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Why would a musical culture, perhaps on another planet, perceive the interval of 1:3 as equivalent as opposed to 1:2?

Factors on any level are welcome, whether it be a specific culture that has tritave equivalence or many species on that planet have tritave equivalence (seeing as octave equivalence has been demonstrated in animals like rats and monkeys, there might be geographical or atmospheric factors that cause tritave equivalence, as opposed to just biological).

The culture probably uses harmony based on odd harmonics only, i.e. the Bohlen Pierce scale, though suggestions that don't encourage that are welcome.

The planet exists inside the same universe as ours, i.e. physics itself is unchanged.

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    $\begingroup$ Related but not actually useful: Ancient Greeks found perfect fourths harmonious and thirds distasteful, suggesting that ‘harmony’ is cultural. $\endgroup$
    – Joe Bloggs
    Commented Jun 8, 2020 at 10:56
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    $\begingroup$ I think the problem you'll have is not explaining why 1:3 does sound equivalent (An octave+5th sounds very harmonious to me), but explaining why 1:2 does not. I think it would be hard to find a system where 1:2 is distasteful but other numeric ratios are fine. $\endgroup$
    – David258
    Commented Jun 8, 2020 at 11:36
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    $\begingroup$ @JoeBloggs: Perfect fourths are harmonious. (They cannot be not harmonious when fifths are harmonious and octaves are equivalent.) (Octaves, perfect fifths and perfect fourths are the only intervals which sound the same in the tuning used in the antiquity and our post-Renaissance equal temperament tuning.) Ancient Greeks used Pythagorean tuning, and Pythagorean major thirds do indeed sound bad (and are different at various points on the scale, to boot). Basically, their thirds and our thirds are not the same. $\endgroup$
    – AlexP
    Commented Jun 12, 2020 at 15:04
  • $\begingroup$ @AlexP I disagree with your justification for the harmony of perfect fourths. Octave equivalence doesn't imply that the same interval inverted or in different octaves have the same consonance. Subjectively, for example, a perfect 11th (3:8) is more dissonant than a perfect fifth (2:3), since it has higher numbers / least common multiple. Though in terms of counterpoint, the categories of consonance and dissonance would refer to different things, I think. $\endgroup$
    – awe lotta
    Commented Jun 12, 2020 at 17:25
  • $\begingroup$ @AlexP: Fair enough. All I could remember was that Ancient Greek tuning sounded bad to modern ears, and they liked perfect fourths while disliking thirds. I equated the two. $\endgroup$
    – Joe Bloggs
    Commented Jun 12, 2020 at 18:07

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Most species find notes raised by one octave equivalent because of their brain structure. However, some species of songbirds do not. The species that inhabits your planet may have evolved to “hear” 1:3 ratios as equivalent, rather than 1:2 ratios.

Check out this study for more information about songbirds and their musical perception: https://pubmed.ncbi.nlm.nih.gov/23354548/. The abstract suggests that songbirds rely more on pitch-height and thus don't "need" octave equivalence.

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  • $\begingroup$ Why did animals' brain structure evolve to demonstrate octave equivalence? I found this website neuroscience-of-music.se/eng7.htm but I don't understand how collapsing octave information was biologically advantageous. I remember coming across some text on the web suggesting it allows communication across vocal ranges, i.e. adults to children, but after recalling it, I couldn't find it while searching. $\endgroup$
    – awe lotta
    Commented Jun 13, 2020 at 22:41
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In a tube open at one end and closed at the other, the resonant frequencies are the odd multiples of a fundamental. (This is why a clarinet or oboe has that ‘quacking’ quality.) If the only musical instruments are woodwinds, octaves might never be heard as consonant.

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  • $\begingroup$ I am aware of this, but I did not mention it in case it might bias the answerers to one type of answer (is that good practice). I was stuck on what geological or biological factors might lead to the adoption of only straight, cylindrical, closed-on-one-side tubes as instruments. $\endgroup$
    – awe lotta
    Commented Jun 9, 2020 at 16:37
  • $\begingroup$ This is only true of cylindrical tubes (cylindrical bore), so oboe doesn't count. Panflute and chalumeau are other examples of cylindrical bore, stopped aerophones. I tried editing, but it got rejected since the changes were understandably too drastic. $\endgroup$
    – awe lotta
    Commented Jun 12, 2020 at 14:21
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Musical Tradition as a Significant Contributor

In regards to octave equivalence, there is actually contradictory evidence (abstract of a study) for its presence, and pitch height tends to play a greater role in the perception of similarity than octave equivalence for non-musicians. This suggests that a specific musical tradition could differ from the laypeople's perception of music partially and still gain footing.

Perhaps there is some religious/mystical prohibition against conical or open-ended tubes, similar to the mathematical/mystical concepts of the Pythagoreans, which would lead to the development of odd-harmonic based music that eventually is taught to nonmusical members of society.

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