Viola Graduations

[Shunyata]

I am making my first viola.  I would appreciate input on the following graduations ideas. (See end of post.)
 

Manifio says he makes the top 3.0 and I developed my technique around thicker violin tops… so I am planning accordingly.

For the back, I really have no idea what to do so my thought is to stay proportionate to violin  graduation.  Your help here is especially appreciated.

Top:

2.9-3.0 most everywhere

3.7 along the C bouts

3.2 at post

 

Back:

5 in center

4.3 along the C bouts

3.0 at top and bottom

[Dwight Brown]

I don't mean to be a one trick pony but I have played one of Manfios violas and it was wonderful.

We also have some other guys around here who can build a box or two :-)

DLB

[Don Noon]

Doesn't it matter what size viola you're planning and what density wood you'll be using?

[Shunyata]

39 minutes ago, Don Noon said:

Doesn't it matter what size viola you're planning and what density wood you'll be using?

15 7/8”

Haven’t measured density. (Got the wood from International Violin so expect middle of the road density.) 

[Shunyata]

Found some comments from Manifio on MN about back graduation.

He uses numbers similar to what I proposed… except 6-7 in the center… much thicker than I was thinking.  I have already rough graduated down to 6.5, so I won’t be trying 7!

[Wood Butcher]

What you are trying to achieve, by asking us to guess at your numbers, is doomed to fail. It's not that simple, as you clearly must know by now.

Without taking into consideration the arching, and material properties, the numbers themselves are largely meaningless. And, you can't replicate how one person makes a graduation scheme work, without considering other factors. If it were as simple as you believe, all really thick violas, would be the most sought after by players, and this really is not the case.

[Shunyata]

Hmmm… on violin graduation questions there is always a plethora of detailed advice, approaches, guardrails, etc.  But for viola the question is without merit?

Perhaps the answer is that viola shapes are more varied, acoustics are more forgiving and there is a wide variation in desired viola sound?

In any case it seems clear that I am not suggesting anything totally out of bounds.  So I will give it a shot and test it in the white.

[The Violin Beautiful]

I would not recommend making the C bouts thicker than everything else. That will stiffen the top too much. 

[Wood Butcher]

It's not that the question is without merit, more that one thing, in isolation, does not guarantee a successful outcome.

Personally, I am considering graduations as part of a wider plan. This would include densities, arching type, string length, even how the neck will eventually be set.

I appreciate it is viola number one, but I would stop and think about things for a bit, before committing to those numbers posted above. Some of them seem way off to me, but I can't see your pattern, or arching.
 

 

[Torbjörn Zethelius]

18 hours ago, Shunyata said:

I am making my first viola.  I would appreciate input on the following graduations ideas. (See end of post.)
 

Manifio says he makes the top 3.0 and I developed my technique around thicker violin tops… so I am planning accordingly.

For the back, I really have no idea what to do so my thought is to stay proportionate to violin  graduation.  Your help here is especially appreciated.

Top:

2.9-3.0 most everywhere

3.7 along the C bouts

3.2 at post

 

Back:

5 in center

4.3 along the C bouts

3.0 at top and bottom

You've got to start somewhere then go from there. In general I usually recommend studying Sacconi's recommendations for thicknesses. I know that Manfio has been very successful.

[uncle duke]

Wouldn’t a m5 tone for a viola plate that size need a reading of 165 hz or close to?

my thinking is since there are no grad specs from others to recommend trying why not just give him a tone hz to maybe shoot for.

[Marty Kasprzyk]

A viola's strings are pitched a musical 5th lower than a violin's which is two thirds the violin's frequencies.  For example the viola's C string at 130 hz and the violin G at 196 gives a 0.66 ratio.

The various vibration mode frequencies f of a plate are proportional to the the plate's thickness t divided by its length squared L^2.  f=t/L^2

We know your viola's length is 15 7/8 in or 403 mm or 0.403m and that a typical violin length is 354mm or 0.354m so their length ratio squared is (.403)^2/(.354)^2= 1.3

So a ratio of viola's plate thickness to violin's plate thickness should be 0.66*1.3=.86.

A viola's plate thickness should only be be about 86% of the thickness of a violin plate because it is expected to produce a lower pitched string range while only being a little bit larger in size.

On the other hand nobody agrees with this.

