Theory Meets Practice in the Music Classroom


"Education is not the filling of a pail, but the lighting of a fire."
–attributed to William Butler Yeats


Overview of this Section

With a growing understanding of kinesthetic teaching/learning and its foundation in certain philosophies of teaching and learning, I set out to engage in the reciprocal process of teaching and learning in the music classroom. My goal was to do this while maintaining an awareness of how our bodies and our sense of movement come into play when we seek to teach and learn. In this section, I relate how my understanding of theory and attempts to put theory into practice worked in the context of the music classroom and the school I worked in during my study. Because my work as a teacher happens in the field of music, I will weave together in this section theory from music education, theory from the previous sections, and reflections from how the influence of theory manifested in my practicum..
This section includes discussions of lessons I created and implemented inspired by my research, how they linked back to theory, and how the experience of bringing theory into practice in the classroom changed me as a teacher. Stories from the laboratory of the music classroom serve as a departure point for literature review in music education.
The theorists I review include Jaques-Dalcroze, a pioneer in combining music with movement in education. Phillips advocates a psychomotor approach in teaching children to sing, and Lessac’s approach to singing involves development of sensory and kinesthetic awareness. Elliott and Small promote music as an activity, as opposed to a thing (musicing and musicking, respectively), and Elliott in particular promotes a praxial approach to music education. Wade and Campbell are creators of the Global Music Series, which presents a musical culture model for musical education, and which looks at the many ways that the people of the world use music to make meaning in their lives.
In this section, I also address the transformational process I went through while examining the context in which I was teaching. As I became exposed to theorists in teaching and learning, kinesthetic teaching/learning and music, and as I lived with these theories in the context of my work life, issues emerged regarding what it means to teach music in a school, or even to be a teacher in a school at all. I include these experiences in this section as well.
During this time I taught music at an elementary school and privately, taught weekly T’ai Chi classes, acted as choir leader and cantor for monthly liturgies, attended professional development seminars for teachers, T’ai Chi seminars and classes, and participated in a variety of bodywork and physical re-education sessions. I hosted three “Sung Shui” community jam sessions and spent a weekend creating an original musical film with a 48 Hour Film Festival team. Working at an independent school for the first time gave me insights into this segment of the educational world I don’t think I could have received any other way. Along the way, ideas about education and kinesthetic learning challenged and inspired me as I discovered and invented ways to integrate theories of learning and kinesthetic learning with my teaching.
This section is about what I learned about kinesthetic learning through the doing of it. I spent a year exploring, integrating and putting into practice the principle of being aware of, taking advantage of, and including the body and sense of movement in seeking to teach and learn.
But it is also about what I learned about doing this primarily in the context of a traditional elementary school.9 Trochim says that even for a single hypothesis or focus question “there are a number of analyses a researcher might typically conduct” (2004) and a number of conclusions that may be reached. This chapter is also about what I learned about myself as a music teacher, as a teacher in general who is finding her place in the world of education.

In the Music Classroom: Overview
My goal as a music teacher is to help others engage in the making of music, and to experience joy in the process. Dewey (1938, p. 27) and Jaques-Dalcroze (1921) emphasize the importance of joy in education, and von Glasersfeld (1983) writes that external rewards (grades, candy) are not required when learning is taking place, as the enjoyment of the experience is all the reward we require. Elliott agrees, saying that “enjoyment is the affective concomitant of self growth... and so we will do it for its own sake” (p. 118). But we cannot expect others to engage in music and experience joy if they are in a state of contraction, feeling insecure, overwhelmed or confused. This is as true in a classroom situation as it is in the rest of life. Teachers must provide an inviting and comfortable way in, with just enough challenge to make it enticing. Elliot, building on Csikszentmihalyi’s theory of flow, points out that the task of music education is “to develop the musicianship of learners through progressive musical problem solving in balanced relation to appropriate musical challenges every step of the way” (p. 122). If, as a teacher, I can successfully provide that balance, I’ll have no need to resort to threats nor external rewards, as the reward will be in the doing of the action.
However, cultivating this joy is not without its challenges. I have discovered that music teachers in this country are up against two major obstacles to teaching music, which Campbell articulates well.
Students from “singing cultures” are likely to sing as they talk, easily, with range and volume, and without embarrassment....Likewise, cultures which pay homage to a “star system” [italics added] in which the talented few “speak” (sing, play, and dance) for the untalented masses will raise people who are uncomfortable with their voices as musical instruments and with their bodies as an expressive means of responding to music.... Classes at all levels contain students at various points of a spectrum of music-making experience, and teachers are challenged to intrigue and entice them to know music in thoughtful listening and active participatory ways (p.9).

I was grateful for Campbell’s recognition of these two pervasive challenges for k-8 teachers of music. The challenge of teaching to classrooms of students with a wide range of experiences, from years of violin lessons to almost no experience at all, is always on my mind. How can a teacher guide and encourage the musically timid or inexperienced while simultaneously engaging the seasoned musician? Campbell also acutely perceives that this condition arises out of the musical “star system,” as she describes it, of our culture. Wade (2004) offers perspective on this issue by setting forth a societal spectrum in which
some societies expect people who make music to be specialists, born into the role or endowed with a special capacity.....[while] in some societies it is assumed that the practice of music is a human capacity and that all people will express themselves musically as a normal part of life (p. 1)

I have found this to be all too true. It means that some students are not simply uninitiated when it comes to playing instruments and singing, they are actually predisposed to avoid even trying it at all costs, having already been told that they are not “musical.” My experience is that the older a group of students is, the higher the percentage of those who feel that they cannot do music, and the more ingrained the damage done from living in such a star system culture. A teacher claiming that “music is the birthright of every human being” and that “everyone can and should play, dance and sing” and that “yes, you in particular can do this and learn to do it well” may be a lone voice in certain school environments.
The condition reminds me of descriptions of learned helplessness, a term originated by Martin Seligman in the mid 60’s when, in exploring the connections between fear and learning with caged dogs and electrical shock, it was discovered that all animals, including humans are able to learn that certain reinforcers are uncontrollable, even when faced with clear evidence that the reinforcer may indeed be controllable. In this case the reinforcer is the “star system” culture. As a teacher trying to entice a student into the world of musicking, I sometimes feel as though I’m trying to cajole the students out of a harmful cage.

