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pearlsngems

Brilliant_Rock
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A 13.5mm pearl is 12% larger than a 13mm pearl.

Round pearls are 3-dimensional-- spheres-- even though photos of them look like flat circles. The mistake is thinking of the size difference in terms of diameter. After all .5mm doesn't sound like a lot of difference. But in terms of volume, a small difference in diameter makes for a large difference in size. The larger pearl is .5mm larger than the smaller at every point radiating out from the center, in all directions.

To know how much larger or smaller a pearl is than another pearl you have to calculate volume.
Volume = 4/3 π (radius cubed)

The volume of a 13mm pearl is 1150 cubic millimeters.
The volume of a 13.5mm pearl is 1288 cubic millimeters.

1288 ÷ 1150 = 1.12
The 13.5mm pearl is 112% the size of a 13mm pearl, which is another way of saying it is 12% larger.
 

pearlsngems

Brilliant_Rock
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The difference in size that, say, 1 mm makes is greater when pearls are smaller, because 1mm is a greater per cent of their diameter.
The following calculations demonstrate that.

Using the volume formula we find that, for round pearls:

1mm pearl = 0.524 cmm
2mm pearl = 4.19 cmm (8x the size of a 1mm pearl)
3mm pearl = 14.14 cmm (28 times the size of a 1mm pearl. It is almost 3 and a half times the size of a 2mm pearl. (3.37x)
4mm pearl 33.51cmm (2.37 times the size of a 3mm pearl and 8 times (7.997) the size of a 2mm pearl.
5mm pearl 65.45 cmm (1.95x (nearly twice) the size of a 4mm pearl.)
6 mm pearl = 113 cubic mm (74% larger than a 5mm pearl)
7 mm pearl = 180 cubic mm (59% larger than a 6mm pearl)
8 mm pearl = 268 cubic mm (49% larger than a 7mm pearl)
9 mm pearl = 382 cubic mm (43% larger than 8mm; twice as large as a 7mm pearl)
10 mm pearl = 523 cubic mm (37% larger than 9mm, 95% larger than an 8mm pearl)
11 mm pearl = 697 cubic mm (33% larger than a 10mm pearl)
12 mm pearl = 904 cubic mm (30% larger than 11mm and 73% larger than 10mm; over 3 times as large as 8mm)
13 mm pearl = 1150 cubic mm (27% larger than a 12mm pearl)
14 mm pearl = 1436 cubic mm (25% larger than 13mm; twice as large as 11mm, and over 5x as large as 8mm pearls)
15 mm pearl = 1766 cubic mm (23% larger than a 14mm pearls)
16 mm pearl = 2144 cubic mm (21% larger than 15mm pearls and over 3 times as large as 11mm pearls.)


This information can be useful when deciding if the higher price of a larger pearl is worth it, and also if the heavier weight is going to be comfortable.
 
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Lisa Loves Shiny

Ideal_Rock
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Our eyes also interpret brighter as bigger, and white is of course brighter to the eye than your darker Tahitian ::)

The cats seem like a reasonable matched pair. @Pearlescence what say you? :bigsmile:

This is so true and important to know when you are stringing white pearls next to dark pearls.
 

Ann

Brilliant_Rock
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Incredible and ever so useful info - thank you so much.
 

CMN

Shiny_Rock
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Question - all things equal does a pearl with a dark body colour versus a light colour (let’s say white) appear to the eyes to have sharper luster because it is dark?
 

pearlsngems

Brilliant_Rock
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I'd say no, but the luster is different.
A lustrous dark Tahitian will look shiny, while a lustrous white pearl will also have a dark circle in the center of the pearl that contrasts with the lighter periphery. The sharper the luster, the greater the contrast between the center of the pearl and the periphery.

See this GIA page:

If you scroll down, there is a photo that shows 5 rows of white pearls. The most lustrous strand is the one at the top. Compare the appearance of the center circle in the very lustrous strand with that of the lower strands.
 

ForteKitty

Ideal_Rock
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Is the WSS actually 13.5, or is it on the upper end of 13.5-14mm? and is the Tahitian on the lower end of 12.5-13mm? Taking my calipers to your photo, the difference looks greater than half a mm!

eta: I zoomed in on the photo till the tahitian is 13mm on my calipers, and at that size, the WSS measures 14mm. Granted this is off a photo and is not 3D, but i think the size difference is greater than half mm.
 
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pearlsngems

Brilliant_Rock
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ForteKitty has the right idea. I took a slightly different approach.

I measured the two pearls just as they appear in the enlarged photo. The enlarged image measures 25mm for the larger pearl and 23mm for the smaller. Since we don't know what size either pearl really is, I calculated two scenarios.

If the smaller pearl is really 13mm, then the larger pearl has to be 14.13mm.
I made a ratio to solve for X, where X is the size of the larger pearl:
25 is to 23 as X is to 13 (Also written as 25:23 as X:13, or 25/23 = X/13)
23X = (25x13)
23X = 325
X = 325 ÷23
X = 14.13

On the other hand, if the if the larger pearl is really 13.5mm, then the smaller pearl has to be 12.42mm.

