Writing Mountain Music - Heitor Villa-Lobos and the technique of "Millimeterization"

Heitor Villa-Lobos

 It may not have been Brazilian composer Heitor Villa-Lobos' (1887-1959) original invention, but he became most renowned for applying the graphical-compositional technique known as "millimeterization" (or milimetrização in Portuguese), mainly in his piece "New York Sky-Line Melody" and in his Sixth Symphony.

What exactly does this particular method of composing entail? In brief, it transfers the outline of, for example a mountain range or the buildings of a city, from a photograph via a matrix, overlaid onto transparent paper, into musical notation, thus creating a melody which rises and falls with the lines of the mountains (or buildings). 

Villa-Lobos may have put this method into practice while teaching music to young people during the mid-1930s, yet he first demonstrated it by the end of the decade in a short piano piece, Melodia da Montanha ("Melody of the Mountain"), based on a mountain range known as the Serra de Piedade do Belo Horizonte, situated in Minas Gerais, central Brazil. 

In a published print of the piece he includes the matrix used to establish the melodic line on top of the score page. On the left hand side, or vertically, we find the notes of the chromatic scale (using sharps and avoiding flats, for practical reasons); horizontally, the lines of the millimetric grid translate into the duration of each note. The composer decides on the curved line (i.e. the outline of the object) where the main points are located, thus being able to determine the exact notes and rhythms. The last step - and the actual creative process - is to harmonise the established melody, to add further voices and to transform it into an actual musical piece.

Melodia da Montanha by Villa-Lobos

Villa-Lobos' best known example of the millimeterization method is his - adequately named - "New York Sky-Line Melody", in its piano version from 1939 which he also orchestrated shortly after. As indicated in the title, the shapes of the skyscrapers and other buildings (including bridges) had been transformed, using a similar matrix, into several overlapping melodic lines, which the composer then harmonised and to which he added underlying rhythmic patterns. By doing so, he created much more of a work of art, albeit equally brief, as in the former example of a mere scholarly demonstration¹. 

The "New York Sky-Line Melody" and its possible derivation.

In a far more complex context, and expanding the technique into symphonic dimensions, Heitor Villa-Lobos' Symphony No. 6 from 1944 - again with the adequate title Sobre a Linha das Montanhas do Brasil ("On the Outline of the Mountains of Brazil") - incorporates a vast mountain range, the Serra dos Órgãos (literally: "Mountain range of the Organs"), a short drive away from Rio de Janeiro. Here he uses different viewpoints of the mountains in various photographs, thereby increasing the thematic material, which is mainly used in the second movement (Lento - Adagio) of this symphony². 

The Serra dos Órgãos and Villa-Lobos' realisations thereof ³.

The so derived themes are then subjected to various processes of symphonic development, until a homogenous full-scale work of both beauty and form has been composed, making this not only one of Villa-Lobos' most interesting and fascinating symphonies, but also one of his most accomplished pieces. 

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Having analysed the principles established by Heitor Villa-Lobos, we should now be in a position where we can put the technique of millimeterization into practice, by following these few steps:

1. Take a photograph of a mountain; we have chosen Ingleborough (one of the Yorkshire Three Peaks), due to its distinguishable outline.

2. Apply a grid with, vertically, the pitches of the chromatic scale, and horizontally, the beats and sub-beats of the bars. Identify the main points of the mountain's curve within the grid, here marked as red dots.

(We have cheated slightly, by "doubling" the height of the mountain, to allow for a larger section of the chromatic scale to be incorporated into our melody⁴.)

3. Transfer the thus identified main points into a musical stave, hereby allocating the appropriate pitches and rhythms. The finished melodic line may look somehow like this:

The red line following the melodic curve should bear, at least, some resemblance to the photograph we took of Ingleborough mountain.

4. Now we can use our creative spirit and incorporate our new "mountain" melody into any form of composition, for example as the beginning of a piano sonata:

... or as a fugato for wind trio:

Certainly, there are limitations to composing by use of the millimeterization technique only, just as there were in dodecaphony or serialism - due to the often more or less rounded shapes of mountains the resulting melody will progress mainly in chromatic steps, with the odd larger intervals being interspersed. But it shows credit to a composer's talent and imagination, being able to create from a rather limited outset such beautiful and original pieces as Heitor Villa-Lobos did with his "New York Sky-Line Melody" and his Sixth Symphony.

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¹ FELICISSIMO, Rodrigo. O processo de criação musical de Heitor Villa-Lobos desenvolvido na peça New York Sky-Line Melody. ANAIS DO III SIMPOM 2014 - SIMPÓSIO BRASILEIRO DE PÓS-GRADUANDOS EM MÚSICA

² FELICISSIMO, Rodrigo; JARDIM, Gilmar Roberto. Interface entre os processos criativos de Paul Klee e H. Villa-Lobos: gráficos para gravar as Melodias das Montanhas. Opus, Porto Alegre, v. 9, n. 1, p. 47-70, jun. 2013. 

Photos courtesy of Museo Villa-Lobos, Rio de Janeiro

³ The handwritten melody at the bottom of the last picture reads as follows:

⁴ In fairness, the mountains in and around Rio de Janeiro seem to be much steeper than our English hillsides, therefore Villa-Lobos did not have to alter the outline of his photographs.