Making music is kinesthetic experience, so the a music classroom is a natural for the exploration of kinesthetic learning. Theorists such as Jaques-Dalcroze,(1921), Phillips (1992, 2001), and Lessac (1996) advocate movement, a psychomotor approach, and a sensory approach, respectively, for the teaching of music. Campbell (2004) presents the teaching and learning of music as multisensory experience (p. 6), of which kinesthetic experience is an integral part. Elliott (1995) and Small (1998) find within our very biology the roots for their musicing (and musicking, respectively), a bodily basis for our human need to understand and make meaning in our lives through the making of, the doing of, music.
My practicum experience began before the students arrived. This was to be my first year at an independent school, and I admit that I was quite ignorant of the term previous to this experience, but I slowly cam to realize that this was just the newer and preferred term for what I grew up calling “private school.”
For the previous eight years, I’d taught music at parochial schools. A K-8 parish school with one classroom per grade typically needs a music teacher for only two days per week, and this was the case at the school I’d been working at. Looking to pick up enough hours to make the benefits package, I’d sent out my resume to to other Catholic Schools in the area. I was aggressively recruited by this independent Catholic school, who wanted me for a 4/5 position spread over a 5 day week, which meant I’d have to leave the school I was at. The independent school offered flexibility for my graduate work schedule. But, since this was a Catholic school, I didn’t expect much of a change from the schools I’d been at before, except that I had a larger salary and a bigger annual classroom budget. Learning about the differences between parochial and independent schools was to become an unanticipated part of my practicum education.
In particular I remember being inspired by the Assistant Head of School’s speech to parents on back to school night about the school’s philosophy of progressive, research-based, student-centered, self-directed learning. My research and my instincts told me that this would be a good setting in which to explore integrating kinesthetic learning in the music classroom.

Setting Up the Classroom
In setting up the classroom to facilitate kinesthetic learning, I remembered Dewey’s discussion of the importance of setting up the environment to provide the right kinds of experiences. My vision was to create a musical playground, a space which beckoned all who peeked in to come in and pick something up and give it a try. I wanted the room to be bright and colorful, yet warm and comfortable as well. I arranged the instruments in a large circle around the periphery of the room, leaving room in the center for movement and dance. I agree with Dalcroze and others that movement is a key to learning music.
I am a fan of the tradition of many communities to sit around in a circle when engaging in music, and I am less and less, as time goes by, enamored of the performance model in which there is a performing group and a separate and separated listening / audience group. I wanted the arrangement of the space to reflect this. Although one side of the room was constructed with the familiar tiered levels so often used in traditional choral work, I rarely used it this way, and it became part of our seating area.
The audience/performer model relates to the teacher/student model in the traditional classroom. One group faces the other in a face-to-face us/them structure. The teacher stands up in front and speaks, the students sit and listen. In a traditional educational setting, it’s difficult to get around this basic structure, and I’m not against using it at times for expediency with certain things, but most often I like to sit among my students in a circle, and I wanted this to be easily possible in the classroom. I provided a wide variety of seating alternatives, most of them low to the floor or on the floor. Very often we’d arrange ourselves in a circle using the alternative seating items I set out in the tiered part of the room.
I gained inspiration for the seating in particular from the SI theory of Ayres (1972) and Kranowitz (1998), and the work of Hannaford (1995) and Gilbert (1977)(see Appendix: Setting Up the Classroom). A variety of seating options promotes sensory integration, mind-body flexibility, alternatives in sensory stimulation, and even proper posture. T'ai Chi teacher and Acupuncturist J. Lang puts it very simply, "Chairs are evil" (personal communication, July, 2005). Correct posture is critical for relaxed, healthy musicking. Seats such as inflatable cushions, zafus, seiza benches and exercise balls, when properly used, allow the pelvis to rest at such an angle that the "sits bones" (ischial tuberosities) are under the body and the spine aligns upright in a relaxed and natural way, almost as if it were "falling up." Perhaps this is why globally, it is not unusual to see musicians squatting, seated on the ground or floor, or seated on low stools and benches. Thus, a music classroom provides a wonderful opportunity for exploring alternatives to typical chair seating.
I wanted the room to visually express aspects of my philosophy of music and music education. I wanted students to feel comfortable with things which may often seem overwhelming, and I tried to do this be making such things accessible. For example, I preferred to keep most of the instruments out on display, inviting students to pick them up and try them. I wanted students to be comfortable with the idea of exploring the whole world in search of interesting things, and to see the world as a whole as their home, so I brought in an inflatable globe three feet in diameter, to use when we “traveled” to different parts of the world to listen to music, so they could actually hold it and turn it and trace their fingers across oceans to arrive at the country we were “visiting.” I created a circular chart of the musical notes, in bright colors, so that students could see that most of the music they have ever heard is made up from a repeating pattern of just twelve notes (see Appendix: setting up the Music Classroom: Circular notes Chart).

Lessons
I set out Ground Rules at the beginning of the year. The idea of establishing rules, although at first this sounds potentially oppressive, is really about creating a common structure for experience within which we can all explore in freedom. These Ground Rules apply to all of us, teacher included, and establish mutual understanding for behavior, so that we may get past the rules and on with the music. It’s during this time that I also introduce myself and my philosophy to the students: they deserve to know something about the person they are going to be working with. As I wrote in my journal:

My goal is to play and make and do music and to help them to play and make and do music. I’m not so much interested in talking about music as I am about doing it and getting them to do it. I tell my students, "Don’t worry if you think you aren’t musical or you can’t do music very well. Don't worry if someone else has told you that you can't do music very well. That’s not important to me. There are plenty of places in the world where everyone does music every day and no one would even imagine that some people can’t do it or aren’t meant to do it. Music is for everyone, it’s our birthright as humans, and that’s a big reason why I come here and do what I do." As a teacher, I set example, and serve as a guide, a facilitator, a support person for their music.

Dewey’s (1938) philosophy of the teacher as a facilitator in a democratic classroom and Anne Green Gilbert’s (1977) observation that “the structuring allows for freedom” are among my influences for beginning the year by setting out the Ground Rules (see Appendix: Lessons: Basic Ingredients: Ground Rules). Support for my philosophy that “Music is for everyone” and my approach of learning music through the doing of it can be found in the work of Campbell (2004), Elliott (1995), Lessac,(1996) Phillips (2001), Small (1998), Tomatis (1991), and Wade (2004).

