Tetraktys in Neon, for just-intonation MIDI Piano, Voice and Computer is an audio/visual work set in a 3-limit just-intonation environment. The piece was inspired by the Pythagorean symbol of the Tetraktys – a triangular figure constructed with four rows of dots, as seen at the beginning and end of the work. In short, the Tetraktys held great significance for the Pythagoreans because it symbolizes the connection between the first four whole-numbers and the number 10. The connection is clear when one considers that the sum of 1, 2, 3 and 4 is 10. After 10, there is a sense in which all of the number are mere repetitions of the first ten numbers. The symbol for the number 11 is, after all, a shorthand for 10 + 1 (one in the ten’s place and one in the one’s place). Thus, there is a completeness in the number 10, and it’s relationship to the first four whole-numbers, that the Pythagoreans held to have supreme importance.
Much of my understanding of this number symbolism comes from the book The Theology of Arithmetic by Iamblichus, an important third century Neoplatonist from Syria. In truth, it appears that Iamblichus was not the author of most of this volume, and that he primarily compiled the work from existing sources. Regardless, it is in the spirit of this Pythagorean number symbolism that I have composed the piece.
The importance of the Tetraktys symbol is distilled in a Pythagorean Prayer quoted by the mathematician Tobias Dantzig in the third chapter of his book Number: The Language of Science. I am not yet sure of Dantzig’s source. Nevertheless, I have used it prominently in the second and third sections of the piece. The text is as follows:
Bless us, divine number, thou who generated gods and men!
O holy, holy Tetraktys, thou that containest the root and source of the eternally flowing creation!
For the divine number begins with the profound, pure unity until it comes to the holy four;
Then it begets the mother of all,
The never-tiring holy ten,
The keyholder of all!
This piece shares some aspects with the version of As Pythagoras Enter Into Heaven that was included in the official recording of Ritual no. 1: (Ascension of the Primes). These “aspects” are as aesthetic and extra-musical as they are musical, and this piece represents the continuation of my growing fascination with Pythagorean philosophy.
For those who are curious the ratios used in the piece are: 1/1, 9/8, 32/27, 4/3, 3/2, 16/9, 2/1.