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.

FriPod: Be the Beginning

1. "BE JUST!" by Martin Bresnick, performed by the Bang on a Can All-Stars on The Essential Martin Bresnick.

2. "Be with you" written and performed by U2, a cool live version with guest artists (including a choir!) joining in.

3. "Beatam Me Dicent a 6" by Heinrich Finck, performed by the Copenhagen Cornetto & Sackbutts with Vocal Group Ars Nova on Winds and Voices 1: at the Court of King Christian III.

4. Beatrice et Benedicte: Overture by Hector Berlioz, performed by Yuri Temirkanov and the Royal Philharmonic Orchestra.

5. "Beats Brand X" by Alex Temple, 12 March 2007 performance.

6. "Beautiful" by Steven Sondheim, performed by Bernadette Peters the actress who plays George's mother on Sunday in the Park with George original Broadway cast.

7. "The Beautiful Galathea" by Franz von Suppé, performed by the John Foster Black Dyke Mills Band on Overtures.

8. "Before I Gaze At You Again" by Frederick Loewe, performed by Arleen Augér on Arleen Auger, American Soprano.

9. "Begin The Beguine" by Cole Porter, performed by Art Tatum on Solos (1940).

10. "The Beginning of a Friendship" by John Williams, on the E.T. The Extra-Terrestrial - Remastered & Expanded soundtrack.

Theorists in the wild

Uh oh, we're being observed.

How singers are like drummers

No, it isn't the start of a joke (though that would be a good opening). Previously I wrote about percussionists that influence the perception of duration through physical gestures. Another study shows how vocalists use head movement and facial gestures to influence the perception of melodic intervals. Listeners were asked to rate the size of ascending intervals that three performers sang. Three physical movements of the singers were measured: head displacement, eyebrow displacement, and lip displacement. All three movements correlated with the size of the intervals, so the singers moved their heads, eyebrows, and lips more with bigger intervals. These movements also influenced the listeners' ratings of interval size, so a bigger physical movement made the listener rate the interval as larger.

William Forde Thompson and Frank A. Russo, "Facing the Music," Psychological Science Vol. 18 no. 9(Sept. 2007), 756-757.

drug-induced synaesthesia?

Mind Hacks directs us to a Wired article on Oliver Sacks and his forthcoming book on music neurology. Sacks describes how Monteverdi's Vespers allowed him to see an indigo hue that he had only seen through drugs. A warning label will now be required on all recordings of music from the Seconda Prattica.

RIP Bruce Benward

The Society for Music Theory just announced that Bruce Benward, the most wealthy music theorist in the United States, died a week ago. I have a great memory of him visiting Eastman while I was a grad student. He and Bob Gauldin started reminiscing about being students at Eastman back in the 40's, and it was amazing how much was the same as my own experiences, even if the names and theories changed. I'll post the eulogy that they sent out:

Dr. Bruce Benward, an eminent pedagogue and influential scholar, died on September 15, 2007 in Fayetteville, Arkansas. He served as professor of music theory for 30 years at the University of Wisconsin–Madison School of Music. Prior to that, he spent two decades as professor of music and chair of the Music Department at the University of Arkansas in Fayetteville. Benward also served as Florida State University’s distinguished visiting professor of music theory in 1992. He earned his master’s degree from Indiana University in 1943 and his Ph.D. from the Eastman School of Music in 1950.

During his career, Benward published several landmark music theory textbooks, including Music in Theory and Practice, Ear Training: A Technique for Listening, Sightsinging Complete, and Practical Beginning Theory: A Fundamentals Worktext. He is credited for being on the forefront of computer-assisted music instruction, having authored or coauthored several pieces of computer software. Throughout his career, he made presentations at conferences and workshops across the country for various professional organizations. In 1995, he founded the Macro Analysis Creative Research Organization, an organization dedicated to music theory pedagogy.

Among his many honors, Benward received the Trochos research grant from the IBM Corporation in 1985 for the development of instructional programs for microcomputers. He was awarded the Joe Wyatt Challenge Award in 1991 and was listed among 100 other technological leaders. At the University of Wisconsin–Madison, he was voted as one of the “Top 100 Educators.”

As an examiner for the National Association of Schools of Music, Benward visited more than 50 accredited universities in the United States. He served on the editorial boards for Computers in Music Research, College Music Symposium, Journal of Music Theory Pedagogy, and Schirmer Books. Benward also served as president of the National Association of Music Schools of State Universities.

Schenker's tonality, Part I

Yesterday I realized that it has been eight years since I thoroughly reviewed the various theories of tonality, when I was studying for my qualifying exams. So I thought I'd create a regular series of posts going through the details of some theories, though the posting schedule will definitely be aperiodic. First I will look at Heinrich Schenker's theory of tonality, as explained in his final monograph, Free Composition.

First, there was the tone. This tone creates overtones, the images of which create the triadic chord, called the Chord of Nature. Most contemporary theorists ignore the chord of nature part of Schenker's theory, for reasons that I listed here. Instead, we accept that Schenker's tonality is based upon the triad, and upon major or minor modes. These postulates are accepted because the music literature of 1600-1880(ish) exhibit this behavior and the analyses based upon Schenker's theory work with this starting postulate. Recent theories suggest that jazz tonality is based upon the seventh chord rather than the triad.

This triadic chord is unfolded through time by stepwise descending motion in the upper voice, from either the third or fifth* of the chord to the root tonic, which Schenker calls the fundamental tone**. Schenker equates this melodic motion, the fundamental line(Urlinie) with our own life-impulses, striving towards a goal. The melodic motion is accompanied by an arpeggiation in the lower voice up a fifth and back down again, as a foundational counterpoint. Why the fifth? From the overtone series, but also from contrapuntal practice: in three-voice strict counterpoint, if the closing scale degrees 2 and 7 are in upper voices, only scale degree 5 is allowable to complete the triad, and was the only leaping bass line found at the close (same as a cadence) in modal counterpoint.

Schenker has a few terms for this counterpoint: background, fundamental structure (Ursatz), and diatony. This fundamental structure is further expanded through middleground and foreground levels by transformations, prolongations, and elaborations, until the actual musical composition is realized (the surface level). The fundamental structure provides the unity, the primary identity of the tonal piece, by marking the goal and the direct path to that goal. Schenker defines "tonality" as the sum of the fundamental structure with all the elaborations and prolongations.

I'll stop here for the first part, quoting from p. 5 of Free Composition:

As the image of our life-motion, music can approach a state of objectivity, never, of course, to the extent that it need abandon its own specific nature as an art. Thus, it may almost evoke pictures or seem to be endowed with speech; it may pursue its course by means of associations, references, and connectives; it may use repetitions of the same tonal succession to express different meanings; it may simulate expectation, preparation, surprise, disappointment, patience, impatience, and humor. Because these comparisons are of a biological nature, and are generated organically, music is never comparable to mathematics or to architecture, but only to language, a kind of tonal language.

Next time I will describe dissonance as it affects the fundamental structure, and begin to explain the transformations that elaborate this fundamental structure.

* Schenker does allow for the traversal of an octave, from root down to root, but later analyses show that he doesn't think it is very common.
**Or at least that is how Ernst Oster translates it from the german.