FILMBOARD: Microtonal Study #1 - 18ifdo — Inverse-Arithmetic Frequency Division of the Octave

FILMBOARD: Microtonal Study #1 18ifdo, or the inverse-arithmetic frequency division of the octave, is an 18-tone tuning built from the ratios: 1/1, 36/35, 36/34, 36/33, 36/32, 36/31, 36/30, 36/29, 36/28, 36/27, 36/26, 36/25, 36/24, 36/23, 36/22, 36/21, 36/20, 36/19, 36/18. Reduced to simplest ratios, the same scale is: 1/1, 36/35, 18/17, 12/11, 9/8, 36/31, 6/5, 36/29, 9/7, 4/3, 18/13, 36/25, 3/2, 36/23, 18/11, 12/7, 9/5, 36/19, 2/1. Instead of dividing the octave into equal logarithmic steps, the pitches come from an inverse-arithmetic progression. The result is an uneven 18-note scale containing a number of simple harmonic relationships, including 9/8, 6/5, 9/7, 4/3, 3/2, 12/7 and 9/5. 18ifdo was chosen as the Monthly Tuning for September 2026 by the Monthly Tunings group of the Xenharmonic Alliance. I made this short piece as an exploration of the tuning and the kinds of harmonic and melodic shapes that emerge from it. FILMBOARD is a series of short audiovisual microtonal studies, with each video focused on a different tuning system. Noah Dean Jordan @noahjordan.music noahjordan.ca