DISCUSSING THE MODEL
The project’s research showed that there were almost countless types of cellos over the centuries.
Following the conclusions drawn after testing the two prototypes the team decided to build the project’s final instrument as a Stradivari-type cello with a slightly smaller size than the usual 4/4 size.
In the meantime Ueda had managed to temporarily lay his hands on a photo (showing several views) and a poster25 (showing all important measurements in the original size) of a five-stringed cello26, built by the Amati brothers Antonio and Girolamo around 1600.
Picture 20: The five string, knee-held cello from the Amati brothers Antonio (ca. 1537-1607) and Girolamo (ca. 1551–1630); Body length: 707 cm – slightly smaller than a 7/8 modern cello; distance from nut to bridge: 640 mm – 30mm less than a 7/8 cello’s.
Picture 21: The complete measurements of the Amati brothers’ five string cello27.
COMPARISON OF THE PROJECT’S CELLOS’ OUTER MEASUREMENTS:
| Prototype I | Prototype II | Amati | |
| LENGTH OF BODY: | 750mm | 710mm | 705mm |
| LENGTH OF STRINGS28: | 690mm | 670mm | 640mm |
| WIDTH OF UPPER BODY: | 340mm | 325mm | 354mm |
| WIDTH OF MIDDLE BODY: | 250mm | 225mm | 235mm |
The Amati model has the smallest body length of the three instruments. It might make its use a little awkward, but the real concern is the considerable difference of length of strings; today’s cellists’ left hands are used to the 4/4 sized cello’s length of 690mm. Switching to an instrument with a difference length of strings up to 5cm will certainly cause adjustment problems.
This problem has to be dealt with when building the project’s final cello.
THICKNESS OF BELLY AND BOTTOM
Picture 22: The Amatis’ cello’s belly. The numbers represent the measurements in millimeters. The + signs indicate the places of measurement.
Picture 23: Measurements of the Amatis’ cello’s bottom.
The pictures illustrate the non-symmetrical structure of the belly and bottom of the instrument. That fact is a very substantial point, supporting the decision to produce a hand-made instrument. Following those measurements requires very cautious, slow work, involving precise and frequent measuring: a mistake like taking off one millimeter too much cannot be corrected. Fast and cheap production cannot deliver that kind of precision.
BELLY:
The Amatis’ and Stradivari’s measurements are the result of careful calculations and countless trials. A violin maker wants the belly and back as thin as possible without risking the static stability of the instrument. A thin belly and a thin bottom allow the body to vibrate more easily, which will result in a better responsiveness of the strings and a bigger sound.
On the other hand, since the tension of the strings cause quite a lot of pressure, mainly onto the belly, a too thinly constructed instrument could end up with a sinking or even cracking belly when the strings are being mounted and tuned to their respective pitch. A thicker body will provide stability but will have worse sound properties.
The Amatis’ solution for this problem was making their cello’s belly thicker than the bottom and using an asymmetrical pattern of thickness for both. It was the same decision their father, Andrea Amati, and later Antonio Stradivari took for their four string cellos. The lower strings are much thicker than the higher strings and thus produce more pressure onto the belly. That is the reason why the masters decided to make the bass sides in general thicker than the treble sides. That way belly and bottom are strong where a lot of pressure is present and thin where less strength is needed.
BOTTOM:
The bottom is generally about 40% thinner than the belly with one exception: the place around the sound post and below the bridge. The sound post transfers considerable pressure from the bridge to the bottom. For that reason the Amati design demands in the area around the sound post’s position 7.1 mm and in the area under the bridge 7.2mm. This is more than the thickest part of the belly (5.7mm).
Otherwise the asymmetric pattern is very much like the belly’s design: the bass side is thicker than the treble side.
Surprisingly the general thickness of this five string cello’s belly and bottom is only very slightly different from a four string Stradivari-type cello’s measures; one would have expected for example a substantially thicker belly in compensation for the additional pressure of the fifth string. Obviously, besides the body length, the general measurements of a five string cello do not have to change to a major degree.
OUTER MEASURES OF THE BODY
CONTOURS
Basically the contour of the Amati five-stringed cello is very close to the final shape Stradivari decided about in the early 18th century for the four-string model. One difference was already pointed out: the lesser length of the Amatis’ cello’s body. Presumably the reason for that were the static and acoustic changes resulting from adding a string – the four string cellos manufactured by the Amati family generally have the usual length of around 750mm.
In the year 1600 Antonio was 63 and Girolamo was 49 years old. They did build cellos before 1600 that were bigger (lengths between 730 and 750mm) than the five string cello (705mm). It also is a fact that their father Andrea Amati (1505-1577) was the first master who established the measurements that became the fundament of the Stradivari model: Andrea’s cellos already had measurements around 750mm (length), 35mm (shoulders) and 44mm (hips). (Stradivari’s models featured only relatively minor changes of the Amati model. Stradivari’s importance lies in the fact that his changes were the last ones.) Therefore it can safely be assumed that the brothers’ five string cello was a try to make a step ahead from the Andrea Amati and the later Stradivari model: it would make no sense to return to the gamba design at a time, when the new four string cello already had proved its superiority.
