Overtones

 
 

Overtones


    The study of overtones (a.k.a., harmonics) is vital for any woodwind performer.  The saxophone is a large cone, making it fairly efficient at producing a complete harmonic series for any given fundamental.  Of course, the saxophone is not a perfect cone, and the harmonic series for any given note is compromised by a variety of conditions, including the length of the bell, effects of the bow, under-venting from open keys, and the overall strength of the internal resonance for a given note.


When producing a note, we are amplifying a standing wave that exists within the saxophone.  With the mouthpiece removed, put your ear to the neck opening and slowly change fingerings to hear these faint resonances.  When supplied with the correct balance of air and embouchure support, the reed will begin to vibrate at the same frequency as the standing wave.  There is a complete overtone series for any normal fingering, but the reed will seek the easiest path to set into motion, and lower pitches are generally easier to produce because resonances are strongest at lower frequencies.  Higher notes (and overtones) have weaker resonances, making them more difficult to produce.  The player must somehow compensate for these weak resonances, especially when transitioning into altissimo register.  In simple terms, the saxophone does more of the work on low notes, while higher notes require more operator assistance. 


Playing a low note at a medium dynamic, one should notice that most of the work is done in supplying ample air, as the reed has a strong tendency to vibrate at the correct pitch.  These low notes can easily be brash and out of control, but let us temporarily postpone the discussion regarding tone quality.  In contrast, high notes must be supported with considerable embouchure strength, or the reed will collapse into a lower mode of vibration.  (This occurs when an amateur attempts to play a high F#, but the note drops to something like an F, one octave lower.)  The lack of high frequency resonance within the body of the saxophone must be balanced with a complimentary resonance in the oral cavity.  This performer-supplied resonance boost is what is meant by the term voicing.


An interesting way of thinking about tone production is to make an analogy to electricity.  The player provides directional energy, in the form of a pressurized stream of air, like the direct current of a battery.  The energy expressed by the saxophone, however, is in the form of a pulsating wave (alternating current).  Remember that electricity from a battery sends electrons traveling through a wire, but in an AC circuit, electrons transmit energy by “wiggling,” back and forth.  For our analogy, the embouchure provides support as the reed/mouthpiece interface converts energy from a one-way stream of air (DC) into sound waves (AC).


In electrical terms, current is the volume of particles (electrons) in a stream, and voltage is a measurement of the pressurization of that stream.  Shifting from electrons to air, imagine blowing air through a drinking straw with a very large diameter.  In this case, a relatively high volume of air would exit the straw at low pressure – a perfect analog to high current with low voltage.  This is comparable to low saxophone notes; with their high resonance and low resistance, they require a large stream of moderately pressurized air. For higher notes, we must imagine the small jet of air that would result from blowing into a very tiny straw, i.e., higher voltage with lower current.  For the upper saxophone notes, resistance is greater (and resonance is weaker), requiring more pressure, with a smaller volume of air moving through the mouthpiece.


Low notes = lots of moderately pressurized air (high current/low voltage)


High notes = a smaller stream of highly pressurized air (high voltage/low current)


The saxophonist should gather two important pieces of information from the above discussion.  Firstly, low notes require large quantities of air.  The saxophone literally consumes more air as the reed makes slow, wide vibrations.  There should be a feeling of air moving through the body and into the instrument.  Secondly, high notes demand a smaller, more pressurized airstream.  There is a feeling of back pressure, as high velocity vibrations require lots of air support, but less air is actually consumed, when compared to notes of the low register.


Overtone Venting


The octave key is used to operate two small vents, one on the neck, and the other on the upper body of the horn.  These vents are distinct from tone holes in that they have very small diameters, and that, unlike the outwardly drawn holes that cover most of the instrument, vents are tiny pipes that intrude into the bore.  Vents serve the purpose of disrupting the fundamental resonance of a given standing wave, leaving the next strongest resonance to control the reed.  A similar effect can be seen by lightly touching a guitar string in the center.  With the fundamental disrupted, only half of the string can vibrate.  This vibration occurs with greater speed, and less amplitude.  The problem of reduced amplitude increases as the vent moves away from its ideal placement.  For this reason, middle D is particularly stuffy, as the ideal venting would occur lower on the bore.  Play a middle D without the octave key, and with the palm D key slightly opened.  This note will speak more clearly, as it is closer to the ideal placement of the vent.  This experiment demonstrates that tone holes can also be used to disrupt lower resonances.  (We will exploit this technique in the exercise Vent, Tap, and Slur.)  Although every note could have its own dedicated octave vent, this would be mechanically cumbersome, and it would create new acoustic problems with too many little pipes reaching into the bore.


Embouchure: Firm but Flexible


Everything in the universe is subject to the laws of physics, and the reed is no exception.  Try the following thought experiment.  Imagine a rubber band, stretched between your finger and your thumb.  When plucked, it will vibrate at a frequency (pitch) and amplitude (loudness) that is controlled by how far the elastic has been stretched.  When loose, it will vibrate in a relatively slow and wide pattern, producing a low pitch.  Under high tension, it will be vibrate more rapidly, but the distance from peak to trough will be considerably more narrow.  There is also a window of acceptable tensions.  If too loose, it will flop about, unable to make a pitch at all.  Stretch it too far, and it will become too tight to vibrate well, and it will eventually break.


Obviously, a saxophone reed does not vibrate in the same manner as a string in free air.  Still, it does behave according to the same laws of physics with similar relationships between frequency and amplitude.  A loose embouchure allows the reed to vibrate widely, and as with a loose rubber band, wider vibrations express more energy in amplitude, leaving less energy for speed.  In other words, a loose embouchure results in a louder tone with a lower pitch.  On the other hand, a tight embouchure limits amplitude, causing the reed to invest its excess energy in higher frequency.  A simple experiment with a tuner will quickly demonstrate that pitch can be regulated up and down with embouchure pressure.  The ear alone will also confirm that biting on the reed will squash tone and dynamics, but a slack-jawed approach will sound harsh and out of control.


For each member of the saxophone family, there is a “just right” amount of embouchure pressure.  Although this pressure will vary slightly for different notes, and at different dynamics, an ideal pressure will result in the following pitches, when the mouthpiece is played alone:


Soprano – concert C

Alto – concert A

Tenor – concert G

Baritone – concert D


Experimentation with the mouthpiece alone will reveal that pitch can be manipulated over a wide range with voicing adjustments, but dramatic changes in embouchure pressure will result in squeaking, or a total collapse of the sound.  As a daily exercise, warm up with the mouthpiece alone, starting on the appropriate pitch, and then bending down, one note at a time.  Play slowly, with a full, consistently supported sound.   It should be possible to eventually play at least a full octave on the mouthpiece alone.  If the sound breaks, or the reed squeaks, make certain that the embouchure is not too loose, and that the jaw is not dropping excessively.  Good technique on the mouthpiece alone will assist greatly in intonation study and tonal flexibility.


Watch the above YouTube demonstration, first looking carefully at the embouchure.  Notice that the embouchure is relatively still, and mainly flexes to support the reed as the performer changes overtones.  The throat area clearly shows the voicing mechanism in motion, working sympathetically with the resonances of the saxophone.  (Try watching the video with the sound muted, and observe the throat and neck without the benefit of audio cues.)  Finally, watch the end of the video and pay careful attention to the adjustments for the slur down to low B-flat: the embouchure firms, the jaw remains still, and the throat pulses to accommodate the lower voicing position, and the increased volume of air support.

Overtones, Electricity, and Vents!