BGM : Piano Y.Kawano 2017
31. Vibration intensity -Measurement 2_2-
[ 12/14/2017 ] Labels: 31..Intensity-TopPlate
Vibration intensity of cello on the top-plate, tailpiece and (this case -->) carbon endpin:
When the tip of endpin is placed on the floor and restricted to vibrate, the vibration patterns of endpin and tailpiece change remarkably and the vibration intensity increases. As a result, the influence seems to extend over whole cello.
There seems to be some difference between the result from a steel pipe endpin and a carbon-fiber, but this phenomenon probably comes from the essential mechanical/structural issue of the endpin-built-in-cello.
エンドピン材質により若干の違いはあるものの、床置きしてエンドピン先端の振動が止められると、チェロの振動は大きく影響を受けて変化します。
Device : Vibration meter VB-8205SD
Cello : 110-year-old German cello
Endpin : 10mm(D) carbon, 28cm(11in) below tailpin
Vibration intensity of cello on the top-plate, tailpiece and (this case -->) carbon endpin:
When the tip of endpin is placed on the floor and restricted to vibrate, the vibration patterns of endpin and tailpiece change remarkably and the vibration intensity increases. As a result, the influence seems to extend over whole cello.
There seems to be some difference between the result from a steel pipe endpin and a carbon-fiber, but this phenomenon probably comes from the essential mechanical/structural issue of the endpin-built-in-cello.
エンドピン材質により若干の違いはあるものの、床置きしてエンドピン先端の振動が止められると、チェロの振動は大きく影響を受けて変化します。
Device : Vibration meter VB-8205SD
Cello : 110-year-old German cello
Endpin : 10mm(D) carbon, 28cm(11in) below tailpin
82..Cello -Response and Resonance 4-
[ 11/18/2017 ] Labels: 94.Video & Study
This exaggerated simulation suggests a simple and important truth.
The sound speed in the air is far faster than the speed of top-plate vibration. Actually it is probably 100 times or more.
If so, cello's all sound color/quality and even overtones might be created by the top-plate(or body)'s mechanical vibrations rather than acoustic resonance.
Furthermore the top-plate/body reflects the influence from tailpiece, endpin and the floor.
Players encounter poor resonance at rainy day. It will be because the resonance is generated by wood plate.
空気中の音速はチェロの表板の振動速度より遥かに速い。
これは楽器の音色・響き・倍音さえも表板自体が創り出していることを示唆しているように見えます。床やエンドピンの影響も反映されます。
雨の日に響きが悪くなるのはなぜでしょうか。楽器のディメンションや音響構造の話ではなく、単純に響きや音を造るエンジンが木製であることに起因すると考えられます。
BGM: YouTube free sound
82..Cello -Response and Resonance 5-
[ 12/02/2017 ] Labels: 94.Video & Study
Cello takes 10-20 Hz slow swing(/vibration) along its whole-length.
Brandenburg Concerto No4-1 BWV1049 - Classical Whimsical by Kevin MacLeod is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/)
Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1100303
Artist: http://incompetech.com/
31. Vibration intensity -Measurement 2-
[ 11/24/2017 ] Labels: 31..Intensity-TopPlate
Top-plate's vibration intensity was measured again including tailpiece data.
MEMO:
When the tip of endpin is placed on the floor and restricted to vibrate, the influence seems to extend over whole cello.
(1)Endpin changes its vibration patterns remarkably.
(2)Tailpiece increases its vibration intensity.
(3)Top-plate slightly weakens the vibration in general or shifts to the flat(/even) vibrations at least along the vertical direction.
Device : Vibration meter VB-8205SD
Cello : 110-year-old German cello
Endpin : 10mm(D) steel pipe, 28cm below tailpin
Data : each 10 measurements averaged
82..Cello -Response and Resonance 3-
[ 10/17/2017 ] Labels: 94.Video & Study
The lowest note of cello, C(66Hz, period:15 milliseconds), needs 25 milliseconds or more before C tone settles.
Inside a cello, what happens during the first 50 milliseconds after a pizzicato?
