Occupation: Music and Math
Author: Boris Andonov
Email: andonov@nearequaltemperament.com
Initial release: 16 August 2021
Latest update: 16 August 2021

Small Scale Stack

Description

Another approach to reduce the amount of steps in the Fast Inverse Stack is to combine a small set of ratios. 3/2 and 5/4 requires at least 9 step to reach a perfect fourth. Stacking 9/8 (3/2 * 2) and 15/16 (3/2 * 5/8) reduces the amount of steps twice.

Following picture shows how could be done for a single tone. For the rest of them, same logic applies as Forward Stack or Fast Inverse Stack.