Make a timbre fits 15-ET
This blog article is a snippet of my article, for more info, please visit: https://docs.google.com/document/d/1LGTcZN83AEFCCjSqfKJOCeIrQKVmdZ8BEUwbBSYOec4/edit?usp=sharing The partial pattern of most strings and wind instruments is in the pattern of harmonic series. In the harmonic series, the 2nd and 3rd partials combine in the ratio of a perfect fifth, 3/2. Stacking the fifth 12 times roughly returns to the original tone in octaves. The 12-ET is the tool to solve the Pythagorean comma. That is the background of why 12-ET fits normal instruments. The challenge right now is I need to build a partial pattern that fit 15-ET. Comparing 12-ET and 15-ET, intervals that line up with each other are major 3rd and octave. Current instruments with harmonic series partials sound really out of tune. The partials have to be rebuilt artificially. The process of building the partial pattern First, calculate all the ratios of 15-ET. 15-ET 1 1.0473 1.0968 1.1487 1.2030 1.2599 1.3195 1.3819 1.4473 1.5