Videos/Sounds - Knut's Acoustics

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Here you will find a number of videos describing phenomena referred to in different texts. The videos are mostly showing simulations of the bowed string. Notice: some web browsers might have a problem with playing back the sound examples. It is important that the browser is set up  to function correctly with Adobe Flash Player and a sound player for wav-files. The website is tested and works correctly  with Chrome.

Helmholtz motion
The string movement referred to most often, is the Helmholtz motion, named after Hermann von Helmholtz, 1821 - 1894, who around 1860 by use of a vibrating microscope, discovered how the string moves when bowed with a "normal, good, musical sound": Under this condition the string is schematically shaped as two straight lines, joined in  a kink or corner that rotates within a parabolic trajectory between the bridge and the nut/finger.

In this video the bridge and nut are indicated on the left and right side, respectively (shown as triangles). The bow is drawn dashed to show its movement. The dashes turn green every time the string slips on the bow's hair. The string's corner is seen to rotate anticlockwise. Had the bow been moving downwards, the corner rotation would have been clockwise. Sound example (simulated).


Bowed-string attacks are not always easy to make clean, as any amateur will confirm. However, most professional players seem to control their tone onsets pretty well, choosing the kind of attack that suits the music they are playing.
Sound examples of attacks from creaky to loose/slipping:

Three major bowing parameters control the outcome. In sustained tones these are:
(1) bowing pressure (correct physical term: force)
(2) bowing position, relativ to the active string length
(3) bow speed
During attacks the third parameter is acceleration rather than speed. For a successful attack to be produced, acceleration on one side must be balanced against pressure and bridge distance on the other side.To make it even harder, this balance will also vary with pitch and string type (higher pitch - faster bow; heavier string - slower bow). However, after the attack transient has expired, you are at liberty to vary the parameters quite a bit without destroying the Helmholtz wave pattern.


A "perfect" attack

In order to start the Helmholtz motion directly, the bow must have reached a certain speed when the string slips off the bow-hair ribbon for the first time. After that, a certain acceleration is required for a short while, for the string to be engaged with a periodic slip-stick pattern. Sound example (simulated).
Important: the term "perfect" should not be interpreted too literally; in this context it is merely referring to the periodicity of the stick-slip pattern, without further consideration to the overall sound quality or timbre!


A "not so perfect" attack 1
(the bow "pressure" is too high)

Here, the bow's "pressure" (correct physical term: "force") is too high for the bow's  position and acceleration. When the first string wave returns to the bow, and a second slip was supposed to take place, the bow won't let the string go right away. The delay causes a chaotic wave pattern. Increasing the acceleration and/or moving the bow closer to the bridge, would have helped.
Sound example (simulated).


A "not so perfect" attack 2
(the bow "pressure" is too low)

Here, the bow's "pressure"  is too low for the bow's  position and acceleration. The string slips back on the bow hair prematurely (i.e., before the first string wave returns to the bow, at what time the second triggering should have happened). Chances of producing the octave above are quite high (see the video example below). Reducing the bow's acceleration and/or increasing the bow-to-bridge distance would have helped. Sound example (simulated).


Low bow "pressure" produces the octave

Here, the bow's "pressure" was too low compared to the acceleration/speed during the attack. The string went into a mode where the fundamental pitch is quite suppressed, while the octave above dominates. Sound example (simulated).



By touching the string lightly, one can suppress all frequencies not having a node there. The video shows the finger (light blue line) touching the string 1/5 of the string length away from the bridge. The remaining frequencies are all multiples of the fifth harmonic, i.e., a major tenth above the fundamental of the open string. Rapid acceleration is required if a clean crisp attack is desirable.

The simulated sound example demonstrates the fifth harmonic of the open violin G-string, i.e., B5. Between nodes one apparently sees five rotating Helmholtz corners, synchronized. The distance between them on the string is exactly one-half wavelength of the harmonic frequency.   

In the video example to the right, the same note is repeated, this time with the finger touching the string 4/5 of the string length away from the bridge.  Here, the starting transient is slightly longer, but on a violin this is hardly audible (smulated sound example).

When the harmonic has a prime-number ratio to the open-string frequency, all nodes can be used for invoking that pitch. During the onset transient, about one-half of the energy should be absorbed by the finger in order to provide optimal reflections (distributing the remaining energy eaqually between transmission and reflection). In steady state, the energy loss should be much less, even with the lightly touching finger pressed against the string with the same force.



Here, the bowing takes place very close to the bridge, and the bow "pressure" is far too low to permit Helmholtz motion. The result is a"glassy" sound, and there occur numerous extra slips per nominal period. Sound example (simulated).(See: 2006: K. Guettler, "The violin bow in action – ‘A sound sculpturing wand’" for further discussion.)