Doing the Blues: Stepping to the Music; Call and Response
Kinesthetic learning can be initiated through oral instruction combined with visual imitation, and through vocal imitation responding to aural input. As I write there is an article in the New York Times Health section about mirror neurons, the cells we have in our brains which specialize in imitating or mirroring the actions we hear, see or think about (Blakeslee, 2006). The old saying “monkey see, monkey do” seems to be even more true of humans. Perhaps this is part of what makes imitation such an effortless and enjoyable way for people to learn. However, imitation for imitation’s sake does not justify its time and energy in the classroom. Dewey (1938) rejects knowledge of the past as an end and sees it rather as a means of helping to deal with issues of the present and future; the connection between these two exists within experience (p. 23). By taking advantage of the inviting ease of the blues tradition, as well as the human knack for imitation, establishing basic fundamental practices in a classroom such as call and response singing or drumming and stepping to the regular beat of a song allows everyone to be able to experience music in no time, building confidence necessary for deeper future exploration.
Jacques-Dalcroze (1921) held that ”musical sensations of a rhythmic nature call for the muscular and nervous response of the whole organism.” His strategy involved using movement of the body to comprehend rhythms and movement of the voice (singing) to comprehend pitch.Typically I do this using a CD called “Blues in All Keys” It’s designed to allow musicians to practice improvising over basic 12 bar blues structures in a variety of keys and tempos, but I’ve found it to be ideal for getting a classroom of learners up and moving and singing relatively painlessly. I play the blues on the CD, and get the class to step to the beat, first moving left for four beats and then to the right. This allows the music to come in through the ears while we respond and actively participate in it with our bodies. This is how I begin teaching scatting as well (see Appendix: Lessons: Basic Ingredients: Doing the Blues).

Moving in a Circle; Passing ‘Round the Circle
Often I will work in circles with the students, as I feel this is a natural form for creating group music. However, for very young learners, the basic skill of forming a group circle may not yet be established. As adults, we sometimes take for granted such a skill, and may have no conscious memory of having acquired it. I imagine that every Pre-K teacher has a way of helping young learners develop this skill, but lacking such training, I had to find my own method.
Jacques-Dalcroze emphasized the importance of working with rhythm “for the coordination of brain, nerve-paths and muscles” (1912) and “to regulate the natural rhythms of the body ... to create definite rhythmic images in the brain” (1921). Each hand percussion instrument has its own feeling and requires its own body action and awareness. I like to use a variety of percussion instruments when working with rhythms, and often use a game such as "Before you Can Play, You Have to Give Away" (see Appendix) to distribute them. However, after a circle of students has had some time with their initial instruments, it's fun to pass the instruments around so that each learner may have experienced a variety of instruments by the end of the time. But, it can be a problem, particularly with very young learners, to get the instruments passed around in the circle. With older students one might simply say, "Please pass your instrument to the person on your left," but what about very young students who have yet to get familiar with such a directive or concept? They may not know left from right, they may not get the idea of passing around in one direction, and they may not want to let go of what they have. In Passing “Round the Circle, I use oral/aural instruction and setting an example for imitation to facilitate a series of movements and actions on the part of the students which results in getting the instruments passed along in the circle to the next person (see Appendix: Lessons: Basic Ingredients: Moving in a Circle; Passing ‘Round the Circle).