This 1/1000second-resolution-simulation suggests strong linkages between the vibrations of string, top plate and the air. That is the mechanical resonance of cello.
The lowest note of cello, C(66Hz, period:15 milliseconds), needs 25 milliseconds or more before C tone settles.
Inside a cello, what happens during the first 50 milliseconds after a pizzicato?
This 1/1000second-resolution-simulation suggests strong linkages between the vibrations of string, top plate and the air. That is the mechanical resonance of cello.
81.. 2mmD steel rod -bowed and plucked-
[ 06/29/2017 ] Labels: 81.Solution & Study1
A 2mmD x 500mmL steel rod behaves like as a string and also an endpin.
(2mmDx500mmLの細い鉄棒、その動きは弦のようでもあり、太いエンドピンのようでもあり、観察に利用できそうです。)
70d. The mechanical resonance of cello
[ 06/06/2017 ] Labels: 95.Video & Study1
- Effect of rebounded vibration from floor
- Flattened vibration beats
- Whole length slow swing
- Vibration center shifting
(床置きしてエンドピン先端の振動を止めることによる影響：
床からのリバウンド、響きの平坦化、全身振動、胴体振動の中心変化)
20. Vibration of C string (arco, on floor, 32 times slower)
[ 04/26/2017 ] Labels: 20.Vibration-Video
When appropriate pressure and speed applied into a bow, the C string takes a pure C vibration( of 1 beat, 66Hz, cycle=15.2ms) from the beginning accompanied with tiny fluctuation.
In this case, the fingerboard also takes 1 beat synchronized, and the G string widely resonates too.
Be noticed, G string's vibration is not of a 'G' but a 'C', because it is just synchronizing to 66Hz(15.2ms) probably taking 4-beat.
If G string can create a real sound by itself, it is presumed as a C 263Hz(= 2 octave above) sound.
We can find such mechanical resonances here and there on our cello.
C note (66 Hz, open)
Cello: 110-year-old German cello
Strings : Evah pirazzi Weich
with steel pipe endpin on the floor
32 times slower
C線を丁寧に演奏すると、C弦は最初から１ビートの純粋な(Cの)振動をします。この場合、テールピースも１ビートで共振し、G線はGの振動でなく４ビートのC音(=２オクターブ上のC)で共振しているのがわかります。
20. Vibration of C string (arco, on stand -floating-, 32 times slower)
[ 04/26/2017 ] Labels: 20.Vibration-Video
50. A(221Hz) Endpin-tip vibration data
[ 04/08/2017 ] Labels: 48..Beat.Endpin
3 sec after a A(221Hz, open string) pizzicato
Cello: 110-year-old German cello
Endpin: 10mm(D) steel pipe, 28cm(11in) below tailpin
----------------------------------------------
Some data might show weakness in intensity. The reason is unknown but it might caused by low-voltage at battery in contact microphone.
50. G(98Hz) Endpin-tip vibration data
[ 4/04/17 ] Labels: 50.Beat.Endpin
On stand, endpin is floating,
pin-tip takes natural various beats.
Placed on the floor, endpin is fixed in place,
pin-tip keeps homogeneous 3-beat.
On Advanced Endpin Holder,
pin-tip takes a mediate vibration beat pattern between above.
----------------------------------------------
3 sec after a G(98Hz, open string) pizzicato
Cello: 110-year-old German cello
Endpin: 10mm(D) steel pipe, 28cm(11in) below tailpin
----------------------------------------------
50. C(66Hz) Endpin-tip vibration data
[ 3/29/2017 ] Labels: 48..Beat.Endpin
[ comment ]
On a stand(,endpin is floating in the air),
bridge takes natural beat pattern (e.g. 4->3->2->3->2-) during fading out, and the endpin-tip unexpectedly ceases the vibration in a short time.
With endpin and placed on the floor,
both bridge and endpin keep mainly constant 4-beat, moreover the endpin has a long vibration duration.
On Advanced Endpin Holder(AEH-011),
bridge has rather a similar beat pattern to the case of 'floating' cello and the beat of endpin-tip is also similar to the bridge. The duration time of the endpin-tip is medium between above.
