Exploring the Relationship Between Pitch, Mass, and Tension

Mass and Tension • Any object that can vibrate is capable of creating a tone. Two factors determine the frequency of the vibration: the Mass of the object and its Tension. • As the Mass is increased, the frequency and hence the pitch decrease. This is quite familiar to most of us. For example, the thick strings on a piano or a guitar produce the lower tones. • Men in general have more mass in their vocal folds than women and hence, have lower voices. • On the other hand as the Tension of a vibrating body is increased, the frequency increases. This also is quite familiar to most of us who have plucked a guitar string while turning the screw to increase the tension of the string. The pitch rises as we turn the screw. As the mass of a vibrating body increases, its frequency decreases, but as the tension increases the frequency also increases. • Mass and Tension: Any object that can vibrate is capable of creating a tone. Two factors determine the frequency of the vibration: the Mass of the object and its Tension. • As the Mass is increased, the frequency and hence the pitch decrease. This is quite familiar to most of us. For example, the thick strings on a piano or a guitar produce the lower tones. • Men in general have more mass in their vocal folds than women and hence, have lower voices. • On the other hand as the Tension of a vibrating body is increased, the frequency increases. This also is quite familiar to most of us who have plucked a guitar string while turning the screw to increase the tension of the string. The pitch rises as we turn the screw. The pitch of one's voice is raised by increasing the muscle tension on the vocal folds in the larynx. • Those of us who couldn't afford a guitar have probably had an equivalent experience by progressively stretching and plucking a rubber band which we held at one end between our teeth. • We would hear a definite increase in the pitch of the resulting "twang" sound, usually for several strums before we felt the excruciating pain of the rubber band as it broke and snapped back. • Then, of course, you would hear the high pitch of someone yelling. • We achieve a high vocal pitch, incidentally, by tightening the muscles associated with the vocal folds to increase their tension, much in the same fashion that we pull back on the reins of a horse. • Some people who live in the "fast lane" find through life a constant need to be on the "red alert". These individuals are often described as "High Strung." A person who is tense may have a habitually higher pitched voice that would be predicted from the mass of his vocal folds. • A high strung individual may generally hold their body musculature at a higher level of tension than is necessary. This can include the muscles of the neck and larynx. • The result of the increased tension on the vocal folds is a habitually higher pitched voice than would be predicted from the size (mass) of their vocal folds. • This can actually cause undo wear and tear on the folds resulting in various types of voice disorders. • A pitch related voice problem confronts boys particularly at around the age of puberty. At this time, the influx of hormones causes, among other things, an inordinate rate of growth of the vocal folds. The increased mass causes the voice to drop in pitch. • Two other factors exacerbate the problem. The first is the role our voice plays in society, The other is the significance of our voice to ourselves. Our face and our voice are two important passports, that determine if and how we will be accepted into society. • The Role of our voice in Society: I always imaged myself to be a good candidate to become a self sufficient solitary mountain man type. I find however, that in reality, 30 minutes into Griffith Park begins to bring on withdrawal symptoms for my health food store, my exercise gym, and my room where my internet connections await. • I am compelled, now, to admit that I am very dependent upon society! • What's more I believe most of use are. But ironically, we need passports to be accepted by others in Society. • One important passport is our face. If I had no nose and no upper lip, but just a gaping hole, the students in my class on campus would cluster in the back of the room rather than choose seats up front. • Come to think of it, they are clustered in the back of the room. What can I say--some people have better passports than others. Our Voice is a major component of our Self Concept • You can imagine where the students (who are predominantly women) would be sitting if Tom Cruise were teaching the course. My wife would even come to class! • Another major passport is our voice. If I had a very high pitched squeaky voice, it would be hard to win acceptance as a leader of men. I doubt if I could ever be elected president. • We are subconsciously aware of these passports, and as a result show major concern for things that diminish them. • How we hate to have warts and wrinkles on our face; or an aberration to our