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It is my understanding that unaccompanied singers (or players of fret less instruments) will naturally tend to sing (or play) just intervals, i.e. intervals whose frequency ratios are ratios of simple whole numbers, and that the complicated tuning systems invented throughout history are compromises made to accommodate fixed-pitch instruments that can’t adjust pitch on the fly. My first question is, is this true regardless of musical/cultural background? I understand the physical reasons why octave equivalence would be a universal thing, and why simple ratios of frequencies sound better together, but how far does physics go in explaining the notes humans use?

I have always been told that non-western music doesn’t use the same system of notes as in the western tradition; the example usually brought up are the microtones in Indian classical music. Before I ever looked into it, I assumed that they may not consider octaves to be equivalent, or that they would actually split the octave into many more notes than we do, and each one would have an important function like the usual western scales. However, it looks like the microtones are usually embellishments or elaborations on more “central” notes, and some scales in Indian classical music split the octave into seven notes that basically correspond to the western diatonic major scale.

So my main question is: Are there any cultures whose music would seem as truly foreign to me as, say, the Bohlen-Pierce scale? Or do most cultures really use simple just intervals like 3:2 (perfect fifths), 4:3 (perfect fourths), and so on, with some small variations?

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    A quite canonical example of non-rational music is Gamelan. Sep 7, 2020 at 17:23
  • Perhaps change 'minor' variations to 'small' ones..?
    – Tim
    Sep 7, 2020 at 17:24
  • I wonder if this is why, to my ear, 50% of singers cannot hit a simple major third on the root chord; there are so many variations [without even including anything that could be considered "blues"] that it often makes my brain hurt. Sharp is much worse to me than flat, as flat can feel bluesy with some singers.
    – Tetsujin
    Sep 7, 2020 at 17:43
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    @phoog Do Indonesians also sing in gamelan tuning with stretched octaves? I think the gamelan example might fall into my “alternate tuning systems to make compromises with instruments” category.
    – Steven
    Sep 7, 2020 at 18:53
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    I agree with Steven - to me the gamelan tunings are an artifact of the inharmonicity of the instruments themselves, not a cultural preference for non-rational intervals. To me the true intersection of the original question and the intricacies of gamelan tuning is whether the instruments of a gamelan orchestra are turned so that the intervals sound just, similar to stretch tuning on a piano is meant to make it sound equally tempered, even as the fundamental frequencies are not actually equally tempered. Sep 7, 2020 at 20:02

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A bit long for a comment but will try to make it kind of an answer…

The human auditory system does not seem to carry any intrinsic relations between tones linked by intervals relations like octaves, perfect fifths or perfect fourth: it does not seem that any geometrical effect (or so) in there is actually allowing the brain to associate such intervals in an innate manner.

But, one may also need to considerate the fact the brain is actually very good to associate things from past experience. A lot of systems that are producing sound for an human ear to hear (pun nearly intended, but these two words does sound a bit the same to me ;) ) are producing periodic sounds, or at least periodic on short timescales (bells are a counter example obviously). These sounds, if they are not pure sines, will carry overtones which frequencies will be a multiple of the fundamental frequency thus. In these overtones, the octave interval (1st, 2nd, 4th (…) harmonics - it may depend if you start counting them from the fundamental or not) and the fifth interval (3rd, 6th (…)) will usually be extremely present.

One could thus think the human brain is educated by nature to find these tones together. Obviously, being surrounded from birth by music would also be a reinforcing effect, and would be a good explanation for the acceptance by the brains of "less natural" intervals than the fifth or the octave (this would work the same way as "training" the ear to appreciate styles of music which make extensive use of intervals not used in "standard popular" music, jazz and psychedelic are the first ones which come to my mind).

Well, this is not much more than an hypothesis, and one of the source I found on this subject is this article in which I do not have much confidence. Maybe something from the scientific literature will pop and I'll edit this…

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  • Yep. As far as I know, there is no musical culture in the world where the octave is not prominent in music. But as we see in the case of gamelan music, even the perfect fifth is not always present: culture plays a deciding role as well. As usual with us fickle humans. Sep 8, 2020 at 10:34
  • @ScottWallace If someone would have been raised in a white noise only (silence make people mad apparently) this would sort it out!
    – Tom
    Sep 8, 2020 at 10:37
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    hmmm. We'd have to try it out to be sure, and that would be pretty nasty. Sep 8, 2020 at 10:54

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