-- Introduction --
Thanks to recent developments in technology, it is now getting easier to a certain extent to take a scientific approach to analyzing the mysterious sounds of musical instruments using commercially available measuring equipment and cameras. The latest slow-motion video camera is able to record the low frequency vibrations of the cello, which are usually within the range of 66Hz to several hundred Hz.
When a note is plucked on the cello, many complex vibrations emerge inside or on the surface of the cello. The vibration itself propagates amazingly quickly inside the wood or metal materials. Although it may seem almost instantaneous, in order to transmit the energy, every component needs to vibrate itself physically, taking at least 10 to 20 milliseconds (msec) to reach the tip of the endpin and then to retrace its route.
When using microphones to record the sound from instruments, we have to understand that the sound we record is merely a combined waveform which is affected by factors such as distance, direction and environmental reflection. Advanced methods are required for a high-definition analysis in addition to the acoustical measurements.
What measuring device should be adopted for complex vibrations? Contact microphones are able to catch a localized vibration like a 'pulse' very clearly and sensitively. New meticulous findings will be brought by comparing the data or stitching the results at various spots.
When a cello is played with a bow, additional uncertain factors may come into the result, such as the player's bowing skills, the condition of the resin, etc. To avoid these factors, 'pizzicato' on open strings is mainly used in this research.
The components of the cello can be divided into the following groups according to resonance and vibration :
1) cello body (top plate, back plate, upper bouts, center bouts, lower bouts, sound post, bass bar, etc.)
2) neck, scroll, tuning pegs, etc.
3) bridge
4) strings
5) tailpiece
6) endpin
[ 7) floor ]
The effect on the cello body from the tailpiece, the endpin and the floor is especially carefully studied.
To different extents, all of the components and component groups transmit the vibration and influence each other; however, only the body can create the real sound.
-- The resonance of the cello without an endpin --
1) cello body:
Only the body can produce real, effective sounds by vibrating the air using its broad surface. The vibration of the top plate is much faster than expected. For instance, the C note (66Hz) needs to vibrate 66 times per second. The cycle period of the fundamental vibration is calculated as: 1 sec/66 = 15 msec, but many beats within the '15 msec' can actually be observed. Some vibrations can be propagated though the sound post to the back plate and back to the top plate.
In many cases, major components such as the top plate or the back plate would probably like to repeat their natural beats. For example, the center area of the top plate generally vibrates 1, 2 or 3 beats, but the upper end or the lower end of the top plate sometimes vibrates 4 beats or more.
Generally, pulses shift as if intersecting with each other; however, if they are taking a completely opposite phase the vibration waves cancel each other, resulting in them suddenly disappearing for a moment, like a 'wolf-tone'.
Without the endpin, the most resonant area of a cello is its body, just at the foot of bridge. In the echo, the typical transition beat pattern is 4->3->2->3->2->1 for low frequency notes. The cello body takes natural resonant vibrations which then fade out.
Such freedom of the resonance could probably produce natural overtones and also make diversity in the player's performance possible.
Well maintained instrument's body may continue the vibration even after it fades out on the strings and at the bridge.
2) neck, scroll, tuning-pegs
These components seem to vibrate sympathetically with the fundamental frequency, basically taking 1 beat.
3) bridge
The bridge transmits the vibration from the strings to the top plate and then back to the strings. In my observation, the vibration beat patterns on the bridge were almost the same as on the top plate.
4) strings
The strings originally take a 1-beat vibration for the fundamental frequency as long as it is not affected by external influences. In reality, however, when a player bows a string, it is rare to be able to maintain a beautiful 1-beat waveform for a long time as in many cases it becomes multiple beats due to unexpected noise or as a result of the player's own bowing skill.
5) tailpiece
The tailpiece anchors the strings at one end while the other end is pulled by the tailgut without touching directly on either the end rest or the bridge. The tailpiece vibrates taking a very characteristic beat for the given note. It is well-regulated either physically or mechanically. It is not like the pattern of the body. For example, a pure 4-beat for C (66Hz) was seen on my cello. We cannot discriminate this 4-beat signals from that of the fundamental 1-beat signals of higher C (263Hz, 2 octaves higher).
