Pythagorean tuning

The following is another way of making a Pythagorean tuning. It has more steps than Guido’s, described below, but is (hopefully) more intuitive.

A Pythagorean tuning uses only ratios made from the first three numbers: 1, 2, and 3, and their powers: 4 (2x2), 8 (2x2x2), and 9 (3x3).

We will be using the ratios 1:2 (octave), 2:3 (fifth), and 3:4 (fourth).

The open string is G Gamut.
Divide your entire string in half to find G (1:2)
Divide your entire string in thirds to find D (2:3)
Divide your entire string in fourths to find C (3:4)
Starting from D, divide the string in thirds to find a (2:3)
Check by dividing D to the end into fourths, and you should be at G (3:4)
Starting from a, divide your string in thirds to find e (2:3)*
Starting from e, divide your string in thirds to find h (b natural) (2:3)
Starting from C, divide your string in fourths to find F (3:4)
Starting from F, divide your string in fourths to find b (b flat) (3:4)

*To find the notes on other octaves, divide that note to the end in half (to go up), or multiply it by 2 (to go down). For instance, after you have found e from a, you can swing your dividers down twice from e to find the E an octave below.