Archive for the 'Reflections' Category

10/20/09 Music-Math Matrices as a Model of Shared Fundamental Concepts

NewsBlog Editor’s Note: We are pleased to introduce to you Justin Stanley, a new CMIE Guided Intern working as Documentation Specialist for Larry Scripp’s Introduction to Music-In-Education course this Fall.

Professor Larry Scripp introduced a number of concepts this week in his class, “Introduction to Music-in-Education.” He began the lesson by drawing a matrix (as shown below) on the class blackboard and playing a recording of a piece by Bobby McFerrin. Professor Scripp, through nonverbal suggestion, portrayed the function of the matrix in the rhythm of the song, and added x’s in single cells to notate clapping or emphasis. Soon, the class was engaged in an activity in which we clapped along rhythmically to the piece in a unified perception of the function of the chart drawn on the board. Professor Scripp gradually added complexity to the exercise by using symbols to imply rhythmic groupings, words to apply to rhythms (antelope for a group of three, salamander for a group of four), and rhythmic solfege for the same.

The basic form of the matrix used in class to show the basic form and rhythm of the song.
The basic form of the matrix used in class to show the basic form and rhythm of the song.

After the exercise and a discussion of what we did, students were asked to compile a list of mental processes that had to be integrated to take part in the exercise. Among many conclusions, students realized that processes of permutation, symbol association, cycle recognition, and grouping and parsing were needed to actively participate. We found that these concepts and brain processes that we used can be applied to a number of different subject areas. This led Professor Scripp to make the following comment: “If music is a fundamental medium and model for teaching and learning, from the point of view of integration, you could say that it is a fundamental medium and model for integrating.” Because of the subtle complexity involved in the activity, Prof. Scripp was able to keep the entire class (perhaps completely subconsciously had we not been conservatory music students) in a state of Flow (as shown in the chart below) during which we were all listening, questioning, creating, performing, and reflecting. Through this lesson, we as students were able to experience some of the cornerstones of the MIE program first hand: shared teaching and learning concepts, and teaching and learning processes. the flow st The integration of all of the learning processes exhibited during this exercise can help students create and strengthen connections necessary for all kinds of education. The subtle complexity of this exercise and any number of exercises like it that integrate music and other curriculum can create and strengthen connections in the minds of any student. Complexity in learning and comprehension can lead to any number of paths for a learner of any age. This lesson pushed me to do two things: 1.    I worked on a new unit plan for my internship teaching brass players at a local upper school that incorporated the use of a matrix to teach solfege. The initial lesson went incredibly well, with students learning how to create their own symbols to notate rhythm and melody. I hope to incorporate the following aspects into the unit curriculum for integration: a.    MATH: unit, sequence, fractions, special learning b.    LANGUAGE ARTS: symbols, syntax/structure c.    SCIENCE: measurement, documentation, inquiry d.    HISTORY: timelines, maps, contextual history e.    ARTS: creation, spatial learning 2.    I decided to focus on flow theory and brain processes/anatomy for a research paper for another MIE class at NEC, “Learning, Brain Development, and Music,” taught by Lyle Davidson.

11/18/08 Of Transcribing and Analyzing: Methods for Evaluating One’s Own Teaching

A few weeks ago, I completed the second major assignment for MHST 537 (Teaching Music History): Substitute teach (or “guest lecture”) for another professor at NEC; videotape your teaching and analyze it. I had the good fortune to substitute for Larry Scripp; he had to travel out of town for the latter half of his MIE 501 (Intro to MIE), so I stepped in.

The agenda I set forth for my teaching was based on an assignment Larry wanted me to give to the class: to get his students familiarized with the CMIE NewsBlog, as readers and potential writers. I worked backwards from his assignment to plan what basic learning outcomes I hoped my students would achieve—an understanding for what makes NewsBlog writers’ postings different from the “rants” that are commonly associated with blogging; a rationale for organizing the kinds of ideas and documentation that get shared on the NewsBlog; and a sense of direction—where, beyond the NewsBlog or MIE program, does this kind of documentation and writing have use and purpose?

Where’s the Video Documentation?

Although I am not able to post my video of teaching here, due to length and filesize, any readers of the NewsBlog who are interested should read the transcription file (posted as a PDF here). In fact, anyone who reads the transcription file will notice that parts of it are highlighted and color-coded; this is a technique for analysis that we encourage MIE students to undertake.

