I've started to analyze your weights which you say are from applying a 15.8% per inch increase to get the weight at a different diameter. The first thing I discovered is that 15.8% is not applied exactly given the numbers you report. It looks like you have rounded your weights as reported above to more even or "nice even" amounts. So the 15.8% is only approximate. In some cases I can't reproduce the numbers you give using the established rules of rounding. I suspect you just shifted the actual results up or down to "nice even" numbers.

The same issue of "rounding to nice numbers" is true in the tables I gave using the allometric and ratio of areas methods. You can see that the 22" weight bands are "nice". That's because the named weight bands were made up for 22" cymbals. As soon as you scale to some other diameter the named weight bands no longer have nice even weights to their endpoints. That's why for 21" the range for Medium goes from 2278g to 2251g (ratio of areas) rather then 2280g to 2250g. But the correct thing to do is to report the result of the calculation exactly in the full modelling results. Otherwise you are just introducing further uncertainty and creating unauditable results.

I would need your raw data in order to look at how the 15.8% was derived and whether it is a good estimate from your raw data. Selecting the most accurate model is all about comparing error rates for different models, and that is not possible with what you have supplied. I will still be able to plot your weights as given against the results from the other two methods to see how the curves differ in shape.

The other question I have is about your use of the model categories Crash, Crash Ride, Ride, Ping. The sequence of numbers you give are exactly the same and just begin and end offset by one position from one model category to the next. Did you actually calculate some mean difference in weight for Ride vs Ping? Was that based on the actual weight distribution of different models? For a particular diameter? Known models from cymbals which still have model ink? In other words, is the average weight of a 22" Ping model really 3180g and a 22" Ride model 2750g to be believed as an accurate difference of 430g on average between the two models? Given the "changed to nice numbers" nature of your reporting I have no way to know which (if any) diameters and known models you actually had measurements for. What's real data and what's just the result of applying some formula?

I have rounded up a few grams to remove the decimals

my method was exactly the following, having some reference 50s 60s avedis, without weight writing (medium, etc)

I started from 13" crashes (550 grams) if you prefer another weight for a 13" crash put your weight here (example 490 grams)

adding 15.8% I realized that I was coming to the reference of the 20" and 22" cimbals with a likely weight

to go from "crashes" to the higher category "crash ride" I added 15.8% again, ie the 13" crash ride has the same weight as the 14" crash , this based on my personal tastes of ear, but here too you can start from a weight that you prefer

I had developed only for my purchases and did not want to be a real study but a rough reference to not buy too much weight

sorry I redid the calculations now and in fact does not correspond to 15.8 , now have passed years and I do not remember well I had a note to add 15.8% but obviously I had changed something ... I try to review the calculations ... ...

ok, yes, it was correctly 15.8% rounded by a few grams :)

Thanks for the clarifications. I'm really in the same boat as you with the allometric method because I don't have the original raw data and model fitting.

Here is a plot of the estimated weighs for the three different methods. I've called the 15.8% method P15R, where R means I used the Ride sequence. I chose to standardize the three curves on a 20" ride so they are constrained to be the same (2050g) at that point.

[img]http://black.net.nz/cym2018/wt-scale.png[/img]

Compared to the ratio of areas method (red), the allometric method (black) makes small diameter cymbals a little thinner. It also makes large diameter cymbals a little thicker. That's what I was mentioning before where larger diameter cymbals need to be a little thicker to stand up to playing. If you compare this to the 15.8% per inch method (green) it gives very similar results to the allometric method at smaller diameters. At larger diameters the 15.8% per inch method predicts an even thicker cymbal than the allometric method.

The next step is to use the data I've got from cymbals of different diameters which actually do have model ink still on them to check on which predictions are closer to the actual weights for those cymbals. I will also need to take what cymbal data I've got for the same model in different diameters and refit an allometric model to see how that goes. Since the original fitting was done on Bosphorus cymbals some years back, there is no guarantee that the results generalize to all Turkish cymbals let alone all cymbals including Paiste, and Avedis Zildjian. It is also possible that the scaling equation works well enough across different brands and production eras, but that you would need different weight category boundaries to get the names to line up with the model ink manufacturers put on their cymbals. We'll see.

I'm pretty sure that the 20" 2050 gram cymbal is medium (ride), while the red forecast of the Area method reaches the 24" cymbal with about 2900 grams which is thin (almost paper thin) which is a crash / crash ride, so that method seems quite unreliable ... I do not know if my 15.8 perhaps with more study could be calibrated yet, but we are not far ... your allometric 24" comes to just over 3000 grams which I think is always a crash (thin / medium thin) , while my 24" reaches 3680 grams, and I've never had a cymbal of that kind ... should hear the opinion of some other expert or in any case a deepening

24" cymbals with MEDIUM RIDE model ink and weight I've got on file (plus a few additions of other models to fill out the picture).

Laser serial 24" MEDIUM RIDE 3798g, 3800g (Orchestral 3357g)

1970s MEDIUM RIDE 4190g

1970s MEDIUM THIN RIDE 3550g

Large Stamp (mid 50s) CRASH RIDE 2900g

I've got a lot more 20" examples

Early 50s Trans Stamp at 1536g (exceptionally light), 2396g (MEDIUM BOUNCE)

Late 50s Small Stamp 2005g and 2260g

60s 9 at 1950g - 2150g (plus one MEDIUM BOUNCE at 1932g and one MEDIUM CRASH at 2060g)

70s 3 at 2380g - 2676g (plus one MEDIUM THIN at 2010g, one CRASH RIDE at 2080g)

80s 8 at 2249g - 2716g (plus one CRASH RIDE 2100g)

90s and Early Laser era 2500g - 2755g (still heavy like the 80s)

2013 Laser era 2324g - 2500g (plus two MEDIUM THIN CRASH 1970g, 2022g)

It's not that the ratio of areas method is unreliable. It is that it answers a different question from the one we want to know. But I suspect that by combining all the data I've got for different diameter cymbals with model ink on them we might start to get something more suited to what we want to know. I've got a lot more data than I've shown above because I haven't included all the CRASH models. Then I've got all the other diameters (although 20" are the most numerous), and even more data for Paiste 602s from different eras and diameters, and then North American K Zildjian cymbals (Canadian and American made).

This plot below doesn't indicate the specific weights for individual cymbals with ink on them. I haven't figured out the best way to add that sort of info in. But it does show why I don't think "universal" named weight bands are going to work well. They don't even work well within the A Zildjian cymbals where there is hardly any overlap between the weight ranges of the Trans Stamps (T) and the 1980s.

[img]http://black.net.nz/avedis/images/A20-weights-by-era.png[/img]

Using the 20" weight of 2050g might be plausible in the Large Stamp (L), Small Stamp (S) and 60s. But things get out of kilter if you go back to Trans Stamps or forward to the 70s and 80s.

this because not only the weight that influences but also unpredictable factors that emerge in the manufacturing phase

I started a distance endorsering relationship with Masterwork and I noticed that for the same size/weight you can have a crash, a crash ride, or a ride, this is because after the production they try it and they see how the cymbal responds

I would say however that in principle the weight is a more than valid reference, only some cymbals deviate due to reasons emerged during the manufacture