In the 17th and 18th centuries, counterpoint and learned polyphony were believed to be earthly manifestations of a heavenly order. Going back to the days of Ptolemy and earlier to Pythagoras, there was a belief in the West of a divine or cosmic music. Pythagoras noted that the movements of the celestial bodies in mathematical relation to one another produced various pure intervals. By Ptolemy’s time, the belief was that the planetary bodies slid along the rims of infinitely fine crystalline spheres creating a vibration that produced the purest of tones somewhat similar to a glass harmonica except these crystalline spheres were nestled inside one another something like a Chinese puzzlebox. The idea of a heavenly music evolved by perhaps a couple of centuries prior to Bach’s birth into an angelic choir that sang in the sweetest of voices in the sweetest of melodies and the sweetest of harmonies which earthly musicians and composers tried to approximate. Hence the importance of producing the highest artistic musical expression possible and, by that time, counterpoint and learned polyphony were considered the highest of the musical expressions that employed the hidden secrets of harmony. Even the more scientifically inclined astronomers as Johannes Kepler (1571-1630) believed fervently in a celestial musical order.
Most people today are unaware just what an influence the idea of a heavenly music had on the baroque composers including Bach and which informs classical music to the present day. One of the most important works in this regard is Antonio Vivaldi’s
L’Estro Armonico from 1711. Christopher Hogwood states that the title defies translation. I have seen it translated as The Harmonic Fancy, The Musical Flush and The Harmonic Inspiration. Perhaps the lattermost translation is the best. But what is the inspiration? The orchestra is being inspired by what? Why, the heavenly music of the angels, of course. Vivaldi, a Venetian priest, worked with orphaned girls in the Conservatorio dell’Ospedale della Pietà. A great many of his pieces were first performed in public by his girls. Charles de Brosses wrote, upon seeing a performance: “They are brought up at the expense of the State, and they are trained only to excel in music. They sing like angels and play the violin, the flute, the organ, the oboe, the cello, the bassoon…” His praise that the girls sing like angels refers to the heavenly music. Today, we take it as simple praise perhaps a bit overblown but, in those days, such praise had a specific meaning. Paintings of angels playing instruments became a very popular theme during the Renaissance. Our modern idea of haloed angels playing harps descends from those paintings.
CD cover Pieter Dirksen’s version of the Goldberg Variations on the Etcetera label shows the heavenly choir and orchestra playing the Secrets of Harmony inherent in this masterpiece of counterpoint.
L’Estro Armonico especially Opus 3 was a huge inspiration on baroque music and defined the structure of the concerto. Bach was greatly influenced by it and structured his Brandenburg Concertos on this great work of Vivaldi’s. We know of six keyboard transcriptions Bach had made from Opus 3. We discussed Bach’s predilection for the number 6 and how many of his pieces contained six concertos or suites; Vivaldi had a predilection for the number 12. Opus 3 consists of 12 concertos as does Opus 7, Opus 8 and Opus 9. Opus 1 consists of 12 trio sonatas.
Vivaldi’s predilection for the number 12 may be because there are 12 months in a year, 12 numbers on a clockface, 12 major and 12 minor scales. The number 12 also appears in the bible a great many times—12 tribes of Israel, 12 disciples of Jesus, Jesus found preaching in a temple at age 12, 12 gates to the celestial city, etc. It is also a number of unity since the numeral 12 is composed 1 and 2 where 1 symbolizes singularity and 2 symbolizes plurality. Pythagoreanism and Neoplatonism were also popular among the educated classes of Europe and so Vivaldi was almost certainly familiar with the concept that if one bisects a square with an area of 1 square unit diagonally, a square with an area of 2 square units is formed from that diagonal and each side is the square root of two (√2) units in length. So √2 was the intermediary between the heaven (1) and earth (2) or God and man in one—the Logos—and this was Christ—the Logos Made Flesh, according to John. Since √2 was irrational and went on forever, it demonstrates the infinity and eternity of heaven and the divine nature of Christ. It was the link between harmony and proportion. Vivaldi being a priest probably knew this and so perhaps chose 12 to symbolize this. This kind of knowledge would be found among the esoteric principles of counterpoint and polyphony. Exactly why Vivaldi relied so much on 12 may never be fully known but we must conclude it held a mystical and/or spiritual significance to him.
One of Bach’s fellow members of the Society of Musical Sciences, Georg Venzky, put it thus: “God is a harmonic being. All harmony originates from his wise order and organization. […] Where there is no conformity, there is also no order, no beauty, and no perfection. For beauty and perfection consists in the conformity of diversity.” Exactly how much stock Bach put in all this is certainly open to question. He was a model Lutheran but also musically a pragmatist. His top priority was that the music had to sound good and if the secrets of harmony helped him to achieve that then great. If not, then Bach wasn’t going to waste a second trying to incorporate them.
The frontispiece from Athanasius Kircher’s
Musurgia Universalis (1650), a book known to every musical theoretician of the 17th and 18th centuries, showing the heavens resounding to counterpoint. Bach was definitely familiar with it. Double counterpoint and canon were seen as a manifestation of the “order of God”—an actual manifestation and not simply as metaphor. Perpetual canon was seen as a symbol of God’s creation of the universe and the eternal harmonies of heaven. Heinrich Bokemeyer, a contemporary of Bach, wrote of the contrapuntist: “There he finds the beginning and end bound together and has discovered the perpetual canon in order to remind himself of the eternal unending origins, as well as the harmony, of all eternity as a rule of nature of the most perfect example of his work.” These beliefs of the secrets of harmony spoken by Bokemeyer were passed to him from his teacher, Georg Osterreich, who learned from his teacher, Johann Thiele, who learned it from his teacher, Dietrich Buxtehude. Every composer made use of it: Heinrich Schutz, Johann Pachelbel (who gave Bach his first keyboard lessons), Johann Froberger, Handel, Praetorius, Telemann, etc. This esoteric belief system permeated the musical intelligentsia of that day.
Exactly where Bach learned the Secrets is not precisely known but he was close to Johann Gottfried Walther (they were second cousins, after all) who corresponded at length with Bokemeyer over the Secrets of Harmony. Bach also studied briefly under Buxtehude when he went to Lübeck to see the organist play and then stayed for three months instead returning to his job in Arnstadt as he had promised his supervisors (In fact, Handel and Bach were offered studies with Buxtehude at St. Mary’s in Lübeck except each was told he would have to marry Buxtehude’s daughter as part of the deal which both declined and promptly fled the city). So, Bach had ample opportunity to learn the Secrets and apply them.