3 sec after a C(66Hz, open string) pizzicato
Cello: 110-year-old German cello
Endpin: 10mm(D) steel pipe, 28cm(11in) below tailpin
----------------------------------------------
Please remember some findings at Label-47.(Propagation).
(1)The beat pattern of bridge very linked to that of the center area of top plate.
(2)Without the endpin, cello body naturally faded out taking beats e.g. 4->3->2->3->2->1, but when with the endpin and placed on the floor, the bridge kept characteristic flat 4-beat.
In this case, 110-year-old instrument is probably consisted of stiff wood, although the results might be slightly different from Label-47., but the structure of the cello is basically the same. Common inclination should also be expected.
50. Research focusing on the vibration of endpin-tip
[ 3/21/2017 ] Labels: 48..Beat.Endpin
Let's make a further research effort focusing on the vibration of tip of endpin.
50. The vibration of endpin-tip
[ 3/19/2017 ] Labels: 48..Beat.Endpin
Two video samples show the the vibration of endpin-tip after a C(open string) pizzicato.
[Top:] (1)Contact(flat) microphone data measured at the tip of endpin and (2)usual sound microphone data in the room.
[Bottom:] A small dental mirror was installed at the tip of endpin. The mirror casts small spotlight about 3 meter away.
In this 40 sec video the endpin mainly vibrated 64-65 times. We can also recognize the vibration in video as '96-100 tempo'.
It just matches the calculation of C(66Hz, 15.2msec, fundamental) vibration : 66Hz * 60sec / 40slower = '99 tempo'
In the measurement, contact microphone detects internal 6/5/4,, beats in a cycle period.
A reflection of light in the mirror takes a stiff oscillation and gives us a premonition of existence of these tiny beats.
Video: 1 sec after a C(open string) pizzicato, 40 times slower
Cello: 110-year-old German cello on stand
Endpin: 10mm(D) steel pipe, 33cm(13in) below tailpin
Camera: SONY RX100-4 ( zoomed to two times )
A0. Advertisement
[ 3/14/2017 ] Labels: A0.Advertisement
Behind their concern about toes, cellos still retain the innate great capabilities to sing and dance.
Need further researches.
A1. Available angle
[ 3/02/2017 ] Labels: A1..AEH
Advanced Endpin Holder(AEH-011, 012) requires your cello to be kept a proper angle from the floor.
In case that the diameter of the tip of your endpin is 8 mmΦ, the placing angle of your cello should be at between 45 and 90 degrees.
Please avoid to take a shallow angle.
浅すぎる(チェロ)角度での利用を避けてください。
70c. The resonance of the modern cello
