sospiri

Rib Taper hypothesis #43,759

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9 hours ago, Bruce Carlson said:

I rather like when it remains a discussion although we've wandered off from the original topic of rib taper. Apologies to Sospiri for this.

Yeah, I ran out of popcorn. But it's not your fault Bruce, thanks for sharing so much wonderful information.

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So, we have only very limited examples from the main Old Cremona names.  However, we can expand our examples a bit by including Stainer, who seems to follow the same principles with the neck and body stops, and by including Cremona makers from the 1790s.

 

So, my assertion is that all of these neck and body stops are based on a primary ratio of 2:3. 

1936950369_2to3.thumb.jpg.5e0df49c28fc273d9f131c8e4880d588.jpg

 

But that as with all old Cremona use of proportions, 'Liberty at the Margins' must always be taken into account.  

With body and neck stops, this means we can not assume the point of measure at the nut or at the neck join to the body.  Rather, we are relegated to observing which points the maker used in each case.

These 'liberties at the margin' are not squishy or nonspecific.  In the case of the body and neck stops, they create four specific and well defined options for the maker using a particular ratio.   For the observer, it creates two options to test.

387810113_MarginOptions.thumb.jpg.801ef1cdbf7aeb6a89a9782ec6465528.jpg

For body and neck stops, that means we must look to see if the maker measured from the string or box side at the nut, and from the purf/rib or outer edge at the neck join.

In each examples below, I show a blue line for each of these choices available to the maker.  And, for the bridge lines, I show them placed simple midway of the notches.

******

 

With the extra large and extra small instruments, the makers adjust the primary 2:3 ratio by taking away or adding 'a part' of the 'stop unit'.   Differences of 'a part' play a big role in the overall old Cremona use of proportions. 

In the case of neck and body stops, we see Cremona style old makers adjusting the basic 2:3 ratio by adding or subtracting 'a part' of the 'stop unit'.   Mostly, we see them adding or subtracting 1/4th, 1/3th, or 1/2 the stop unit.   In theory though, this same concept could extended to smaller parts like 1/6, or even to adding a whole stop unit. 

Augmenting the 2:3 ratio by adding a part:

245770631_2to3augmented.thumb.jpg.dbbcd4b7b02ff8f8267f71bd72d950e5.jpg

 

Reducing the 2:3 ratio by taking 'a part' away:

1132569380_2to3reducedbyapart.thumb.jpg.3e96ca9868c42d5e3b4da30f0b6714a5.jpg

 

This notion of the primary 2:3 ratio being adjusted by 'a part' difference leads to a specific family of ratios.  And in deed, these are the specific ratios found in the old examples.  

This is also the very same family found primarily used in modern methods, though expressed differently.  With cellos for example, we do not have old examples to test.  But notice, the modern 7:10 cello ratio is part of this old family of ratios.   

And despite, the lengthening of necks, the stop to body ratio in new violins mostly reflects a numeric measure expression of the 2:3 ratio.  And the old violins we can observe show the same ratio, just with different choices at the margins for applying the ratio.  

And, it is plausible to believe that modern standards start from a transitional period that did its new sizing work within the old system of ratios and 'liberty at the margins'.    Again, though examples are few, the existing examples show a very similar trail of changing choices within the old system's framework for the lengthening of the fingerboard, all the way to the modern standard length.

Just as an aside, let's look at the modern 7:10 cello stop ratio in terms of the old system.   In terms of the old system, the 7:10 ratio is augmentation of the 2:3 ratio by a tenth::

(1/10 + 2) : 3   ===>   (1 + 20) : 30  ===> 21 : 30 ===>  7:10

*******

 

Example instruments:

1613 Brothers Amati piccolo.    Ratio is 2:3 augmented by 1/4

142978915_1613BrosApiccolo.thumb.jpg.10c92cc47152af74ccb5236f0d4dd8f9.jpg

 

1650c Stainer tenor:    Ratio is 2:3 reduced by 1/2

1295754613_1650cStainertenor.thumb.jpg.0f5214b75e97c804f28bdeaf194eecc0.jpg

 

1664 Andrea Guarneri tenor:  ratio 2:3 reduced by 1/4

585659216_1664AGuarneritenor.thumb.jpg.e1a401247a63530e26145c56f37e9ec1.jpg

 

