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PHI


polkat
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I believe this came up here a few years ago, but I don't remember any conclusion. The book; The Da Vinci Code got some people in luthery talking when it was siggested that Strad used PHI in the placement of his F holes. Some here said no way. Others disagreed. I've been studying this Golden Number, measuring the dimensions of various old violins such as lengths of various parts, compairisons of bout sizes, etc. etc., (of both 4/4 and smaller instruments) and indeed this proportion does seem to come up (or comes very close) in a lot of these compairisons.

Now, I'm no math pro, and most of my violin work is in repairing and restoration, not making anymore, but I'm courious about any further thinking on this in recent years. PHI was known by many during the Golden Period of violin making, so it stands to reason some luthiers of the time may have experimented with it.

Anyone?

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The golden ratio will come up in violin design but it's far from the only proportion that apply. Here is my F-hole layout for 'generic Strad models' that I developed at the violin making school (around 1989). Although I have moved beyond it since then, it can still be useful. I gave this to Alvin Thomas King who was asking if anyone had done work on this. He later published his own variant in the Strad.

1. On a paper, draw the outline of the belly and mark the center line. The length to be measured equals the full length of the body.

2. Then draw a cross line at the golden section (phi) from the bottom. It's the height for the lower lobes, we may call it line (A).

3. Mark the golden section from the top; the same measurement as nr. 2. Point B.

4. Draw a line across the c-bout for the upper holes. It's located at the golden section between the first two phi's. Line C.

5. Find the widest points at the lower bouts. (In the original geometric design (which we don't have) they would be at an exact location.)

6. Then draw a triangle from point B to these two points. Where the triangle crosses lines (A) and C is where the lobes in the f-holes are placed on the belly as seen from the front.

Note: The triangle may be adjusted at will by geometric means to suit the specific model.

Note on transforming the above drawing to a template for the f-hole layout á la Stradivari: When Stradivari made his f-hole layout templates he adjusted the width between the upper holes to be slightly narrower on the paper to compensate for the curvature in the arch. The lower lobes are quite flat and doesn't need adjustment.

Edited by Torbjörn Zethelius
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There might be some kind of mystical input in violin designed (after all the golden age for violin was still an age of alchemistry beliefs and everything that goes with it) but I want to believe that the position of this or that on a violin also serves some practical and important purposes ! :)

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There might be some kind of mystical input in violin designed (after all the golden age for violin was still an age of alchemistry beliefs and everything that goes with it) but I want to believe that the position of this or that on a violin also serves some practical and important purposes ! :)

Here's an excerpt from Dizionario delle Arti e de Mestieri, Francesco Griselini, Marco Fassadoni, Venezia 1770 vol. 8 page 196: " Everything connected with the true way of positioning the two holes in the shape of S which are carved in the violin belly; the placement of the soundpost and the bridge is essential for the goodness of the instrument." (Translated by Luca Primon, Pio Montanari, T. Zethelius)

Geometric positioning of the f-holes is the true way. IMO

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Yes, I've read Torbjorn's method of F hole placement elsewhere. I understand PHI and certainly don't think of it as something mystic, and while I realize that the golden age of violin making was also a time of strange scientific beliefs, I also realize that the real properties of PHI remain effective scientific fact today long after the days of trying to make gold from lead have disappeared.

My question was really less aimed at PHI in setting F holes, and more about wondering if PHI or any other early math formulas came into play in the original form (Amati?) of the violin? The original dimensions had to come from somewhere at a time when there were few other violins references!? I don't think I'm really putting this right.

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My question was really less aimed at PHI in setting F holes, and more about wondering if PHI or any other early math formulas came into play in the original form (Amati?) of the violin? The original dimensions had to come from somewhere at a time when there were few other violins references!? I don't think I'm really putting this right.

