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Is there a way to measure consonance of intervals that are played by pure sine waves? I am looking for a list that shows the order of consonance between intervals of sine waves with no overtones. Also, I am assuming the tuning is in just intonation.

I have seen some posts, but it seems like they often include some of the overtones into the calculation. Some claim that the lower number ratio intervals are more consonant than higher number ratios.

SirPiano
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    A complicating factor: interval ratios *very close* to simple ratios such as 3:2, even if their numbers are absurdly high, will be graded as more consonant than some ratios with lower numbers (e.g. 8:7). For example, the interval ratio corresponding to the equal temperament perfect fifth is approx. 1.498307:1, and it still sounds more consonant than a major second (9:8 or 10:9). – Dekkadeci Mar 04 '19 at 07:04
  • @Dekkadeci Oh, I know I've seen a graph like that, where the closer one gets to certain intervals (like the fifth), the more consonant, like a rounded peak, since 700.1 cents is pretty much just as consonant as 700 cents. – user45266 Mar 04 '19 at 18:10
  • The accepted answer of the duplicate is clearly an answer to this question, as it is specifically about the sense of roughness or dissonance between two sine waves. – Todd Wilcox Mar 05 '19 at 23:16

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The answer could be as simple as 4-1-5-2-6-3-7 ... the intervals with more basic fractions are more consonant to the tonic ... or perhaps this...

Is there a way to measure the consonance or dissonance of a chord?

or perhaps:

https://www.reddit.com/r/musictheory/comments/5tn4p9/what_are_the_intervals_in_order_from_most_to/

Randy Zeitman
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