# Computational Technique to Predict Two-Note Dissonance? [duplicate]

Many of us are taught that the "complexity" of the ratio between two frequencies predicts its dissonant qualities. Is there a way to find a numerical value for dissonance? I have created a method, but I don't have the technology to test it.

My method is as follows: Take a = frequency 1, b = frequency 2

Ratio = a/b Dissonance = LCM(a, b) where LCM(x, y) is the least common multiple between two values x and y

This is rather simple, but I cannot find any mention of it online: I suppose it is either wrong or considered a given.

Take a few examples of different intervals' "dissonance":

Unison: 1/1 --> 1 Octave: 2/1 --> 2 Perfect Fifth: 3/2 --> 6 Major Third: 5/4 --> 20 Triple Octave: 8/1 --> 8

As a note, while doing research on the subject, I am attempting to remain in the realm of the non-extensive overtone series, and avoiding delving into synthetic ratios created through equal temperament and other tuning styles.

• You might want to look at William Sethares's work: sethares.engr.wisc.edu/ttss.html. You'll need to decide on a precise and measurable definition of "dissonance" rooted in whatever musical practice you're seeking to explain. Commented Apr 18, 2022 at 10:19