Transcribing, Coding, and Analysis

The process I have engaged myself in—of videotaping my teaching, watching it, transcribing it, coding it for objectivity, and finally analyzing and reflecting on it is one that I have observed as being useful for emerging and experienced teachers alike. It is a method that we showcased and published in the Journal for Music-In-Education (Scripp, Keppel, Wong, eds.), and that we encourage throughout the MIE department. Its value lies in the fact that words do not lie, and it is often easier to quickly see the ‘big picture’ when scanning transcripts than from sitting and watching a videotape. The benefits of watching the videotape, and doing one’s own transcription from that tape, are obvious: Body language, tone of voice, eye contact, movement, and other physicalities of teaching are easily recognizable. From watching my own tape, I was surprised to learn that my teaching voice was not as loud or enunciable as I thought it had been. I suppose that is something to continue to work on. I didn’t do an ‘exact word’ transcript here, but what I learned from the tape is that there were multiple times that I had to re-phrase questions, transitions, and other verbiage. I already knew from past experiences that off-the-cuff presentation is not my strong suit; the introductory Ten-Minute Presentation we did at the beginning of Teaching Music History is testament to that (I scripted that presentation and practically read it). Because of the limited amount of time I had to prepare this teaching session, scripting nor rehearsing were barely possible, but I did have to time to make a short Powerpoint presentation that I used as an outline of sorts.

Connection to MHST 537 course

Although the class session I taught is not a Music History course, I believe that many of the same principles that we have been studying in Anne Hallmark’s MHST 537 Teaching Music History course still apply. The past several weeks have seen discussions in class based on readings that articulate how college classrooms are run; the pitfalls and mistakes of ‘wet behind the ears’ teachers; ways to engage students in discussion; and organizational tips for lecturers, among other things. These readings are balanced with seminar-style class sessions moderated by Hallmark, which in and of themselves serve as models for successful teaching in a graduate setting.

As is evident in my coded transcription, I tried to incorporate some of the techniques that Hallmark and others are suggesting as worthwhile ways to engage students in discussion and classroom learning. Granted, there was less discussion than I would have liked, and the majority of communication was responsorial, but I think a good effort was made.

The teaching session was also an opportunity for me to go into a situation not as well rehearsed or prepared as I usually would be. There is, as Warren Senders or Larry might say, a certain amount of improvisation that that is a part of any teaching experience, and that a seasoned teacher would need to be comfortable with; things hardly ever go ‘as planned.’

Finally, I did make it to the end-point Larry projected for me: A MIE NewsBlog blogging assignment that students would need to complete, and connect, to the knowledge they’ve so far acquired on documentation, for inclusion in their process portfolios.

Download PDF:

11/12/08 10/22/08 Folk Communities

We began this session by learning a few folk rounds. The first was a bluesy MoonDog tune that reads as follows:

Nero’s expedition up the Nile
Failed
Because the water hyacinths
Had clogged the river
Denying Nero’s vessel’s passage
Through the Sud of Nubia

(I found a transcription online if anyone is interested in joining along!)

The second was a curious tune that compared a frog to a strange form of bird. This piece reminded me of a showtune more than a folk melody. Its text read:

What a queer bird a frog are
When he sit he stand almost
When he jump he fly almost
When he sing he cry almost
And he ain’t got no tail
Hardly he ain’t got no tail
And he sit on what he ain’t got almost…
What a queer bird a frog are!

When we broke into canon (I believe at one point we were in 4 or 5 parts) I began to get so excited that I couldn’t help but sing at the top of my lungs and by the end I had definitly broken a sweat. At times I stopped (just briefly) in order to experience the composite harmonies and rhythms as they flew by. This is the music that shaped me into the man (and musician) that I am today. My mother sang folk songs from her youth to me when I was an infant (and in fact even before I was born). When I was older she bestowed unto me her collection of LPs that contained her favored renditions of these tunes (they are still in frequent rotation on my record player). There is a strange sense of community that is lost when these songs and their traditions are ignored and undermined.

Later that night, after our class, Joanna and I took a couple friends up onto a friend’s rooftop deck. We taught them the songs that we had learned, and while a number of intoxicated college students stumbled home on the streets below, we rounded off the roof above them. This type of community is profoundly valuable. The sense of sharing is so unique and there is such a strong energy of liberation from all things ego. It is as though the music soaks into your skin and you feel such ecstasy from its internal resonance. These moments are rare (and increasingly so). We speculated in class on what life might be like if the price of gas escalated to an unreasonable and unaffordable height. Luxury as we now know it would cease to be an option. Touring musicians and ensembles would become rare and would force our community into a tighter knit microcosm. I believe that our scope of perception would narrow and we would begin to look inwards for entertainment. It is likely that our culture would return to an orally driven tradition with a focus on sharing, trading, familial communities, and the immediate experience of being. It is possible to speculate that within our current global community these things become insignificant and tend to disappear.

