Geometric derivation of 22 srutis
This is a continuation of my earlier post showing the derivation of 22 srutis, as a geometric construction in a log-log plot. This was created using LibreCAD . Figure.1, shows a cycle of pure fourths and fifths. Figure.2, shows a cycle of 53EDO tempered fourths and fifths. The numbers shown are frequency ratios in cents . An octave (2:1) is 1200 cents wide. Standard Western tuning divides this in 12 equal semitones ( 2^(1/12) : 1 ) 100 cents wide. How to read this construction. The X and Y axes are 1200 cents long, and they represent frequency ratios between 1 and 2. zero cents represents the ratio 1:1 1200 cents represents the ratio 2:1 Because of octave equivalence 1:1 and 2:1 refer to the same musical note. We are interested in finding the optimal number of frequency ratios that we can fit inside this space. We introduce a new ratio by adding a fret. If our instrument has two strings tuned an octave apart, each new ratio that we introduce ( say 'a' ), also introduces its ...
