October 8: Order and Chaos; A Study of Vibrations

In Wednesday’s class we began by pairing up and experimenting with long ropes in order to visualize the vibration of a string. One person stood holding their end in front of them while the opposite person swung the rope at different speeds. We attempted to create, at first, one broad swing of the rope (like you might see in a game of jump-rope). Then we doubled the speed so that the rope was divided into two equal parts, each rotating conversely (while one side swung upwards, the other rotated downwards). This increase in speed was continued until it wasn’t possible to divide the rope into any smaller sections (usually occuring around five divisions of the rope). Each dividing point between rotating sections is considered a ‘node’, or a place where the vibration is zero.

We then gathered into a circle in the classroom and used a monochord (an instrument consisting of a single string) to discover the specific ratios that create each interval above the tonic pitch. We began by splitting the chord in half (done by lightly touching in the center of the vibrating string) so that each section of the string was vibrating at twice its original speed. This is the same as what we had just experienced with the rope when we doubled our initial speed in order to create two vibrating sections. This time with the string of the monochord, an octave occured above the original pitch (shown by the ratio 2:1, where the higher pitch is vibrating two times for each one vibration in the lower note). We continued to use this same method to achieve the 5th (ratio of 3:2), the 4th (4:3), and so on through each of the twelve intervals. We discussed that frequency ratios always come in pairs that add up to an octave. For instance, the ratio 3:2 will be paired with the ratio 4:3 (a 5th plus a 4th equaling an octave).

The class reminded me of Stuart Isacoff’s book “Temperament” which addresses the history, problems, and evolution of tempering the Western scale. After the class, I went back and read the section concerning Pythagoras and his original discovery of the geometry of music. Pythagoras, who invented the monochord, stated that “music’s rules are simply the geometry governing things in motion: not only vibrating strings but also celestial bodies and the human soul.” Pythagoras believed that the most pleasing of harmonies arose from the simplest of proportions and that complexity would insight chaos. What is fascinating about this is that behind his discoveries of pure musical geometry there lies a forbidden and volatile darkness. He found that pure octaves and fifths, according to his ratios, are incommensurate (also referred to in Greek as ‘alogon’ meaning ‘the unutterable’). Fifths will never complete a perfect circle (as suggested by the widely accepted circle-of-fifths), but will reach toward infinity in an unending spiral. This essentially boils down to the fact that octaves are based upon multiples of 2 (2:1) while fifths are based upon multiples of 3 (3:2). In this case, no multiple of 2 will ever meet a multiple of 3. If one were to compare the pitch achieved by an octave and that achieved from the completion of a circle of fifths, they would be very similar yet “out of tune”. This spiraling phenomenon hints at a more complex mathematic sequence, that of the golden ratio. Even so, these simple ratios were believed to be an expression of the divine. It is easy to find similar ratios present within nature. Saint Augustine, in fact, believed that churches and cathedrals were to be more than just shrines, and instructed that proper proportions were to be used in their construction. Thus the heights, lengths, and depths of the structures formed the proportions of Pythagoras’s “celestial harmonies” (1:1, 2:1, 2:3, and 3:4).

So what difference does this make to us, as musicians and as people? What effect does this really have on our performance? I think it is crucial to understand the fundamentals of the creation of sound, of pitch, especially when such things are taken for granted everyday. I remember the feeling I had when I first discovered the ratios involved in music. Once I got past the initial migraine acquired from my first lecture on equal temperament, I began to look a bit into proportions. It made perfect sense (and also supplied an interesting and practical perspective to my high school math classes). This is the real foundation of what I do every day, of each note I play. It is a fundamental that comes before technique, before fingerings and musicality. In a sense it is the DNA of music (more specifically of pitch). Yet as crucial as these fundamentals are, an understanding of them is not essential for the enjoyment of music. Recently, Warren mentioned a workshop that he was conducting years ago. During the course of the class, he plucked two notes on a string, the second a fifth higher than the first. Soon after, a young boy came running into the room exclaiming “What was that beautiful music?!”. Like the young boy, a single, simple fifth can produce a level of joy bordering on ecstasy. Warren also noted that infants are particularly drawn to simple intervals. This has been quite a meal for my thoughts (even just thinking back to our class sends my head spinning!). Every time I try to find a solution to these musical systems I find that I develop more and more questions. It is truely amazing how much chaos lies within order!

