The diagram below illustrates the notes played on the open strings of the violin, and also for two other members of the violin family, the viola and the cello.
The strings of the violin are tuned a fifth apart, as is true for those of the other instruments described in this diagram; those of the double bass are tuned a fourth apart, so it and related instruments are described in another diagram.
In addition to the violin, viola, and cello, the tunings for six of the eight instruments in the Violin Octet of Carleen Hutchins are shown in this diagram.
An earlier proposal for additions to the violin family, by Dr. Alfred Stelzner, is also noted in this diagram. He had also proposed a change in the shape of the instrument to improve its acoustic properties; among other things, the difference in size between the upper and lower halves of the body was increased slightly.
The violin family as we have it today does present some difficulties.
This image which I produced from an old photograph of a violin and a viola side by side shows that the viola is quite a bit larger than the violin. However, the viola is tuned a fifth lower than the violin; it may be larger, but it is not one and a half times larger in every direction.
To improve the viola, Jean-Baptiste Vuillaume invented an instrument called the contralto. This instrument basically looked like a viola with its body split in half, with an additional rectangular piece inserted, thus making it wider without changing the shape of its sides. While the result was found to have a satisfactory tone, and the principle of its design was intended to make it possible to play it in a similar way to which the viola is played, the instrument was found to be unwieldy.
More recently, the pellegrina was invented by David Rivinus in 1993 as a way to reduce the large size of the viola, thus helping to protect viola players from injuries such as carpal tunnel syndrome. The instrument has a somewhat unattractive appearance, looking like two left halves of a violin joined together, one upside down.
At first, I wondered if it might be possible to achieve the same thing with a shape like that of the contralto, but with the bridge, strings, and neck in an off-center position. On further consideration, in order to enlarge the instrument, but have everything reachable, while retaining a symmetric appearance, perhaps a solution would be to turn both sides of the instrument upside down, so that the smaller round part is nearer the player, which would then allow for the instrument to be widened as the contralto. Another option would be to thicken the instrument, as we will see below was done for the violoncello, except with a part at the bottom cut off so that a chin rest could still be used.
On the left, there are images of the front and the side of a violin, from an old photograph; on the right, images of the front and side of a cello, from another old photograph.
The images are not to the same scale; for comparison, the two instruments have been made the same height, whereas a cello is in fact much larger than a violin.
As can be seen from this image, a cello is considerably thicker, in proportion to the size of its front and back, than a violin.
This was done to increase the internal volume of the cello, thus lowering some of its resonant frequencies, while limiting its size.
So what is illustrated here is that the wide range of musical pitch, of audio frequency, covered by the violin family cannot be matched by a proportionate increase in size, because the awkwardness of having larger instruments is not felt to be a reasonable disadvantage to accept for the improvement in tone that would be obtained. Of course, since the cello exists, a larger viola that would have to be played like a cello could still be played; and since the double bass exists, a cello that has a larger front and back, but more violin-like proportions, again, could still be played; but in both cases, making the instrument larger would limit what players could do with it in performance, and it would make it awkward to seat as many players of each instrument in an orchestra.
So a balance was found between the notes each type of instrument would produce and how much of the agility of a violin player performers in that range of sound would need to enjoy for the purpose their parts would serve in music.
To allow a clearer comparison of the sizes of the violin, the viola, and the cello, the diagram on the right shows several dimensions of such instruments, following the notation used in the book Antonio Stradivari: His Life and Work by W. Henry Hill, Arthur F. Hill, and Alfred E. Hill. This book included, as an appendix, tables of the dimensions of a number of instruments by Stradivari and others.
Here are just a very few of the measurements given there, to give an idea of the relative sizes of these three instruments:
A B C D E Stop Violin 14 1/16 8 1/4 6 5/8 1 1/4 1 3/16 --- Stradivarius, 1720 Violas 18 7/8 10 3/4 8 5/8 1 11/16 1 9/16 10 1/4 Stradivarius, 1690 (Large size) 16 3/16 9 9/16 7 5/16 1 1/2 1 7/16 8 5/8 Stradivarius, 1701 (Small size) Cellos 31 3/8 18 1/2 14 1/2 4 3/4 4 1/2 16 3/4 Stradivarius, 1690 (Tuscan) 29 7/8 17 3/8 13 5/8 4 5/8 4 1/8 15 3/4 Stradivarius, 1711 (Duport)
The Duport cello, being made after 1710, is an example of one made using the "Forma Buono" cello mold, and these proportions are now considered the ideal for a cello.
Metal-wound strings are not a recent innovation; they were what enabled Francesco Ruggieri to reduce the size of the cello to what we are familiar with today, to sizes such as 760 mm and 740 mm. The body size of cellos was originally around 32", or 812 mm. As can be seen from the table above, Stradivarius made cellos in both of these ranges of size. Guadadnini went further, making cellos with a body size as small as 711 mm or 28", and this would still be considered a full-size cello today.
As for the viola, current violas are all in the "small size" class. If the size of a viola were in proportion to its pitch, it would have a body size of 21 3/32 inches, and a thickness at its base of 1 7/8 inches, which would be completely impractical, unless it were to be played as a cello is played.