Words into Rhythms
I have found that learners become more confident about playing percussion instruments when they realize how much they already know about making rhythms. In every word and phrase we say, there is a rhythm pattern. When children realize this, they can begin to explore and play on their own with rhythm patterns; all we have to do is help them make this connection (see Appendix: Lessons: Basic Ingredients: Using Words to Make Rhythm Patterns). This can provide learners with opportunities for internal exploration which may manifest as external expression, as they think about the rhythms of word in their heads, and then speak or tap or otherwise play them out in the rhythm. Additionally, in using words to make rhythm patterns, there’s an integration of language that I like. It is empowering for the students, as they already have a substantial vocabulary, so learning that this can be used to discover and invent rhythms gives the already comfortable tool of their vocabulary another use.
As I articulated in the previous section, kinesthetic teaching/learning may be internal, external, or a combination of both. The body may be many instruments, and kinesthetic learning can be learning about the body and how to use it. I encourage children to discover and inventory the instruments they have on their own bodies, “the instrument you have with you even in the bath tub.” Then we can explore the rhythms within words and try them out using our body instruments (claps, stamps, whistles, snaps, and so on). The sounds we make with our mouths all the time (words) without thinking about their inherent rhythms may now be felt and expressed through our bodies. Because there is verbal direction, the impetus for the kinesthetic experience is external, coming from the teacher or student who comes up with the word or phrase to rhythmically explore. However, because the students enter a process of speaking and playing, then listening internally to the word while playing, then lastly trying to play without thinking of the word at all, just the rhythm pattern, there is a movement from oral/aural experience toward internal and external kinesthetic experience.
Kinesthetic learning may be a body-on-body direct experience. Sometimes a student has trouble clapping a steady beat, even when surrounded by a group of students playing the same beat. Inspired by the body-on-body definition of kinesthetic learning offered by Bateson and Mead (1942), I now stand behind such students and lightly tap the rhythm on their shoulder or upper back as they are trying to play it. If they still have difficulty, I’ll ask them to stop playing for a moment, and just tune into the feeling of the rhythm on their body. When they do this, you can almost see the internal brain paths developing by the focused concentration on their faces. Without stopping the beat on their back, I then ask them to try to play again. I have had great success with this approach.
Getting to Know the Notes and the Pitch Matching Game
The world of music involves a potentially confusing combination of the two kinds of information that von Glasersfeld (2005) identifies when he advises teachers that “whatever is conventional must be learned, so to speak, verbatim; what is based on rational operations, should be understood.” It makes sense to me that learners deserve to know which kind of information in music is which, but teasing apart the two can be sticky.
Recall that von Glasersfeld further states that conventional information is necessarily political, whereas that which is based on rational operations is politically neutral (2005). Perhaps there is a link between this distinction and the distinction Elliott discusses between the aesthetic versus artistic qualities of music (1995, p.90). The asethetic qualities being “directly noted,” “immediately perceptible” and being “the qualities that belong to something” and which “do not manifest indications of their contextual embeddedness,” perhaps these would be akin to information which “is based on rational operations.” The artistic qualities being “attributes of works that are directly reflective of the practices and traditions of which they are a part,” may be the equivalent of von Glasersfeld's conventional information. By extension, perhaps Elliott’s point that “Most music education philosophers make no distinctions between aesthetic qualities and artistic qualities” (1995, p. 90) is an indication that he may agree with the advice von Glasersfeld offers to teachers in the words above.
The science of sound reveals a harmonic overtone series of aligning and harmonizing sound waves generated by a fundamental vibration which is well known in the world of physics. The physics of sound is a natural aspect of the field in which we engage in music, information about which falls into von Glasersfeld’s category of rational operations, that which must be understood. However, the ways that humans decide to play with and manipulate those natural physical aspects of sound generates information which falls into the other category, that which is conventional and must be learned verbatim.
Elliott acknowledges the place of the physics of sound in the world of music, stating that “works of music are physical events,” (1995, p. 81) and that "Pitch is a phenomenon like few others. Music makers from around the world tend to recognize that from "high to low" along the pitch continuum, every pitch duplicates itself almost exactly at regular intervals called octaves”(p.88). However, this statement sheds light on the confusion as well, because “high” pitches are not really high, they are made up of waves of greater frequency, whereas pitches we perceive to be low are of lesser frequency.
Small (1998) acknowledges that the tonal harmony of Western musicking is “a paradoxical technique...extremely logical...lucidly rational...based on acoustical logic” (p.127) and notes that “the idea of a triad...does have some basis in the physical nature of sound” (p. 124). But he also points out that what he refers to as the Western system of tonal harmony is simultaneously rooted in cultural norms as well.
The basis of music in the physical nature of sound is evidenced in the harmonic overtone series, in which the fundamental tone plus its first five overtones comprise the elements of what the Western system of tonal harmony calls a major chord.10 Add the next overtone and you have the elements of a major 7th chord (but the notes of the overtones recede in volume as the series progresses). Small advocates demystification of the Western tonal harmony system (p. 126). To allow students in my classroom to discover the basis for this for themselves, I kept a collection of whistling tubes, flexible ribbed plastic tubes about a meter long which are played by holding one end and swirling the tubes around in circles. Air rushing past the end of the tube provides friction enough to create vibrations in the column of air inside the tube, and a whistling sound. As speed increases, the whistles progress along the sequence of the harmonic overtone series, and students can experience how certain pitches go together, at least in terms of physics. Political neutrality is certainly the case for the major chord, for any given note has a major chord built into its overtones. However, Elliott reminds us that “music listening is not restricted to cognizing purely sonic information” (1995, p. 84) and Small agrees, pointing out that the identity of a musical work does not lie in the sounds of which it is made (1998, p.112). Still, the physics of sound is based, as von Glasersfeld would say, on rational operations, and must be understood.