There is only one possible explanation for the brothers’ experiment: They wanted to build a five string cello that stayed as close as possible to the new cello’s shape but offered new opportunities.
Those new opportunities and the true reason why they wanted to construct a five string instrument at that time can only be speculated about; they probably wanted to expand the tonal range of the cello, either on a general purpose or for the easier execution of some particular pieces that could be performed easier with a fifth string.
(The Amati five string cello is presently in the posession of the museum of the Royal Academic of Music of London. It is equipped as a baroque cello and can therefore not serve as a material for comparison to any cello with modern equipment.29)
BODY HEIGHT
The term body height here refers not to the length from the top of the scroll to the end of the tail piece but to the height of the bouts (ribs) of the instrument.
Picture 24: Lower treble side rib of the Amati five string cello.
The Amati has rib measurements of between 112 and 130mm, with128mm at the shoulders and 130 mm at the hip, including the edges from belly and bottom. (If one sees a cello one assumes that its shape is perfectly symmetrical and regular. The measurements of the lower treble side rib (picture 24) and the measurements of belly and bottom (pictures 21 and 22) however illustrate that the Amatis obviously decided about several deviations from the principle of symmetry. That is true not only for this particular instrument: other Amati and also the Stradivari four string cellos show asymmetric measurements of body thickness and height. As mentioned before, this is the way how the masters dealt with the irregular distribution of pressure on belly and bottom.)
The rib height of the Amati five string cello is somewhat surprising: the Stradivari models have an average height of 120mm (shoulders) and 130mm (hips) and the 7/8 PROTOTYPE II has respective measurements of 122 and 126mm. Considering the reduced length (705mm) of the Amati (Stradivari’s average length is 750mm) one should expect a proportionally reduced body height. But the Amati has the same rib height at the hip as a Stradivari full-size cello and its shoulder is even a little higher than a Stradivari’s average shoulder. The comparison of PROTOTYPE I and II showed that a slight sacrificing of body length results in better sound properties. However, reducing the height proportionally would not affect sound properties30: the ribs do not play a significant role in the acoustic system of a string instrument; they do not really transport vibrations from the belly to the bottom: that task is the sound post’s main job. (Touching the ribs while playing will not change the sound, while touching belly or bottom will considerably disturb vibrations and muffle the sound.) The Amatis obviously wanted to keep the body volume as big as possible.
A Stradivari-type cello has basically the same proportions as a violin but is approximately twice the size. The only major difference is the height: the cello’s height is four times the height of a violin. Like to the Amati brothers with their five string cello it seemed important to Stradivari to get the biggest body volume possible, probably in an attempt to make up for certain acoustical losses, caused by enlarging the size. It is a surprising fact that the sound volume of string instruments becomes smaller with growing size. For example the viola (average body length: 41cm) is not much bigger than a violin (average body length 36cm) but has a distinctly smaller sound. The by far biggest string instrument, the double bass, has the smallest sound of all the orchestral string instruments.
The lower registers and the longer strings with their lower speed of vibration are one reason for the loss of volume with bigger instruments. Another important factor is the size of the body: bigger bodies require more material and have to feature thicker bellies, bottoms and ribs which results in some loss of responsiveness to the vibration of the strings.
After having studied the Amatis’ instrument’s measurements it was concluded to basically follow the inner construction’s design ratio of the Amatis’ cello. Overall a general increase of thickness will be taken into consideration.
However, the string length of only 640mm cannot be tolerable: the project’s final cello should be an instrument that can be used by any cellist without major special adaption. Preserving the Amatis’ outer body measures and only change the strings’ length to an acceptable 660 to 670mm by prolonging the instrument’s neck would result in a general esthetic misbalance of the instrument and also might cause negative changes concerning sound and usability.
Thus it was decided to use the outer measurements of a small, master-made four string cello.
25 Both were photo-copied and returned to their owner.
26 Photo and poster were a supplement to an edition of the magazine ‘The Strad’.
27 The photos of the Amatis’ measurements were taken from the poster created by John Dilworth that came with an edition of the magazine ‘The Strad’.
28Measured from bridge to nut.
29 Modern equipment mainly means stronger strings. That seems to be a minor factor but with the development of stronger strings over the centuries the violin makers had to adapt their instruments’ bodies to the growing pressure on the body. That is the reason why a modern cello’s structure is quite different from a baroque cello’s. A baroque cello could not take the pressure of steel strings.
30 The 7/8 PROTOTYPE II does have smaller height than a 4/4 instrument. The reason for this is the intention of creating a usable cello for small persons while accepting the possible downside of having a smaller volume.
