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.

A good day

Yesterday was a good day. I got to see my daughter sing in her choir robes for the first time. I took part in an interesting Bible study. I watched the Colts win a squeaker against the Texans with excellent clock management, which then switched over quite nicely to the Packers-Chargers game so I could watch Brett clinch that win. I took my wife out for a good meal and good conversation. And I got to see eighth blackbird perform the opening concert of their residency here at DePauw. I had never heard De Mey's Tafelmusik (literally performed on a table, really a dance of six hands), which was a great opening. The ending of Rzewski's Pocket Symphony was like giant wood blocks pounding out chimes that rattle the soul before moving away. The recited poetry of Bresnick's In the Twentieth Century was not amplified well for most of the speakers, but the piece had some incredible shifts of musical space, especially through timbre. And Higdon's Zaka was a virtuoso finish, even if lacking in deep emotional content.

Closing the book

I just got back from blowing shofar at the closing service of Yom Kippur. It was a lovely service, the student rabbi has really become comfortable with the DePauw community. Unfortunately an argumentative comment knocked me out of the balanced place I had found, so I'm not much for blogging tonight. I'll provide two links, and knock off until Monday. Both links are from Mind Hacks:
1) Musicogenic epilepsy, when music causes seizures. Not to be confused with Celebrity epilepsy.
2) Clive Wearing, the pianist who has forgotten everything except how to play the piano and that he loves his wife. Elaine Fine has also blogged about this.

FriPod: Every thing

I stole this idea from Fred Clark, but it works well for personal reasons.

1. "Every Little Bit Hurts" by Ed Cobb performed by The Spencer Davis Group on The Best of the Spencer Davis Group.
2. "Every Mornin'" by M. Longo, performed by Dizzy Gillespie on New Faces.
3. "Everybody Loves Louis" by Steven Sondheim, performed by Bernadette Peters on the Sunday in the Park with George original Broadway soundtrack.
4. "Everybody's Jumpin'" by Dave Brubeck, performed by The Dave Brubeck Quartet on Time Out.
5. "Everything Happens When You're Gone" composed and performed by Michael Brecker on Don't Try This at Home.
6. "Everything I Said" composed and performed by The Cranberries on No Need To Argue.
7. "Everytime We Say Goodbye" by Cole Porter performed by John Coltrane on My Favorite Things.
8. "You're My Everything" by Harry Warren, Joe Young, and Mort Dixon; performed by the Miles Davis Quintet on Relaxin' With Miles.

Tin Ear Test

Henkjan Honing directs us to an online test for amusia, the inability to consciously perceive musical pitches and/or rhythms. The test was developed by Isabelle Peretz, well-known in music cognition circles.

Syntax vs. Semantics

In the comments to a previous post, Fred Himebaugh asked me to explain the difference between syntax and semantics in music. First, I will give a general definition of the terms. "Syntax" is the description of proper construction following rules of grammar. Thus in language, syntax describes the proper order of words following the grammatical rules of that language. "Semantics" is the description of meaning assigned to a statement (or to symbols if we are going to be very general).

In tonal music, syntax is easy to describe as the expected order of harmonic progressions, melodic pitches and rhythms, both at local levels and in hierarchical systems. The expected order is based upon rules that have been (slowly) developed by observing the behavior of tonal music composed between about 1600 and 1880. Stefan Koelsch calls these rules "certain regularities." There is debate as to whether this syntax is learned by exposure to music of that culture or if this syntax is hardwired. This same debate exists in linguistics. But regardless of the means of development, there is no debate that music has a syntax.

Musical semantics is a different story. Some say that musical semantics are identical to musical syntax, that any meaning gleaned is only a perception of structure. But others say that music can communicate a variety of meanings. Koelsch describes four different aspects of meaning: 1) analogies to similar sounding objects or to qualities of objects, such as imitating birdsong; 2) emotional meaning, such as happy or sad; 3) extramusical associations, such as literary references or conventional uses of a particular musical work (anthem, folk song); and 4) perception of syntactical structure.

The question that Koelsch's team has been investigating is if our brains process musical semantics separately from musical syntax, and if these neurocognitive processes are similar to the processes of language syntax and semantics. Previous research has identified two electrical signal changes (called event related potentials) associated with harmonic expectancy. When a harmonic expectancy is violated, the ERAN and the N500 peaks are affected. By playing musical excerpts coupled with sentences in the native language of the listeners, said sentences containing either violations of syntax or violations of semantics, Steinbeis and Koelsch found that syntactic violations in the sentence reduced the effect of the ERAN, and that semantic violations in the sentence reduced the effect of the N500. Thus, if one accepts the premise that these two ERP peaks do correspond to harmonic expectancy, this harmonic expectancy has two different processes that correlate to language's syntax and semantics.