I made a ratio to solve for X, where X is the size of the smaller pearl:
25 is to 23 as 13.5 is to X (Also written as 25:23 as 13.5:X, or 25/23 = 13.5/X)
25X = (23 x 13.5)
25X = 310.5
X = 310.5 ÷25
X = 12.42

Either way the difference is diameter is over 1mm.

It's also possible neither pearl is the size described.
An object of known size in the photo would help, such as a coin we know the diameter of, or a ruler.
 

ForteKitty

Ideal_Rock
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ForteKitty has the right idea. I took a slightly different approach.

I measured the two pearls just as they appear in the enlarged photo. The enlarged image measures 25mm for the larger pearl and 23mm for the smaller. Since we don't know what size either pearl really is, I calculated two scenarios.

If the smaller pearl is really 13mm, then the larger pearl has to be 14.13mm.
I made a ratio to solve for X, where X is the size of the larger pearl:
25 is to 23 as X is to 13 (Also written as 25:23 as X:13, or 25/23 = X/13)
23X = (25x13)
23X = 325
X = 325 ÷23
X = 14.13

On the other hand, if the if the larger pearl is really 13.5mm, then the smaller pearl has to be 12.42mm.

I made a ratio to solve for X, where X is the size of the smaller pearl:
25 is to 23 as 13.5 is to X (Also written as 25:23 as 13.5:X, or 25/23 = 13.5/X)
25X = (23 x 13.5)
25X = 310.5
X = 310.5 ÷25
X = 12.42

Either way the difference is diameter is over 1mm.

It's also possible neither pearl is the size described.
An object of known size in the photo would help, such as a coin we know the diameter of, or a ruler.
That's what i usually do when buying diamonds on ebay with almost no description! They almost always have ring size, so I'd ask for a profile pic and calculate diamond diameter based on inner ring diameter. Works like a charm and a few times the diamonds were much larger than they said!
 

SparklyBandit

Rough_Rock
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Feb 19, 2020
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34
The Tahitians are from a local jeweler, I suppose I could go back and have him size them in front of me. I would be very upset if they were not as described.
The WSS are from Moline and have a separate appraisal. I trust Moline’s number to be correct. Can’t say I trust the local guy as much. Now I want calipers.
 

SparklyBandit

Rough_Rock
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So, back after using my husband’s mechanical calipers, gently measured the pearls. While these calipers are not as sensitive as jewelry calipers, the WSS is a solid 13.5. And the Tahitians, not 13.0. They are slightly under, but much closer to 13 then 12.5. The matching pendant is a solid 13. Of course now I cannot find the receipt for the Tahitians, we moved this summer and all my files got messed up. But I recall the receipt noted very close to 13, maybe 12.9 or so. I do have more appreciation for measuring pearls so perhaps I am off a bit in my recollection.

6878F8E2-36E9-4B0C-82F0-59B50DA6F33D.jpeg

And better pics with a ruler. My eyesight isn’t good enough to even use this ruler to measure these!
 

LilAlex

Brilliant_Rock
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A 13.5mm pearl is 12% larger than a 13mm pearl.

This is true and we often forget to think in three dimensions!

That said, I think the diameters are way more than 0.5mm different. Can check with calipers but one of those two is way off. On my screen, I "measure" one as 29mm and one as 26mm so that is an almost 12% difference in diameter whereas you were expecting < 4% difference in diameter. With my estimated diameters, the black pearl is ~ 40% larger in volume and that fits with what my eyes "see."

At least one of those diameters is way off, imo...

Alternatively, one is a button (or at least non-spherical) and I can not see the "short" dimension or one is closer to the camera. I don't think either scenario is likely.

EDIT: I get 8% difference in diameter in the second photo vs. 12% in the first. Closer but still more than 4%.
 

SparklyBandit

Rough_Rock
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What I am sure about, the Tahitians were not as big as I thought...... and I strongly suspect we’re not accurate on my receipt (if I could find it).
 

pearlsngems

Brilliant_Rock
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I googled the diameter of a dime, and it's 17.91.
In the photo it measures 37mm with my ruler. (sorry for all the edits, I kept typing it wrong.)

I find it harder to see the precise edge of the white pearl than the Tahitian on that light background (might do better with a dark background), so I will calculate the diameter of the Tahitian using the dime for comparison.

By my ruler the Tahitian is 27mm.

So the ration is:

37 (image diameter of dime) is to 17.91 (true diameter of dime) as 27 (image diameter of Tahitian) is to X (true diameter of Tahitian.

37X = (17.91 x 27)
X = (17.91 x 27) ÷ 37
X = 13.07

I now get 13.07mm for the Tahitian, using the dime for comparison.

If you post a photo of the dime and the WSS on a darker background I'll try calculating the WSS diameter again.
 

LilAlex

Brilliant_Rock
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Oh wait. They do not throw away the ones that are not exactly 13 or 13.5mm so I'm guessing that they are binned in 0.5mm "buckets." In which case you could have a 13.74mm "13.5mm" pearl and a 12.76mm "13mm" pearl -- and that is an 8% difference in diameter.
 

yssie

Super_Ideal_Rock
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No measurements of round pearls using their dimensions as they appear in images (ie. Measuring the diameter in the photos) is going to work. Unless you’ve got extraordinarily high resolution photos taken from a few feet away!