[ 2/07/2017 ] Labels: 95.Video & Study1
-- 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/s400/76b_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.
-- 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.
70b. チェロ(モダンチェロ)の響きについて
[ 1/24/2017 ] Labels: 95.Video & Study1
－－前置き(introduction)－－
近年の技術進歩のおかげで、楽器の神秘的な響きについても、一般に市販されている測定機器やカメラを利用してある程度の科学的アプローチが可能な時代になっています。
とくにチェロについては、表現できる周波数範囲が、通常最低音C(66Hz)から数百Hz程度であり、低周波数振動についてはスローモーション動画も十分に撮影可能です。
奏者によってチェロの一つの音が発音された時、楽器内部では実際にきわめて複雑な振動が生成されます。振動自体が木や金属の中で伝播する速度は極めて高速であり、ほとんど瞬時に伝わると考えて良いのですが、実際には弦が振動を開始し更に表板などが物理的に大きな振動を行うには若干の時間が必要と思われます。しかしその時間もせいぜい10～20ミリ秒と考えてよさそうです。
つまり私たちの感覚としては、弦に与えた刺激はほとんど瞬時にエンドピンの先端に届いていると考えるのが正解のようです。
音声マイクを使って測定する場合、測定している音は楽器から発生する様々な音波が合わさっていて、測定位置(マイクロフォン位置)での合算された波形でしかありません。実際の楽器の振動をとらえるためには楽器の各部分の振動を個別に調べて並べてみるしか方法がありません。この観点から言えば、接触マイク(壁マイク)が利用可能でした。接触マイクは強弱の絶対的比較には不向きですが振動の存在に対しては「パルス」のように検知でき、極めてセンシティブです。
弓を使って発音する場合、奏者の技量・弦の違い・松脂などにより発生する振動がきわめて大きく左右されます。そのためこの一連の測定では、極力'解放弦'のピチカートから生成される振動(残響振動)を中心に比較しました。
また、さまざまな測定を行う中で、チェロの響きまたは振動パターンに関して、チェロを構成する部材について次のグループ分けができるようです。
①チェロ胴体(表板top-plate・裏板back-plate・側板center-bouts・底板lower-bouts・魂柱soundpost・バスバーbass-barなど)
②ネック(neck)・渦巻き(scroll)・糸巻き(tuning-pegs)
③ブリッジ(駒bridge)
④弦(strings)
⑤テールピース(tailpiece)
⑥エンドピン(endpin)
[⑦床(FLOOR)]
とくに、⑤⑥⑦がチェロ胴体①へ及ぼす影響について着目して調査しました。大小の差はあるものの①～⑦の全てが何がしかの振動をしている(または振動が伝えられている、または関与している)が、実際実質的にサウンドを生成しているのはチェロ胴体のみです。
－－エンドピン無しのチェロの響き－－
(1)チェロ胴体
唯一、音を生成しています。想像を上回り表板などが高速に振動して空気の濃淡を作り出しているようです。
例えば最低音C(66Hz)では、基音振動は１秒間に66回の振動です。間隔は1秒÷66=15ミリ秒です。実際にはこの15ミリ秒の間に多くの振動が観測されます。魂柱経由で伝えられる裏板からの振動・弦からの多数の信号・それらの相互影響などの為です。この１周期中の振動数(ビート数)は実に刻々と変化します。
一般に、表板・裏板の中心付近では、3または2または1ビートで振動していますが、表板の上下端・側板などでは多数振動しています。色々なところから到来する振動がぶつかり重なっていると言えます。
わずかにずれる二つの振動が交差する時、多くの場合はパルスがお互いを横切るようにシフトして行きます。しかし僅差の二つのパルスを表現できない場合は、ちょうどウルフトーンのように、位相が打ち消しあって一瞬消失する場合もあります。
チェロにエンドピンを付けないで浮かせた状態で測定すると、表板は駒の直下付近を中心に大きく振動して、低音では例えば、４→３→２→３→２→１というように残響の中でビートが変化します。胴体が調和しながら自然に変化(推移)していきます。この自由で自然な変化こそが、自然な倍音を生み演奏時においては多様な表現を可能にするベースとなっていると考えられます。
よく作られた楽器では、弦や駒の振動が減衰した後でも、胴体部分の振動と残響が残るでしょう。
(2)ネック・渦巻き・糸巻き
基本的に、基音振動に対して１ビートで共振しています。
(3)駒
弦の振動を表板に伝え、逆に表板の振動を弦に伝えています。駒では表板とほぼ同様のビート・振動パターンが見られました。
(4)弦
与えられた刺激(基音)に対して、基本的に１ビートで振動しているようです。しかし実際に演奏者がボーイング演奏する時には１ビートの美しい波形を長時間維持することはおそらく稀で、多くの場合は雑音を含む多ビートとなっているでしょう。
(5)テールピース
駒とテールピンの間で弦と"テールガット"でつながっており、4本の弦を引っ張っていますが、与えられた音(基音)に対して独自の固定ビートで振動しています。この振動は極めて個性的で特徴的です。ただしエンドピン無しの場合、この機械的振動は駒には影響が及んでいないようです。
例えばC音(66Hz)に対しては非常に規則的な４ビートが見られました。測定データで見る限り２オクターブ上のC(263Hz)で振動しているとも言えます。(区別がつきません。)
(*6*)エンドピン