The implications of this? I'm not sure, beyond a a possible negation of that one opinion that music syntax and music semantics are identical. I suppose it opens up the possibility that there are universal meanings in music, with varying potential levels to "universal." And it could lead to investigations on whether music-making evolved as a byproduct of language development or vice-versa.

Don't give up your day job

I'm pleasantly surprised to admit that I agree with Norman Lebrecht about something. He wrote a post about the principal 'cellist of the Sydney Symphony Orchestra. Said 'cellist, Nathan Waks, once was head of music at the Australian Broadcasting Company. That part isn't important. What is important is that Mr. Waks has another job alongside playing with the orchestra, as CEO of a winery (Nathan Waks also wrote a comment to the post). Mr. Lebrecht points out that this model leads to a much happier life, compared to full-time orchestral players who get burned out. What struck me about the post is that the concertmaster, Dene Olding, has a similar arrangement to the new concertmaster of the Indianapolis Symphony Orchestra, Zack De Pue. He is in the popular chamber group Time for Three. The ISO has also hired Alexander Kerr, a professor at Indiana University, to be the principal guest concertmaster when Zack is on tour with his other chamber groups. The day job can be teaching, composing, playing in a chamber group, or running a bistro.

Is it over?

(I'm in a questioning mood today.)

Adam Baratz has found an interesting topic to blog about from an unusual source, an LSAT study guide. The topic of discussion is Historically Informed Performance practice, which I have blogged about before. More specifically, Adam isolates possible answers to why symphonies may have played final finales more slowly in Mozart and Beethoven's days, and why audiences don't applaud between movements anymore. Alex Ross has looked at the latter phenomenon closely, supporting the comment I made on Adam's blog. You'll have to visit Adam's site to see what I said.

Do you see what I hear?

Michael Schutz and Scott Lipscomb have published a study that shows how percussionists use visual cues to make audiences think notes are of different lengths, when the actual notes are the same duration. A world-class percussionist was video-taped performing long and short notes. The video was split into visual and audio components, which were then cross-matched so Long note visuals were sometimes matched with Short note audio and vice-versa. Listeners were told that some of the videos had mismatched visual and audio cues, and were instructed to judge duration solely by the sound. However, the duration ratings varied according to visual cues rather than audio cues.

This is another reason why live music creates a much different experience than an audio recording. The visual cues actively change our perception of the musical sounds, even when they are acoustically exactly the same as a recording (which is rarely the case).

Schutz, M. and S. Lipscomb. "Hearing gestures, seeing music: vision influences perceived tone duration." Perception (2007), 36/6, 888-897.

Harmonic tension as meaning

A study published in Cerebral Cortex may be of interest to those who followed the recent harmonic theory bruha. The junior research group at the Max Planck Institute for Human Cognitive and Brain Sciences measured the electric response potentials of listeners' brains when harmonic expectation was violated, combined with another factor of syntactic or semantic language violation. They found that both types of language violation affected different locations of brain waves, a strong argument that harmonic tension-resolution is a grammar, but also has associated meanings. The study does not reveal whether these meanings are universal, merely that individuals do interpret harmonies beyond a syntactic level. The authors presented preliminary research of this at the Neurosciences and Music conference I attended in 2005. And Dave Munger has written about this line of research.

Steinbeis, N. and S. Koelsch. "Shared neural resources between music and language indicate semantic processing of musical tension-resolution patterns." Cerebral Cortex 2007 (eprint).

"I just let gravity pull me down, I don't give a ****"

I have survived the Reach the Beach Relay, and have the medal to prove it. Our team, Go Swim, finished 197 out of 350 teams, and 70th out of 154 Mixed Open teams. We ran 203 miles in 29 hours and 30 minutes, giving a pace of 8:36 per mile. My personal pace was a little slower, though still faster than my predicted 10 minute-mile. I ran 14.8 miles in three separate legs of 3.5, 4.5, and 6.8 miles, with times of 30, 40, and 60 minutes (surprisingly these times do not involve rounding beyond a few seconds). So my overall pace was 8:47 per mile. I ran at three in the afternoon, one in the morning (50 degrees with a light rain), and eleven that same morning (just after a heavy rain, slightly warmer).