voice quality and/or articulation. • The significance of our voice to ourselves: One of our most singularly important possessions is our self concept. As part of this, we are obviously very fond of our body parts and feel great loss, over and above the inconvenience, when one of them is amputated. • One of the most important body parts, ironically, is not strictly a body part at all--the voice. When the teenager's voice begins to change, a major part of his self concept is threatened. • Whereas we see little of our body parts unless you carry a full length mirror around, as I do, we constantly hear our voice. It is almost symbolic of our daily existence and who we are. If we lose our voice, we have almost lost ourselves! • Now we can begin to see the potentially massive psychological problem that is confronting the young teenage boy as his vocal folds begin to rapidly increase in mass. • His voice begins to drop in pitch. His "Comparitor" sends error messages to the Mixer that the pitch is not right. The Mixer sends messages to the larynx to raise the pitch. • But this is becoming more difficult as the mass of the folds continually increases. • There will be frequent sudden pitch breaks. The resulting deep voice is an aberration -- not part of the teenagers concept of himself. Whatªs more people may laugh. In a desperate attempt to maintain the status quo for vocal pitch, some teenagers may adopt a falsetto register. • All this, of course, is occurring at a time of life when the teenagerªs concept of himself is most liable anyway. Teenagers are struggling for self identity as their bodies and social roles change, and then their voices begin to go haywire. • Still most teenagers cope with it and eventually accept the change. A few, however, find it overwhelming. • In a desparate attempt to keep their pitch close to what it was, at least in their minds, and to preserve their self concept, they throw their voices into a falsetto register which is now more easily sustainable. • Although people may be startled to see a six foot, 200 pound volatile teenager with a voice like Shirley Temple, they may elect to say nothing about it in his presence so as not to aggravate him. If mass and tension of a vibrating object are held constant, there will be one frequency at which it vibrates best. • But in time the problem becomes increasingly compelling. An inability to get preferred jobs or dates drives the now young man to seek professional help. • A speech pathologist may be able to correct the voice in 30 minutes, but it may take a year of counseling for the young man to accept and use the "new" voice in public. But back to mass and tension. • What happens if the mass of a vibrating object is held constant and the tension is not changed? • Under these conditions there will be one frequency at which that object vibrates best. That frequency is called the Natural Frequency. • The farther away in frequencies an object vibrates from its natural frequency, the more intensity it requires to produce a desired loudness. • Take, for example, the person who speaks habitually at a higher pitch than their natural frequency. A body will resonate if the original vibration matches the Natural frequency of the resonator. • The vocal folds of a person who speaks too high (or too low) have to work much harder to maintain a desired loudness. • This abuse to the folds leaves the door open in time for a myriad of voice disorders. • Resonance: Some vibrating objects are not the original source of the vibration. They are set in motion by some other vibrating object. Probably most people have witnessed a window that vibrates when a vehicle, maybe a truck, passes by. • What is important is that not every vehicle that passes causes the window to vibrate. Only those engines which generate sound waves that match the natural frequency of the window will start it to vibrate. • Another example is that when soldiers march across a bridge, they are told to break cadence. Otherwise, if they all happen to be stepping in time to the natural frequency of the bridge, they can cause it to resonate so violently that it will actually collapse. A resonator is a screen that lets some frequencies of a complex tone through while inhibiting others. • There was a case of a large suspension bridge in Washington State (the Tacoma Narrows Bridge) which in 1940 was whipped so vehemently by wind gusts which matched the natural frequency of the bridge that it collapsed. You can see this in the notes below. • The point is that frequencies that match the natural frequency of a resonator are facilitated whereas those that do not match are inhibited. • Hence, the resonator acts as a screen which can eliminate some frequencies in a complex tone while facilitating others. • This is the function of the modulators, which we will discuss soon as part of the Expressive Transducer for the Aural Modality (e.g., the mechanism of speech). We will discuss how they change the pattern of overtones produced by the larynx to create the vowel sounds of speech.