チェロを空中に保持したままエンドピンを装着した場合、エンドピンの先端は非常に大きく振動します。これは主にテールピース-エンドレスト-テールピン経由で伝えられた振動がエンドピンを共振させるためです。しかしこの場合(空中に浮かせている限り)、チェロ胴体への影響は比較的少なく、胴体優位の振動が保たれているようです。この時エンドピンは呼応する独自の振動ビートをとっています。いわばチェロに重いアクセサリーを取付けたような状態と考えることができます。
－－モダンチェロの響き－－ (チェロを床置きする影響)
チェロを空中に保持したままエンドピンを装着した場合、大きく振動しているのは、a.駒を含めた胴体の中心付近、b.上端のスクロール、c.エンドピンの先端、の３ケ所でした。ところが、演奏者がチェロを床の上に設置し、床がエンドピンの先端の振動を止めた時、状況は大きく変化します。
(1)弦に与えられた音振動は駒を経由して表板に伝えられます。同時にその振動は(主に)テールピース・テールガット・エンドレストを経由してエンドピンにも伝わっています。
チェロを床の上に設置するとエンドピンの先端の振動が止められるため、エンドピンの振動エネルギーはリバウンド(逆流)して、結果としてエンドピンではテールピンの若干下周辺が大きく振動するようになります。
さらにこのリバウンド振動は先ほどのルートを逆流してテールピースへ戻されます。楽器の部材の中でも本来脇役であったテールピースがエネルギーを得て、実際に駒の振動(さらに表板の一部まで)に影響していることが確認できました。
(2)弦と'テールガット'に両端を張られたテールピースは与えられた音振動の周波数に対して独自の規則的・機械的なビートで共振します。このビートはチェロ胴体に直接影響を与えていますが、テールピースを弁護するならば、それはいわば'poxy(代理)'です。原因はエンドピンの振動メカニズムの変化です。さらに真の原因は、床がエンドピン先端の振動を抑止することであり、演奏者がチェロを床置きすることに起因していると言えます。このエンドピンからテールピースまでのいわばアクセサリー部材の連携した共振が楽器の中で優位に立っているように見えます。
エンドピンは、材質・長さ・与えられる音の周波数によって異なりますが、基本的には独自の固定ビートをとっています。
(3)しかしもっと広い観点から言えば、チェロ胴体への影響は直接影響(上記)というより間接影響が重大であると考える方が正しいかもしれません。チェロ胴体は、上記の「アクセサリー連携」(固定振動がベース)に対して、'胴体全体'の振動を同様に均質・平坦化して共振して対応しているように思われます。この胴体全体の「均質化・平坦化」こそがモダンチェロの音色を作っている大きな理由と考えられます。振動の均質化によって自然な倍音が生み出されるチャンスは少なくなります。
(4)さらに、エンドピンの中膨れした振動は次の二つ変化を誘発しているようです。一つは僅かですがテールピンを振動させていることです。もう一つは底板の振動が、このエンドピンの振動の(てこの)支点となっているために全体として若干抑制されることです。この結果特に低音域の音では、全体的にチェロ胴体の響きの中心点が胴体の上方にシフトし、低音の豊かな響きが若干抑制されることになるようです。
演奏者は芯のある音が自分の胸に強い振動としてとらえられ、音も大きく聴こえるように感じるかもしれませんが、単に低音の響きが抑制され響きの中心点が上方にシフトしているだけではないか検証される必要があります。
チェロにエンドピンを装着して床置きした場合、さらなる影響が発生します。それはエンドピンを含めたチェロの「全身振動」です。この全身振動にも２種類あるように思われます。
一つは前項(4)のテールピンで見られたビート振動です。与えられた振動から誘発され共振する４～１ビート(66Hz以上)の振動です。(これはチェロ胴体の均質な振動との関係があるかもしれません。)
奏者は弓の毛を軽くに弦に触れる程度では芯のある十分な響きが得られないため、楽器が均質化した安定状態に達するまでの十分なエネルギーを注入する必要があるかもしれません。発音するたびに振動状態をリセットする為のエネルギーが加算して必要であることを示唆しています。
もう一つは、音としては成立しない超長周期(20Hz前後)の全身の揺れです。
おそらくこの全身振動も、奏者が演奏時、弦から抵抗を感じる原因のひとつであろうと思われます。新たな音を発生させたい場合、現在のチェロ全体の(質量に対応する)振動エネルギーをリセットさせる必要があります。そのリセットに必要なエネルギーは、かつてエンドピンを装着していなかった時代にはせいぜい、弦・表板・テールピース(・あるいはネック・・)程度で良かったものが、現在ではエンドピンを含めたチェロの全質量になっていると考えることができます。
どのような音と響きがチェロにとって理想的なのか、演奏者と演奏を聴いてくれる人にゆだねられます。
モダンチェロの響きは、かつてストラディバリやモンタニャーナが設計し製作していた当時から若干そのメカニズムが変化している可能性があると言えます。
エンドピンはチェロの演奏性を改善する上で大いに貢献しています。しかし同時に副作用を持っていることも忘れてはなりません。
47e. Comments on -without endpin-
Meanwhile the bridge(BR) weakens at around 2.5 seconds. We can image a scene that the cello body is still resonant in the echo even after the fading of bridge, strings and tailpiece/endpin. Such behavior will probably be familiar to violins or violas.
