# Violin's sound holes

#### Icebreaker

Does anyone know the relation between integrals and the sound holes on the violin?

Related General Discussion News on Phys.org

#### brewnog

Gold Member
Icebreaker said:
Does anyone know the relation between integrals and the sound holes on the violin?
What, the way that the F-holes look like an integral sign?

#### Icebreaker

Yes. I read somewhere that they were incorporated onto the violin after some violin maker was impressed with calculus. But I can't find the source.

#### fourier jr

james stewart's calculus text has a violin or something on the cover. seeing that cover for the first time was the first time i noticed that. it made me think that math is 'musical' in some (superficial) way, the way it looks on the page or something like that.

edit: on second thought i'm not sure that i believe that. euler was the first to use a stretched-out latin summa for an integral sign (i think) but he was around after the old-school baroque violins were made & they had the same soundholes as later ones. i think that's all true but i may be wrong. if i am wrong i'll of course look like a total bull****ter lol.

Last edited:

#### zoobyshoe

I should think Mentor Integral would know the history of the symbol, when it first came to be used.

#### FredGarvin

Icebreaker said:
Does anyone know the relation between integrals and the sound holes on the violin?
I have seen papers on vibration analysis of violins in which they discuss the formation of chladni pattern formations at various resonant frequencies. From what I remember, the sound holes seemed to always be enveloped by the nodal lines. They didn't seem to cross them. I am not sure if that is coincidence or not. But by the looks of it, the general envelope of where to put the holes is somewhat driven by the tuning of the top and the "integral" shape came from stylization that was popular in the day. I will have to keep digging on this one. Interesting question.

It doesn't exactly reference a direct expalination, but I think it's a start. I'll have to read the whole thing later.

Last edited:

#### Icebreaker

If Euler was the first to use the stretched out S, then it was probably the other way around, that Euler used the shape of the violin sound holes. Then again, it could be a coincidence.

#### hypatia

I've sent a email to this gentleman. I bet he knows the answer, hope hes not on summer break
http://www.ecu.edu/physics/George.htm [Broken]

Last edited by a moderator:

#### russ_watters

Mentor
My professional bass guitarist roommate isn't sure but thinks its stylized based on a treble clef symbol. We think the area of the hole probably matters because it needs to let a certain amount of air move in and out, but other than that the geometry shouldn't matter.

#### hypatia

from: Dr. George Bissinger
Professor of Physics
East Carolina University
Howell Science Complex

Hypatia,

knows many details about the origin/originator during the 1500-early
1600 period of many of the things we accept as commonplace today. This
includes f-hole shapes, which are quite variable and certainly not
always f-shaped. In fact modern makers often change proportions to suit
their personal whims - and in some cases this significantly affects the
sound. So seeing integral signs prior to actual integrals is probably a
vapor state pursuit.

George

#### zoobyshoe

That's a nice letter.

What, though, does he mean by a "vapor state pursuit"?

#### hypatia

The f-hole shapes were made befor the integral, so the pursuit of this is not realistic?

lol Now I wonder if the person who made the integral sign, got it from the violin?

It is a very eye pleaseing shape

#### zoobyshoe

hypatia said:
The f-hole shapes were made befor the integral, so the pursuit of this is not realistic?
It sounds like a physics term he is using to indicate that there may not be any single actual origin, no one violin or violin maker you could point to and say "Here we have the first, classic violin sound holes."
That's my impression, but I need to know if there is actually such an endeavor in physics as a "vapor state pursuit" and what the attendent difficulties are, to be sure I'm understanding him.
lol Now I wonder if the person who made the integral sign, got it from the violin?
Fourier jr said it's the greek symbol summa, stretched out:
fourier jr said:
euler was the first to use a stretched-out latin summa for an integral sign (i think)

Last edited:

#### Jelfish

zoobyshoe said:
Fourier jr said it's the greek symbol summa, stretched out:
I'm pretty sure summa is latin. Summa, which means "sum," was written with a stretched "s" (the integral sign)
$$\smallint \text{VMMA}$$ (perhaps something like this?)
while the modern day "s" was used as a terminal "s" (that is, used when the "s" sound ended a syllable). The greeks have something similar: sigma $$\sigma$$ and terminal sigma $$\varsigma$$.

#### hypatia

well I asked up in the physics threads..maybe someone will help us with "vapor state pursuit".

#### GOD__AM

Sounds like hes saying: trying to relate the f holes to the integral sign is wrong since the holes existed before the sign... Its a fruitless endeavor or a vapor state pursuit. In other words a waste of time.

Another thought may be that since the f-holes were created so long ago that the original reason it was selected has since been lost or changed. Much in the way and story is changed over time after being told many times by many people. Hence the information is in a vapor state.

Last edited:

#### hypatia

thanks for the imput

#### zoobyshoe

Jelfish said:
I'm pretty sure summa is latin.
"...but, for mine own part, it was greek to me."

Casca in Julius Caesar
Act I, Scene II
by William Shakespeare

#### zoobyshoe

Jelfish said:
I'm pretty sure summa is latin. Summa, which means "sum," was written with a stretched "s" (the integral sign)
$$\smallint \text{VMMA}$$ (perhaps something like this?)
while the modern day "s" was used as a terminal "s" (that is, used when the "s" sound ended a syllable). The greeks have something similar: sigma $$\sigma$$ and terminal sigma $$\varsigma$$.
Looks like you're more or less right about all this:

Integral Sign -- From MathWorld
The stretched out S to mean "summation" is due to Leibnitz.

#### zoobyshoe

Musical Instrument Q & A: Violin

Origins of the violin
Q:I am a violinist and I am interested to know about the history of violin: who was the inventor of the first violin (I suppose the first maker of the violin is unknown.). My sister is a flutist. She is 12 and she is researching about the same thing - the history of violin - for her school. She goes to a French school and therefore she needs this information in French. She tried hard to find the information but she didn't succeed.* Quebec* 1/20/2004
A: This is a complex question that depends on what you define as a true violin. As you suspect, the violin was not so much invented as evolved from precursors. It is widely accepted that the concept of bowed instruments began in the Middle East around 1000 AD. The essential shape we know as a "modern" violin became standard in Italy around 1550, but may have evolved as early as the previous century. At the time there were many variations on bowed instruments (largely classified by whether they were played on the shoulder or on the lrgs - viola da bracchio or viola da gamba), but the violin family eventually took prominence. Among the earliest "great" violin makers beginning from around 1540 were the Amati family: Andrea Amati, his brother Nicolo, and Adrea's sons and grandsons.

Last edited:

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving