I like this type of research, but I think these results are not really new or surprising. In fact, there is almost a kind of "circular reasoning" at work - the Euler lattice (or Tonnetz) was constructed for the purpose of trying to represent the relationship of the basic music musical intervals. The fact that the basis of scales is the set of simple harmonic ratios of an initial pitch has been asserted by theorists for centuries, and that is what these star-convex structures correspond to. In other words, this research confirms that the established and traditional theory of scales and harmonic relationships is indeed the basis of human music of most cultures.
I agree with the feeling of "circular reasoning" in this paper. First you restrict yourself to integer ratio pitches, then you lay them out such that simple ratios occur close together, then you claim that scales contain pitches close together.
Further more, nothing is "universal" until it holds for all of the relevant set's elements. In fact, now that they've identified star convexity as a candidate for a universal, the next obvious step for an avant garde musician is to create music out of pitches picked from non-star-convex sets :)
The question is, will any of such music be considered 'beautiful'. The underlying philosophical consequences are what are (to me) most interesting in research such as this - they are another piece to add to the argument for aesthetic objectivism.
Music history has great examples of now considered beautiful music that was once (figuratively) spat on. The audience created a ruckus during the first performance of Stravinsky's Le Sacre du Printemps, Wagner looks like, in modern terminology, a "sleeper hit". Past masters who were once ignored are being re-celebrated in Indian classical music. You can tell I have my doubts that aesthetics is objective :)
Oh there are no doubt such examples; I don't consider them as an argument against aesthetic objectivism though, just as examples that our epistemology, to put it mildly, needs work :) It's an argument I've had many times and that has been fought over for 1000's of years and in countless papers and journal articles - to the point where I've given up hope of convincing anyone who knows what the argument is about, because those who do usually have thought about it so much that it's unlikely I will bring up an argument they haven't heard already, and vice versa :)
> In fact, now that they've identified star convexity as a candidate for a universal, the next obvious step for an avant garde musician is to create music out of pitches picked from non-star-convex sets :)
First, this is cool. As someone who studied Sound Engineering it's not often that you see this type of post on HN.
Second - The scientific journal that published the article looks really interesting - The Journal of New Music Research. I wasn't aware of this. Now to find out if the local college library subscribes!
http://www.informaworld.com/smpp/title~db=all~content=t71381...
I've just skimmed the article. If you know music theory (scales, intonation) and a little math you can at least get the gist of it. I agree with mycroftiv's comment. It's nice in the sense that it formalizes in a new way some knowledge we already had, but it doesn't seem to be anything new or surprising.
Concerning just intonation scales, this paper boils down to saying that, if a given ratio appears in a scale, then ratios with prime factors removed tend to appear in the same scale.
Since intervals whose ratios' numerators and denominators high LCMs tend to sound dissonant, it is not surprising that these complex ratios are present only when the simpler ratios are already "taken". Seems like the same evolutionary processes that result in languages with simple speech sounds may be at work here.
As far as even-tempered scales go, this is silly.
From section 2.2, on reducing even-tempered scales (think, transcendental numbers) to just intonation scales (ratios):
> In an Euler-lattice [...], unison vectors can be found which represent very small ratios,
...of COURSE if you approximate the tones with very small ratios, they will likely form a convex lattice, since very small ratios are all near the center of the lattice!
> of COURSE if you approximate the tones with very small ratios, they will likely form a convex lattice, since very small ratios are all near the center of the lattice!
I don't think that's what that part is saying. Small ratios i.e. ratios close to 1 like 16/15, 24/25, 27/25 don't appear near the center. Simple ratios such as 3/2 etc are the ones that appear near the center. If I understand it correctly this section is simply describing a transformation that collapses several points into one, equivalent to collapsing several similar notes into one.
It should also be pointed out to non-musicians that the chance that you have ever in your life heard music that uses a just intonation scale, which this study is restricted to, is very small.
I dunno, if you ever played a brass instrument, then you're playing on an (approximately?) just-tempered scale -- each valve combination is a harmonic series starting from the 2nd harmonic. Whether it's just-tempered over the entire scale depends on the way the valves are tuned, I guess, and it's likely that the tuning reference is equal-tempered most of the time, so it's kind of a hodgepodge. It probably has a name.