No, you're not. I will try and answer you anyway. I am convinced that Andrea Amati lay the foundation for violin design and that every luthier in Cremona was basically just repeating what he (or his teacher) did, if they were interested in design at all. Stradivari may have had help developing new designs from an architect that he knew quite well, Alessandro Capra. According to my research, I have concluded that the start for the design was a fixed pattern that consisted of lines and circles. The geometer can find every proportion that Euclidean geometry is capable of. A violin can be designed using 'themes' such as Phi, Pi, or Pythagorean numbers, and they will all be different from each other. Themes can also be mixed in the same design according to the designers' will. This is a big and complicated topic. It doesn't lend itself easily to a discussion board.

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Thanks, but your response is a bit confusing in itself. You say "I am convinced that Andrea Amati lay the foundation for violin design and that every luthier in Cremona was basically just repeating what he (or his teacher) did..." Hummm, so if Amati did in fact have a teacher (and who was that person?) then the teacher came up with the design? Lines and circles?...okay, based on what?

You also say, "This is a big and complicated topic. It doesn't lend itself easily to a discussion board." Well, sorry for wasting everyone's time here! I thought the original question was pretty simple. Where can it be discussed or read about??

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Thanks, but your response is a bit confusing in itself. You say "I am convinced that Andrea Amati lay the foundation for violin design and that every luthier in Cremona was basically just repeating what he (or his teacher) did..." Hummm, so if Amati did in fact have a teacher (and who was that person?) then the teacher came up with the design? Lines and circles?...okay, based on what?

You also say, "This is a big and complicated topic. It doesn't lend itself easily to a discussion board." Well, sorry for wasting everyone's time here! I thought the original question was pretty simple. Where can it be discussed or read about??

Anyone?

Indeed it was a simple question. I haven't written anything about my method yet, and I'm not sure if I ever will. Francois Denis did write a book which is quite popular among violin makers. I have declared pretty much what I have on Phi. I'm sorry if it wasn't enough for you. You did mention the Da Vinci Code and that's the reason for my first post. My method precedes the book.

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You can already see here that violin-shaped instruments were made probably before Amati made his violins. And this Lyra da Braccio was most likely itself an evolution of earlier string instruments with similar shape but different. Evolution is evolution, whether it's animal, vegetal or musical... :)

It's pretty rare to start from scratch and come with a completely new design.

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Andrea Amati introduced the complete working system which was continued until the mid 18th century. He also introduced the violin design which was perfect and followed closely by the later Cremonese luthiers. His instruments set the standard for the Cremonese tradition. The arching in the best of his few surviving instruments is on par with the best of Stradivari/Guarneri. His varnish was used by the Amati family until the very end. He also delivered a full orchestra of bowed instruments to the royal court of France.

A self taught luthier would certainly not be able achieve all this, however skilled. Until we find out who his teacher was (if we ever do), we should accept that Andrea Amati was the great genius of luthiers – ever. What has followed is merely variations on a theme. The sad thing that has obscured this fact is that so few of his instruments have survived.

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I was also looking for this. Even older but the shape is already there with the 2 "E" holes. The painting on the right is from Hans Memling who lived from 1430-1494. I find the picture interesting because the man is depicted holding the vielle on it's left shoulder like a modern violinist. I had read somewhere that this technique was introduced much later.

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Well, this subject is an interesting subject and worthy of discussion, though I'm not sure it's worth losing sleep over, or getting huffy over, since everyone who has an opinion on the matter has a seemingly equal chance of being right - if there is such a thing as "right".

I tend to agree with much of Robertdo's thinking on the matter.

To me it seems obvious that the first design constraint is the size, shape and construction of the average adult human body. It's such a basic limiting factor that the tendency may be to overlook its importance or influence on design, but surely it was the (a) main primary consideration in the evolution of the violin's general size, shape and design.

Secondarily, there are the physical (mechanical) demands of playing a bowed instrument. (CC bouts for bow clearance, etc. Neck width to accommodate the size, shape and articulation of the average hand, string length determined roughly by the size allowed between the neck or shoulder, and the hand with the arm in extension allowing for horizontal movement along the neck in order to reach the various positions of different notes. Curved bridge/f.b for the bow - etc.) These thing arise out of need first, in order to satisfy mechanical demands.

