For a given instrument (violin, viola, cello, bass is more complicated), the tuning of a fractional size instrument (1/16, 1/8, 1/4, 1/2, 3/4 are commonly seen, 7/8 used to be frequently called "lady's cello") is always the same as the full size instrument.
viola is a bit complicated because professionals have different sizes (15', 16', sometimes 17' for body length, remove about one inch for string length), so that one refers to the body length and string length (the last one being the more important for buying strings).A good rule for chosing one's viola size is : are you able to confortably stop on each string the first tone after the empty string with the index as well as the fifth interval with your little finger ?
(For the A-string : try to stop a B and a E, for the C-string : try to stop a D and a G).
The size matters for the sound, but a lot less than the quality of construction.
A good violin maker will change the internal measurements, the position of the f-holes, to maintain the best body resonance for the intended tuning.
I have played several good 1/2 cellos that sounded a lot better and more powerful than ordinary full size ones.
The only reason to buy a fractional size is the age and body measurements of the player, not the sound.
Also make sure that the player will have time to play and study say two years on this instrument.
This is not about economy, just so that he/she will develop enough is ear and finger skills, so that the transition to a larger one will be really easy.
music.stackexchange.com/users/48/ogerard
3/4 means three quarters size as opposed to full size.
The tuning can be the same, but the scale length is different, which means string length and tension (and thickness) are different.
So while you use the same techniques, the finger positioning will vary.
The reason for these different size instruments is the difference in tonal quality.
The resonant frequency of the body will be different between two instruments of different sizes.
music.stackexchange.com/users/104/Doktor Mayhem
Usually the three-quarter or other smaller than standard violins are for younger, smaller children.
A full sized violin would be way too much for a three or four year old to handle.
The bow is appropriately smaller, as well.
The spoken lengths of the strings are obviously in proportion, and a child will have to re-adapt when it grows big enough for the next size violin.
Most adults would, I believe, use a full-size 4/4 violin.
music.stackexchange.com/users/2808/Tim
In the bass world, size matters.
:)
Very few players use a full size bass (it's huge), except some orchestral players.
The standard size is ⅞, and ¾ size basses are popular, too.
music.stackexchange.com/users/9337/Robert Fink
1/4, 2/4... 4/4 are instrument proportion measurements.
A child will often play in a 1,2 or 3 quarters of original size (4/4).
Normally a professional instrument is a 4/4 size.
The term 4/4 is most used in Schools/Student context.
What changes between them is the string length, and with that the space between fingers to tune properly.
The proportion between instrument size and arm length is important for the hand to have a good ergonomic position and reach naturally the fingers place.
The size of the instrument means also a weight difference.
a 4/4 violin is heavier than a 1/4 violin.
I have seen many colleagues, playing for example viola, having to exercise the upper body so they can compensate the heavy instrument when playing many hours.
Last but not least, the bigger instrument the more resonance body and larger string wave length.
A 1/4 violin will not produce a open string tone as long lasting as a viola (which can be compared with a measure like 5/4 or 6/4 of a violin).
You can see it as a concert piano.
The longer the tail is the better sound you will get.
music.stackexchange.com/users/6511/Sergio
The tuning is always the same.
The "3/4" fraction of full size is approximate, as a moment's websearching reveals.
Intonation is easier on larger instruments, because less precision is required.
Sound is louder from larger instruments: larger resonating body, more energy imparted to the string.
Tone is better on larger instruments, because a longer string's harmonics align more closely to its fundamental frequency.
(That's why a piano is tuned in "stretched" octaves: its ideal bass strings would have to be dozens of feet long.)
All these generalities assume that the instrument is not so large as to be uncomfortable to play.
music.stackexchange.com/users/8794/Camille Goudeseune
In the string family, you can buy instruments that are described in fractional sizes, like 3/4 violin.  Is the tuning always the same, no matter the size of the instrument?Why is the instrument size important/what difference does it make?  Also, what does the term 3/4 or 4/4 mean?  Example : 4/4 Violin Maplewood
Why does bowed string instrument size matter?
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music.stackexchange.com/users/5839/Ivan Ivković
The reason for these different size string instruments is the difference in tonal quality. Sound is louder from larger instruments: larger resonating body, more energy imparted to the string. Tone is better on larger instruments, because a longer string's harmonics align more closely to its fundamental frequency. The tuning is always the same.   The only reason to buy a fractional size is the age and body measurements of the player, not the sound.  The tuning of an instrument is always the same regardless of size. However, the size can impact other things such as tone, weight and intonation. "3/4" and "4/4" are instrument proportion measurements, and fractional sizes normally are used to cater for the body measurements of the player.
The size of an instrument can have a big impact on the sound and tone that the instrument produces. Intonation is easier on larger instruments. The tuning is always the same regardless of the size of the instrument. "3/4" and "4/4" are instrument proportion measurements. Fractional sizes exist to suit the measurements of the player. The size of the instrument will also impact the weight of the instrument.