TTT - without timbre, interval is meaningless

The graph below demonstrates when two pure sine tone is played, how we perceive the dissonant on each interval. The horizontal axis displays the semitone steps away from the original tone; the vertical axis shows the level of dissonance. This graph demonstrates a very weird situation compared to our normal perception of intervals: the fifth sound exactly the same to octave, sixth, seventh; basically every interval beyond fifth is the same. The peak of the dissonance is the semitone interval which fits our normal perception. Within a semitone, when two sine tone is playing together, the combination tone results in a beating sonority; while the distance is further, the beating becomes faster, and hear two tones.

To explain this phenomenon, the sine tone does not carry any overtone, unlike all other acoustic instruments. The harmonic generates complex interval combinations, for example, the major 2nd interval at the 7th and 8th harmonics, the minor 2nd interval at the 11th and 12th harmonics. When two tones are played with harmonics, the upper harmonic partials with finer steps (smaller than four semitones) crash with each other, generating different levels of dissonance, resulting in the interval that we normally perceive.
The above graph is what we hear in normal circumstances, tone with harmonics. The harmonics not only provide timbre, but also the presence of consonant and dissonance.

Both graphs are from:
The role of timbre in the memorization of microtonal intervals - Scientific Figure on ResearchGate. Available from: https://www.researchgate.net/figure/Roughness-and-ratios-adapted-from-Sethares-1999_fig2_215646531 [accessed 10 Mar, 2022]

 

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