The atmosphere was crazy, about 700 vans driving around the highways and backways of New Hampshire. The vans were decorated with horses, kangaroos, shaggy dogs, lewd sayings, etc. Some running teams wore pirate hats, or tutus, or capes. You would expect that runners who agree to run 15-25 miles on three hours sleep would be more sane. And now my sore calves and I are going to bed.

*The title was a quote from one of my teammates, giving advice on how to run down hills.

AMS Midwest Chapter

Those in the Chicago vicinity can see musicology in action on October 6-7 at National Lewis University. The program includes a roundtable on teaching music history with Matthew Balensuela, my office neighbor, participating. He has developed an interesting series of activities for students based on compositional treatises and pedagogical sketches that are often included in music history textbooks. I think it's a great integration of theory and history, and must think of a way to repay the favor. The cost of the conference is $10, which also gets you a membership in the Chapter.

The Robe and Crown

A reader from Dublin wrote me to ask if I knew about the connection between "Down to the River to Pray" and the Underground Railroad. A friend of hers said that the person who wore the robe and starry crown was next to be freed from slavery via the Underground Railroad. I found some sources on Gospel songs used for secret communication, but I couldn't find anything that confirmed this story. Does anyone out there know more details?

FriPod: Feel the Spirit

Today I had a meeting with my rector, in which spirituality was discussed.

1. Symphony No. 2 in D, Op. 73, 4th movement, Allegro con spirito. Johannes Brahms, performed by George Solti and the Chicago Symphony Orchestra.

2. Canzon I "La Spiritata." Giovanni Gabrieli, performed by (1) Paul McCreesh and the Gabrieli Consort & Players; (2) American Brass Quintet.

3. Con spirito from Heldenmusik. Georg Phillip Telemann, performed by the Empire Brass

4. Concerto For Trumpet, Bassoon & String Orchestra; 1. Allegro Spiritoso. Paul Hindemith, performed by Jouko Harjanne et al.

5. Concerto for trumpet in E Major I. Allegro con spirito. Johann Nepomuk Hummel, performed by (1) John Wallace; (2) Wynton Marsalis (performed in E-flat).

6. "Possente spirito e formidalbil Nume," from Orfeo. Claudio Monteverdi, I don't remember who performs this.

7. Sonata for Trumpet and Piano - III. Spiritual. Jean Hubeau, performed by Thierry Caens, Yves Henry.

8. Sonata for trumpet In D - Spiritoso ed adagio. Arcangelo Corelli, performed by Crispian Steele-Perkins.

9. Sonata for trumpet in D Major: I. Spirituoso (Allegro). Georg Phillip Telemann, performed by Stephen Burns.

10. Symph. #103 E Flat Maj "Drum Roll": I. Adagio - Allegro Con Spiritu - Adagio. Franz Joseph Haydn, performed by Herbert von Karajan and the Berlin Philharmonic.

11. Symphony No. 8 in E flat "Symphony of a Thousand": 1. Hymnus: Veni, Creator Spiritus. Gustav Mahler, performed by Seiji Ozawa and the Boston Symphony Orchestra.

May the shouter rest in peace*

Most people who are interested in classical music already know that Luciano Pavarotti died this morning. It was interesting seeing how students reacted to the news. The ones that were saddened were also horrified when other students said "who?"

WGBH has posted a 1972 interview with Luciano on their website. They also sent a press release with details of the interview:

On Monday, April 10, 1972 during the radio program Morning pro musica hosted by Robert J. Lurtsema, WGBH 89.7 in Boston featured an interview with a rising opera star named Luciano Pavarotti. The interview was recorded from a phone conversation between WGBH 89.7 host Ron Della Chiesa and the tenor that took place on March 14, less than a month after Pavarotti's now legendary 1972 New York Metropolitan Opera appearance. This was a pivotal point in the tenor's career. He was making musical history at the Met, singing the role of Tonio in Donizetti's "Daughter of the Regiment". The role includes the demanding aria "Ah! mes amis, quel jour de fête!" Often called the "Mount Everest" for tenors, the aria features 9 exposed, high Cs in rapid-fire succession--requiring monumental vocal dexterity. According to the Kennedy Center biography for Pavarotti, he made history by being the first tenor to sing those 9 high C's loudly, musically, in full voice (i.e. not falsetto.) As Pulitzer Prize-winning journalist and cultural critic Manuela Hoelterhoff described the triumph, "Pavarotti stepped to the footlights and sang all nine as if he were flipping pancakes into his mouth. The crowd roared." This is when he was crowned the "King of the High C's". In this historic interview, Ron Della Chiesa speaks with the tenor about his childhood in Modena, his thoughts about the great tenors of the past, his plans for future recordings, and --of course-- the unprecedented musical accomplishment that launched him to international superstardom.

