The Elements of Harmony > Intervals (basic) > Consonance > Proportional Increase

                                            
Non-linear Frequency Increments

Adjacent notes in a scale are characterized by non-linear increases in frequency. In passing from one note to the next, we increase the initial note's frequency by a fixed proportion of that frequency. We do not simply add or subtract a fixed number to the starting frequency to obtain the next. So the higher the frequency of the starting note, the larger the increase in frequency to get to the adjacent note. Consequently, a specific proportional increase (or decrease) in frequency will preserve the privileged relationship of consonance between any two notes, irrespective of what frequency the starting note has. See Figure 2 in Intervals (in-depth).

For example, if we start with a note C and then empirically identify a higher note G which is consonant with the note C, and then measure that the note G has 3/2 the frequency of the note C, we have also identified what proportion any frequency must have with respect to the lower frequency in order to produce the same degree of consonance. So, for example, in order to obtain this consonance between a note D and a note A above it, the proportion, or ratio, of A to D must again be 3/2 or 3:2.

However, the numeric value of the frequency increment in moving from C to G will be different from the numeric value of the frequency increment in moving from D to A, because consonance depends on proportional relationships, and not fixed, linear relationships.