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The string

the left hand

Left hand position

The left hand controls not only pitch, but also timbre.  A pitch played on the A string can be played higher up the fingerboard on the D string, and even higher on the G and C strings.  Shorter, thicker strings (high positions on the G and C strings) have fewer overtones and shorter decay.  The reduced decay time is particularly noticeable for pizzicato, as shown in the video below.

acoustical information

Summary

 

The position of the stopping finger decides the pitch of the tone and the relationship between string width and length (string width increases relatively as the left hand stops shorter lengths of string).  This has important implications in overtone content of the sound because the frequency of the highest possible overtone (set by string width and other factors) remains constant for changes in string length.  Therefore, overtone content decreases as stopped string length decreases. 

acoustical information

Detail

 

The overtone exclusion/inclusion for particular left hand positions can be viewed as ‘potential’ overtone content under particular conditions.  I define potential overtone content as the maximum number of overtones that may take part in the spectrum for a fixed left hand position.

 

For a particular stopping position, the highest overtone that can be present in the sound is set by finger pressure and density, and overtones are encouraged/excluded by changing point of contact.  If the left hand shifts upwards, finger pressure and density remain constant, therefore so does the frequency of the highest overtone.  In other words, although the fundamental pitch has risen, the pitch of the highest possible overtone has remained constant.  This overtone is a lower order relative to the new fundamental; therefore the potential overtone content has been reduced.  The fact that potential overtone content reduces as the left hand shifts upwards implies that the scope for varying overtone content by changing point of contact is reduced, i.e., a less extreme ‘sul ponticello’ effect is possible in higher than lower positions.  To an extent, a more extreme ‘sul tasto’ timbre is possible under these conditions since overtone content is reduced for every contact point.  However, the former effect is more extreme, therefore the overall scope for varying timbre is reduced.  When choosing between alternative positions for a particular pitch (for example C4 in first position on the A string vs. fourth position on the D string vs. thumb position on the G string vs. upper third of the C string), the cellist is selecting timbre under these terms.

 

In addition, string stiffness increases from A to C string.  Increased stiffness rounds the shape of the curve of the vibrating string.  This has the effect of restricting higher partials. Therefore, a less extreme sul ponticello effect is possible on the D string than the A, an even lesser effect on the G and still less on the C string.  

Video 37

C4 is plucked on each string, with a similar force and plucking direction.  The overtone content is weaker and decay time is shorter on the lower strings.  I dampened all of the strings that I wasn't playing (firstly with the chin, then with the fingers of the left hand) to prevent resonance from the other strings interfering with the impression of decay time. 

Left hand finger pressure

There is a scale of finger pressure.  From high to low pressure: tones are overtone-rich with a long decay, harmonics and stopped string sound are combined, harmonics, harmonics combined with the open string, multiphonics and a noise component are heard.

High pressure

High pressure at the stopping finger allows an overtone-rich sound with a long decay.  Stopping the string with the fingernail or another dense object is overtone-richer and has longer decay times.

In context

Too much pressure with the left hand is counter-productive; it can cause unwanted tension in the right hand that restricts loudness and overtone content. 

Slide effects

If a dense object stops the string (a pen, a glass rod), even without pressing it to the fingerboard, long glissandi are possible, like the guitarists’ slide techniques.  Cello map link 

Harmonic pressure

For harmonics, the finger touches the string without pressing it to the fingerboard.  Within the range of ‘harmonic finger pressure’ there is scope for some variation and many sounds are possible.

 

At high harmonic finger pressure the string is slightly depressed but not in contact with the fingerboard.  This is often called a ‘half harmonic’.  The pitch of the harmonic (probably slightly sharp) and the tone at the stopping point are both heard.  The sound is overtone-weak.  

At mid-high harmonic finger pressure, the harmonic sounds alone, usually slightly sharp with weak overtone content.  As pressure decreases, the harmonic’s pitch falls to normal and overtone content becomes richer.