1679 Stainer violin:  ratio 2:3

1654109990_1679Stainerviolinunaltered.thumb.jpg.d06ac493423244bb1c279a8456c33acf.jpg

 

1690 Strad tenor:    2:3 reduced by a 1/4

536240953_1690Stradtenor.thumb.jpg.e87b3026beb4c100ee1e05d782eb6ed3.jpg

 

1721 Strad Lady Blunt  (unreset neck):   ratio 2:3

 

1082609925_1721LBStradunreset.thumb.jpg.90dd96ef44d10037eb0949f663b6ac45.jpg

1793 Mantegazza viola:   ratio 2:3

690414077_1793Mantegazzavla.thumb.jpg.08fc1b2fc4412d1ff54de63487455d87.jpg

 

1793 Storioni small violin:  ratio 2:3 augmented by 1/4

 

621105472_1793Storionismallviolin.thumb.jpg.273287927d26e6496cd7954fb41d48c0.jpg

 

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Hi David,

 that is interesting, 

 what do you think could be the reference length for you?
I see 3 obvious possibilities (and some others less obvious to demonstrate like those proposed by Kevin)

-the string length
-the stop
-the neck

For example, if we choose, the string length = L
like reference quantity of calculation
we would have a theoretical length L = 20 parts
which gives by a split of fifth
12 + 8 ratio 3: 2 (fifth)
then we subtract a part
12 + 7 ratio 12: 7 (?)
and the next expected ratio would be
12 + 6 ratio 1: 2 (octave)


Otherwise I allow myself to correct a point;  the 7:10 ratio is NOT increase of the 2: 3 ratio by a tenth.

The ratio 7:10 is a (close) tritonus interval (actually √2)  that means a measure between the fifth and the fourth (fourth augment of a major semi-tonus )

We have very strong clues that all the relative dimensions of the instrument (middle age in western country) were initially calculated following the tradition of the division of the monochord -

 (Boèce give us a nice glimpse about this forgoten and little-knowed approach.)

 

PS: Again, mm measurements could allow us to check your data 

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When things are strongly and cleanly related, it isn't necessarily obvious which starting point is the actual reference length.

I tend to think the body length is either the fundamental starting measure, or close to it.   But, of course, I consider that the maker might not always measure this from edge to edge.

The bridge line tends to near or slightly above 4/9ths the body length.  But the exactly placement of the bridge line is not simply dependent on body length, but ends up depending more directly on the soundhole work.  

So, for the string and neck system, I think the body stop, from bridge to top of plate as the maker takes it (either outer edge or purf/rib) is fundamental.

1/3 this distance is always the stop unit. The neck length then comes from this, as do other things. In fact, both the volute height and the span across the upper eyes (between for cellos) each appear to derive from the stop unit.

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Well, 

49 minutes ago, francoisdenis said:

Hi David,

 that is interesting, 

 what do you think could be the reference length for you?
I see 3 obvious possibilities (and some others less obvious to demonstrate like those proposed by Kevin)

-the string length
-the stop
-the neck

For example, if we choose, the string length = L
like reference quantity of calculation
we would have a theoretical length L = 20 parts
which gives by a split of fifth
12 + 8 ratio 3: 2 (fifth)
then we subtract a part
12 + 7 ratio 12: 7 (?)
and the next expected ratio would be
12 + 6 ratio 1: 2 (octave)


Otherwise I allow myself to correct a point;  the 7:10 ratio is NOT increase of the 2: 3 ratio by a tenth.

The ratio 7:10 is a (close) tritonus interval (actually √2)  that means a measure between the fifth and the fourth (fourth augment of a major semi-tonus )

We have very strong clues that all the relative dimensions of the instrument (middle age in western country) were initially calculated following the tradition of the division of the monochord -

 (Boèce give us a nice glimpse about this forgoten and little-knowed approach.)

 

PS: Again, mm measurements could allow us to check your data 

You seem to assume the choice of ratio should be musically meaningful.   But that is not at all what I've found. 

And you seem to assume for an intial principle measure to refer and correct back to.  

 

No.  The assymetry we see in their work contradicts the use of an initial principle measure to correct back to.

No. The examples themselves show rhe old makers 'follow rather than corrected' as variances develop while the worked.

