Music Teacher's Helper Blog

In 7th grade, our music teacher tantalized us with ideas about the harmonic series. I remember asking him about it after class, and he gave me a copy of the Instrumentalist magazine with an article and diagrams showing the connection between music and the frequencies of sounds.

I was fascinated, and I’ve seen students be equally interested, and even taken by surprise, at this meeting of music and science. It adds another dimension to learning about music besides the struggle of trying to coordinate hands on an instrument and understand the organized beauty of melody and harmony.

The harmonic series explains why anyone can match two pitches, and why octaves have notes of the same name, and are almost as easy to identify as unison pitches. The fact that one octave is double the frequency of the lower one helps string players understand why a string rings sympathetically if the octave note above it is played in tune.  Even beginners can hear this, and since there’s a physical, scientific reason for it, they don’t have to worry that it’s tied in with talent, or years of study. 

It’s fun to point out that anything in the world that vibrates at high speed will create a musical pitch–a hummingbird wing, or a card buzzing on bicycle spokes–and if we know how fast it’s vibrating, we know what pitch it is.  For example, the hum in our houses and our sound systems is between an E and an F, because it’s a multiple of the 60-cycle vibration of our electric current.

It’s amazing to see that if a string divided in half, the resulting pitch is an octave higher. Even more surprising is to find out that if you divide the string in thirds, you hear a note a fifth higher than the octave. Wind players work with this all the time, and for string players this fact helps understand why the fifths our open strings are tuned to are pretty easy to hear–the next easiest thing to identify after the octave.

So the revelations add up: one-half the length of a string (or column of air) makes a vibration double the frequency of the full length, and sounds an octave higher. One-third the length triples the frequency, yielding a note that’s a fifth higher than the octave. One-fourth quadruples the frequency of the vibration, adding a fourth (resulting in a note two octaves above the original). One-fifth quintuples the frequency and adds a major third.

On it goes, adding a minor third, a major second and so on. Some say the history of Western classical music follows the harmonic series, with each generation spotlighting the next level of the series as its featured interval. This idea doesn’t apply too well to some of the baroque composers who loved playing with dissonant intervals. But it seems to fit the general historical pattern of succeeding generations of composers moving from unison to fifths to thirds to seconds to twelve-tones to even quarter-tones in their compositions.

I say Western classical music, because music of other cultures or of local populations, whose music is categorized as folk or traditional or world music, have developed other sound patterns.  For example, the Ottomans went so far as to divide the octave into 57 pitches, and this can be heard in classical Turkish music.  Some Indian music apparently divides the scale into 22 pitches.

It’s especially intriguing, I think, that the two most ambiguous notes in the harmonic series–the multiples of the original frequency that don’t quite match our seven-note scale–are the third and the seventh notes of the scale.  It’s no coincidence that these are the notes most freely toyed with in most musical cultures. In classical music, these notes determine major and minor.  Harmonic and melodic minor scales play around with the seventh note of the scale.

The blues likes to bend primarily the third and the seventh notes. Many old fiddle traditions play the thirds and sevenths ambiguously, sort of halfway between the major and minor thirds and sevenths. This can be done easily on a violin by spreading the fingers out evenly:  place the second finger halfway between the first and third, instead of next to one or the other to form a half step. You might assume a player might do this only because of a lack of training, but in fact, this ambiguous pitch is maintained by some fiddlers even in other keys, so it’s clearly part of a way of hearing the pitches. An example is the playing of Joe Cormier, a great Cape Breton fiddler, or old recordings of traditional Shetland fiddlers.  A musician unfamiliar with those traditions would simply assume the player is out of tune.

We often view science as making things better known and more predictable, but it seems to me that learning about the harmonic series and the science of sound only makes musicmaking more engaging, mysterious and awe-inspiring.

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One of my students is a professional educator who has gone through all the ranks of teaching, on up to top positions in education administration. You would think he would be a good student, and in some ways he really is: he respects my suggestions, works to understand them, comes faithfully to lessons, is proactive with ideas he wants to pursue, and is generally patient and persistent.

But there are often moments when he can’t seem to do the simplest actions, or even follow the simplest instructions. And if I insist he focus on those simple instructions, he can eventually get it, but there is an unspoken sense that I’m treating him a little like a child, even though I have no intention to do so.

The problem, I think, comes down to acknowledging one of the ways in which learning music is different from other kinds of learning.

In many arenas of education, the instructor wants to teach a piece of information but knows it isn’t helpful simply to give it out when the student isn’t ready to understand it. Sometimes I like to test people out by offering advanced information to see if it makes sense–my own judgment of whether they’re ready to understand may not be perfect. But more often than not, if someone doesn’t know enough to ask the right questions, they aren’t ready to hear the answer.

So it is a common teaching strategy to lead the student bit by bit to where s/he is ready to grasp the new information. And it is common learning strategy, in response, for a student to try to figure out what the teacher is getting at, because if the student can go there and understand the point, s/he can grasp it and move on. This is especially important to an adult student paying good money for lessons!

But music isn’t like that. It is a combination of information and physical sensation, and it comes to nothing if not set in motion, down the river of time.

When I ask my student who is a professional educator to try a simple exercise with three notes, and he can’t seem to get it, sometimes I think he is just trying to figure out in his head what exactly I’m getting at, so he can understand the point and move on, rather than follow the simple instructions as if being led by baby steps.

What he may not realize, though, is that I’m not always getting at anything other than exactly what I’m asking him to do. Sometimes in music, you need to experience the smoothness of playing two notes on the upbow leading into a strong downbow on a beat note, and this feeling needs to be felt and built into the hands and ears several times in a row, for its own sake. It’s not always a mental exercise or a piece of information to understand. There’s no ulterior motive to jump to. It is what it is. And when that bowing in that spot becomes comfortable, that spot in the music flows better, and the mind can focus on more important things. The repertoire of muscle memory has just broadened, and doors to better musicianship have opened.

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Last weekend, we were an exhibitor at the Utah Music Teacher’s Association (UMTA) Conference, and it was a great success! This was our first time exhibiting at such a conference, but the response was overwhelmingly positive. Everyone who took more than 30 seconds to see what our booth was amazed at what Music Teacher’s Helper could do to simplify business management in their studio. We also did a showcase and demonstrated Music Teacher’s Helper to a larger group, and got a lot of great interaction and feedback. Some of the most oft-requested features were a photo album on the studio website (to put up recital photos, etc.), and a way to track Federation (NFMC) points and trophies, etc. So, these are things we’re currently looking into. Actually, we already finished the photo album. 🙂

I, personally had a lot of fun getting to meet more teachers out there and learning the different ways teachers have of handling billing and scheduling in their studios. I especially loved seeing their faces light up when they realized how much time and headache Music Teacher’s Helper could save them. We had such a great time that we’re considering going to the Music Teacher’s National Association (MTNA) Conference in Toronto next year. We’re hoping it will be just as big of a hit there as it was here in Utah. What do you think?

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