Special thanks to Iason Marmaras, Johannes Menke, Felix Diergarten, David Erzberger, Leonard Schick, and Anne Smith.