It's a different concept. It's not a plan or blueprint mapped out ahead.

The ratios appear to be merely pragmatic and traditional.  And mostly in parterns that can be seen as 'a part different'.

Of course, since these are simple integer ratios many of them coincidentally correspond to musical ratios.

But I believe in the evolution of their actual choices they begin from what was most traditionally and recently successful and migrate toward choices that where they like the outcome bettee, either visually or performance wise.

So, for example, the body to width ratio choicea are alway from the family of ratios given by 'a part less than double'.

Which gives 2:3, 3:5, 4:7, 5:9.  There is no musical concept running through this collection of ratios. No.  But these give a pratical range of body lengths to widths sufficient for all the violins, viols, cellos, viola, piccolos etc we see coming from old Cremona.

No. Simple ratios between parts.  The is no need for one thing to be a fundamental refernece measure.  That seems an incorrect concept, somerhing that hangs on to an 'a piori' concept of design.  I don't think that squares with classical making somehow.

It's a late hour here in Santa Barbara, so please pardon me if my thoughts are completely coherent right now.

But no. I don't expect, look for, or believe there should a 'reference measure'.

Rather, I think of the geometry and proportions my research has observed in classical examples as something like a collection of recipe for working features of an instrument, one by one as you go, not as formulas for working up a plan ir blueprint ahead if time.

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3 hours ago, David Beard said:

The bridge line tends to near or slightly above 4/9ths the body length.  But the exactly placement of the bridge line is not simply dependent on body length, but ends up depending more directly on the soundhole work.

I don't understand what 4/9ths the body length.

A 355 mm corpus used for length to get a 4/9ths ratio gives me a figure of 157.77 mm.  

In plain terms 4/9 of 355 is 157.77.

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We aren't talking computer age.  We aren't talking in .01mm terms.

What we are talking about walking dividers nine steps along the body length, either edge to edge or purf to purf, with that choice belonging to the maker and not the observer.

So we're talking a practical accuracy for the fourth divider step from the bottom of about .5 to 1mm.

And this is just a very rough guide for bridge lines.  Some do actually sit right there, but must are acctually placed somewhat higher to that.  And the final placement of the notches and the actual bridge line placement end up depending on the soundhole work.

But yes, in a 355mm violin, if we measure from the edges, then 4/9 by dividers would be within .5 to 1mm of 158mm from the bottom.  And, in old Cremona work, we'd very strongly expect the actual bridge line to be marked by the notches at somewhere from 158mm upto maybe 168mm from the bottom.

Notice that modern numerical standards would place the bridge at 190mm down from the top edge, which equals 165mm up from the bottom edge.

 

 

 

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I don't have an unattached Stradivari violin top plate here at the moment to test.  Does anybody know if the balance point of his plates are at the bridge line?

A similar question is if his plate area below the bridge is equal to the plate area above the bridge.

 

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57 minutes ago, Marty Kasprzyk said:

I don't have an unattached Stradivari violin top plate here at the moment to test.  Does anybody know if the balance point of his plates are at the bridge line?

A similar question is if his plate area below the bridge is equal to the plate area above the bridge.

 

I think the answers to all those questions is generally no, though there might be occasional counter examples when one of those things might be true in a odd instrument now and then.

 

On the other hand, there are some very interesting relationships that emerge between bridge line, body length, and rectangles based on lower bout by upper bout.  This relates to bridge line to some extent, and seems to be part of what makes violins a little different than violas and cellos.

But these things lay deep in the forest.  With a crowd that still struggles with allowing the maker rather than themselves decide to measure from the center, treble side, or bass side of a circle, there is zero room to get into these further things.

For now, my task is get people to view 'liberties at the margins' not as me cheating as an observer but as the makers taking control in their work.

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On 11/13/2020 at 11:18 AM, David Beard said:

So, for example, the body to width ratio choicea are alway from the family of ratios given by 'a part less than double'

Not always.... but often yes 

 

On 11/13/2020 at 11:18 AM, David Beard said:

Which gives 2:3, 3:5, 4:7, 5:9.  There is no musical concept running through this collection of ratios.

 

We have testimonies that Musical ratios have been involve in architecture, 

difficult to imagine than this was not apply to the musical instruments ...

the question is may be more  how?

