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John Cadd
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 Posted: Fri Oct 01, 2021 9:29 am Post subject: curtate cycloids |
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There was a young man called Green
Who invented a funny machine
Concave and Convex
It would suit either sex
The Goddamnest thing ever seen.
(Best done with an Appalachian accent). |
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John Cadd
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Location: Hoylake
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| Posted: Wed Oct 27, 2021 3:33 pm Post subject: curtate cycloids |
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| Basically it`s not important what we call the curves because most makers copy what Strad and Guarneri did. If they want a really exact copy they just follow what is there .If you create your own model and it is different and not so good that`s the price paid for experimenting . No need to worry about the name of the curve . |
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John Cadd
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| Posted: Wed Nov 10, 2021 1:48 pm Post subject: curtate |
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| One problem . The write up about the Vieutemps violin shows a low angle photo of the belly plate and it says there is little to no recurve . So where does that leave us ? Akiko Meyers plays a simple slow tune in a video and , blow me down , even though it`s the most expensive violin in the world it`s still playing out of tune . |
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Oleg Vostyakov
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Joined: 13 Sep 2021
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| Posted: Fri Nov 12, 2021 4:42 am Post subject: Re: Curtate cycloids....What would Strad do? |
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| John Masters wrote: | | R Mac wrote: | Just looking at the math for curtate cycloids makes my head hurt, and I have difficulty imagining a working luthier crunching numbers.
Mac |
To ease the pain and do away with disks, it is much more accurate and easier to calculate numbers you can measure at any point you wish. To calculate the T that corresponds to a given X is more elaborate, but not especially useful. You can choose a T close to what you in X and then use that X, it will give good results.
You can do these on an Excell spreadsheet. Just put the t variable in a colume and run it at intervals of .1 or whatever other increment you decide. I have made changes of variables in order to make the curtate cycloid centered on the Y axis and put the ends on Y=0. These formulas are for one cycle with ends wherever you want the deepest channel. This occurs at L. (Making L less than the width will make the rolling disk rotate more than one revolution because L is the circumference of the disk.)
The function is so-called parametric in t, but it is essentially Y=Cosine plotted on a distorted X-axis.
X = T+.5*h*sin(T*pi/L)
Y = .5*h*(1+cos(T*pi/L))
T runs from -L to +L where L is the half-width of the violin at the particular position on the long arch.h is the height of the long arch at that position.
choose t = T*Pi/L
X = t*L/Pi+.5*h*sin(t)
Y = .5*h*(1+cos(t))
Here, t runs from -Pi to +Pi
If you want an arching template, make a graph and cut it out. Many of you may have graphing programs, but make sure the scaling is full scale for any template you wish printed out. |
Can you please "translate" that maths into english please  as easier as you can.
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John Cadd
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| Posted: Sat Nov 13, 2021 8:55 am Post subject: curtate |
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| One feature of Strad bellies shows up when you see the relief map diagrams . Looking at the area between the soundholes on the maps ( the lines about half way between edge and centre ) the lines never (hardly ever ) bend inwards . I think that would be described as "Pinched". Moving from the soundhole area upwards and downwards the "straightish " lines then curve inwards . That "shell shape " leaves the outer surfaces with a Recurve to get to the sides . It might be described mathematically in a curtate formula but it may arise from the shell shape that seems to be a Strad feature . |
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Michael Darnton
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| Posted: Sat Nov 13, 2021 10:47 am Post subject: |
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Are you referring to what is usually referred to as a. "barrel" shaped arch, in contrast to "egg" or "figure-8"? That comes partly from the height at the widest part of the bouts being higher than the same spot on the back. . basically flattening of the long arch in the middle.
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John Cadd
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Location: Hoylake
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| Posted: Sat Nov 13, 2021 4:16 pm Post subject: curtate |
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I don`t know of the egg or figure 8 . I am connecting something about the c bouts being straightened out too . This is guessing what Strad was thinking . Apart from visual things that I always noticed but never tried to understand .
Some violins maybe from Germany seem to make their arching based literally on the outer edge shape of the violin and at the corners there is almost a triangular buttress designed to prevent vibration. |
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John Cadd
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Location: Hoylake
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| Posted: Thu Nov 18, 2021 6:06 am Post subject: curtate |
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| One reason the for the curtate shape that levels out as the top and back reach the sides could be connected with the Italian way of doing the purfling after the plates were glued on. Some Guarneri outline shapes are so lopsided the idea of pre fitted purfling would be impossible. Having the surface edges flat would allow the wayward garland to be fitted . |
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Mike Shuman
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Location: Denver
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| Posted: Wed Nov 24, 2021 1:52 am Post subject: |
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| Michael Darnton wrote: | Not in modern times that I know of. One of my workshop participants made a disc for me one year, though.
On Andrea Amati instruments the curve bottoms out on the purfling. The diameter of disk needed to make the templates for the c-bout and lower bouts are about 31.5mm and 63mm. Anyone who's been following what I do for a while knows of my fascination with the 31-32mm dimension, which is scribed on ALL of the extant Stradivari forms. The precise number in that range depends on the overall length of the instrument form.
For instance:
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One year? How can it be technically possible?
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John Cadd
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Posts: 830
Location: Hoylake
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| Posted: Tue Nov 30, 2021 6:25 am Post subject: curtate |
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What I have managed to understand so far about curtate cycloids ( I don`t want that to sound negative ), is , these curves are adaptable in the way a lampshade makes a shadow curve on a wall . Move the lamp and the shade makes a different curve but its in the same group of curves mathematically. That shadow curve is not a curtate cycloid though .
So take one curtate cycloid curve to match the top height of a belly and that can be manipulated (proportionally )to match all the heights and widths on a violin ---without using a computer . Do it with a calculator to keep an eye on what is happening. There are other ways without a calculator. Stradivari could have done it like that . But that is adapting from just one good curtate curve. Do I need more than one curve to begin the process ? |
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Michael Darnton
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| Posted: Tue Nov 30, 2021 9:12 am Post subject: |
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No, that's not right. It's imperative that you find a cycloid designer on the web and plug in some numbers, especially at the extremes. The whole point is that they do NOT do what you say: The curves are not the same, changed. They have the same mathematical description, but can look completely different, depending on height/width. Further, the changes match exactly what happens with a violin arch, which is not as you describe.
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Michael Darnton
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John Cadd
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Joined: 23 Jul 2009
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| Posted: Sat Dec 04, 2021 12:16 pm Post subject: curtate |
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| Thankyou so much . I appreciate that . |
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