Why is there no simple relation between fractional size and metric size?

January 1, 2012 at 12:16 AM · Don't the fractions refer (at least roughly) to the volume of the space inside the body? Fill a quarter, half, 3/4, and full-size violin with water and see if this is so!

January 1, 2012 at 08:15 AM · Lisa, no, they don't. Not even roughly. For that, the length of an 1/8 violin would have to be 1/2 that of a 4/4. It is much more.

January 1, 2012 at 03:25 PM · Hello Bart:

It is a very intelligent question and, I am not sure if my answer is correct but neverthless, I think that it is and so I will try. I think the logic is based on Scaling Principles - (i.e., sizing logic and not to be confused with scales of music!!!). For that we have to understand what is the range of sizes we are trying to cover. When you have a small range to be covered, then the Scaling Principle is based on Arithmetic Progression - i.e., Constant Additive to the previous size to get to the next size. This is the principle that is used in sizing says shirt sizes or say, shoe sizes because the body size or feet size range is small. So, from Small size to Medium size to Large size to Extra Large size of shirts is a Constant Additive. You use Constant Additive because, the Extra Large size guy is not 4 times as large as Small size guy. Same logic applies to shoe size - it will be a Constant Additive from one size to the next size. When a large range is to be covered, say size of Power Plants that a company is offering in its Product Portfolio, then it will a Geometric Progression - i.e., Constant Multiplier to the previous size to get to the next size. So, for example a company is offering 100 MW to 1000 MW power plant then, can be covered in 5 steps as follows - 100 MW, 160 MW, 250 MW, 400 MW, 600 MW, 1000 MW - wherein each size is multiplied by 1.6 - i.e., 5th root of 10 - i.e., 5th root of (1000/100) in order to get to the next size. That means, in 5 steps you go from 100 MW to 1000 MW or 10 times your initial size = final size. You apply Scaling Principle because you don't want to carry an infinite sizes in your Product Portfolio because then it would be uneconomical to do so in terms of part sizes that you will have to carry.

With the above background on Scaling Principles, we can deduce that the Violin Scaling would have to based on Arithmetic Addition because the range covered in arm sizes is rather small between a child and an adult - pretty much like the example of shirt sizes or shoe sizes that was covered before. The Constant Additive in length between 1/64 size to 1/4 size is 4 cm; then the Constant Additive reduces to 3 cm between 1/4 size to 1/2 size (assuming that there is a hypothetical 3/8 size in between the two) and it further reduces to 2 cm between 3/4 size to 4/4 size. Since, the growth rate of children taper off, the Constant Additive also reduces from 4 cm to 3 cm to 2 cm. Hope the above helps.

January 2, 2012 at 09:26 AM · Hi Shiv,

Thank you. That must by why the actual sizes are what they are. One half of the puzzle solved. Now for the other half: what do those fractions refer to? Or was it just the way sizes were named in those days?

Bart

January 2, 2012 at 11:29 AM · Lisa, I trust your suggestion to fill the violin with water was merely metaphorical and not to be taken literally! Or we'll be having someone telling us to fill the violin with foam next ;)

January 2, 2012 at 04:31 PM · Hello Bart:

Once again conjecture on my part - using adjectives* like Large, Medium, Small Medium, Medium Small, Extra Small, Very Extra Small etc. etc. as nomenclature to denote various violin sizes can only end up confusing everyone. Instead if we have numbers and their fractional sizes like 4/4, 3/4, 1/2 ... 1/64 etc. etc. for nomenclature of the various violin sizes it is less confusing. Long and short, both the nomenclature and the scaling logic used seems to indicate a very profound/ scientific thinking by our elders of bygone era. Of course, violin is an instrument based on scientific principles, is it not?

Best regards

Shiv

* Precisely for this reason you will find good engineers and scientists will not use adjectives in their communication but, instead quantify things in order to avoid subjectiveness and confusion.

January 2, 2012 at 08:15 PM · Hello Shiv,

This is too deep for me.

In our times we would perhaps have had the body length in inches as a designation, as with violas.

I would have liked that better.

But that's not the way it is:)

Best wishes,

Bart

January 13, 2012 at 09:39 PM · Shiv Dinkar is right: from a full-size (4/4) violin, we take off about 1 inch each time to get a 3/4, 1/2, 1/4, 1/8, and 1/16 sizes.

Then we find that proportionally there is too big a change from 1/16 to 1/8 for 3-to-4 year-olds, so we insert a 1/10 (which sounds a whole lot better than the 1/16).

There is also a 7/8 "lady's violin" for delicate "ladies".

Too simple? Century-old french quarters correspond to our present eigths (but with a wonderful tone, and a wider finger board for our chunky western fingers!

Got it? Good thing the question wasn't about violas!

Adrian