Tolkowsky Cut Diamond vs 60/60 Ideal Cut:
“Hello, I am seeking advice regarding the table % for a round diamond. I want to choose a table that will display the greatest brilliance with a balance of dispersion. More brilliance. Period ha ha. I found an article [on United Diamonds] which at the bottom says that the president of the GIA shared the ideal table size for exceptional brilliance. It says we should choose between 59 and 62 for table % yet I have found other tables that open the range to 53-58 as excellent and 58-60 is very good, so it has confused me. I read some texts here and it seems whoever does these reviews and articles is as picky as I am ha ha ha so my main concern is what should I aim for? Currently I am on the hunt for a diamond with these specs: Shape: Round; Carat 1.75 +-; Cut: Excellent; Color: G; Clarity VS-2; Polish and Asymmetry: Excellent. Certification: GIA; Fluorescence: None. Thanks a lot !!! F.M.”
Ha Ha, I remember when Bill Boyajian, the former lab director of the GIA, made the statement which you are referring to back in 1997, what he actually said was “One example discovered in our investigation of modeling proportions of a round brilliant cut diamond revealed that, by our method of calculating brilliance, a 59 percent table is more brilliant than a 53 percent table, which was defined by Tolkowsky as “ideal”. This calculation was based on maintaining all other angles defined by Tolkowsky.”
I’ve always thought the statement was issued because the GIA was reeling from getting knocked off their pedestal and was scrambling to try and discount the importance of proportions grading because the AGS Laboratory had just introduced their proportions grade study and it resulted in a substantial loss of business for the GIA Gem Trade Laboratory. From my perspective, the GIA tried to dismiss the findings of the AGS Laboratory for and when it became clear that tactic was not going to work, they introduced their own cut grade system almost a decade later. The amusing part was that the AGS Laboratory knocked them back to the stone age once again by introducing their Light Performance grading platform right about the same time.
The Tolkowsky Cut Diamond:
In 1919, Marcel Tolkowsky, a member of a Belgian family of diamond cutters, published Diamond Design, the first recorded analysis of diamond proportions for the round brilliant cut diamond. His work was based on modern theories of light behavior and his opinion of what proportions resulted in what many industry professionals considered to be the best possible balance of brilliance and dispersion of light until the mid-1990’s.
Tolkowsky’s calculations indicated that for optimum brilliance a round brilliant cut diamond should be cut to the following angles and proportions:
- 34.5° Crown Angle.
- 40.75° Pavilion Angles.
- 59.3% Total Depth (excluding girdle thickness) with 16.2% of the depth being comprised of the crown (top half of the diamond) and 43.1% representing the pavilion lower half of the diamond.
- 53% Table based on diamond’s overall diameter.
Tolkowsky’s design is frequently referred to as the “American Ideal Cut” because diamond cutters in the United States began cutting it first… Marcel Tolkowsky’s early model of brilliance set the stage for the modern AGS Round Brilliant Ideal Cut Diamond and Hearts & Arrows Round Brilliant Ideal Cut Diamond which are widely recognized as exhibiting superior Light Performance and Visual Performance.
Note that Marcel Tolkowsky’s Diamond Design did not take girdle thickness into account, this means that a diamond truly cut to Tolkowsky proportions would have a zero percent, razor sharp, girdle edge which would be prone to breakage and is essentially impossible to produce. Allowing for a minimum girdle edge of 0.7% thin would bring the total depth of the diamond up to approximately 60% which is a more durable and realistic design.
Tolkowsky Cut vs. Tolkowsky Range:
Do not be confused or misled by the appearance of the words “Tolkowsky Cut” on some diamond grading reports. The words “Tolkowsky Cut” do not necessarily mean that a diamond has been cut to Tolkowsky’s exact specifications. Some laboratories like the European Gemological Laboratories (EGL) will say that a diamond is “Tolkowsky Cut” or within “Tolkowsky Range” if the diamond’s proportions are “within tolerance” of Tolkowsky’s original calculations. According to the EGL the specifications for their “Tolkowsky Range” are as follows:
- 33 – 36° Crown Angle.
- 40 – 41.5° Pavilion Angles.
- 56 – 60.5% Total Depth (excluding girdle thickness) with 14 – 16.5% of the depth being comprised of the crown (top half of the diamond) and 42 – 44% representing the pavilion lower half of the diamond.
- 53 – 57% Table based on diamond’s overall diameter.
However we have evaluated “Tolkowsky Cut” diamonds that scored overall proportions ratings as low as AGS-2 Very Good on our Sarin DiaPort computerized proportions analysis machine. Recently we have even seen the words “Tolkowsky Cut” used by the EGL Laboratory to describe the overall proportions rating of fancy shape diamonds such as Flanders Brilliant, marquise, and princess cut diamonds… What gives with that? How is it possible that the results from Tolkowsky’s analysis of the modern round brilliant cut diamond can be applied to a diamond with a completely different shape and facet structure?