I would also like the mention the great attention devoted within our current cultural machine to the standardized process of test taking. This continues a conversation we began in class that Jenny also spoke of in her previous blog. As Jenny mentioned, learning to take a test, such as the SAT, targets strengths that you might use when balancing a check book. The strategies you learn when training for these exams in no way helps one to develop into a better artist, writer, musician, or creative thinker. Much of the way that high school English classes are conducted reflects this. Conversations surrounding literature and higher art are more often than not guided towards a specific end result or “correct answer” as defined by a teacher’s handbook. These so called ‘guided conversations’ are not real conversations and do not express anything but a prescribed formula and its subsequently derived answer. It leaves little room for creative thinking and no room for a student to learn freely. In tighter knit societies, we want people to sing with, to talk to, to be part of a community with.

We discussed in depth how much of what we learned as students was not what our teacher had been attempting to teach. For many of us, we learn in a variety of free-associative ways. We make connections and draw conclusions based upon previous experiences and our current understandings. It seems obvious, with this in mind, that our system of education can many times create a barrier for the minds of learners. In my view, education is something that cannot be prescribed. It is something that, when most effective, is coordinated with the specific needs and current situations of each student group (and in the most ideal situations, for each student individually). We have a long way to go in fulfilling the needs of our students, but I believe that in-depth speculation on the unique qualities of folk based communities will yield positive and provocative results.

11/06/08 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!

10/18/08 The “Model Minority” and Some Implications for Teaching

Two weeks ago, we were given an assignment for MHST 537 (Teaching Music History) class: Find a reading outside the syllabus that is connected to prejudice in the classroom, and introduce that reading to the class.

The reading I chose—Strangers From A Different Shore: A History of Asian Americans (Ronald Takaki)—is one that was part of the syllabus for a course (”Asian Americans and Education”) I took while at the Harvard Graduate School of Education. That course, the reason I took it, and what I got out of it are posts for perhaps another time. I remembered this Takaki reading because of one particular section titled “The Myth of the ‘Model Minority’” that resonated with post-grad school experiences I’d had. Takaki writes:

Today Asian Americans are celebrated as America’s “model minority.” In 1986, NBC Nightly News and the McNeil/Lehrer Report aired special news segments on Asian Americans and their success, and a year later, CBS’s 60 Minutes presented a glowing report on their stunning achievements in the academy. “Why are Asian Americans doing so exceptionally well in school?” Mike Wallace asked, and quickly added, “They must be doing something right. Let’s bottle it.

[A] Pattern of Asian absence from the higher levels of administration is characterized as “a glass ceiling”—a barrier through which top management positions can only be seen, but not reached, by Asian Americans. . . . Asian Americans complain that they are often stereotyped as passive and told they lack the aggressiveness required in administration. . . . Asian American ’success’ has emerged as the new stereotype for this ethnic minority. While this image has led many teachers and employers to view Asians as intelligent and hardworking and has opened some opportunities, it has also been harmful. (Takaki, 474-477).

I grew up in a society predominantly Asian and Polynesian, so I was largely insulated from the “model minority” views that Takaki relays. However, while studying for an additional degree beyond my Harvard one, I did encounter some of the reverse racism that Takaki might suggest would come about as a result: That because Asian Americans are perceived as success stories, it becomes acceptable by others to taunt, berate, and bring up Asian ethnicity as a means of “leveling the playing field” for those of other racial or ethnic backgrounds.

Here are a few short anecdotes that I feel relay my experiences:

  • At one point, when I was taking a historical survey course (and was doing rather well in it, because of a lot of effort I’d put into studying the material), the instructor insinuated that my success was ethnically based rather than on my skill set.
  • Another teacher commonly made analogies that somehow connected musical scores with Chinese menus and Oriental massage.
  • I also had new acquaintances remark, “You’re the first Asian friend I’ve had—the others are so nerdy” and “Why are you damn Asians so good at everything?”

Though I wanted to take those experiences and remarks in good faith, I found it increasingly difficult to tolerate and stomach them. While the easiest way to interpret some of these experiences may be as harassment (racial and sexual), I see them as being related to the “Model Minority” syndrome. At no time during these occurrences did I observe members of other minorities or ethnic/racial groups receive similar treatment.