(2)Tailpiece(:TP1) keeps characteristic flat 4-beat. However in this case, the bridge(BR) is less effected and the beat-pattern is similar to the top plate. Bridge(and also strings) seems to be acting as a member of top plate group.
[ 1/13/2017 ] Labels: 47..Propagation
47d. Comments on -on the floor-
The endpin is getting the vibration energy mainly through this route(TailPin-TP-BR) not through lower-bouts.
When the vibration of tip of endpin is restricted at one point on the floor, the rebounded energy will probably come back to the tailpiece through this propagation highway. Getting energy, tailpiece can probably keep the vibration powerfully and clearly for 3 seconds or more.
(2)An another important peculiarity was found at the upper part of tailpiece(TP1). TP1 shows a characteristic vibration beets for C note(66Hz) that keeps constant(/flat) 4-beat. This vibration is supposed to be caused from structural reason.
In this case, it is shocking to say, the 4-beat vibration is also observed broadly in bridge(BR), and partially in the top plate(T-3, T-2). This particularly flat vibration from the tailpiece seems somehow affecting the cello body.
(When we look back at the "Label: 20.Vibration Video(slow-motion) -> Tailpiece", tiny 4-beat vibration can be seen on the string between bridge and tailpiece.)
(3)In my former posts, the lower-bouts showed a tendency of fading out rather in a short time at the case of 'on the floor'. Besides this, the lower part of top plate(T-4) also slightly weakens the vibration at around 3 seconds. These phenomena probably suggest some shrinkage of resonance at the lower hemisphere of cello body.
[ 1/13/2017 ] Labels: 47..Propagation
46e. Vibration beat--B(496Hz)--COMPARISON--Top plate--
Note:
The duration time of the vibration of B(491Hz) note on cello A string after a pizzicato, like other notes, was following order: top plate > endpin > lower-bouts.
In these measurements, sometimes some fundamental B(491Hz) beats were missing.
This phenomenon is very similar to the 'wolf-tone'. The impacts/influences on sounds are currently unidentified.
(高音のA線上のH音-491Hz-、ところどころでウルフトーンのように基本振動の欠落が見られた。どういう音響影響があるのかは不明。)
[ 1/08/2017 ] Labels: 46..Beat.Data-B
45e. Vibration beat--E(331Hz)--COMPARISON--Top plate--
[ 1/03/2017 ] Labels: 46..Beat.Data-E
(E note on A string)
The vibration of Lower-Bouts fades out in short time. However top plate and endpin continue the vibrations for a long time.
How can endpin get the energy? Why? Ooooops!
Possibly the endpin is mainly communicated not through lower-bouts but an another route:
Top plate/bridge--strings--tailpiece--tailgut--endrest--endpin--(floor)
We have to check this 'communication highway' later, especially bridge and tailpiece, these components may tell us a hidden truth.
(E音(331Hz)ではチェロの底板はいち早く振動を止めるのに対しエンドピンは表板とともに振動を続けています。別ルート：テールピースなどを調べる必要がありそうです。)
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