** 6) endpin **
We have to take into account the special case of fixing the endpin to a cello floating in the air or on a stand supported at the edge of the lower bout. In this special case, the tip of the endpin can take a large vibration. The induced vibration of the endpin is also characteristic, and both physical and mechanical. However, as long as the cello is floating, its resonance seems to be dominated by the body's behavior (vibration). We might understand this case as a state in which a heavy accessory is merely fixed on the cello.
![[ www.AdvancedEndpinHolder.com ]](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgheZ_3TRYfX2mCQbMcstwSWOjWMzJvuhPk_hIK-kVri4FFdtuy8k4syAC32RpHFG6vhyli5V_MeinKjI0l6E48jzrCZS79KW0FeSEv9slFiA-VC7DkMiYphnpG88EUr2dHY24z_gpSN2A/s1600/76b_ConceptualMechanism_StandVsFloor5.jpg "76b Conceptual Mechanism -StandVsFloor5-")
- The resonance of a modern cello with endpin attached and on the floor -
A floating cello has three major vibration areas: the body center, the scroll and the tip of the endpin. This situation dramatically changes, however, when a cello player places their cello on the floor and the floor stops the vibration of the tip of the endpin.
1) The vibration caused by drawing a bow or plucking with a finger is transmitted from the string to the top plate through the bridge. Simultaneously, the tailpiece sympathetically resonates. The vibration then reaches the endpin through the tailgut and the end rest. At this moment, the tip of the endpin is unable to take enough vibration. As a result, the energy maximizes the vibration of the endpin at the area just beneath the tailpin instead.
Additionally, this rebounded and amplified vibration is also transmitted backward to the tailpiece through the route mentioned above. The tailpiece, originally a supporting component, can now influence the cello's sound quality. The beat pattern of the tailpiece sometimes dominates the bridge and can partially reach to the top plate.
2) The tailpiece, being stretched at both ends by anchors, one end by the strings, the other by the tailgut, seems to vibrate with a very characteristically regular, mechanical beat. However, it is, in reality, just a 'proxy' of the endpin. The reason is that the mechanism of resonance of the cello has changed due to the fact that the floor stops the vibration of the endpin. This is something which most players fail to take into consideration when they place their instrument upon the floor.
The tailpiece and the endpin take a certain regular beat pattern for a given played note. Of course, they are influenced by their weight and length. It has to be said again that the 'accessary alliance' of the endpin and tailpiece supported by the floor plays a leading role in the resonance of the modern cello.
3) From a broader point of view, the cello is indirectly influenced more seriously because the cello body has to vibrate sympathetically with the accessory alliance with flat/plain/homogeneous beat patterns. This might be the most important point about the modern cello. When an instrument takes a mechanical/homogeneous resonance, there should be less chance to create more overtones.
4) Moreover, the center-area bloated vibration of the endpin might cause another harmful effect. The lower bouts seem to slightly restrict the own vibration because they are obliged to act as a fulcrum for the endpin. This phenomenon might force the low tone sound to become slightly thin on the cello. The resonant center of the cello body might also be shifted slightly upward. Although a cello player might sometimes hear a louder sound nearer to their ears, or feel a stronger vibration on their chest, this hypothesis might also advise us to check the location of the resonance 'epicenter'.
-- Whole-length vibration - Another side effect of the endpin --
We have captured some whole-length vibrations of the cello in our slow-motion videos.
There seems to be two types of whole-length vibration. The first is a 'slow swing' taking around 20Hz frequency. It is created by some physical oscillation that the body obtains. This slow oscillation does not make any real sound.
The second type of whole-length vibration is seen at the tailpin. It has tiny beats (66Hz or higher) which might be the same as that of the tailpin and may be related to the homogeneous resonance of the body.
When cello players create a new sound note, they need to pour some additional energy in order to firstly re-set the homogeneous vibration, secondly re-set the slow swing(: re-start the whole mass of cello included the endpin), and thirdly create a new sound and stabilize it well. The accumulation of these adjustments could explain why cello players meet some resistance from the strings when they perform.
What is the best sound for cello? That is a matter of the preference of both cello players and audiences. However, the mechanism of cello resonance might have changed when compared with the era when Mr. Stradivari or Mr. Montagnana designed and made cellos. While the endpin helps to greatly enhance the instruments performance, we should not forget that it also produces some serious side effects.