Significantly, Asian-American “success” has been accompanied by the rise of a new wave of anti-Asian sentiment. On college campuses, racial slurs have surfaced in conversations on the quad: ‘Look out forthe Asian Invasion.’ ‘M.I.T. means made in Taiwan.’ ‘U.C.L.A. stands for University of Caucasians Living Among Asians’. ‘Stop the Chinese before they flunk you out.’ (Takaki, 479).

Implications for Classroom Teaching

Clearly, one lesson that I can draw from reflecting on my own experiences is that teachers must strive to be pro-active and conscientious individuals who value objectivity equal to their own interpretation and analysis. Another is that we must always consider what misunderstandings could result from the ambiguities of language and metaphor. I would also argue that organizing coursework and work products in a way that students’ learning processes are most evident can help to counteract any perceived obstacles for students that will come from a variety of cultural, ethnic, racial backgrounds.

10/15/08 Theta and The Music We Experience Together

As an introduction to what we focused on in class this past week, here’s a project:

Take five stickie-notes and on the first write “beta.”  The second should read “alpha,” the third “theta” the fourth “delta1” and the last “delta2.”  Now, stick the first on your forehead; you’re alert, and your mind is working at “beta.”  Walk over to your pensive cat that spends hours every day staring out the window and stick “alpha” on her back.  “Theta” belongs on your son who is staring out of the same window, gathering his thoughts for another painting.  The sleeping dog on the floor gets “delta1” and your snoring husband should wear the “delta2.”

 

I’ll explain:

This week we learned that our brains functioning capacity has been categorized into cycles per second.  When we’re alert and actively engaged we’re in a state called beta, functioning between 15-40 cycles per second (cps).  Conversely, in deep sleep (Delta2) our neurons are transmitting information at the rate of only 1.5-3 cps.

 

Alert, Active

Beta

15-40 cps

Reflective, quiet

Alpha

9-14 cps

Daydreaming, Creative

Theta

5-8 cps

Sleeping

Delta1

3-4 cps

Deep Sleep

Delta2

1.5-3 cps

 

Lyle Davidson said that “Theta is a good place to be,” and decided that we needed to be brought down to the 5-8 cps range right away.  We were asked to sit still and quietly with our eyes closed and allow ourselves to really lean into our chairs.  We were to relax all of our muscles and really let our minds be free.

After five or ten minutes we opened our eyes and shared our experiences.  Some class members shared that they were able to organize their thoughts, allowing distractions to come and go without ever focusing on them.  We were also able to focus on different things in our environment, an example of what attention really is.  Also, we could remove ourselves from the current environment address a bigger issue without the current “brain noise.”

The next time you find yourself in a stressful situation, try theta.  Let me know how it works.

 

Something I’ve noticed outside of NEC

A close friend of mine, a double bassist, is one of the many artists you may find down in the bowels of the city, better known as Boston’s subway system.  If you go to Downtown Crossing on a Friday night you’ll probably see him with this bass plugged into a loop pedal and an amplifier.  He layers loops one on top of the other and then improvises on them, some of the tunes being mellow, others joyful, and he often delves into the realm of raga, which is the genre in which the following experiences occurred.  He moves between arco and pizzacato, and people absolutely love it.

It’s very common for a crowd to build around him, many people staying to watch as two or three of their trains come and go.  Last week I observed a man very interested in the music and exhibiting many of the characteristics and behaviors of a person with mild autism.  He would be silent and introspective, and then would start clapping furiously at some points in the middle of an improvisation.  During the music, after he’d really gotten into it, he was alive in a new way.  It was fascinating; I’d never seen anyone respond that way. 

Last Friday I was sitting on the same bench a few yards from the show and a man sat beside me.  He clearly hadn’t showered in a while and was mumbling to himself in a frustrated voice.  My friend had taken a break and when he started again the man was silent, lowered his head, and began clapping the beat the way a small child would.  When the music reached a place that became really repetitive and, I think, a little boring, the man got up, started mumbling again, and staggered away. 

These people who behave in a way that’s less than socially acceptable have unequivocally positive reactions to the music.  Their behavior moves from one of silence and frustration to a peace and a joy.  I’m sure I’ll have another opportunity to experience someone’s ecstatic happiness inside beautiful music and I’ll be sure to share it. 

I’d love to hear about a similar experience you’ve had, whether it’s a snoring husband or someone being awakened by peaceful tunes.