 

In your exemple It depends which dimensions you consider - (and that was the sens of my previous question) 

If you take 5 parts of a quantity that you have divided in 9 parts  you find the ratio 5 to 9 which is nothing in music

but you have 4 remaining parts 

so  dividing in 9 parts  you have also the ratio 4 to 5   which is a major third

and also a ratio 4 to 9 which is nothing in music

 

 

 

 

 

 

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12 hours ago, Marty Kasprzyk said:

I don't have an unattached Stradivari violin top plate here at the moment to test.  Does anybody know if the balance point of his plates are at the bridge line?

A similar question is if his plate area below the bridge is equal to the plate area above the bridge.

 

I

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12 hours ago, Marty Kasprzyk said:

I don't have an unattached Stradivari violin top plate here at the moment to test.  Does anybody know if the balance point of his plates are at the bridge line?

A similar question is if his plate area below the bridge is equal to the plate area above the bridge.

 

I don't know, but, Sacconi did say in his book that his observation was that the bridge was always placed at the balance point of the top in Stradivari's instruments, sans bar. He wrote that he thought the bridge placement and f hole layout of each model was determined by trial and error, and then cemented once he found the perfect position. 

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Suppose the bridge divides the lower end to have a 4/9 length proportion and the upper end to have a 5/9 length proportion and the lower bout width proportion is 5/9 and the upper width proportion is 4/9. The areas of the two rectangles enclosing these lower and up bouts then have equal areas:

(4/9)(5/9)  = (5/9)(4/9)

2.222222222222...=   2.222222222222...

Its not out of proportion to think about this 2 much.

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12 hours ago, Marty Kasprzyk said:

I don't have an unattached Stradivari violin top plate here at the moment to test.  Does anybody know if the balance point of his plates are at the bridge line?

A similar question is if his plate area below the bridge is equal to the plate area above the bridge.

As you demonstrated to me a while back, the balance point does not necessarily prove equal area above and below. The shapes are too different. Of those I have tested the balance point is usually further towards the upper bout from the bridge position. I've never found one that balanced right on the line of the inside bridge notches. Same for 'del Gesù'.

It's usually nearer 190 mm. In addition you have with or without bars, possibly some regraduation, cleats and doubling that could skew the test.

Edited by Bruce Carlson
readability and emphasis

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5 hours ago, francoisdenis said:

 

Not always.... but often yes 

 

 

We have testimonies that Musical ratios have been involve in architecture, 

difficult to imagine than this was not apply to the musical instruments ...

the question is may be more  how?

 

In your exemple It depends which dimensions you consider - (and that was the sens of my previous question) 

If you take 5 parts of a quantity that you have divided in 9 parts  you find the ratio 5 to 9 which is nothing in music

but you have 4 remaining parts 

so  dividing in 9 parts  you have also the ratio 4 to 5   which is a major third

and also a ratio 4 to 9 which is nothing in music

 

 

 

 

 

 

Well, when I look at the overall picture, I don't see the makers generally favor any philosophic or musical implications in their ratio choice.

But, they do use the notion of 'a part' different extensively.  And that happens to correspond to a harmonic series.  So, for example, in harmonic series, 1:2 corresponds to an octave, 2:3 the perfect fourth, 3:4 the perfect fourth, 4:5 the major third, 5:6 a minor third, etc.

But, they don't seem to old any actual musical attachments in the use of these.  So, typically, in a place where a maker uses 6:7 in one example instrument, which is a minor third, the ratios tradition to that spot will likely be the neighboring ratios 'a part different'.  And really, their is no musical similarlity between 6:7 or 7:8, which in some spots where 6:7 gets used is a traditional alternative.   6:7 is a type of minor third, while 7:8 is a type of whole step.  Musically very different, but in pragnatic Cremona use, treated very similarly.

So, my first point is that when you use simple integers ratio, you can help but accidentally use harmony ratios all over the place, but it isn't necessarily implying anything meaningful.

