While it may appear on first glance that the major key scale -- to take the simplest iteration of tone structure as an example -- must be arbitrary, there's an interesting relationship between the frequencies of the notes. Middle C, for example, has a frequency of about 260 hertz (depending on how your piano is tuned), and the C above middle C (usually written C') has exactly twice that frequency, 520 hertz. Each note is half the frequency of the note one octave above. The frequency of G above middle C (which musicians would say is "a fifth above") has a frequency of 3/2 that of the root note, or tonic (middle C itself), or 390 hertz. The E above middle C (a third above) has a frequency of 5/4 that of middle C, or 325 hertz. Together, these three make up the "major triad" -- a C major chord. (The other notes in the major scale also have simple fractional values relative to the frequency of the tonic.)
[Note bene: Music theoretical types are probably bouncing up and down right now and yelling that this is only true if the scale is in just temperament, and that a lot of Western orchestral instruments are tuned instead in equal temperament, where the notes are tuned in intervals that are integer powers of the basic frequency increase of one half-tone. My response is: (1) yes, I know, and (2) what I just told you is about all I understand of the difference, and (3) the technical details aren't really germane to the research I'm about to reference. So you must forgive my oversimplifications.]
Because there are such natural relationships between the notes in a scale, it's entirely possible that our ability to perceive them is hard-wired. It takes no training, for example, to recognize the relationship between a spring that is vibrating at a frequency of f (the lower wave on the diagram) and one that is vibrating at a frequency of 2f (the upper wave on the diagram). There are exactly twice the number of peaks and troughs in the higher frequency wave as there are in the lower frequency wave.
Still, being able to see a relationship and hear an analogous one is not a given. It seems pretty instinctive; if I asked you (assuming you're not tone deaf) to sing a note an octave up or down from one I played on the piano, you probably could do it, as long as it was in your singing range.
But is this ability learned because of our early exposure to music that uses that chord structure as its basis? To test this, it would require comparing a Western person's ability to match pitch and jump octaves (or other intervals) with someone who had no exposure to music with that structure -- and that's not easy, because most of the world's music has octaves, thirds, and fifths somewhere, even if there are other differences, such as the use of quarter-tones in a lot of Middle Eastern music.
Just this week a paper was published in the journal Current Biology called "Universal and Non-universal Features of Musical Pitch Perception Revealed by Singing," by Nori Jacoby (of the Max Planck Institute and Columbia University), Eduardo A. Undurraga, Joaquín Valdés, and Tomás Ossandón (of the Pontificia Universidad Católica de Chile), and Malinda J. McPherson and Josh H. McDermott (of MIT). And what this team discovered is something startling; there's a tribe in the Amazon which has had no exposure to Western music, and while they are fairly good at mimicking the relationships between pairs of notes, they seemed completely unaware that they were singing completely different notes (as an example, if the researchers played a C and a G -- a fifth apart -- the test subjects might well sing back an A and an E -- also a fifth apart but entirely different notes unrelated to the first two).
The authors write:
Musical pitch perception is argued to result from nonmusical biological constraints and thus to have similar characteristics across cultures, but its universality remains unclear. We probed pitch representations in residents of the Bolivian Amazon—the Tsimane', who live in relative isolation from Western culture—as well as US musicians and non-musicians. Participants sang back tone sequences presented in different frequency ranges. Sung responses of Amazonian and US participants approximately replicated heard intervals on a logarithmic scale, even for tones outside the singing range. Moreover, Amazonian and US reproductions both deteriorated for high-frequency tones even though they were fully audible. But whereas US participants tended to reproduce notes an integer number of octaves above or below the heard tones, Amazonians did not, ignoring the note “chroma” (C, D, etc.)... The results suggest the cross-cultural presence of logarithmic scales for pitch, and biological constraints on the limits of pitch, but indicate that octave equivalence may be culturally contingent, plausibly dependent on pitch representations that develop from experience with particular musical systems.Which is a very curious result.
It makes me wonder if our understanding of a particular kind of chord structure isn't hardwired, but is learned very early from exposure -- explaining why so much of pop music has a familiar four-chord structure (hilariously lampooned by the Axis of Awesome in this video, which you must watch). I've heard a bit of the aforementioned Middle Eastern quarter-tone music, and while I can appreciate the artistry, there's something about it that "doesn't make sense to my ears."
Of course, to be fair, I feel the same way about jazz.
In any case, I thought this was a fascinating study, and like all good science, opens up a variety of other angles of inquiry. Myself, I'm fascinated with rhythm more than pitch or chord structure, ever since becoming enthralled by Balkan music about thirty years ago. Their odd rhythmic patterns and time signatures -- 5/8, 7/8, 11/16, 13/16, and, no lie, 25/16 -- take a good bit of getting used to, especially for people used to good old Western threes and fours.
So to conclude, here's one example -- a lovely performance of a dance tune called "Gankino," a kopanica in 11/16. See what sense you can make of it. Enjoy!
This week's Skeptophilia book recommendation made the cut more because I'd like to see what others think of it than because it bowled me over: Jacques Vallée's Passport to Magonia.
Vallée is an interesting fellow, and certainly comes with credentials; he has an M.S. in astrophysics from the University of Lille and a Ph.D. in computer science from Northwestern University. He's at various times been an astronomer, a computer scientist, and a venture capitalist, and apparently was quite successful at all three. But if you know his name, it's probably because of his connection to something else -- UFOs.
Vallée became interested in UFOs early, when he was 16 and saw one in his home town of Pontoise, France. After earning his degree in astrophysics, he veered off into the study of the paranormal, especially allegations of alien visitation, associating himself with some pretty reputable folks (J. Allen Hynek, for example) and some seriously questionable ones (like the fraudulent Israeli spoon-bender, Uri Geller).
Vallée didn't really get the proof he was looking for (of course, because if he had we'd probably all know about it), but his decades of research compiles literally hundreds -- perhaps thousands -- of alleged sightings and abductions. And that's what Passport to Magonia is about. To Vallée's credit, he doesn't try to explain them -- he doesn't have a favorite hypothesis he's trying to convince you of -- he simply says that there are two things that are significant: (1) the number of claims from otherwise reliable and sane folks is too high for there not to be something to it; and (2) the similarity between the claims, going all the way back to medieval claims of abductions by spirits and "elementals," is great enough to be significant.
I'm not saying I necessarily agree with him, but his book is lucid and fascinating, and the case studies he cites make for pretty interesting reading. I'd be curious to see what other Skeptophiles think of his work.
[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]