This piece, "Toccata of the Hexaflora, No. 1024," is based on the YouTube video "Fukashigi no Kazoekata (How to Count the Incomprehensible)" from the National Museum of Emerging Science and Innovation (Miraikan), which I previously supervised: https://www.youtube.com/watch?v=Q4gTV...

Considering major and minor triads and their inversions as the most basic chords combining three pitches, for instance, there are six possibilities for chords with C as the root (e.g., CEG, CEA, CEsG, CEsAs, CFAs, CFA). Thus, a total of 72 distinct triads can be formed within the 12-tone equal temperament system. Here, if a chord can be transformed into another by shifting only one of its three pitches, these chords are defined as adjacent. When the adjacency relationships among these 72 chords are diagrammed, they form a beautiful geometric pattern resembling a hexagonal snow crystal (also known as "Rokka" or "Hexaflora").

Within this diagram, when the all-white-key chords 049 (CEA) and 047 (CEG) are designated as the start and goal respectively, there are 15,702,821,337 possible paths (sequences of chords) that do not revisit any chord. Furthermore, upon investigating whether paths exist that traverse all 72 chords exactly once, it was found that precisely 20,464 such paths exist. (These calculations require state-of-the-art algorithmic technology.) One of these, the 1024th solution, was used to compose "Toccata of the Hexaflora, No. 1024." We hope you can sense the dedication of "Fukashigi Oneesan" (Ms. Incomprehensible), who tirelessly counted these paths.