The Myth of the 60/60 Ideal Cut Diamond:
When I first started as a diamond buyer back in 1985, the majority of old timers told me that diamonds with a 60% table diameter and a 60% total depth were the most brilliant diamonds available. Interestingly enough, no mention of crown angle or pavilion angle was ever mentioned and when I asked them about whether the actual measurements for crown and pavilion angle mattered, I was told that if the table diameter were cut to 60% and the total depth were cut to 60% then the crown angle and pavilion angle would automatically fall into place. Apparently anything with a 60% Table and 60% Total Depth would do and at the time I honestly didn’t know better… There wasn’t any such thing as mathematical ray tracing or computerized proportions analysis and the GIA which was the leading gemological laboratory at the time never made any reference to the crown angle or pavilion angle measurements on their diamond grading reports, so it was a relative free for all.
Needless to say that the 60/60 “ideal cut diamond” died a quick and tragic death the moment that the AGS Laboratory introduced their proportions grade rating system and the public began to become aware of the importance of the crown and pavilion angle of a diamond. We were one of the first online diamond companies to purchase a Sarin computerized proportions analysis machine and quickly realized that the diamond cutters were wrong, there was a wide range of possibilities in terms of what the crown and pavilion angle measurements could be with a 60% table diameter and a 60% total depth.
What else can Mathematical Ray Tracing tell us about a diamond?
I believe that Bruce Harding first introduced mathematical ray tracing to the diamond industry around 1986 and his work was later incorporated into various platforms such as computerized proportions analysis machines [Sarin, OGI, Helium] as well as the DiamCalc Software developed by Moscow University and the Holloway Cut Adviser which was first introduced to the public in November of 2001. The Sarin, OGI and Helium machines and DiamCalc software are routinely used by the diamond industry in every spectrum of the production and buying processes. The Holloway Cut Adviser is best suited for consumer use and provides people with an easy to understand evaluation of the potential of a diamond in terms of light return, fire, scintillation and spread.
Here is a screenshot of the HCA results for a “Tolkowsky Cut Diamond” produced to the original exacting standards outlined by Marcel Tolkowsky in “Diamond Design” back in 1919 with the exception of the total depth being increased from 59.3% to 60% to account for the fact that a girdle edge of at least 0.7% is required to complete the diamond design:
The HCA results indicate that the diamond is likely to exhibit Excellent light return, fire, scintillation and spread. Assuming that the diamond cutter also took the time to carefully align the position of the facets across from each other and from top to bottom to avoid Azamet Shift AND maintained consistency of facet size, shape and meet-point-alignment in accordance with the standards necessary to obtain the grade of GIA Excellent or AGS Ideal for Symmetry, the diamond most likely does exhibit an exceptional amount of Light Return and will also exhibit an exceptional amount of Visual Performance (Sparkle Factor).
Now according to the statement which Bill Boyajian made back in 1997 “One example discovered in our investigation of modeling proportions of a round brilliant cut diamond revealed that, by our method of calculating brilliance, a 59 percent table is more brilliant than a 53 percent table, which was defined by Tolkowsky as “ideal”. This calculation was based on maintaining all other angles defined by Tolkowsky.” Let’s just put that concept to the test by punching those measurements into the Holloway Cut Adviser:
As you can see, while the estimated light return of the diamond remains excellent, the estimated fire and scintillation of the diamond dropped down to Very Good. This is not really surprising because the “sweet spot” in terms of the offset for crown and pavilion angle is 34.5 degrees for the crown angle and 40.8 degrees for the pavilion angle. The table diameter of a diamond has very little to do with light return because it is not one of the primary reflective mirrors of the diamond which direct light around the inside of a diamond and back up towards the viewer, but as Bill Boyajian noted in his statement it does have an effect upon the type of light return in terms of brilliance and dispersion.
Clarification of Gemological Terms:
In my 25+ years of experience in the diamond industry, I have come to realize that people usually use the term brilliant to describe the overall visual impact of a diamond while diamond cutters and professional diamond buyers break it down into the categories of Brilliance, Dispersion, Scintillation, Light Performance and Visual Performance.
Brilliance is reflected white light or white sparkle.
Dispersion or “Fire” is reflected colored light or colored sparkle.
Scintillation is the flashes of light or sparkle created when you or the diamond is moving…
Light Performance is the amount of light being reflected back up towards the viewer as it exits the diamond.
Visual Performance is the amount of Sparkle Factor being created by the diamond as the direct result of precise facet alignment and structure.
With this in mind, when a consumer says something to me like “I want to buy the most brilliant diamond possible” I tend to assume that they are actually looking for a diamond which is vibrant and offers a virtual balance of brilliance and dispersion with a high degree of scintillation based upon the actual gemological terminology outlined above. To that regard, I always recommend that people search for round brilliant ideal cut diamonds within the following range of proportions:
Table diameter between 53 – 57.5%
Total Depth between 59 – 61.8%d
Crown angle between 34.3 – 34.9 degrees
Pavilion angle between 40.6 – 40.9 degrees
There are other combinations of measurements which will produce similar amounts and types of light return, but this range eliminates a lot of the guesswork and will save you from having to punch the numbers into the HCA every time you turn around.