The twelve tone scale system of Western tonal harmony, on the other hand, is a hybrid, being based on particular combination of the two kinds of information. The (untempered) scale of Western tonal harmony is generated for the most part by the products of the physics of sound in the harmonic overtone series, and so at first may seem like a product of rational operations and therefore, politically neutral, but untempered scales are rarely used in this system of music, and this does not tell he whole story. The tempered scale is definitely political, the "great compromise" of our traditional Western music. But without it, we would not have the piano.11 It is beyond the scope of this paper to discuss the matter fully, but the point here is that a learner needs only a few seconds playing with a theramin or slide whistle to discover and understand that there are many more pitches possible than are represented on a pitched instrument. Yet out of countless possible pitches within the range of human hearing, the pitched instruments in our music classroom had only twelve. Why, and why these particular twelve? This is the other kind of information, conventional, which von Glasersfeld points out must be learned verbatim, as there is no possible way we could ever come to discover it on our own. I find that once you explain to students where this conventional information begins to figure in, such as in the names of the pitches (we could just as easily have used names such as “green” and “yellow” or “Harry” and “Theodora”) and the fact that A=440 vibrations per second, they relax. They are no longer trying to figure the information out, because you have explained to them that this is the kind of information you cannot possible figure out on your own. It’s an arbitrary thing people came up with a long time ago.
I would tell my classes, “this is where we are; this is what we have; it’s not the only way, it’s not even necessarily the best way, but it’s the way of our culture, and most of the instruments in this room and most of the music you’re ever heard is based on it.” I would hold up a page of sheet music and tell them, “this is not music; it’s just a set of instructions for how to make a certain piece of music.”
Small acknowledges the need for this information, and its limits:
“All ways of musicking have some kind of syntax, some way of controlling the relationships between the sounds that are made; it is a necessary condition for the creation of shared meanings between those taking part....but not a sufficient one.” (1998, p.22).

Elliott (1995) also cautions that although “Part of the musicianship of many (but not all) musical practices worldwide is knowledge about notation,...the ability to decode and encode a system of musical notaion...is only one part of the formal and procedural dimensions of musicianship (p.61). Notation, then, should be taught “as a coding problem to be gradually reduced within the larger process of musical problem solving through active music making.” Given a classroom full of pitched instruments (5 keyboards, 18 xylophones, 2 steel drums, 14 guitars) and the goal of wanting students to be able to play with them, I introduced students to the names and frequencies of the twelve pitches of the Western system of tonal harmony, “the notes,” to de-mystify them so we could move past this to the playing of music.
My creation of a Circular Notes Chart on the wall arose from a desire to do just this I created the chart in bright colors, to make it cheerful and friendly, and made it simple, so that students could see that most of the music they have ever heard is made up from a repeating pattern of just twelve notes. Getting to Know the Notes and the Pitch Matching Game are both lessons which use the circular notes chart I created for the classroom. In Getting to Know the Notes, a student points to one of the notes on the chart, such as “C,” and students look for this note on their instrument and play it12. We can hear and see that the same twelve notes may be found on all kinds of instruments, though they may be in different octaves and have different qualities. In creating the notes while playing the Pitch Matching Game, students engage in exploration of pitch as students alternate playing notes, observing/listening and trying to match the pitch being played with adjustable pitch instruments such as glasses of water, rubber bands wrapped around shoe boxes, or a theramin. They engage in the process of discovery, and are asked to notice the way one can feel the vibrations of the sounds as their overtones line up.
The Getting to Know the Notes lesson requires setting up the classroom in a circular seating pattern, variations of which I used for several lessons (see appendix: Seating Charts). As in the usual classroom situation, the circle features many different types of seating, this time combined with a variety of instruments, offering a range of physical experiences. Following Bateson’s emphasis on the importance of balancing participation with observation and von Glaserfeld’s parallel theory of the need for reflection in order to properly process experience, I was inspired to intersperse “listening seats” with “playing seats” in the circle. At first I was reluctant to do this, as it effectively cuts the time students have with the instruments by half, but the benefits were immediately obvious (more on this below).
The Getting to Know the Notes lesson asks one student to point to note names on the Circular Notes Chart, while other students find and play these pitches on their instruments (xylophones, glockinspeils, steel drums, pianos, guitars). Still other students observe and listen to the process. In a more advanced version of the activity, students also sing the note as they listen to it and play it. Through this process, students come to understand that the same pitches may be found on a variety of instruments, and that these pitches are the building blocks of most of the music they are familiar with.
The lesson integrates kinesthetic with aural and visual experience. Visual aspects come in through visual cues (the rhythm of the pointer and the Circular Notes Chart) used to initiate action on the part of the students, and the visual observation opportunities the listening seats provide for as well. Kinesthetic aspects can be found in the feeling and playing of the different instruments and the movement to different seats of different heights and qualities. In the Pitch Matching Game, the set up is very much like that of Getting to Know the Notes, but interspersed with the pitched instruments are instruments on which one must find and make the pitch (rubber bands, slide whistles, glasses of water, a theramin). Students using these adjustable pitch instruments must engage in the physical act of moving and manipulating the rubber bands, slide whistles, amounts of water and even electronic fields (theramin) while trying to create pitches which blend with the vibrations of the dominant tone being produced by the students on the pitched instruments. This activity links manipulation of movement in space and matter to create varying pitches and asks students to listen with their whole bodies to feel the alignment of the vibrations (See Appendix: Getting to Know the Notes and Appendix:The Pitch Matching Game).
Jamming in Circles