Hints tips and extra bits

At the harmonic node closest to the bridge, the harmonic pitch and the stopped pitch are always the same.  Therefore, for a ‘half harmonic’, it is impossible to hear two combined pitches at this point.  However, overtone content is noticeably reduced.

low pressure

Under very low finger pressures, the pitch of the open string is introduced into the sound in addition to a harmonic.  It is possible that two or more harmonics (including the open string) sound simultaneously.  This is called a multiphonic. 

 

A NOTE ON BOWING

Under low pressures, there might be a forced, ‘stuttering’ sound.  This is particularly strong at low bow speeds. 

 

 

multiphonics

For more detailed information about multiphonics, see Cello map link

 

In this context I will define a multiphonic as the simultaneous sounding of two or more harmonics on a single string.  This can include the open string (which is the first harmonic).  Multiphonics are easier to produce in certain areas of the string; especially at points on the string where there is a cluster of harmonic nodes.  Multiphonics also require some manipulation of the sound in the right hand.

Hints, tips and extra bits

The flexibility and the outcome of varying finger pressure changes for different positions on the fingerboard. 

 

Lower harmonics are more flexible: it is possible to change the sound and maintain the relatively constant presence of a harmonic.

 

Higher harmonics are more sensitive: a change in finger pressure sometimes causes the harmonic to ‘jump’ to a neighbouring harmonic.  

 

scale of finger pressure

It is possible to summarise a scale of finger pressure:

 

Finger pressure    

Output

Using the finger nail/other dense object.

Very high pressure

Overtone-rich sound, high duration

Gradual reduction in overtone content and duration

Normal pressure

‘Normal’ sound

              

 

 

 

 

 

 

Stopped string pitch with low overtone content and harmonic (possibly slightly sharp). 

The harmonic becomes louder relative to the stopped pitch as pressure decreases.

High harmonic pressure

Sharp harmonics with reduced overtone content

‘Ordinary’ harmonic pressure

In-tune harmonics

Low harmonic pressure

In-tune harmonics with high overtone content

 

 

 

 

 

 

 

 

Very light pressure

Multiphonics: mixture of two or more harmonics and possibly increased ‘noise’ component and/or the open string pitch is heard with the harmonic.  The amplitude of the open string increases relative to that of the harmonic as pressure reduces.  The stopped string pitch might also be faintly present. 

Video 38

A scale of finger pressure for the bowed string. 

Hints, tips and extra bits

In the first example in this video, the stopping finger is at the third harmonic on the D string, not very close to a cluster of harmonics.  Therefore, the transition to the harmonic sound is relatively clean.  In the second example, the finger is very close to both the sixth and seventh harmonics on the G string.  The transition to harmonic sound is more complex, with some fluctuation between sixth and seventh harmonics and some multiphonic vibration.  

acoustical information

Summary

 

As the pressure and/or the density of the stopping finger increase, fewer overtones are lost to damping when vibration is reflected at the stopping finger.  Therefore, the overtone content of the tone increases with pressure and/or density of the stopping finger. 

 

As finger pressure is reduced from ‘stopping’ to ‘touching’, at first a harmonic is introduced into the stopped string sound (the harmonic is possibly slightly sharp due to increased string tension).  For further decreases in pressure, the harmonic sounds alone.  As pressure is reduced further, the open string, or neighbouring harmonics might be introduced into the sound, in a multiphonic.  Finger pressure is relative to harmonic order; higher harmonics are more sensitive to changes in finger pressure. 

acoustical information

Detail

 

Within ‘normal’ stopped string sound, the pressure and density of the stopping finger/‘object’ influence timbre by the extent to which they dampen the string’s vibration.  As pressure and/or density increase, damping decreases, i.e., less energy is lost at the stopping finger and more is reflected back to the bridge.  Therefore, loudness and overtone content (since damping affects higher overtones more than lower) are proportional to finger pressure/density.  Decay duration is also proportional to finger pressure/density since, as less energy lost through damping, the string is able to complete more cycles of vibration before ‘spending’ the excitation energy.

