Note that the tonic triad (C chord) has notes with these relative frequencies: (1/1,5/4,3/2). We can simplify this by restating the fractions in a common denominator: (4/4,5/4,6/4). Note that the relative ratios of these fractions is (4,5,6).

What is interesting about the just tuned scale is that the same relative (4,5,6) ratios are maintained for the subdominant triad (F chord) and dominant triad (G chord). The subdominant triad is (4/3,5/3,6/3) and the dominant triad (12/8,15/8,18/8).

Apparently the (4,5,6) relation is very fundamental.

Note that just tuning is not perfectly consistent. For example, the ratio of the minor third (E,G) is (5,6) but the minor third (D,F) is (27,32). In a sense, these intervals are not really the same. If the other intervals are examined, similar inconsistencies will be found.

This document is ©2003 by Bill Grundmann.