[Dr. Mark]

16 minutes ago, Marty Kasprzyk said:

On the other hand nobody agrees with this

Why should they?  Within somewhat uncertain bounds, where's the relationship between plate modal frequencies and tone?

[Don Noon]

1 hour ago, Marty Kasprzyk said:

On the other hand nobody agrees with this.

I agree with that statement.  What works for the player is the only important thing, not some theoretical nonsense about what "should" work (based on the unproven... or disproven... idea that scaling a violin vibrations is a good idea).

As for some data on my viola that won a VSA certificate for tone, it happened to be exactly the same body length in question.  The back grads were similar to what is proposed, although the top was slightly thinner.  And the wood densities were extremely low:  .49 for maple, .31 for spruce (both torrefied).  M5 was 346 for the back and 262 (291 with bar) for the top.

Anybody using these numbers as a goal will likely get something horrid... don't do it.  I didn't.  It's a viola, so nobody knows anything for sure.  I just did something a bit thicker than a violin, and it came out however it came out.

[Marty Kasprzyk]

1 hour ago, Dr. Mark said:

Why should they?  Within somewhat uncertain bounds, where's the relationship between plate modal frequencies and tone?

Equation 11.24  in the chapter section 11.2 General laws for plates with bending stiffness in Cremer's book "The Physics of the Violin" describes the modal frequencies dependendence upon plate size squared and thickness. I don't think there is much disagreement with him.

A viola has a lower string pitch range than a violin CGDA vs. GDAE so there's no diagreement there either.

But many people disagree about what a "good" violin and viola should sound like with regard to plate modal frequencies..  So some people might like the sound character of thick plate violins or violas having plates with high modal frequencies while others might like sounds thinner ones.

You have to choose who you are trying to please.

[Dr. Mark]

2 hours ago, Marty Kasprzyk said:

Equation 11.24  in the chapter section 11.2 General laws for plates with bending stiffness in Cremer's book "The Physics of the Violin" describes the modal frequencies dependence upon plate size squared and thickness. I don't think there is much disagreement with him.

Please let me expound a bit on what I meant by my question - you calculate with the following formula:

'The various vibration mode frequencies f of a plate are proportional to the the plate's thickness t divided by its length squared L^2.  f=t/L^2'.

I think the general consensus in recent discussions was that, within rather uncertain bounds, plate modal frequencies and tonal quality weren't correlated.  Unless there's a relationship between violin plate modes and violin tonal quality what's the point of scaling violin plate modes to a viola?

As an aside, is there experimental verification of Cremer with violin plates?  I could accept some correlation according to that formula but I'd expect that the scatter would be pretty horrendous - not that I think it matters much.

 

[Don Noon]

1 hour ago, Dr. Mark said:

Unless there's a relationship between violin plate modes and violin tonal quality what's the point of scaling violin plate modes to a viola?

The point is formulas and a precise goal.  Observation and honest logic doesn't tell you what the goal should be... and mostly leads to the conclusion that there isn't a clear "goal".    Some folks don't like that, but I have made peace with reality and the "kindasorta seems about right" approach, in spite of being an engineer.

[Marty Kasprzyk]

On 12/22/2023 at 4:28 PM, Shunyata said:

I am making my first viola.  I would appreciate input on the following graduations ideas. (See end of post.)
 

Manifio says he makes the top 3.0 and I developed my technique around thicker violin tops… so I am planning accordingly.

For the back, I really have no idea what to do so my thought is to stay proportionate to violin  graduation.  Your help here is especially appreciated.

Top:

2.9-3.0 most everywhere

3.7 along the C bouts

3.2 at post

 

Back:

5 in center

4.3 along the C bouts

3.0 at top and bottom

If you like the sound of Manfio's violas and his have a length of 16.3 in. or 415mm and a top plate thickness of 3.0mm and you want to get something similar sounding with a shorter length of 15 7/8 in or 403mm then the your thickness would be around 2.8mm with the same wood, arching etc. which never happens.

thickness ratio = length ratio squared, thickness ratio = (403/415)^2 = 0.943

3mm * 0.94= 2.8mm

[Dr. Mark]

21 hours ago, Don Noon said:

The point is formulas and a precise goal

I'm probably coming across as a curmudgeon lol - really, being guided by mathematics is as good or better than many alternatives.

