With this transformation [4], I generated two chords: one built using the series from the planet B to H, and the second from the planet H to B:


 

 






I used this transformation as the main harmonic material to compose the Overture and the four Mélodrame sections[5] of the opera The Flowering Desert. These showcase the point of view of the Measurer, a character that represents a scientist witnessing the discovery of TRAPPIST-1. With this decision, I wanted to embed an important feature of the system for the scientific community (its harmonicity) into the character and the sections that represent them and the process of the discovery.

 

One of the most striking features of the planetary system TRAPPIST-1 is its harmonicity. The orbital periods of the seven planets are locked in a chain of resonances (Luger et al., 2017). This means that the relation between the orbits of neighbouring planets can be expressed as simple ratios. For example, while planet H rotates twice around the star, planet G rotates three times. These ratios can be expressed musically as intervals as follows:

Figure 1

Table 1

Orbital period ratios

Example #1 

Use of harmonic material generated with orbital period ratios (marked in blue in the score). Chord B-H (transposed):

Example #2 

Use of harmonic material generated with orbital period ratios (marked in blue in the score). Chord H-B (transposed):

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