Getting Down to the Diamond Selection Process:
All right now that I’ve had the chance to thoroughly explain all of the reasons why I believe that diamonds with a 59% table diameter are not necessarily more brilliant than diamonds with a 53% table even when the other measurements of the diamond fall within my exacting standards, let’s go ahead and search for options which meet this particular request… The first thing that I’m going to do is Search for Diamonds at Blue Nile and set the advanced options to a total depth of 60% and a table diameter of 59% with a clarity grade of VS-2 and a color grade of G and GIA Excellent polish and symmetry with faint to no fluorescence. My Search for Diamonds at Blue Nile produced four possibilities:
Note: Blue Nile changed the format of how deep links were created when they switched their affiliate network from GAN to CJ, and thus the original links to the following diamonds were broken and have been replaced with links directed to their diamond search engine, which is fine since these options have probably sold by now. Please use my free Diamond Concierge Service if you would like me to help you find the best options currently available, but the information that can be obtained by reading the article is still applicable even if the diamond details pages can not be accessed.
Blue Nile 1.70 carat, G-color, VS-2 clarity diamond which has a table diameter of 59% and a total depth of 60.9% with a crown angle of 33.5° offset by a pavilion angle of 41.2°with a medium to slightly thick, faceted girdle and no culet with an overall cut grade of GIA Excellent. If we punch the numbers into the HCA we get a rating of Very Good for light performance, fire, scintillation and spread. I think we can do better…
Next we have this Blue Nile 1.71 carat, G-color, VS-2 clarity diamond which has a table diameter of 59% with a total depth of 60.9% with a crown angle of 34.5° and a pavilion angle of 40.8° with a thin to slightly thick, faceted girdle and no culet with an overall cut rating of GIA Excellent. Note that this diamond actually does have the crown angle and pavilion angle defined by Marcel Tolkowsky in his Diamond Design of 1919, but if we punch the numbers into the HCA we get Excellent for Light Return (no surprise, I explained this previously) but only Very Good for Fire, Dispersion and Scintillation. It is however the best of the choices currently available from Blue Nile within the confines of this particular diamond search request.
Finally we have this Blue Nile 1.73 carat, G-color, VS-2 clarity diamond with a table diameter of 59% and a total depth of 60.5% with a crown angle of 35.0° and a pavilion angle of 41.2° with a thin to medium, faceted girdle and a very small culet and an overall cut grade of GIA Excellent. Punch the numbers from this diamond into the Holloway Cut Adviser and you get Very Good for Light Return, Good for Fire, Good for Dispersion and Very Good for Spread.
The next diamond which I found is this 1.706 carat, G-color, VS-1 clarity Signature Hearts and Arrows Diamond from Brian Gavin which has a total depth of 61.9% with a table diameter of 55.9% and a crown angle of 34.8 degrees which is offset by a pavilion angle of 40.9 degrees with a thin to medium, faceted girdle and a pointed culet with negligible fluorescence. While the HCA still gives this diamond a rating of Excellent for Light Return and Very Good for all other factors, this diamond was graded by the AGS Laboratory on their Platinum Light Performance grading platform which takes into consideration a scan of the diamond using their Angular Spectrum Evaluation Tool (ASET) which evaluates the diamond from approximately 244 different vantage points.
This diamond also exhibits a crisp and complete pattern of hearts and arrows which indicates that the diamond is not suffering from a significant amount of Azamet Shift and thus the Visual Performance or Sparkle Factor of the diamond is going to be top notch. It also looks phenomenal through an Ideal Scope. Now the Blue Nile 1.71 carat, G-color, VS-2 clarity diamond might look equally as good through when viewed through a Hearts and Arrows scope and an Ideal Scope, but they don’t provide those images on their web site, we might however be able to get them by request if you’d like for me to ask… I have direct access to the diamond buying department and can bypass the regular customer service department, it’s a perk of being a member of the trade 😉
I continued my search and located this 1.71 carat, G-color, VS-2 clarity diamond from James Allen which has a total depth of 61.0% with a table diameter of 59% and a crown angle of 34.5 degrees offset by a pavilion angle of 40.8 degrees with a medium to slightly thick, faceted girdle and no culet with an overall cut rating of GIA Excellent. The HCA gives this diamond Excellent for Light Return and Very Good for all other factors. Like Blue Nile, James Allen does not provide images of this diamond as seen through the various scopes which would provide us with additional insight into the diamond cut quality and visual performance, but I should be able to get the images upon request.
Finally we have this 1.76 carat, G-color, VS-2 clarity diamond from James Allen which has a total depth of 60.8% with a table diameter of 57% and a crown angle of 34.5 degrees offset by a pavilion angle of 40.6 degrees with a medium to slightly thick, faceted girdle and no culet. The HCA gives this diamond a rating of Excellent for Light Performance, Fire and Scintillation which is promising… now I’d just like to see the scope images, let me know if you want me to ask for them.
Would you like help finding a diamond?
As you can see from this detailed response, I take the challenge of finding the right diamond for our clients quite seriously and provide an impartial review of each diamond regardless of who the vendor is. Drop me a note if you’d like help finding a diamond or if you have diamond related questions.