Science and Art
Now that I am seventy and my engineering and horn performance careers are more in the rear view mirror than in front of me, I feel obliged to offer my own take on the many ways in which art and science can be combined to the benefit of both the artist and the scientist. I have pursued this goal for the better part of half a century and I have been fortunate to have a reasonable number of successes. The time has come to go back to my roots and focus this work in a way that benefits my horn playing colleagues. Horn playing was my introduction to the world of the arts and leading up to that, my interest in things mechanical was the reason I chose to join the school band in junior high school. Others before me have made use of some aspects the science of sound to advance our understanding of the instrument. To date, there have been number of horn playing physicists who have have tried their hands and interpreting mathematical models for the acoustical functioning of the horn and for that I am grateful.
I will be approaching the topic as a horn playing engineer. As an engineer, I treat mathematical models as a handy tool for developing an understanding of the general acoustical functioning of the horn. However, the engineer has to be very aware of the limitations of mathematical models when applying them to the real world. When the limit is reached, other forms of knowledge are put to use. In acoustics, relying exclusively on mathematical models can lead to an unfortunate situation of very carefully and precisely solve the wrong problem. As my brilliant colleague and mentor, Dr. Marcelo Epstein said “the trouble with reality is that it is such a poor approximation of mathematics”.
I will focus specifically on demonstrating the use of engineering design and creative problem solving in bending the science of music acoustics into something useful for the horn player. Sometimes, I will be interpreting mathematical models like my Physicist colleagues have done, but the end goal will always be to acknowledge what aspects of science are useful to the horn player in equal measure with what science does not or cannot know about the art of horn performance. For me, that in-between space is where the fun and useful knowledge lies.
Throughout my dual careers as a horn player and an engineer, I noticed that a considerable number of my horn students went on to careers in math, science and engineering. As well, the professional horn players and teachers I met as a horn player and teacher often displayed a talent for analytical thinking and an interest in the science behind music instrument design and music acoustics. This might be due to the fact that the horn, being such a treacherous instrument to play reliably and consistently, requires that the performer use every available bit of information to achieve a level of mastery in performance. Consequently, the horn player must necessarily be a problem solver, gathering information and concepts from any source, in unique combinations that will yield a successful result.
My main teachers were Eugene Rittich, principal horn with the Toronto Symphony, Arnold Jacobs, tuba and Richard Oldberg, third horn, both with the Chicago Sympnony. Each of these excellent teachers used scientific analogies extensively in their teaching. Arnold Jacobs, in particular was renowned for his extensive knowledge about the bio-mechanics of breathing although that was only one of the ways that he integrated the art and science of music performance.
If I were to begin this adventure from a purely scientific standpoint, I would start by introducing the fundamental acoustical concepts of music in general and horn playing in particular. However, I would soon loose my intended audience of horn players who would rightly have little patience with the opaque mathematical concepts that provide the limited understanding of music as it is presented in the sciences.
Instead, I will chart a different path and begin right away with stories of how the art of music and the science of acoustics can work together successfully to the benefit of the horn player. With each story as a foundation, I will then develop the relevant problem solving and acoustical and musical concepts in a manner that draws on common experiences of horn playing. Hopefully, this will keep my fellow horn players reading long enough to recognize that there are indeed useful practices and knowledge in science and engineering that can, with careful handling, give further credence to performance concepts already in practice and perhaps offer new ways to approach the challenges of horn playing that have a bit of science behind them.
The First Music Story:
This is a story about one of my long time horn playing colleagues. John Ellis was a pianist who decided in his early twenties that he wanted to be a horn player. Although, with such a late start the odds were stacked against him, he persevered and eventually landed a job in a German orchestra after cutting his teeth on an orchestra job in South Africa. John had gotten wind of the fact that I was doing my PhD engineering research on sound reflectors for the horn. During a phone call to bring him up to date on the research, John lamented that the horn solo in the Franck D Minor Symphony was impossible to play without mis-pitching the high A because the clarinet, with which he had to play in unison, was always flat and trying to bend the pitch down inevitably resulted in cracking the A. I was in the midst of my research into sound reflectors for the horn and, based on one aspect of the research, suggested to John that, if he used the F side of the horn and took his hand out of the bell when playing the high A, he should be able to place the pitch wherever he needed it to be without falling off the note. John tried it and it worked. Removing the hand from the bell eliminated the “notches” for the notes above G and the A could be bent in any direction without cracking.
The First Science Story:
I begin my own story by describing my struggles to bring together years of professional horn playing and teaching along with as many years of engineering study, practice and teaching. As a horn player in the 1970’s, the thrill soon wore off from winning enough auditions to land full time jobs with the Canadian Opera Company and then the Calgary Philharmonic Orchestra. The jobs did not offer the creative and artistic outlets that I wanted. The final straw was when I attended post concert receptions given by the local engineering companies who sponsored the orchestra. Very often, I would find myself listening to one or another enthusiastic engineer who would go to some length to educate me about how my horn worked. I was mystified as to why an engineer who had one or two classes in wave theory would imagine that this provided him with more knowledge about the horn than my ten plus years of working every day to learn to coax music from a French horn. My angst was only increased by the fact that the engineer was using the language of science and I could not understand it. In 1982 I gave up the holy grail of a full time, tenured position with the Calgary Philharmonic Orchestra and began to train as an engineer at the University of Calgary.