Video, Reflection & Analysis: “Exoticism of Taboo” (Mini-Lecture Assignment for Teaching Music History)

NewsBlog Editor’s Note: This post is the first (of hopefully more) to share documentation from the Fall 2008 semester of Anne Hallmark’s Teaching Music History course, a MIE cross-listed course. The assignment given was for students to present a ten-minute straight lecture on a piece of their choice, then watch the videotape of their presentation and write a reflection/analysis following the viewing of their tape. This report comes from CMIE Program Coordinator Randy Wong.

Hello, CMIE NewsBlog readers! This semester I am taking Anne Hallmark’s “Teaching Music History course” and will be acting as one of its Documentation Specialists—that is, posting my class experiences to the CMIE NewsBlog so that others in the MIE community can get a bird’s eye view of the course, and articulating my work in a public forum with the hope of receiving constructive feedback, etc. Expect to read some more blog posts from me over this semester. I will also make a MIE portfolio for the course as an example of what a MIE portfolio would look like for a cross-listed course. I look forward to your comments and feedback!

The Assignment

In our first class, Dr. Hallmark announced that we’d each have to give a short lecture on the piece of our choice. I think she made this assignment as a ‘diagnostic’, of sorts, so that we could each figure out what we already bring to the table and set some goals for the semester. Our assignment had three parts, and this post is a partial extrapolation of the second part. (I wrote a more fleshed-out analysis that you can download here). Here’s the assignment:

  1. Give a short lecture to the class on a topic/piece of choice (and videotape that lecture). 
  2. Watch the videotape and write a reflection/analysis paper based on your reactions to the video. 
  3. Meet with the instructor for further discussion of your reactions and to set goals for the semester.

The presentation requirements, as I understood them, were open-ended: Choose a piece to introduce to your classmates. Use a ‘straight lecture’ format. Use of Powerpoint presentations, hand-outs, audio or video recordings, etc. would be allowed; the only real requirement would be that each presentation must fall strictly within ten minutes. Following each presentation, the floor would be opened for questions or comments from the audience (our classmates). Comments from the audience could pertain either to the lecture style and presentation attributes, or to the content itself.

Pre-Viewing Reflection on Lecture Success

As it is for many, pre-presentation anxiety is one of my faults. I think my biggest worry is getting up to present and either forgetting what I want to say, or trying to say it but not being articulate enough and thus getting a lot of blank stares. Ancillary worries are: rambling (in which main points and others get tangled, and so the audience doesn’t know what the presentation’s ‘take-aways’ are) and running out of time and having to leave off main or important points. Thus, I scripted my lecture… but at the risk of reading my presentation instead of actually presenting it. I know the audience caught on to this pretty quickly, but I might not know until viewing the tape what reactions they each made, and how that affected the overall quality of my presentation.

The Video of My Lecture

Post-Viewing: Analysis of Videotape & Goals for the Semester

The same thoughts I had post-presentation (pre-viewing) applied when I watched the tape. Although the tape does not show the audience while I was presenting, my guess is that if it did, there would be body language from the audience that shows them being ‘turned off’ by my reading from the script vs. me presenting in an organic way.

The videotape also reveals how my body language plays into the way I suspect my audience interprets the tone and formality of my lecture. For much of the video, I am leaning on my hands, slanted diagonally towards the lectern/computer, and the eye contact I make is in short spurts—not for long periods, neither with audience members nor with the projected slides. This coupled with my script reading was surely a turn-off and disengaged my audience.

My main goal for this semester is to feel comfortable giving lectures, short and long, without the crutch of a script or extensive notes. I have long felt comfortable internalizing subject matter and leading discussions on it and buttressing these conversations with audio-visual material. But giving straight lectures is a different animal, and it’s a skill I must master if I continue public speaking in any context.