Like when you stick your finger in front of the moon, and you can hide the moon. Or when you take a selfie without a selfie stick and your nose is huge. Subtend angle - here’s a page that explains it nicely. https://www.onemathematicalcat.org/Math/Precalculus_obj/angleSubtendedByGeomObj.htm
A coin that had exactly the same real-world diameter as the WSS would have a smaller diameter measurement than the WSS in close range photos, because the WSS is sticking up further - the plane of its diameter is closer to the camera lens.

Same thing’s happening with these pearls. The white pearl measures bigger in pics both because it actually IS bigger, and also because the plane of its diameter measurement is closer to the camera lens... That second adds a tiny bump but we’re talking about tiny differences here!

Long way to say - don’t sweat any measurements taken from photos folks, they’re kinda doomed anyway ::)
 
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LilAlex

Brilliant_Rock
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Same thing’s happening with these pearls. The white pearl measures bigger in pics both because it actually IS bigger, and also because the plane of its diameter measurement is closer to the camera lens...

If they are on a flat surface and the imaging plane is parallel, then the relative relationship should be preserved -- unless there is a huge difference in diameter. The quarter-mm (250 microns!) difference in distance of the pearl diameter from the camera is not going to do much of anything to that photo taken from a foot away -- it's < 1/1,000th of the distance. I don't think my same-height son will look taller than me if he is 1/10th of an inch closer to the camera in our family portrait.

I was hoping you would weigh in on this part since you deal with this a lot:

They do not throw away the ones that are not exactly 13 or 13.5mm so I'm guessing that they are binned in 0.5mm "buckets." In which case you could have a 13.74mm "13.5mm" pearl and a 12.76mm "13mm" pearl -- and that is an 8% difference in diameter.

Couldn't it just be a big 13.5mm pearl and a small 13mm pearl?
 

yssie

Super_Ideal_Rock
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Sounds like @SparklyBandit has exact measurements on the WSS?

South Seas and Tahitians are often sold by the 1mm range - 11-12mm, 12-13mm, 13-14mm. I would look sideways at a vendor who called a 10.9mm pearl "11mm", as that's not the way most reputable vendors choose to band their sizes, but... The lack of standardization of both grading and reporting means that they wouldn't be wrong to do so... So it'd be a sideways look and a note on this forum to watch out for it, not screeching "lies!" :lol:
 

yssie

Super_Ideal_Rock
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If they are on a flat surface and the imaging plane is parallel, then the relative relationship should be preserved -- unless there is a huge difference in diameter. The quarter-mm (250 microns!) difference in distance of the pearl diameter from the camera is not going to do much of anything to that photo taken from a foot away -- it's < 1/1,000th of the distance. I don't think my same-height son will look taller than me if he is 1/10th of an inch closer to the camera in our family portrait.

I don't think those photos were taken a foot away - I think it was probably more like 5-7 inches? The difference it makes is actually kind of shockingly non-trivial!

The pearls are 9.7mm and 7.4mm.

- - - - - - - - - -

First view

I aligned the pearls such that the tops of the pearls are almost on the same plane. Setup for reference below.

1616381675837.png

Here's how the pearls look face-up (iPhone XS 4.6" above the top of the bigger pearl). No manipulations except cropping.

1616381558450.png

- - - - - - - - - -

Second view

This time I aligned the pearls such that the bottoms (where post meets pearl) are on the same plane. Not exactly the same, but very very very close!

1616381345579.png

And here's how the pearls look face-up (iPhone XS 4.6" above the top of the bigger pearl, just like before). Again - no manipulations except cropping.

1616381776013.png

- - - - - - - - - -

Comparison

Here, I
1. Rotated the face-up pic from the First view to be directly vertical
2. Cropped the First view pic so that only the second column of pearls is visible
3. Cropped the Second view pic so that only the second column of pearls is visible
4. Resized the Second view pic (down, maintaining image proportion) so that the bigger (9.7mm) is exactly the same size as the same pearl in the First view
5. Copied the Second view second column of pearls into the First view photo, side by side
6. Shifted the pearls slightly so that they're exactly aligned in a grid view - you can see where I cut and pasted to align the pearls ::)

So some cropping, resizing, and shifting, but no image manipulations that affect the proportions of any of the pearls relative to each other.

1616384643835.png

Same exact pic, I just screenshotted with a grid to make it easier to see the sizes. The 9.7mm pearls are exactly the same size. In proportion, the 7.4mm pearls look quite a bit larger/smaller depending on whether they were vertically aligned to top or bottom of the bigger akoya...

1616382965911.png

The further away the camera is the less proportional difference between large and small you'll see in this sort of comparison, of course. I think from a full foot or two away it'd become negligible. And it's exaggerated when you use a (single eyed) camera - stereo vision compensates a lot! All of @SparklyBandit's photos were taken like my Second view so they'll understate the real-world size of the smaller pearl. Probably not a lot. But enough that relying on dimensions from pics is a bit of a problematic proposition.

... How unpopular did I just make myself? :lol:
 
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