My second point is that at most points, the cremona work shows the makers had choice amount several tradition ratios in most features and situations.  But these families of ratios we can observe don't hang together in a consistent musical idea, just in a consistent pragmatic 'a part' different idea.  So, take overall body to width ratios. The whole ratio family seen is easily expressed as 'a part less than double'.   And yes, accidentally some ratios in this family are musical, but the family isn't.  So, 2:3 is the most musical ratio in the family. But it doesn't occur in the  violin family.  Only when going to make something like a viol do the Cremonans use this.  The next ratios are used frequently, 3:5, 4:7, 5:9.  Musically these represent interval differences beteen important scale degrees, 5th scale degree versus 3rd, which is a kind of minor third.   Octave versus minor 7th degree, a whole step. And supertonic versus 3rd, a kind of whole step.  But I don't see any of that as meaningful, just accidental.

On the other hand, when I watch the generations of their tinkering with ratio choices relating bout width to bout width, that's the one use where I suspect they might have at times considered the musical parallels to their ratio choices.

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hum, that makes many accidents ...

If you enlarge the picture , you will notice that musical ratios has been widely used as a key element of the conception of the world.

You know that music was also part of the quadrivium -

Furthermore, knowing the place of the monochord in the teaching of the quadrivium, that musical instruments could have been set appart of this would be weird.  

Ignore this  is just historically difficult to defend. 

Of course,  I understand that the survival these ideas into what you curiously call  "old traditionnal Cremonese ratios..." is difficult to grasp  (may be because only a small part of the picture is spotted)
Don't make of our ignorance a truth,

more probably we just don't know yet how it could have been connected to the music 

As we say in french:
" l'absence de preuve n'est pas la preuve de l'absence"

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No, again.

I went into the research quite willing to find a preference for musical ratios, just as your expectations impose.

But, looking into the full geometry of examples, and the usage across very many examples across the families of old Cremona and the generations of making taught me otherwise.

It is looking extensively and carrying the research far that forced me to acknowledge a consistent but pragmatic use of ratio is what is actually there to observe in the historical examples.

These were Italian violin makers, not French philosophers.

Just as today, some people will measure everything in their workshop by a ruler and milimeters, these old Cremona violin makers measured everything by ratios.  It was an habitual practice, shared in common throughout a community. Or, in equivalent words, a traditional way to work in the workshop. Dividers giving ratios.  Simple.

When we approach exploring an actual lost practice like old Cremona violin making, it is unhealthy to go in expecting or desiring to see things we decided to find before hand.

It is better to examine and neutrally observe as much as possible first. And only later try to see if the things we can observe somehow fall together and suggest ideas or common practices behind what we observe.

Neutral observation, then hypothesis.  Rinse and repeat.

 

Note, that neither Cennini, Theophilus, nor Vitruvius mention any form of infusing the underlying technique of artisans with extra philosophic implication. 

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Not if you mix in some self honesty and the habit of challenging all your hypothesis and testing and retesting against as much historical evidence as is available. No.

If they had no principles behind their work, then honest persistence will ultimately break your hypotheses because they would only hold in some cases.

And, if they did have consistent principles, then honest persistence will push you to find those and let go of baggage, because again the false hypothesis is going to fail against more and broader evidence.

Is the prospect of pulling this veil back really so disappointing or disturbing?

One town, a handful of families.  Is it so surprising that there appears to be a consistent tradition behind the two centuries or so of classical Cremona making?

Most modern makers today are still using certain things and working in general ways that began in Vuillaume's time.  Even though we have much less cultural homogeneity than old Cremona would have.  And, at this point, Vuillaune is further in the past for us than Andrea Amati was for Bergonzi.

 

 

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The honest questions are not of the form 'Can I make this thing be what I wanted to be?'   They are instead of the form, 'what can be seen here?'   'What might this represent'.   Is the same thing present in other examplwes, or not.

And no, just having a XY coordinate system does not 'give you' everything that could potentially be drawn in an XY plane.  It just 'gives you' an empty coordinate reference system.   But, r^2 = (× - a)^2 + (y -b)^2 'gives you' a circle with radius  r and center at (a,b) in your XY system.

How would you give us any VSO in your XY system, let alone explicitly the full range of classical Cremona violin family instruments?

 

Why stand so stubbornly and frivolous against these efforts?  Is it so hard to allow the possibility that Cremona masters taught their sons and aprentices a system that was consistent and robust, and happend to be based on dividers and ratios used in a way that left enough trace in the resulting instruments for us to be able to unravel and read most of their methods again now, today?

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