I play brass (trumpet) and was always warned on assuming the tuning was accurate; even with the perfect player using the perfect compensation on the relevant valves the lower notes are definitely iffy (they tend towards flat and the compensation slides can't push them sharp).
That perfect player is improbable though. On the lower notes I can bend them by in the order of a quarter tone without touching the valves. If I pick up the instrument on a cold day without first warming it, not just me, up then it will be probably a quarter tone or so flat for the first few minutes. If you leave it on your chair and come back to find someone's turned the heater on while you were away (happened to me before), it can easily be a semitone sharp, IF it's cool enough to hold in the first place!
I love my trumpet but it's one of the last instruments I'd use to illustrate really precise tuning.
> This is used to lower the pitch of the 1-3 and 1-2-3 valve combinations.
In other words, the tuning slides described in that section of the article are solving a different problem (which is described in a bit more detail in the previous section). As a1k0n said, a given valve combination is a harmonic series. If you play a major third on a trumpet without moving your hands, the distance between the notes will be 386 cents, not 400. Of course, a good player will do whatever they need to do to sound in tune with whoever they're playing with. My understanding is that the lips are the main thing used to get harmonics of a particular valve combination in tune with each other.
It's much easier to play with two dimensional shapes than on a regular keyboard once you get the hang of it, especially if you're a visual thinker.
I'm currently using a layout with horizontal spacing in thirds and vertical spacing in fourths, but I'll see if I can get a clue with the lattice from the paper.
For those interested in more publications in my dear field of music information retrieval (MIR), see the ISMIR conferences: http://www.ismir.net/. All ISMIR conference papers are available for free! Great place to learn about the state of the art in music transcription, source separation, classification, search and retrieval, and more.
“Universal property of music” is something quite a different from “universal property of musical scales”, at least for me. Music is something very abstract and scales are just a tool that helps dealing with it in practice. As Gustav Mahler put it, “the most important things in music are not in the score” (paraphrasing, don’t remember the exact quote).
If there is a cognitive universal, I wonder if it is absolute. Does it describe the nature of cognition itself or does it only describe cognition we do it here on earth.
IOW: will sufficiently evolved lifeforms on other planets have similar experiences (and therefore a basis for common ground) or will we be completely unable to understand them? Maybe we're receiving transmissions right now and we just don't see it.
If a cognitive universal exists, then true artificial intelligence must -by definition- "think like us" because that's how thinking works.
I'd be interested to see how these convex structures relate to neural patterns... I'm sure these shapes some how mathematically can be traced back to the structure of the neural connection patterns that are fired when we hear these scales.
This idea of scales being the basic patterns that music is based on also reminds of color schemes - scales seem to be to hearing as color schemes are to vision.
Ha put that together and... web app idea! A scale generator for musicians just like the color scheme generators that we have for web designers. :P
The article closes with the thought that there may be a related 'cognitive universal'. This list reads like a bare-bones version of the human experience: http://en.wikipedia.org/wiki/Cultural_universal
A number one in the UK Charts within three months of purchasing the book, or you money back!
This book was a great insight into the music industry of the 80s and had quite an impact on me - I was a teenager when I read it. (I'm not a musician)
Well... just like HN has an impact on me today.
Heh, there was article on HN a while back explaining that in order to be truly creative, you have to first master your domain.
So I wonder if this new information will allow master composers and musicians to gain a deeper insight into their craft and then achieve creative advances they might not otherwise have. I've recently gotten into trance, dubstep, and their many, continually emerging sub-genres, hence my interest.
As for me, I'd be happy to just be able to make stuff I could post to Newgrounds or Youtube and get decent ratings. Though now that you mention it, I wouldn't turn up my nose at #1 pop hit-generating startup either.
The basic idea, in one sentence, is that our preferences in art are a result of our ancestral environment.
He cover various ways in which both natural and sexual selection pressures have shaped how we appreciate various artistic products and how we create them. He explores aesthetics from Aristotle to post-modernism and looks, from the Darwinian perspective he's formulated, why we regard forgeries and modern art "readymades" the way we do.
Daniel Levitin has also written a book (This is Your Brain On Music) that explains recent interesting discoveries dealing specifically with sound and music cognition. Awfully interesting stuff.