James Wilkinson, author of the “Varieties of Teaching” essay in The Art and Craft of Teaching (Margaret Gullette, Editor), refers to the varying skills a successful teacher needs:

A good lecturer may experience problems leading a successful discussion; the discussion leader skilled in asking questions may feel ill at ease when conducting a monologue from the lecture podium. But it should be a teacher’s goal to master the full scale of teaching styles, and to know the strengths and drawbacks of each (Gullette, 1984).

This straight-lecture format was definitely good practice for me, because as much as the topic and content is put front and center, so are my methods of organizing and presenting that material. I suppose another crutch I have is to put the student at the center of the conversation; after all, there is a huge push for education these days to be learner-centric rather than topic-centric, and my own philosophy and background in education is from that standpoint (learner-centric) as well. So, this was all a good exercise.

Further Thoughts

As an aside, I think that this course (like other education-focused courses at New England Conservatory) is an important parallel to the school’s performance-based curriculum; particularly because it encourages budding teachers to freely and openly explore and develop each’s own personal teaching style. So often teachers-to-be (also known as pre-professional teachers) are thrown into classrooms with little preparation or minimal chance to practice teaching.

While at NEC, I spent many hours practicing pieces in small motifs, and then slowly linking those motifs together to create longer phrases. Those phrases then had to be linked to each other, and so any transition that occurred between phrases would have to be carefully planned and executed, in accordance with accompanying parts, harmonic structure, rhythm, and form. In other words, it would all have to make sense. I have since come to understand the art of presenting and teaching to be no different. As is stated by Wilkinson, part of the trickiness of lecturing is in the way that one must analyze the subject matter and present it in a logical, flowing, way:

How to argue a point and not simply present data; how to link arguments in a logical chain; how to sum up with a sure sense of what is essential and what is merely extrinsic to your case are skills that require coaching and practice. Students need to be helped to present their ideas with grace and to strive for the control, confidence, and economy of means that help make what Alfred North Whitehead once termed a “sense of style.” (Ibid.)

I have already spent many nights working on this from the standpoint of the written word, and have slowly begun spinning this experience out, into other forms of teaching that I am comfortable with: double bass & music reading lessons; ensemble coaching; and informal lecturing on Exotica music and the Hawaiian culture. However, what I need more practice with is working in more formal venues, with a larger and/or mixed audience, and in extended time periods. Thus, I am excited to conduct the 50-minute classes that are part of the assignments for this course, and hope to further develop the “sense of style” that Wilkinson, Whitehead, and others often refer to as being a crucial characteristic of effective teaching (Ibid).

Read my Reflection & Analysis Paper (PDF)

Work Cited

Wilkinson, J. (1984). Varieties of Teaching. In M. Gullette (Ed.), The Art and Craft of Teaching (p. 4). Cambridge, MA: Harvard UP.

Powerpoint Slides (click to enlarge)

Welcome to the 2008-2009 academic year!

Dear Music-In-Education students, faculty, research associates, and NewsBlog readers alike: 

This is just a quick note to welcome you to our new year, and to thank you for your continued readership of the CMIE NewsBlog. A number of projects, like the NEC Focus School project at The Atrium School (Watertown, MA), are continuing this year, and by reading this NewsBlog, you will learn of their endeavors, successes, and triumphs. Michael Glicksman, who just graduated from NEC in the Spring is now heading up the Atrium School’s music program as its Music Director. Michael is taking the reins of the Atrium project from Jessica Reed, a MIE Concentration alum whom will be moving back to California late this Summer. 

You will also be hearing more from our MIE Documentation Specialists, who will be giving us a bird’s eye view of the discussions and work surrounding Concentration courses and students’ Guided Internships. Though posting to the NewsBlog was a recommended part of the Documentation Specialist internship in the past, it is now a required component. 

We will be enhancing the Digital Portfolio section of our website and also be adding the capability for readers to view Powerpoint slides without having to launch the application. This should save some time and hassle for those who are unable to visit class, yet want to see presentations made by their teachers and peers. 

Finally, this will be the first semester that readers will gain insight into Anne Hallmark’s Teaching Music History class—a MIE cross-listed course. Both myself (Randy Wong, CMIE Program Coordinator) and Charles Morgan (CMIE Documentation Specialist and 2007-’08 MIE Guided Intern Fellowship Recipient) are taking the class; we’re eager to post our experiences and share documentation from the course with you. 