 

Under harmonic finger pressure, as above, increasing the density of the touching finger reduces damping.  Contrary to above, however, damping increases with finger pressure.  Since string vibration passes the touching finger (rather than the finger reflecting vibration, as above), damping is limited by decreasing pressure, minimizing the energy transferred to the touching finger.  Therefore: overtone content, loudness and decay duration of harmonics are proportional to finger density and inversely proportional to finger pressure. 

 

In general, a reduction in overtone content has a more pronounced effect for harmonics than for stopped strings of equivalent pitch.  Since fewer overtones are present in ‘normal’ harmonic sound, the exclusion or weakening of upper partials has a larger impact on timbre in relative terms. 

contact time between stopping finger and string

If the stopping finger is removed from a vibrating string, it interrupts the decay of a tone. Harmonics work in the opposite way: the decay duration of harmonics is maximised by removing the finger very soon after excitation.  In fact, harmonics have an optimum left-hand contact time at which decay duration and overtone content are maximal.  This optimal contact time is inversely proportional to the frequency of the harmonic (i.e., longer for lower harmonics).  In general, even for low harmonics, this optimal time is very short.  For very long contact times, plucked and struck tones become a short, muffled ‘thud’ (in the latter case the clavichord-type pitch is very present).  For bowed tones, the harmonic barely sounds after the stroke.  

Video 39

Plucked, struck and bowed sounds are firstly allowed to ring, then their decay is interrupted by removing the stopping finger from the string.

Video 40

A harmonic is plucked, struck and bowed.  At first, the finger is in contact with the string for a short time, then it stays on the string for a longer time, muting the harmonic.

very short contact times and multiphonics

Contact times shorter than the optimal time for a particular harmonic encourage a second harmonic or the open string into the sound.  Because of this, short contact times can produce multiphonics.  This is especially effective for pizzicato multiphonics.

Video 41

Pizzicato multiphonics produced by short left-hand contact times.

Hints, tips and extra bits

I help encourage the multiphonics by plucking with the very tip of the right-hand finger or the fingernail.  

A note on bowing

In some cases, particularly for loud tones, if the finger is removed before the end of the bow stroke, the harmonic continues to sound for a short while.  If the speed and tension of the stroke remain constant, this effect can continue for a few seconds.

acoustical information

Summary

 

The duration of stopped string vibration increases with contact time between finger and string because the vibration can be reflected again and again at the stopping finger, until the excitation energy has been exhausted.  The situation regarding harmonics is the opposite.  Since vibration passes the touching finger, and in doing so always loses a certain amount of energy through damping, duration is maximised when contact between finger and string is as short as possible.  However, there is a minimum contact time that allows the harmonic to vibrate at a stable pitch.  This is usually very short, but is relative to the frequency of the harmonic.  If the finger is removed from the string before this, it is likely that other neighbouring harmonics and especially the open string will also be present in the sound. 

acoustical information

Detail

 

The decay of a particular sound is maximised if reflection of the kink in the vibrating string is allowed to continue until it runs out of energy, i.e., if the string is allowed to ‘spend’ all of its excitation energy.  If the stopping finger is removed from the string during a tone’s decay this process is interrupted, vibration may continue for a short while as the vibration decays in the cello body and the room.  Since these effects are weak compared to the vibrating string being radiated to the body/room, removing the stopping finger can be an abrupt damping of sound.

In the case of harmonics, the optimal contact time between touching finger and string, usually very short, is the time taken for the string to vibrate for a few wavelengths at the particular harmonic’s frequency.  In this time the string begins to vibrate stably at the harmonic pitch and continued contact with the left hand serves only to dampen vibration because, since vibration is reflected at the nut rather than the left hand finger, the kink of vibration passes the touching finger with every cycle, loosing energy in the process through damping.  Since contact time is dependent on wavelength, optimal contact time reduces for ascending harmonics.  

Video 42

Bowed harmonics continue to sound even if the finger is removed from the string.