Construction of the Just Diatonic Scale

The Just Scales
The Just Scale is built to maximise the number of consonant intervals that have exact frequency ratios. The major triad, ratios 4/5/6 is the starting place. One of the features that makes the Just Scale so attractive in the West is that most of Western harmony is built around this triad.

Step 1: Form a major triad:

Step 2: Form major triads from the top and bottom notes of this triad:

Step 3: Bring the ratios from step 2 within the range of a single octave:

Step 4: Arrange notes in ascending order:

This is known as the Just diatonic scale. Examining the intervals between each step,

There are two whole tones:
9/8 = 1.125 (called the major tone), and
10/9 = 1.1' (called the minor tone).

The semitone has a ratio of 16/15 = 1.06'.
The minor third between notes 2 and 4, (4/3)/(9/8) = 32/27 = 1.'185' , does not have the desired ratio of 6/5 = 1.2.

The perfect 5th between notes 2 and 6, (10/6)/(9/8) = 40/27 = 1.'481' does not have the desired ratio 3/2 = 1.5.