Monday, October 14, 2019

Some hitherto unkown genealogical trees of music


In last week's post, I discussed Petter Hellström's recent doctoral thesis: Trees of Knowledge: Science and the Shape of Genealogy. In this thesis he discusses three "genealogical tees" in detail. Augustin Augier’s tree of plant families and Félix Gallet’s family tree of languages have already been covered in this blog (you can look them up using the Search box, to the right), but Henri Montan Berton’s family tree of chords has not.

Indeed, the historical literature at large has pretty much ignored the idea of a genealogical tree being associated with music. Nevertheless, the tree itself is explicitly labeled a Genealogical Tree of Chords. This tree, and its predecessor by François Guillaume Vial, thus deserve examination.


Henri Montan Berton (1767–1844) is well known within the history of music; and his tree was published as an independent broadsheet as two (almost identical) editions in c. 1807 and 1815. It seems to have been produced as a teaching tool, as indeed were also the trees of Augier and Gallet. As Petter Hellström notes, for these authors "genealogy did not necessarily involve chronology or change ... the introduction of family trees into secular knowledge production had more to do with the needs of information management, visualisation and communication".

Berton himself states (translated from the French):
In composing the Genealogical Tree, one has has had the intention to present to the eye, at a single glance, the reunion of the great family of Chords, and to demonstrate to the eye that there is only one Primordial [Chord], and that it is the source of all Harmonies.
At the base of the tree is a fundamental bass note along with its 12th and 17th major — this was the harmonic series in 18th century music theory. From here the tree produces 8 branches above, each labeled (at the bottom) with a musical chord, and with another 20 chords labeled further up the branches (all highlighted by arrows at the left). The main trunk (denoted A) is labeled Perfect or Constant Chord. The eight branches are intended to show the relationships between "8 fundamental chords [bottom arrow] and 20 inverted chords [the upper arrows]".

The tree thus displays the harmonic relationships among the chords, rather than any sort of chronological development. It was devised as an aid to learning the fundamentals of music composition.

Berton was not the first to use this idea within music theory. Four decades earlier, in 1766, François Guillaume Vial (1725–?) had produced another broadsheet, this time labeled Genealogical Tree of Harmony.


Like Berton's tree, this is not about chronology, but is about "family relationships" in a different sense. Moreover, in this instance the branching aspect of the tree is abandoned, and the tree foliage is simply festooned with medallions, labeled with chords — it is the different sections of the tree's crown that show relationships, not different branches.

The objective here was to illustrate "the most natural order of harmonic modulation", once again devised as a teaching tool. The two compass roses at the bottom left and right show the circle of fifths (left), guiding horizontal modulation among the chords, and the circle of thirds (right), guiding vertical modulation among the chords.

Vial himself states (translated from the French):
This Genealogical Tree simplifies and allows those who are capable of intonation [to practice] the art of preluding not only on a leading note, but even to change between the most desired modulations of any instrument.
Hellström traces these uses of the "family tree" metaphor in music back to Jean-Philippe Rameau (1683–1764), an influential music theorist. Thus, he concludes that we should:
read the trees of Vial and Berton as graphical codifications of an already established metaphor and manner of thinking about harmony, especially as both authors were informed by Rameau in their understanding of harmony in the first place.
In constructing their respective tree diagrams, Berton and Vial both seized upon an already existing metaphor and made it visible on paper. Their trees are not 'genealogical' in the sense that they charted family history or cross-generational relationships, they are 'genealogical' in the sense that they depict presumably natural, organic relationships, in which every part has its place in the whole, and where every part can be referred back to a common source or root.
These trees do not, therefore, fit into the usual history of genealogical trees, as this blog recognizes them, denoting a chronological history. They, would, however, fir neatly into the post on Relationship trees drawn like real trees.