freshman sums

"Freshman sums" are the results of an arithmetical process (also called "mediant averaging" ) popularized by Ervin Wilson, who also coined the term.

The freshman sum of two fractions is the sum of their numerators divided by the sum of their denominators.

For example, the freshman sum of 5/4 and 4/3 is 9/7. The operation is briefly described also in Lloyd and Boyle (1978).

[from John Chalmers, Divisions of the Tetrachord]

---

(to download a zip file of the entire Dictionary, click here)

For many more diagrams and explanations of historical tunings, see my book. If you don't understand my theory or the terms I've used, start here

I welcome feedback about this webpage: corrections, improvements, good links. Let me know if you don't understand something. return to the Microtonal Dictionary index return to my home page return to the Sonic Arts home page