Sunday, September 30, 2007

Pythagoras in the Brain

Here's an interesting cognitive study: A.H. Foss et al used fMRI (the brain scans in the scary tunnel that show blood flow) with exposure to various intervals based upon the Pythagoras ratios. Quick review of Pythagorean ratio rules: musical intervals can be described as ratios of the frequencies of the two pitches. Those ratios that are simplest (2:1, 3:2, 4:3, etc.) correspond with the intervals that Western civilization has judged as the most pleasant (octave, perfect fifth, perfect fourth), while the dissonant intervals of our culture (major seventh, minor second, tritone, etc.) have more complex ratios (243:128, 16:15, 45:32, etc.). The fMRI tests found that in trained musicians, five areas of the brain show activity with the interval performances, showing more activity as intervals progress from perfect consonances to imperfect consonances to dissonances. These five areas of the brain are the inferior frontal gyrus, superior temporal gyrus (location of the primary auditory cortex), medial frontal gyrus, inferior parietal lobule, and anterior cingulate (rational cognition). Nonmusicians (that horrible term used in music cognition to describe a population of listeners that have not had training in music) only had one area of their brain activated in the same consonance/dissonance pattern: the right inferior frontal gyrus.

I haven't yet had a chance to read the full article to see whether the intervals were actually played in just intonation, how many intervals were played, and how many participants were in the study (fMRI studies usually have smaller numbers due to the expense of MRI time). If the intervals were played in equal temperament, that would go against the whole ratio-rule interpretation.

AH Foss, EL Altschuler, and KH James. "Neural correlates of the Pythagorean ratio rules." Neuroreport 18, no. 15 (2007), 1521-1525.


Daniel Wolf said...

Scott, when you've read it the article, could you let us know whether the article (a) distinguished among imperfect consonances between pythagorean (3-limt) ratios and simpler just intervals, for example between 81:64 and 5:4 major thirds, and if (b) ratios involving primes larger than 5 were considered.

The experiment sounds interesting, but there are some important, if somewhat subtle issues here and the description here of "pythagorean ratio rules" has to be qualified in a number of ways -- e.g. for every simple ratio, there are an uncountably large number of complex ratios that will be, in most musical cases, indistinguishable from one another, and in many cases there are pairs of relatively small intervals that are close but distinguishable which are mapped onto the same interval class -- for example the major thirds above as well as their tempered equivalents. The test does sound promising for sorting out some issues related to our capacities -- or at least those of musicians -- for distinguishing intervals and for intervallic tolerance.

Scott Spiegelberg said...

Very good point, Daniel. I have to get the article via ILL, so it will take a couple of days before I can read the full article.

ThumMeister said...

A paper in the forthcoming Winter 2007 Computer Music Journal provides a framework for discussing the extent to which two intervals of different width can be considered to be "the same." A draft can be found here:

brain girl said...

Ok, so trained Western musicians have less brain activity associated with more 'pleasing' intervals that also happen to correspond to simple Pythagorean intervals, which is how Western music is structured. My question is: so what? If they had conducted this study with an additional set of musicians trained in a completely different musical culture that preferred the intervals that are considered 'dissonant' in Western music (perhaps even a discipline that uses microtones,) I may have found this more interesting or insightful. Would their brain activity correlate more to what was considered culturally pleasing, or to simpler Pythagorean intervals? There's no way to tell from this post which one is at work here.

kieran said...

brain girl: the answer to the question "so what" will be made clear in a study i will be presenting quite shortly, and hopefully publishing soon afterwards. you might find once you pair a study like this up with one such as the following:

T. Egner et al. Ecological Validity of Neurofeedback: Modulation of Slow Wave EEG Enhances Musical Performance, Cognitive Neuroscience and Neuropsychology Vol. 14 No. 9, pp.1121-24 (2003)

that there is definitely something to this. where the former relates to composition and the latter to performance, it is clear that a new model for the arts is emerging with the help of neuroscience, what is lacking is a tuning system that allows the best of both worlds to be merged (Equal Temperament with Pythagorean/Just Intonation), and a method of ensuring note-perfect performances, both of which I am currently working on.

We will see a new period of the arts like never before come from such advances. So I would say that asking a question like "So what" is a bit naive if you have any experience with neurofeedback, which a name like "brain girl" would suggest.