Jamming in is a very natural way to learn music. I asked students to listen to the Blues in All Keys CD with one ear and o their own instrument with the other ear. I would explain that when you do this, you are receiving and giving at the same time; you are responding and creating simultaneously. This is what makes it fun, and it feels really great. You have to do two things at once, so it may be tricky at first, but you get used to it. You can also think of it as having one half of your brain on the music that's coming in from the CD and the group, and the other half on the music that's going out, which is what you are creating. This asks them to notice the distinct feelings they experience during the process. It reminds me of the proprioceptive aspects of Bohm dialogue, in which you are asked to notice your impulses to speak and respond and how they feel as they are arising within you. In the jamming in, I ask students to notice the internal experience of music coming in from the outside, and simultaneously notice and monitor the music they are creating on their instruments, and try to make them work with each other, relate to each other. This reflects Campbell’s "engaged listening" (p. 91) and Elliot’s distinction between thought-less and thought-full listening (p,78). The listener is active and is not just a passive recipient of sound. This is the distinction between listening and hearing. The ear hears, but the self listens. This is an active process; it's not just sound waves on an ear drum. I would tell students,"If you're having trouble getting the beat, try to relax, let the music come to you, let it hit your skin. Feel it vibrate inside your bones. Let it move you. Tune in to it, then try again. If you get off track, just stop and start the process all over." Part of me being able to give such a suggestion has to do with the understanding of the skin I gained from Montague, and the understanding of bone conductivity of sound I gained from Tomatis and Lessac.

Although we started our Jamming In Circles with the blues, after the classes became comfortable with the process of jamming in, I began providing a wider variety of music for the sessions. In the early jam sessions in particular, I’d have students switch to the next seat every thirty seconds or so (every twelve bars).Thirty seconds may seem like a very short amount of time, but particularly at the beginning it's a useful strategy for many reasons. Foremost is that in the beginning, the students can't wait to get a chance to play all the instruments. Keeping things moving ensures that everyone will get around the entire circle and play each instrument at least once. Another is that, because students keep alternating playing seats with listening seats, the distinction between the performers and the listeners blurs as the switching continues, so that the goal of everyone being equally comfortable, and equally involved, in either position may be reached-a cure for Campbell’s star system culture.
When I first used listening seats in a Jamming in Circle, I immediately noticed the positive difference they made. Previously in Jamming In circles, I set up the room so that students could move from instrument to instrument. All students played something at all times. By alternating the playing seats with listening seats, several things happened. First, there was half as much noise coming from the students at any given time, and that meant it was easier for students to key into the CD being used for the jam. Second, allowing the students time and space for observation and reflection allowed them to better integrate and prepare for their playing experiences. Despite the fact that they now had less time on the instruments, their playing improved more quickly, even though they now had half as much time on the instruments. This recalled Dewey’s observation that providing experiences is not enough, as they must not be the wrong kind of experiences (1938, p.6). Having the opportunity to really observe others in the same exercise and evaluating what they observed would spark new ideas in them about how to play when their turn to play came up.
Jamming in to music invites improvisation, extemporaneously inventing music as we are creating it. This does not have to be intimidating. As Bateson says, we are constantly improvising without being aware of it. Our daily lives are improvisation in action. But, as Gladwell points out, improvisation requires structure and the agreement to accept whatever comes out.
Improvisation also requires confidence. Particularly working with students who have not had a lot of positive musical experiences, we need to help them feel safe from the fear of making mistakes. Recall again Gilbert’s 3 kinds of problems, the third of which has unlimited number of correct answers and is, in her estimation, the best kind of problem. This is the situation with improvisation. But, although there may be an unlimited number of correct answers, this does not mean that all answers are correct, and learning that distinction can help with alleviating the fear of improvisation. I accomplish this by explaining the concept of key and starting small. If we’re playing a blues in the key of “C” and you just play the “C” note with a rhythm that fits, it’s going to sound pretty good just about all the time. After students try this and find it to be true, they are encouraged to add a second note, the “G” for example, and bounce between the two on whatever pitched instrument they have.
Music is a curious blend of the two kinds of information von Glasersfeld talks about, and helping learners identify which aspects of it are conventional, and which are based on rational operations can go a long way in helping them build confidence and understanding in the field. Although designating “A” as four-hundred and forty vibrations per second is arbitrary, and therefore, conventional, once we decide that we’re playing in the key of “A” we enter the realm of information which can be based on rational operations. That is, any “A” will sound like it “fits” as it is in the key, as will any “E” for the same reason: it’s the second most dominant note in the overtone series which the note “A” generates. Helping learners understand that the reason these notes sound “right” together is a matter of physics allows them to develop an understanding of what is happening when these vibrations meet and align. If we pay attention, we can feel the harmony. It is tangible.
Dewey and Campbell both regard the teacher’s role as that of facilitator. As the students became for familiar with the jamming in process, I was able to take myself out of the process more and more. I saw this as a positive thing because I became more of a facilitator and less of a gatekeeper. I was providing the students with the service of helping them to create their own music. My goal was for them to depend on me less and less for their own musical experiences, and become more autonomous musicians. This was also influenced by von Glasersfeld’s idea that we all construct our own world one experience at a time. This means the job of the teacher is to provide experiences from which the learner may construct her world. Again, Dewey cautions us that these must be the right experiences. I wanted my students to own their own music. I grew to see myself as a resource person, a helper for their own self-directed exploration.
Challenges of Kinesthetic Learning in the Classroom
As I indicated in the previous section, introducing kinesthetic learning experiences into the classroom can present several kinds of challenges for the teacher. These were certainly not insurmountable, and from my perspective the challenges, logistical, administrative, even psychogenic, were well worth meeting.
The kinesthetic approach to teaching can present logistical challenges. In several of the above lessons I had to set up the classroom properly in order to conduct the class. Another consideration in planning kinesthetic lessons may be space and a need for an environment where the noise generated by the involved students will not interfere with other teaching activities going on in the school. In order to play the bullroarers I mentioned in the previous section, a student swings the instrument around her in a 2-3 meter diameter, and safety requires at least another meter on all sides. These create a loud low buzzing noise, and we had many going at once. We were fortunate to have a large playground away from the classrooms, and nice weather.
Kinesthetic teaching/learning lessons can present administrative challenges. The school I was working at required teachers to do curriculum mapping for their classes. Trying to write teaching plans for kinesthetic teaching/learning lessons made me realize that our language does not have an extensive or specific vocabulary for this sort of teaching/learning, and that resulted in the work being quite time consuming. The standard operation of writing a lesson plan seemed better suited to a reading and writing curriculum.
I found that kinesthetic learning lessons may present a unique set of demands on a teacher psychogenically. Inspired by my experience walking a labyrinth, I became increasingly intrigued by the idea of providing people with situations where they can simply enter in and do, without a lot of instruction. This requires forethought and planning, but it also requires the ability to sit back and observe, allowing the unfolding of events to happen. This can be quite difficult. When I asked students to engage in the Pitch Matching exercise, I had to resist the urge to rush over and tell them that, for example, they already had too much water in the glass, and had gone past the note they were trying to match. I had to inhibit, as Alexander (1932) might say, or as Bohm (1991) might say, suspend. I had to trust the process and allow the students to find it for themselves. But we always want to talk, we always want to explain, and it is so easy to forget that the direct experience is the whole reason you have planned the lesson in the first place. I learned that I had to let go of my agenda in order to allow new possibilities to arise.
Lastly, kinesthetic learning experiences can be messy. During the pitch matching lesson we spilled water, we broke glass, and there was wet newspaper all over the floor. It was wonderful, though, and apparently memorable. Weeks later when I was tuning my guitar to a xylophone at the beginning of a class one of the students piped up with, “Hey, listen! She’s pitch matching!”