Raucous/Creaky sound

When bowing with too high "pressure", or too slow bow, the sound will turn out either creaky or raucous. The wave forms become quite irregular.   Sound example (simulated). (See: 2006: K. Guettler, "The violin bow in action – ‘A sound sculpturing wand’" for further discussion.)


Anomalous Low Frequencies (ALF)

When bowing with excess "pressure", or too slow bow, the stick-slip triggering might in certain cases synchronize to a regular pattern with a pitch far below that of the open string. The string waves take one or more extra rounds before causing a slip. This is utilized by certain musicians like
Mari Kimura (who calls it "subharmonics"). The physical background of this phenomenon was explained in K. Guettler, 1994:  "Wave analysis of a string bowed to anomalous low frequencies". Sound example (simulated). While the bow pressure increases linearily, four different pitches are heard. The third one is near one octave lower than normal, as shown in this video.  (See also: 2006: K. Guettler, "The violin bow in action – ‘A sound sculpturing wand’".)


Bow resonances (is this what you really want to hear?)
In several papers on the bow, Askenfelt and I have claimed that the resonances of the bow have a difficult path to go in order reach the audience. And, one should certainly be glad that it is so! The sound examples below were recorded with a contact microphone on the bow (accelerometer signal integrated) during two long strokes including bow changes. One can clearly hear how the bow hair vibrates independently of the strings pitch, making quite unmusical glissandi. This is something we really don't want to hear! That being said, bows do indeed leave a sound signature recognizable by skilled violinists (see "Bows and timbre — myth or reality?" from 2001); we simply do not know what is happening...
Sound examples:

By carefully positioning the bow and a lightly touching finger on the string, the impression of more than on tone played can be achieved. There are two classes, dependent on where the left-hand finger is placed between the bow and the bridge (class one) or vice versa (class two). Although the first kind is easier to play, the latter is more often used, since it is more easily combined with normal playing. On each open string of the double bass, some 150 different sonorities can be invoked, all with the open-string pitch as the fundamental. Muliphonics is not limited to open strings, however, but possibilities are more restricted for the "artificial" positions.
Sound example of a series of multiphonics played on an open double bass A-strng (performed by Håkon Thelin).

Multiphonics 1

Example of a class one multiphonics on a double-bass E-string, where the softly touching finger (marked as cyan line) is placed closer to the bridge (on the right side) than the bow. The finger is positioned at F# (node of 9th harmonic), while the bow is placed at D right below (node of 7th harmonic). Notice that the wave pattern, which is somewhat like the Helmholtz motion, has three kinks and provides three quickly successive slips instead of just one. The harmonics 2, 9, and 10 are emphasized.  
Picture of Fernando Grillo:          Sound example:
Picture of waverform etc.:


Multiphonics 2

Example of a class two multiphonics on a double-bass E-string, where the softly touching finger (marked as cyan line) is placed between the bow and the nut. The finger is positioned a quarter tone above G#, while the bow is placed at D (node of 7th harmonic, as before). The harmonics 9 and 13 are emphasized.  
Picture of waverform etc.:     Sound example:


Multiphonics 3

Example of a class two multiphonics on a double-bass E-string, where the softly touching finger (marked as cyan line) is placed between the bow and the nut. The finger is positioned at G#, a major decim above the open E (node of 5th harmonic), while the bow is placed at D (node of 7th harmonic). The harmonics 2, 3, and 5 are emphasized.  
Picture of waverform etc.:     Sound example:


The waveform of the plucked string differs substantially from the wave form of the bowed string. At the bridge, the force signal of the plucked string is in principle a series of square-wave pulses, while the bowed string produces a series of sawtooth pulses. (Watch the string's angle in the vicinity of the bridge; it tells you about the relative force, and when it changes sign.)  In pizzicato excitation, the higher partials fade out first - leaving essentially the fundamental frequency alone at the end (the string goes rounder). In the bowed string, the bow sharpens the string's kink every time it passes the bow, thus at all times providing high-frequency energy to make up for what was lost.


Wolf tones
Wolf tone is the topic I get questions about most often. In the literature, the phenomenon is most often explained mathematically, but as this video shows, it is quite simple to grasp from a mechanical point of view: The video starts with four normal Helmholtz periods, during which the bridge/body, having a strong resonance at the fundamental frequency, starts oscillating with greater and greater amplitudes (here drawn as the string moving on a fixed bridge).  In the middle of the fifth nominal period, the bridge is moving so much down while the bow is trying to bring the sticking string up, that the string is torn off. In the continuation we get some eight nominal periods where the string slips twice per period, producing the octave. During this time, the bridge, not being feed with the energy of the fundamental frequency anymore, "cools down" and becomes more quiet. Then everything is back to normal, and the whole show can start over again... Sound example (simulated):

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