Symmetrical Design No. 6 presents an eight-element symmetry by means of tetrachords varying in the musical dimensions of high-low, near-far, and fat-thin. It moves from tetrachord to tetrachord by twelve-note “promenades” sharing pitches with both neighbouring elements. A three-tetrachord progression forms a brief coda. In this version, No. 6b, the tetrachords lie in a 31-tone equal-tempered scale, and the sounds are those of vintage synthesizers by Arp, Moog, Sequential Circuits, Oberheim, and Roland. These sounds are reproduced by Kontakt, Native Instruments’ software sampler, using their Retro Machines Mk2 library. Multiplication of the unit quaternions {±1, ±i, ±j, ±k} is a canonical realization of the underlying symmetry.
! 31 tET 31 ! 38.70968 77.41935 116.12903 154.83871 193.54839 232.25806 270.96774 309.67742 348.38710 387.09677 425.80645 464.51613 503.22581 541.93548 580.64516 619.35484 658.06452 696.77419 735.48387 774.19355 812.90323 851.61290 890.32258 929.03226 967.74194 1006.45161 1045.16129 1083.87097 1122.58065 1161.29032 2/1
John L. Baker writes mildly experimental music, mostly in small forms loosely based on classical models. He lives in Vancouver, Canada, where his music has been performed by outstanding artists such as Ariel Barnes, Iman Habibi, Heidi Krutzen, the Microcosmos string quartet, Standing Wave, and the Turning Point ensemble. Much of his music is organized around four-member pitch-class sets (tetrachords) characterized by pitch-symmetry. An example in the 31-tone context is {E-, Gb, Ab, B}, comprising two 7-step intervals around a 5-step one; this occurs in “Symmetrical Design No. 6b”. His electronic works have been included in a number of VoxNovus (New York) presentations. A version of this piece has been performed on the Fokker 31-tone organ in Amsterdam by Ere Lievonen. He began formal training in music somewhat late in life, studying for a few years at Washington State University under Loran Olsen and Charles Argersinger. His earlier post-graduate study was primarily in computer science, culminating in a Ph.D.