Additional Experiences and Reflections
Although it is not possible to relate all of the experiences I had while trying to bring kinesthetic learning into the music classroom, the above examples may serve to illustrate something about my process and progress in these efforts. However, there are other aspects of this work that the lessons themselves cannot show. Classroom teaching happens in the context of a school, and each school has its own identity, values and culture. Trying to implement kinesthetic learning in the context of a traditional school, even one that espoused a philosophy of child-centered, self-directed education, made for additional lessons and, as the ersatz ‘Chinese curse” is reputed to say, interesting times.

Encountering the Culture of the Previous Teacher
As a new music teacher coming into a school, I had the thought of starting with a clean slate. However, I soon learned that walking into the legacy of the previous teacher has an impact on your experience. Everything from the state of the classroom to the state of the students operates in this shadow as the new teacher tries to get her bearings.
I think that someone who has never played the piano before has just as much right to sit down and play as someone who has been playing the instrument for thirty years. Imagine a child running onto a playground and heading for the slide, and, when asked later if she's thinking of trying out another activity, responding "Oh, no, I only do the slide" This is what some of my students were like. It is a shallow confidence which serves to limit exploration into new areas of life. As teachers, we must know our material, but we also must know the people we are working with, as we are working in the context of their prior experience. Recall that in the section on Philosophies of Teaching and Learning, I presented von Glasersfeld’s idea that when we as educators are helping a learner memorize conventional information verbatim , we are engaged in training. If, while working with a learner, we discover that, as a result of certain training, a learner becomes reluctant to venture beyond the realm of the training, it may be appropriate for the teacher to become the tyrant.
I was conducting a unit on songwriting, with an emphasis on collaboration. Certain students expected to be allowed to work together as they were in a band already. At first I allowed this. These were trained musicians, many of whom took regular lessons after school in a popular rock band music school centered around covering recent and classic rock hits. However, problems quickly developed. Given time in a group with guitars, bass and drums to come up with a composition, they presented a piece they already knew. I reminded them that they were supposed to be creating original material. They came back with a very slight variation on a tune they already knew, arguing that the variation made it original. This actually prompted a class in which I taught the famous My Sweet Lord / He's So Fine plagiarism case, in which George Harrison inadvertently plagiarized the song He’s So Fine when composing My Sweet Lord. Even though the plagiarism was not intentional, Harrison had to pay royalties to the publishers of the earlier song. Wehn we compose, we must be mindful of this issue.
Still the problem continued; if a piano player was allowed to work on piano, she'd just do what she already knew how to do. It was the same with the guitar players and drummers. In a room full of new and unusual instruments, they never ventured into new territory. They seemed ossified in their ways of relating to music; their concept of music and music making seemed ingrained into their minds. They complained about not being allowed to just play what they already knew. They wanted to settle into their area of confidence and familiarity and stay there. I was getting much more inventive material from the self-proclaimed “non-musicians” of the class.
At some point I learned that the rock school teacher was my predecessor as the school's music teacher. It was his pre-established culture that I had walked into. He was idolized by some students and resented by others.
I recalled the tour I had take the previous year when I had interviewed for the position. We first came upon five students bewildered with guitars sitting in the vestibule outside the classroom, trying to play from a chord chart they had been given. Nothing sounded right, they complained, so I listened and discovered that the guitars were completely out of tune, which none of them seemed to even realize. I quickly tuned their guitars, helped them to understand how to read the chart, and we then continued with the tour. In the music classroom, the teacher was energetically working with a group of four students in one corner of the room.You could hear that another group was practicing out on the adjacent stage. Other students were sitting reading or doing math or other school work, not involved in musical activities at all.
As I thought about this and pieced it together with my experiences thus far, I realized that the previous teacher had cultivated a star system culture within the school. Some students received lots of attention and played at area parties and events, while others were largely ignored. The ones who adored the previous teacher were now taking classes with him at his rock band school. I though of Jaques-Dalcroze’s statement that, “all teachers should understand the difference between education and instruction.” These students had been instructed, but had they been educated? They had been trained and rehearsed to perform, but training and rehearsing only for the sake of performance is the musical equivalent of teaching to the test.
I wanted to offer lessons that complimented and supported but were not at odds with whatever was happening in the students’ world of private lessons. I needed to figure out how to achieve this, yet still get them out of their stuck places. I wanted to find a way to connect with their musical selves, but also to help these musical selves develop autonomy and independence. It was a new kind of challenge for me. Once when a group was playing a cover song and I mentioned that something didn’t sound right to me, one student explained, “well, it’s supposed to be louder.” I ended up getting a copy of the song and learning it, only to discover that the student had no idea about how to sing the song in the key she was playing it in.
The next trimester’s songwriting class brought in a new batch of students, but the same set of problems. This time I tried a different approach. I created the composition groups myself, deliberately combining and recombining groups of students to mix the seasoned musicians with the less experienced or less confident ones, and I dictated the elements they were to use. I would give them odd combinations of instruments to work with so they might be nudged into new territory. I also gave them very little time, asking them at first to only to come up with a short riff. I might say, “this group will use a kalimba, tube, maracas and finger cymbals, you have 7 minutes before you present.”
I wanted the students to be in a situation where they could openly explore and create. Perhaps they had less confidence with these instruments, but they also had no habits with them. This allowed those who were not confident in any area of music (and it's heartbreaking to find a student who has had music class at least once every week for 7-8 years to be absolutely devoid of any confidence in the subject) to be on a more equal footing with the "experts" of the class, most of whom had, as von Glasersfeld puts it, had training, but not necessarily understanding. The simplification of elements got to the point where I gave a group of the most experienced rockers in the class rubber bands and boxes to work with to come up with a riff. It was as if I had to take them to an area almost of musical disorientation in order to shake loose some of that mind stiffness that had set in and reclaim some natural flexibility and a more open musical perspective. When they emerged on the other side of this process, The results were wonderful--a classroom full of innovative original material. “Fourteen is too young to be set in your ways,” I told them. “Getting stiff and stuck and hard is not a sign of youth.”
Self directed learning can only take a learner so far. Learners also need the benefit of experience, and as Dewey notes,
basing education upon personal experience may mean more multiplied and more intimate contacts between the mature and the immature than ever existed in the traditional school, and consequentially more, rather than less, guidance by others. (1938, p.21)