10/15/08 Reflection and Analysis of Recent Class Sessions

Learning through Oral History and Morphogenetic Family Fields

In one of our first classes, Warren taught us the first verse of a traditional Indian song. He began the class with a drone and had us repeat vocal warm-ups in order to acquaint ourselves with the intervals in the scale. These fragments were then, piece by piece, combined to form a small melody. At this point, he broke away from the melody to have us repeat 5 or 6 spoken syllables. He then sang the completed piece with the full text and had us sing along when we heard the syllables that we had just learned. Now we had a somewhat ‘fleshy’ skeleton of the piece that we were able to fill out with the missing syllables. After about 10 or 15 minutes the class had successfully learned the verse.)

In our session this week, three of us recollected the song to Krishna that we had learned a few weeks ago while the other five members tried to learn it. This time, though, it only took about 4 or 5 minutes for the class to be able to recite it (as opposed to the 10 or 15 minutes the time before).

This reminded me of Rupert Sheldrake’s studies with morphogenetic family fields. Stated in a question to anthropologist Terence McKenna, a morphogenetic field is “a non-material organizing collective memory field that affects all biological systems. The field can be envisioned as a hyper-spatial information reservoir that brims and spills over into a much larger region of influence when critical mass is reached – a point referred to as morphic resonance.” Basically, one can understand it as a collective memory bank where a species, through adaptation and evolution, stores knowledge that is passed on through future generations of that species. Sheldrake elaborates that

each individual both draws upon and contributes to the collective memory of the species. This means that new patterns of behaviour can spread more rapidly than would otherwise be possible. For example, if rats of a particular breed learn a new trick in Harvard, then rats of that same breed should be able to learn the same trick faster all over the world, say in Edinburgh and Melbourne. There is already evidence from laboratory experiments that this actually happens.

In this case, knowledge is not limited to growth by future generations, but in fact is immediate.

This seems to be evident in our classroom. It took half the time for the class to learn the song when there were members present who had already learned it than it did when none of us knew it. In relation to this, Sheldrake determines that “animals inherit the successful habits of their species as instincts. We inherit bodily, emotional, mental and cultural habits, including the habits of our languages.” This could also go to explaining the pattern of oral history and tradition that makes our species unique. Warren mentioned in class that oral tradition was learning based upon the human love of imitation. I agree with this, but I also believe that, on a similar scale, oral tradition exists because of our innate capability of memory. Sheldrake in fact proposes that memory is inherent in nature. In this way I see oral learning and history as divided into these two factors; imitation and remembrance.

I watched a series of video clips this week on YouTube of Warren and his teacher, S. G. Devasthali, in a lesson (http://www.youtube.com/watch?v=W4qibmXtTN0). The way in which he learned the ragas was similar to the way in which he taught pieces to our class. There was a call and response throughout the lesson, where his teacher would sing a fragment of the melody which Warren would repeat. The fragments were eventually compiled and through this repetition, he remembered them. This is the basis of oral tradition; imitation and memory. Repetition may also be listed as a component of oral tradition, perhaps as a subset of imitation.

It is interesting that, while he worked with our class, the song was essentially shattered in numerous fragments (phrases, pitches, syllables, physical expressions of the mouth, etc.) which we pieced together in a variety of different ways. I could almost envision a matrix of possible combinations, which after a number of these combinations had been tested, an image of the piece as a whole became more clear. It seems to me that this method is effective in that a deeper understanding of the material is achieved, where one not only learns the song front to back, but now knows its inner workings and could perhaps sing it back to front, or even from middle outwards. This also relates to a matrix, lets say in 12 tone music, where all possible combinations are visible at once (all of the inversions, retrogrades, and retrograde inversions for each transposition of the prime series).

Later in the class, we began to learn the second part of the Krishna lullaby. I was reminded of a piece by Milton Babbitt for soprano and piano (or tape) where, in addition to his systems of 12 tone and duration rows, he devised a system where each pitch was assigned a syllable. In this way, the text of the piece emerged from the music or from the system, rather than the music emerging from a set text. For me, this was similar in that learning this Indian song (where my knowledge of the language is next to none), each pitch or melodic fragment was assigned a syllable or, in a sense, a syllabic motif. It is interesting that in this case, in both pieces, there is a supreme unity to the sound. One piece (the one from class) the music emerged from the text, and the other (the Babbitt piece) the text emerged from the music. Either way, both utilizing a language unintelligible to my ears, both pieces felt solid and complete.

-Chris