Using sizes from the table above, which don't necessarily correspond to the actual instruments the old pictures of which were used in preparing this image, here is an image providing a graphical comparison of the size of a violin, a viola, and a cello:
If a cello were made as a scaled-up violin, its body height would be 42 3/16 inches, but the thickness at its base would only be 3 3/4 inches, less than that of today's cellos, which indeed, as noted, use a larger depth as a substitute for a full height.
Looking at an adult playing a cello, one might think that there would be no problem in making a cello in that larger size resulting from maintaining the same proportions as a violin, since the metal rod reaching down to the floor from the bottom of the cello, called the pin, is certainly much more than one foot in length. However, this would also enlarge the distance between the points at which the fingers would have to press the strings to the fingerboard to play different notes. To reduce this distance is the reason Francesco Ruggieri took the opportunity afforded by the development of metal-wound strings to reduce the body size of a cello from about 32" to 29", so a cello with a 42" body would clearly be impractical. This is also the reason why the strings on a double bass are tuned in thirds rather than in fifths, so that fewer notes need to be made with any one string.
Of course, one could imagine a cello of this form being made with its strings tuned an octave higher than the strings of a double bass. The lowest note that could be played would be E instead of C, but it would cover much of the same range.
A viola that was a scaled-down cello instead of a scaled-up violin would be 14 15/16 inches in height, but 2 5/16 inches thick at the base; perhaps such an instrument is too thick to hold under the chin, but as there appears to be room to put a shoulder rest under a viola, perhaps not.
Note that all three instruments are slightly wedge shaped, being thicker at the bottom than at the top (in the sense of towards the neck, not towards the belly).
The diagram below shows the tunings for the double bass and related instruments.
Shown there in addition are the two remaining members of the Violin Octet, and the Octobass, proposed by the noted luthier Jean-Baptiste Vuillaume.
Next, we will look at how the viol was tuned; as it is a more complicated case, it may be appropriate at this point to look into the basis on which tunings are designed.
Above is a simple diagram of the circle of fifths, a very important concept in Western music as it is today.
Because the seven natural notes are consecutive on the circle of fifths, when strings are tuned a fifth apart - or a fourth apart, since that interval is complementary to the fifth, corresponding to a counter-clockwise step around the circle of fifths, as a fifth is a clockwise step - many choices of tunings are available which avoid having any open strings tuned to a sharp or flat.
A four-string bass guitar is tuned to the same four notes as a double bass. But bass guitars can also have five or six strings; the six string bass guitar extends the sequence of notes to B E A D G C, with another fourth available in both directions that leads to a natural note.
A six-string instrument tuned in fourths could also start the sequence at E, for E A D G C F, again using only natural notes.
Thus, based on that principle, one could have a whole family of six-stringed instruments, two per octave, with the space between them alternating between a fourth and a fifth.
For comparison with the tunings of the two parts of the violin family, here is a diagram of the tunings for the viol family, which preceded the violin family:
The tuning for the Great Double Bass is a presumed one given in Wikipedia.
Note that the six strings of a viol are divided into two groups of three strings that are tuned in perfect fourths, like those on the double bass and related instruments, separated by a major third between the two central strings.
This allows three different instruments in each octave, and the compass is less wide than a straight tuning in fourths over six strings would provide; this is reasonable, as one reason violins only have four strings is the same as the reason the members of the violin family differ in size: a given instrument of a particular size produces the best quality of sound for notes within a limited range of pitch.
While the violin family consists of three instruments that follow one pattern, and a fourth instrument that differs, the viol family includes seven instruments that all follow the same pattern. But because the successive instruments are separated by fourths instead of fifths, and the conventional violin family omits a possible instrument between the viola and the violoncello, the range of notes covered is about the same.
Since the sixth string is tuned to the same part of the scale as the first string, it is possible to see that the possible tunings of this instrument correspond to the possible tunings for an instrument with five strings, all tuned in fourths.
Additional members of the viol family which don't fit into the regular pattern of those appearing here are shown at the bottom of the diagram. An instrument higher than the treble viol, the Pardessus, added at a late date, usually had only five strings. The Wikipedia article on the Pardessus shows two possible tunings for the six-string version, both the one which doesn't fit the pattern, shown at the bottom of the diagram, and the one that does; the article on the Viol only showed the one that didn't.
The Alto Viol in C, like the non-conforming Pardessus, had two strings tuned in perfect fourths, followed by a major third, followed by four strings tuned in perfect fourths, proceeding from the lowest string. In the case of that instrument, however, the deviation from the pattern was required, since the string tuned to A, if it was a perfect fourth higher than the one tuned to F, would be tuned to A sharp or B flat, not to B natural - and having open strings tuned to notes other than the natural notes of the diatonic scale seems to be something that is generally avoided.
As well, the standard tuning for the guitar is shown on this diagram, although it is plucked only and not bowed, because its tuning is also very similar: in this case, four strings tuned in fourths, a major third, and then two strings tuned in fourths. This time, the major third comes earlier rather than later, but it can be seen that the tendency to tune a six-stringed instrument in fourths with a major third near the center has survived the eclipse of the viol.