There are 5,040 possible variations for each of the 462 heptatonic scales (or seven-note chords) possible in 12-tone music. The Harken Music system proves this mathematically using combinatorics to calculate every combination and permutation possible in 12-tone equal temperament. With the Harken Music system we can calculate there are 5,544 heptatonic combinations in all, with 2,328,480 permutations.
Can you play 5,040 variations of a Dorian scale? The Harken can. Right now. Before your eyes and ears. Watch the video. Check out the demo. Use the code. It’s all free and open-source.
For a detailed explanation of the high-school-level math used in creating the Harken Music system, please read, “The Future of Music is Math” by Mitch Kahle.
See also: “Harken Music: A New Mathematical Framework for 12-Tone Harmony”, by ChatGPT 4o, and for an even deeper dive into the mathematics, read Factorials and Fractions “Navigating the 12-tone matrix,” by Mitch Kahle.
Try the free open-source demo* at harkenmusic.com. You can choose any combination size (from 1 to 12 notes) from the pull-down menu; then select any particular combination from the numbered list, to see and hear all permutations, reflections (inversions), and rotations (transpositions).
*Note: a desktop or laptop computer and current web browser (Chrome, Safari, etc.) are required for using the demo; however there are no downloads, sign-up, or subscription requirements.