Some things, traditions in particular, cannot be discovered through self discovery. Other things may not be optimally navigated without the guidance of an experienced teacher. On the other hand, teaching which is limited to training may leave a learner hamstrung. Also, as teachers we must respect a learner’s prior experiences while trying to balance them. An experienced eye can see when a learner is becoming stuck or heading down a potentially problematic path. There is a delicate balance which must be struck.
In this instance, I became the teacher as a gatekeeper, a controller, an approach I would not normally take. But this was not control for the sake of controlling, it was control for the purpose of liberating the students from a falsely internalized external control they were beholden to. Perhaps sometimes you have to take away a lot in order to help someone reconnect with their essential musical self, so trained and covered we may become if we’re saddled with the burden and label of being “talented” in the context of a star system.

Challenges of Engaging in Kinesthetic Learning in a Traditional School Setting
Kinesthetic learning activities can present challenges when introduced in a traditional school setting. Recall Hannaford’s observation that “A majority of teachers continue to believe that learning only occurs when a child is quiet, still, listening, and handing in all their homework” (p.196). The same might be said for school administrators. As it is said of law and sausages, school officials may verbally support the validity of kinesthetic experiences, but they do not want to have to watch them being created.
We were studying timing and flow as an aspect of improvisation. It’s particularly important to understand this in terms of music, as music doesn’t stop for you to find the right note. The time is coming, and then it is here, and then it is gone, so music allows you to experience time, but you must learn to create within these parameters. After going over the theory with the students, I wanted to give them a bodily-based exercise to integrate the idea that the time and the notes keep moving. I threw out Squidgy balls, which are soft and pliable and very non-threatening when they are coming at you quickly, and my directive was to just keep them moving; don’t stop, don’t think, just do. This is a state wherein you can access flow, when you are just doing and not thinking, and how you do what you do comes out based on what you have done before, but now it is too late to think about it or plan or put it in you now, now you just have to let what comes out come out. As soon as you get it, throw it. If you drop it, pick it up and throw it out. just keep all the balls moving. The feeling you get when doing this exercise is very close to the feeling of being in the middle of playing a very fast musical piece when the flow of the piece itself seems to take over and you are just moving along with it, trying to keep up.
This is why we were throwing balls and giggling when the admissions director, unannounced, walked in with a tour. I turned around and saw a group of people staring with their mouths hanging open. I went over to them and cheerily explained what we were doing, something about my studies, and the theory behind the activity, but their faces did not change much.
The following day the admissions director came into my classroom when I was working alone. She asked me “what on Earth” was happening when she came through the day before. Once again I reminded her of my work and explained the theory behind the exercise. She told me that she really liked it when she brought a tour through and the children were all sitting quietly and tapping on xylophones or singing, but she could not have something like that happen again.
Perhaps the most wonderful thing about this incident was the feeling I had when my teaching method was being questioned. I had spent months grounding my work in theory, and my confidence was solid. I felt as if I had a roomful of theorists in my field standing up right behind me, supporting my work. I calmly replied that she was always welcome in the classroom, and she could bring in anyone she liked, but to please understand that this is the way I teach. I offered that if she wanted to let me know in advance when a tour was coming through, I would try to be sure to have the students engaged in activities that were more conventionally presentable. I am quite sure that this incident resulted in the school’s decision not to renew my contract.
There’s a saying in the entertainment business and in politics, “you’re always on camera and you’re always on the mic.” But a school cannot run this way. Education is messy business, and kinesthetic learning can be particularly messy.
Mission Statements
Schools are an expression of a mission; that is, they have a reason to be, which tells the world something about who and what they are. This mission may be explicitly articulated, but even if not, it is implicit in the way the school conducts the business of educating. The school may have its own carefully developed mission statement, but there may also be an agenda of default resulting from any number of unexamined habits or influences. These things affect all individuals who come in contact with the institution. If a school’s mission is not clearly articulated and defined, and furthermore mutually understood by all parties involved, the purpose and identity of the school may become muddied, and problems result.
I became increasingly aware of the critical and conjoined issues of a school’s mission and identity through a string of professional development seminars and incidents during the year which punctuated my learning experiences in this area.
At an Introduction to Independent Schools panel discussion presented by the Association of Independent Schools of Greater Washington (AISGW), I learned that independent schools are mission-driven institutions, run by a board of directors. The board of directors has one employee, the Head of School. The Head of School then implements the plan for the school and “makes the school happen” in accordance with its mission as articulated by the board. More importantly from my own perspective, agreeing to teach at such a school is voluntarily agreeing to carry out this mission. I was not previously aware of how mission-driven independent schools are. I came away from the seminar wondering: what is the mission of the school I’m working at?
As I mentioned above, the Assistant Head of School envisioned the school as progressive, research-based, child-centered, and focused on self-directed learning. This vision aligned with theorists I was reading (Jaques-Dalcroze, Dewey, Gardner, Gilbert, von Glasersfeld and more), and with my evolving personal philosophy of teaching and learning.
At the end of the first trimester, the upper school students presented their original compositions in a performance in the school hall. The various groups let me know which instruments they would be using so I could arrange to have them moved into the hall prior to the performance. We had two upright pianos. One was a recent gift from a grandparent, the other I had discovered in the back of a storage room at the beginning of the school year. It wasn’t pretty, but all the keys worked, and it sounded pretty good. I taped a guide to the keys above the keyboard and put colorful letter stickers on the keys, making it more friendly to unfamiliar players. This was the piano one of my groups chose for their performance. They said they were more comfortable with it.
After the concert, the Head of School asked me, “Why didn’t you use the new piano? It looks so much better.” I told her I was trying to follow the school’s philosophy of child-centered, self-directed learning, and had allowed the students to choose their own instruments. The old piano was what they chose. “That’s good,” she said, “next time make them use the new piano.”
Some time after this, I attended a day-long professional development workshop on “Creating a Brain-Friendly Classroom.” The seminar was a fairly good re-working of the auditory/visual /kinesthetic theories of learning, but what really impressed me was the host school. Their mission was “Joy,” an educational imperative which Dewey and Jaques-Dalcroze also espoused, and it was written on the walls of every hallway and room in the school. This was a school that knew itself and its purpose.
Again I wondered, what is the mission of the school I’m working at? This time I began to ask around, but none of the teachers seemed to know or think it was of much importance. What about the Assistant Head, who spoke of child-centered, self-directed learning? Certainly he would know the school’s mission statement; certainly these values would be expressed in it? In fact he did not know it, he was not sure what it said, but he would try to check. I soon discovered that the mission statement was a vague statement about being a “challenging K-8 school.”
In the middle of the school year, the Head of School expressed frustration about the music for the school’s liturgies, which I voluntarily provided on guitar (as I had done in other schools for many years) along with a group of students on drums, shakers, xylophones and other instruments. She wanted more traditional music; she wanted a piano. I do not play the piano. I said I would be very happy to step aside and let someone else do the music for the liturgies. But stepping aside was not enough; she wanted me to find the piano player. Did she want me to hire one? Did the school have a budget for this? No, she wanted someone in the school community to do it voluntarily. This question had come up before earlier in the school year, and one student in particular, a very accomplished guitar and bass player, had been suggested to me. I had asked him about it back then, and he had told me that he was not interested; he no longer played the piano. Now the possibility of having him play piano for the liturgies was being fielded again. Couldn’t I make him do it?
I have deep respect for my students, and the Rubber Bands and Boxes story above notwithstanding, I am loathe to coerce them. Saint Augustine said that when you sing, you pray twice. Given that music of liturgies may be regarded as an expression of prayer, it seemed particularly problematic to try to force someone into service to provide it. When I said this I was told, “Call his parents. They’ll twist his arm.” I wondered, is this the kind of school we are?
I was not the only teacher struggling to figure out what the school was about, and I was not the only person to experience problems resulting from the school’s fuzziness about its purpose. The consequences of the school’s lack of a clearly articulated mission which was universally understood and embraced by faculty, staff and families, and the resulting lack of a solid identity, continually presented themselves as the year wore on. There seemed to be a schism between progressive and conservative camps. A number of new and more progressive faculty and staff members chose not to renew their contracts. Others (like me) were not invited to (a first for me). A number of difficulties were blamed on the controlling parents of the students. It was the problem of dealing with difficult parents that organizational psychologist Rob Evans was asked to address in his Changing Families, Changing Schools professional development workshop.
Evans’ main message articulated what I had gradually come to understand through direct experience: when a school is solid on its identity and clearly knows and articulates its mission, it doesn’t have the kinds of problems with parents that the teachers and administrators at our school had been having. If questions or problems arise, they can usually be resolved in light of the stated mission of the school. I would add that such a school doesn’t have the kinds of difficulties we had experienced with staff and faculty, either. Near the end of the school year, I heard that the school’s mission statement was in the process of being rewritten.
In retrospect I was blessed to spend time in a school which was struggling as a result of its lack of a clear identity. I learned how schools, teachers and perhaps all humans, can benefit greatly from a mission statement. I stumbled into teaching music in schools as a result of a phone call many years ago. But, if I am to stay in this field, I need to figure out how I am going to stay in it, and what and where I am going to be in it. I need to know my mission.

9
As in the earlier section on the Philosophies of Teaching and Learning,, I’m using the term “traditional” as related to education as Dewey defines it (1938, p. 17).
10The fundamental is note 1; the first overtone is a wave of half its length, creating note 2, the octave. The second overtone, note 3, consists of a wave 1/3 of the fundamental’s length, generating what in Wesstern music is called a perfect 5th above the first overtone. The next overtone, note 4, is another octave of the fundamental, with waves 1/4 the length of the fundamental. This is followed by a wave 1/5 of the wave length of the fundamental, note 5, creating a pitch called a major 3rd in relation to the previous octave pitch generated. Note number 6 is twice the wavelength of note 3, generating another 5th.
11
Small discusses the twelve tone scale system of Western tonal harmony in his book Music, society, education (1977).
12
Instruments such as xylophones and steel drums have the note letter names labeled on the instrument. On other instruments, such as the piano or concertina, I write the letter name in pencil or put a sticker on or next to the key or button.