*The title comes from an appearance Luciano made on David Letterman. He was explaining to Dave how to sing, and said it was basically controlled shouting.

What's out there

A colleague in the math department sent me this link to a great explanation of violin acoustics.

Stephen Casales has finished the Unfinished Symphony.

Composer, teacher and critic Stephen Casale studied theory and composition at the New England Conservatory of Music and musicology at New York University. The project to realize a performing version of the Scherzo movement of Schubert's "Unfinished" symphony based on Schubert's piano sketch for the movement took shape in Martin Chusid's graduate course on Schubert at NYU, where it was performed in 1978. A studio recording of the Scherzo was subsequently made by the Czech Radio Symphony under Vladimir Valek in 1995. The present performance by the Toronto Philharmonia is the first professional concert presentation of this realization of the movement.

A new e-company is trying to connect music instructors with students at ClickForLessons. I have no idea how effective it is.

This Saturday there is a symposium celebrating John Cage's 95th birthday at the University of New Hampshire.

John Cage in 2007: Reception, Performance Practice, Analysis

Symposium, 1:00 p.m. to 5:00 p.m., M-223, Paul Creative Arts Center, UNH

Our Memory of What Happened is Not What Happened: Cage and the Power of Myth
Brent Reidy, Ph.D. candidate, Musicology, Indiana University

On John Cage's Late Music, Analysis, and the Model of Renga in Two2
Rob Haskins, Ph.D., Assistant Professor of Music, UNH

Interdeterminacy and Performance Practice in Cage?s _Variations_
David P. Miller, Boston, MA

Thinking About Cage and Nature, Back Then and Right Now
David Andrew, Ph.D., Professor of Art History, UNH

Concert, 8:00 p.m., Bratton Recital Hall, Paul Creative Arts Center, UNH

Music for One
Margaret Herlehy, Oboe

Four6
Rob Haskins, David Miller, Laurel Karlik Sheehan, and Brent Reidy, performers

Two2
Rob Haskins and Laurel Karlik Sheehan, pianos

The long walk

Today I made the last tiny adjustments to my tenure files, and walked them over to the Committee on Faculty (COF) Coordinator's office. I had three files: Teaching, Professional Growth, and Service. The first two were pretty fat files, the third and skinny file was mostly letters from colleagues thanking me for serving on committees or other service. The next step is for the Personnel Committee of the School of Music to review my files during the next three weeks and to write their report with a recommended decision. The School Personnel Committee (SPC) consists of all full-time faculty, except those in their first or last year at DePauw. Plus untenured faculty can recuse themselves, as I did for my colleague's tenure review that is immediately after mine. I get to read the SPC's report and write a response if I see fit, and then these are sent on to COF. They write their own report with recommendation to either concur or disagree with the SPC's decision, which is sent on the Vice President of Academic Affairs and eventually to the President. Theoretically either of these people or the Board of Trustees could overrule the previous decisions, but I'm told this is unlikely to the point of never happening.

It feels much like when I submitted my dissertation, concerned whether I caught all the typos and logical flaws. But nothing is perfect, and I feel the files do represent my work, which is the important thing.

Running fool

This morning I ran my longest distance, 7.7 miles at exactly a 10.0 min/mile pace. I wasn't shooting for this pace, I was only trying to see if I could run over seven miles. I needed to know this, because I foolishly agreed to join my brother's team for Reach the Beach. That's right, 200 miles in 24 hours. The legs range from 2.8 miles to 9.3 (gulp!) miles, with many in 7+ mile distances. To make my little test more accurate, my route included several killer hills and I only slept four hours the night before. The latter feature wasn't intended, I was suffering from some insomnia and decided to make it useful. The cool thing is that I finally reached that runner's high. I could have kept going past my house, my lungs and legs felt perfectly fine. Granted, I had energy lows later, so I don't know how well I will do after my first leg, especially as I will be going at a faster racing pace. But while I still feel completely daunted by this relay race, I know it is possible. Of course, my students will have to prod me with sticks to get me through the following Monday's classes.