Hope everyone has a great year and be sure to continue reading the CMIE NewsBlog!

-Randy Wong

CMIE Program Coordinator & Research Associate

Director, Guided Internship Programs

Intro to Music-in-Education

Larry Scripp’s Intro to Music-in-Education class is an obvious forum for exposing students to the various aspects of teaching, but a closer look shows that not only do we hear about these methods through Larry’s teaching, we also experience them in the way he teaches us, and we experiment with them by teaching our own lessons in front of the class.

In these past two weeks we have been using different colored plastic cups to represent either rhythm or pitch, and creating impromptu performances led by members of the class. Follow the link at the bottom of the article to see Alex Powell directing the class in a pitch exercise. He assigned a pitch to the first cup, and assigned the second scale degree to the second cup. When he pointed to the third, we deduced that it would mean to sing the third scale degree. The confusion came when he assigned scale degree 5 to the fourth cup, and then directed us to sing back down the row. We mistakenly sang scale degree 4 instead of 3 for the third cup. Alex made us aware of our mistake, and we corrected ourselves. In a later discussion, Larry showed how Alex might have corrected our confusion by starting from the first cup and ascending to verify the correct scale degree on the third cup. I think this was a most valuable lesson – that it’s better to allow students to correct their mistake by verification, rather than simply telling them they’re wrong or correcting the mistake for them.

  • Watch Pitch Representation movie (Quicktime video file)
  • -Kristen

    An Update from Paul Burdick’s Performance Outreach Class

    We have currently had 6 classes and in these classes we have discussed everything from poetry to the average attention span of a 3rd grader. I found that I have the attention span of a 5th grader at times, especially when this class meets at thursday between 4 and 6. This past week we took a field trip to the South End Settlements, it is an old building that houses a pre-school program, before and after school program and a community arts center. In December our class will be performing for the after school program and we went to check out the performance space and the types of activities that occur there. While there we had to oppurtunity to watch an African Dance Class, where the emphasis was not perfection but movement and enjoyment. It gave the kids time to figure out what they were doing with gental instruction. We then walked through two classrooms where math and reading were being taught. Each group was no more than 10 students with 2 teachers/tutors. We learned the basics of how an after-school program is run, and was given time to look around the all purpose room. The last stop on our tour was the art center located next door. Inside we found the youngest group that the afterschool program has. They were finishing their pumpkin patch mural by cutting out silver stars and rocket ships. Our trip ended with some time of reflection where the class talked about the size of the program and how it was run. This trip was interesting and I am looking to discuss it further in class on thursday.


    Hope for the Cross-Listed


    I am writing to you today from the strange but powerful world of MIE Cross-Listed courses. I hope by now it is common knowledge that there are many courses, some that may even be required of your degree program, that also count towards your MIE concentration. If there is a more striking interest beyond what the MIE department offers, chances are there is a cross-listed course that will suit your fancy. For me, my course was the Wind Ensemble Conducting course with professor Bill Drury, but what I didn’t realize was just how much (even at this early stage) this course would delve into my entire MIE experience and the model of an artist/teacher/scholar.

    Only two classes in, I’m already realizing that this course isn’t only about conducting, but also about performing and reflective study. The way I see it, this is the highest level of performing that there can be because you are essentially the performer for the performers. You have to be on top of your game in such an extreme way in order to even begin to be effective. The amount of confidence is uncanny, and as you can imagine has seeped into my artistry as a trumpeter.

    But, much of the time on a podium isn’t about performance it’s about rehearsal. And in this regard knowledge of the score is key. This is where it is necessary to be the best possible scholar one can be. Even at a beginning stage of conducting it is helpful to have studied the phrases and contours of the music, not just as they lay on the page but how they were historically intended. This too has seeped into the other aspects of my life as both a student and a performer.

    And in rehearsal a conductor literally becomes a teacher. I realize now that the way someone acts on the podium directly relates to the way things function in any type of classroom, even in a private teaching setting.

    As you can see, this conducting class has a lot of implications for the Artist/Teacher/Scholar model, and my MIE concentration as a whole. I’m looking forward to seeing how these notions play out over the course of the semester.

    Stay tuned,