During the time leading up to my decision to expand my world, I had the great privilege of travelling to Chicago to study with Arnold Jacobs over the course of seven years. There is a very good story about why he put up with my visits for so long, but that is for another time. During one of my lessons, he pulled out a sound meter and had me play with different hand positions while he measure the decibel level associated with each different position. There were remarkable differences in the sound power emanating from the horn bell with more or less of the hand covering the bell. Mr. Jacobs told me that he had used the sound meter while trying to convince Phil Farkas to use a less covered hand position in order to get more sound power with less effort. He surmised that maybe Farkas would have had a longer playing career if he was not working as hard to get a sufficient volume of sound for the demands of the legendary Chicago Brass Section.
As I began my engineering training, one of my goals as a student in mechanical engineering was to develop a more scientific basis for the role of the hand in controlling the tone and pitch of the horn. Placing the hand in the bell is something that no other instrumentalist has to deal with and, for a horn player, the hand in the bell is as important as the mouthpiece in creating proper tone and pitch. Every professional horn player has his/her own theory about how and why to use a particular hand position.
Throughout my undergraduate engineering years, I had tried many times to use high quality sound measurement research lab equipment to clarify the acoustical functioning of the horn under actual playing conditions. My undergraduate efforts were not successful because, with my limited knowledge of sound analysis instrumentation, I had to assume that whatever showed up on the sound spectrum charts was correct and precise. Neither I nor my engineering professors could see anything in the sound spectra that shed any light on the subject other than displaying a graph of the sound spectrum that was a general characteristic of the horn. As mentioned, I was not yet proficient in setting up sound experiments and my professors, who were much better at interpreting the data, were not able to understand the unique acoustical characteristics of the horn other than the simplistic mathematical models that were available.
In grad school, I finally had the opportunity to dig into the actual mathematics involved in sound measurement equipment. To my surprise, I learned that even the best sound analyzers (costing many tens of thousands of dollars) had to condition and filter the sound information coming from the source ( in this case, from the horn). Sound measurement can only be accurate if the sound under analysis is “steady state”. This means the sound is assumed to be unchanging through out the experiment’s time frame. If it is not steady state, the analyzer captures a very short sample, duplicates it over and over and analyzes it as though the stitched together bits are an accurate version of the real sound.
Unfortunately, it is the nature of musical sound to constantly change from moment to moment. Otherwise, it is decidedly dull and not at all musical or artistic. Therefore the adulteration of the original sound through techniques of sampling, filtering and windowing in order to manufacture a steady state approximation of reality eliminates much of the subtle, everchanging acoustic information that makes up a musical sound.
What to do? I decided to address the problem in two ways. First, I would use the existing sound analysis methods only to the extent that there was a reliable, steady state aspect of the horn sound that would show up in the sound measurement. Secondly, I decided to build my own sound analyzer that would use a mathematical technique called “wavelet analysis” to operate only on the raw, infiltered, unadulterated sound coming from the horn.
Both methods yielded useful results. The position of the hand in the bell vs the hand out of the bell provided enough of a steady state condition that useful information could be drawn from the analysis. My own wavelet sound analyzer was designed to capture and display unadulterated information about the makeup of the horn sound from moment to moment as it spread out into the room.
The three graphs shown here were produced by a research quality sound analyzer. The experiment was set up to create a steady state, single frequency tone that would produce reliable results. Rather than a real (ie.changeable) player, a speaker was hooked up to the mouthpiece end and it input a single frequency sound wave into the horn. Of course, the sound coming out of the horn was nothing like a real horn sound because it had only one frequency. A microphone was set up at the bell end and the measurement machine was programmed to run through every frequency from the C two octaves below middle C to high C.
The graphs show the resulting acoustic impedance versus the frequency. I have added the location of the pitch names for the natural harmonics of the horn.
The acoustic impedance in the graphs requires a bit of explanation. Acoustic impedance is an indication of how readily the molecules of air inside the horn can transmit sound energy. Strangely, high impedance is better than low impedance. Figures 4 and 5 give a visual context of the acoustic impedance of the air molecules inside a horn. A Jacob’s ladder also demonstrates this principle very well.
If the impedance is at a maximum, the sound energy from the vibrating lips is instantaneously transmitted to the bell and into the room. Each impedance peak coincides with a resonant frequency of the horn which is what we as horn players know as a natural harmonic of the horn.
The usefulness of the analyzer output is in its ability to indicate how well defined the high impedance frequencies are. The first graph ( horn with no hand in the bell)t shows that, at the high end of resonant frequencies, the separate impedance peaks are not well defined. There is not much of a hump near the resonant frequencies. An advanced horn player can readily demonstrate this by attempting a slow glissando from third space C to high C on the F horn. There is clear definition of the C, D, E, F# and G but from G to high C there is a smooth smear of all the frequencies. Next, looking at the second graph (hand properly in the bell) the humps in the high frequency are much better defined which means that the resonant frequencies are more discernable as G, G#, etc. Playing the same slow glissando will result in clear “notches” for the notes from G to C. This clearly demonstrates one of the most important functions of the hand in the bell.
Already, without delving into heavy mathematical analysis, one of the roles of the hand in the bell is clarified: the notes of the high register become better defined. Figure 3, the superpositioning of Figures 1 and 2 clearly shows a second effect: the presence of the hand in the bell lowers the pitch of the natural harmonics. These two bits of knowledge provide two tools for the horn player. The first is the ability to gain control over bending of the pitch in the difficult high range of the horn by momentarily removing the hand from the bell. The second is a further refinement of control achieved by varying how much of the hand is in the bell. For example, if removing the hand from the bell still leaves the pitching of the high A bit sharp, placing the hand slightly back in the bell can provide some additional lowering of the pitch. Of course this kind of practice is only for emergency situations, but it opens the door for considering other types of fine adjustment of tone and pitch.