[Don Noon]

30 minutes ago, Dr. Mark said:

I'm probably coming across as a curmudgeon lol - really, being guided by mathematics is as good or better than many alternatives.

As time goes on, I have gotten more curmudgeonly.  The math used as a guide is only as good as the assumptions underlying it... and for instruments, I think that the assumptions are usually unsupported and there are better alternatives than taptones and scaling.

[Shunyata]

 

9 hours ago, Don Noon said:

As time goes on, I have gotten more curmudgeonly.  The math used as a guide is only as good as the assumptions underlying it... and for instruments, I think that the assumptions are usually unsupported and there are better alternatives than taptones and scaling.

Can you talk more about the alternatives you mentioned, Don?  Certainly there must be underlying principles involved… even if they are not definitive by themselves.

[Don Noon]

42 minutes ago, Shunyata said:

 

Can you talk more about the alternatives you mentioned, Don?  Certainly there must be underlying principles involved… even if they are not definitive by themselves.

My main measurement is plate weight.  Unlike taptones and glitter patterns, it doesn't change completely when assembled to the ribs.  Graduation patterns too.  And arching.  And wood properties.  They also stay mostly the same assembled or not.  I won't use spruce with abnormally low speed of sound; maple is mostly aesthetics, but I'll use the lower density stuff on violas.

Lower density wood I'll compromise between thicker grads and lighter weight (a little of each).  Denser wood thinner/heavier.  I DO look at taptones, but only as a vague check on the stiffness neighborhood I'm expecting.  I might tweak a couple of grams one way or the other if the taptones are higher/lower than usual... although my best guess is that it's not significant in changing the outcome.  Everything is baked in at that point.

That's my approach; there are plenty of good makers that do things differently.  Probably all of them.

[Marty Kasprzyk]

14 hours ago, Marty Kasprzyk said:

If you like the sound of Manfio's violas and his have a length of 16.3 in. or 415mm and a top plate thickness of 3.0mm and you want to get something similar sounding with a shorter length of 15 7/8 in or 403mm then the your thickness would be around 2.8mm with the same wood, arching etc. which never happens.

thickness ratio = length ratio squared, thickness ratio = (403/415)^2 = 0.943

3mm * 0.94= 2.8mm

If you are making a 403mm small viola and you like the sound of larger 415mm violas you can also scale the top plate weights by the same length ratio squared.

If the average top weight of some good sounding 415mm violas is around 82g then your top weight should weigh around 82* 0.943= 77g

However some people will disagree with this too.

 

Attached is a summary of some different top plate strategies for making violin plates which are quite standard in size.  Violas vary quite a bit in size and sound character.  In general small violas will tend to sound bright and large ones darker and different people have different preferences.

The thickness and weight scaling I have suggested is if you have some sound viola character you like   and if you want to duplicate this sound with a different size one. 

 

Different plate thinning strategies 7_25_2019 .pdf

[Don Noon]

1 hour ago, Marty Kasprzyk said:

However some people will disagree with this too.

Me.

Sound doesn't scale.  With arched plates, some vibrations scale one way, others scale a different way.  I don't think you can ever use this kind of math to get different size instruments to sound even remotely the same.

It's too complicated.  Give up analysis and build stuff to find what works.  And look at good stuff that others have built.

[Marty Kasprzyk]

1 hour ago, Don Noon said:

Me.

Sound doesn't scale.  With arched plates, some vibrations scale one way, others scale a different way.  I don't think you can ever use this kind of math to get different size instruments to sound even remotely the same.

It's too complicated.  Give up analysis and build stuff to find what works.  And look at good stuff that others have built.

Sound does scale--big instruments have a low pitch range and small instruments have a high pitch range and the Hutchins-Schelleng Violin Octet is an example which is described in chapter 18 in Rossings' book "The Science of String Instruments", Springer 2010.  The Octet was intended to duplicate a violin's sound character over a 3 1/2 octave range with eight different size instruments.

The equation I used for making the thickness for Shunyata's small viola slightly thinner than bigger ones was taken from chapter 18.4.3 "Flat Plate Scaling Equations" which were derived by Schelleng.

Two weeks ago I went to a youth orchestra's Christmas concert and there were about 70 kids aged about 5 to 15 playing fractional sized  violins, violas, cellos, and double basses.  They played great but the orchestra's sound was terribly harsh.  I attribute this to the excess plate thicknesses of all these small instruments.