Then, and most likely further down the road in order of "evolutionary demands", are the aesthetic refinements. ff hole shape and placement - scroll design - corner and edge treatment, varnish.

To me, there seems to be a great deal of obligatory primary physical constraints necessary (length, width, depth, scale, etc., etc., etc.) that limit other possible design considerations, in order to satisfy the BASIC physical demands that exist.

So it seems somewhat valid to consider that the refined shape we see today may as well been the result of a sort of drawn-out agonizing enforced classical design evolution...

On the other hand, it may well have been that the roughly finished design "evolved" or simply emerged as a result of a particular individuals inspired vision or as a result of individual aesthetic drive or decision, somewhat like the mandolin design for the F-5 model mandolin that was created by Loyd Loar.

He may have agonized over the Golden Section, PHI, Classical Design limitations - or he may have simply sat down and designed what was aesthetically appealing to him.

In which case we can back engineer anything we want to in order to discover something that may or may not have even been intentional.

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Andrea Amati introduced the complete working system which was continued until the mid 18th century. He also introduced the violin design which was perfect and followed closely by the later Cremonese luthiers.

... Until we find out who his teacher was (if we ever do), we should accept that Andrea Amati was the great genius of luthiers – ever. What has followed is merely variations on a theme. ...

Perhaps Andrea Amati's continued tweaking indicates one of two things: (1) His design tweaks were made to 'customize' an instrument's projected sound spectrum for an individual Player; or (2) He in fact did not understand the underlying design principles [of his Teacher?] and engaged in empirical design changes as is still done today.

Jim

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I'd love to see a guitar designed by Andrea Amati [i don't believe one exists though]. IF he was using PHI to design violins, you'd expect to see the same design principles applied to plucked instruments as well.

Stradivari made The Rawlins Guitar which shares very little in design proportions with his many many violin 'Models'.

Jim

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Perhaps Andrea Amati's continued tweaking indicates one of two things: (1) His design tweaks were made to 'customize' an instrument's projected sound spectrum for an individual Player; or (2) He in fact did not understand the underlying design principles [of his Teacher?] and engaged in empirical design changes as is still done today.

Jim

What do you mean by tweaking? blink.gif

He probably did what every luthier does; customize instruments for his clients. Since he's the first known Cremonese violin maker, and with all the qualitites that I listed in a previous post, I think that we can safely assume that he knew what he was doing. rolleyes.gif

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What do you mean by tweaking? blink.gif

For example, he made some 'small' 4/4 violins.

He probably did what every luthier does; customize instruments for his clients.

Some customize with a completely new violin 'Model' [change body outline; change the ffs, change arching; etc.]. Some simply 'customize' with a different set-up [only].

Jim

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I think that we can safely assume that he knew what he was doing.

I have met and talked with many good modern makers, and I don't know any of them that claim they really know what they're doing. In fact, it is the other way around... they admit they don't know, and continue to seek answers and try things a little differently to see what happens. It is only the bad makers that claim they know.

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I have met and talked with many good modern makers, and I don't know any of them that claim they really know what they're doing. In fact, it is the other way around... they admit they don't know, and continue to seek answers and try things a little differently to see what happens. It is only the bad makers that claim they know.

I mean, of course, in the context of the discussion. wink.gif

Another thing that we have, that they didn't, is the dawning of the Enlightenment and the uncertainty that it brought with it. Back in Andrea's days, I think that science was more seen as an artform. They had the certainty that God was the ruler of all things scientific, and hence there was certainty in science. Today's makers don't have that.

I think that this paradigm shift was partly the reason why the Cremonese violin making tradition died out. Things went from certainty to uncertainty. It rocked the very foundation of the Tradition.

Edited by Torbjörn Zethelius
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