hello there is an approximate method of calculating the weight of a cymbal?
ie. if I have a 19" cymbal weighing 1600 grams, I would like to take one with the same characteristics (same series) of 20" with the same balance stick / wash, I find an equation to guess the weight?
There are two methods I use. One is based on the ratio of areas. That models a cymbal as a disk of even thickness throughout. We know that is a simplifying assumption given that cymbals have bells and taper (thinner metal towards the edge) and profile (how much curvature there is in the bow). We don't know how much the simplifying assumptions decrease the accuracy of the method.
The second method is based on an allometric ratio with an exponent of 2.5 which was empirically derived by looking at different diameter cymbals of the same model (eg medium ride) within the same line of Bosphorus cymbals. This was done some years ago when Tony Costello (cymbalsonly) had a big stock of them. The goal was to do just what you are asking about: predict the weight of same model different diameter cymbal which will sound the same excluding pitch (as related to diameter). I don't have the original data and I didin't do the original estimation. In fact I would have to go looking in my archives to thank whoever did it, although I think it was ThomasL. Forgive me if I've got it wrong.
An equivalent for a 19" at 1600g is a 20" at 1773g by the ratio of areas method. The sonic equivalent for a 19" at 1600g is a 20" at 1819g by the allometric ratio with an exponent of 2.5
What I tend to do is use the two values to provide a target range, so a 19" at 1600g is most likely to be matched if you go for a 20" cymbal in the range 1773g to 1819g. However, this modeling still leaves out lots of factors we know influence the sound.
I've got a program which does these things, as well as provide the "named" bands for different weight ranges (eg Medium Light vs Medium). It is in a Mac only format and I'd need to do some work to convert it to a spreadsheet or an internet tool for general use. I was going to get to that some day but I've got a lot of other projects on the go which I give priority to.
That uses the ratio of areas method and it just tells you the category names for a given weight and diameter. But I did think about starting from that code to create a web available version of my calculators. Falling Do
Here's a better place to begin (but still not as good as having a calculator for this specific task) if the silly attachment system leaves it large enough to read...
well it might be clear enough. Let me know if you need a bigger one.
...An equivalent for a 19" at 1600g is a 20" at 1773g by the ratio of areas method. The sonic equivalent for a 19" at 1600g is a 20" at 1819g by the allometric ratio with an exponent of 2.5...
ok, thanks so much! 2.5 ? some time ago I had calculate an increase of 15.8% per inch, based on the 50s 60s avedis study, obtaining these forecasts
crash
13 550
14 630
15 730
16 850
17 990
18 1150
19 1350
20 1550
21 1780
22 2050
23 2370
24 2750
crash ride
13 630
14 730
15 850
16 990
17 1150
18 1350
19 1550
20 1780
21 2050
22 2350
23 2750
24 3180
ride
13 730
14 850
15 990
16 1150
17 1350
18 1550
19 1780
20 2050
21 2350
22 2750
23 3180
24 3680
ping ride
13 850
14 990
15 1150
16 1350
17 1550
18 1780
19 2050
20 2350
21 2750
22 3150
23 3680
24 4260
... I would like to hear more opinions about it
the method is certainly reliable on vintage avedis, but I do not know if it can be a universal method!
exact, would be a prediction based on another cymbal, thanks anyway :)
I can go as deep into the mathematics of this as you want. But be warned I'm a retired PhD with decades of work in mathematical modeling, statistics, and data analysis. So my replies can be a bit long and technical. ;)
Allometry is a specific discipline as well as a general fitting method and I did a bit of work in that area as part of my PhD, although I am woefully out of touch with the latest work in this area. Allometry comes into play when trying to scale objects up and down and factors such as gravity and material come into play. These factors mean that simple linear scaling (make an animal twice as big) doesn't work very well. The discipline started out in evolutionary biology, but the same analysis issues apply to cymbals.
The ratio of areas method is the equivalent of an exponent of 2 in the allometric method (from memory anyway). The ratio of areas is the simplest geometric model. A linear increase such as 15.8% per inch might approximate the behavior of the ratio of areas model or the allometric model, but in order to assess that we need all the raw data to do the fitting and assessment of patterns in the residual errors.
The 2.5 came up empirically but it seemed reasonable given what we know about the "incorrect" assumptions in the ratio of areas. I mentioned some before: taper in cymbals so they aren't a uniformly thick disk. Also the (relatively) fixed area taken up by a bell leads to inherently non linear modeling being likely. In overall diameter terms the bell of a 26" cymbal takes up a lot less area than the bell of a 20" cymbals. Also we believe larger diameter cymbals need to be thicker over much of their area otherwise they would suffer structural failures more frequently than they do. This last observation has yet to be experimentally verified. My research budget doesn't really run to commissioning a bunch of cymbals in different diameters and thickness just so I can test them to failure. :(
^^ ok, but the allometry how is it measured??? I looked on the internet and I did not find anything fast, I tried 1600 x 2.5 but obviously it does not work, what is the calculation to do ? 2.5 to what corresponds in %, if there can be a correspondence ... I have done ancient literature and philosophy so imagine my rapport with the math ...
I'll have to make a few graphs and show how the predictions vary for the three different models (ratio of areas, percentage increase, allometric). That should shed some light on things. I'll give the equations as part of that since to get the graphs (and other statistics) out of the R system I'll also need to code them up. I've got two other specific tasks I'm working on at the moment. One is price modeling for 17" Paiste 602 cymbals as context for Bright Ride prices, and the ongoing discussion on bell sizes on different models.
I've got about 1930 weights recorded for various production eras, models (where known) and diameters of A Zildjian cymbals. That's counting pairs of cymbals sold as a pair although I've got each weight recorded separately. I've also got 680 weights for K Zildjian Istanbul cymbals, 287 for North American made K Zildjans, and 1838 for Paiste 602 and Sound Creations. Not to mention 123 Spizzichinos. That would give us a bit of data to work with to see how the formulas need to change to cover different sorts of cymbals. ;)
An interim solution for you (and anybody else who is interested) is this Excel spreadsheet which gives
[LIST]
[*]The table of 22" weight bands scaled to other diameters using the ratio of areas
[*]The table of 22" weight bands scaled using the allometric method
[*]The named weight bands for 22" cymbals which started this off
[*]A calculation area which uses both methods to tell you the "equivalent" weight for a cymbal of a different diameter.
[/LIST]
To download the spreadsheet you can now just click on this link and it will download to your computer.
Note this spreadsheet was produced by an automatic converter from LibreOffice to an older version of Excel after an initial export from Mac Numbers. Since I don't have Excel I can't say how it will behave in Excel itself. If there are any problems I can try the spreadsheet with Excel on other people's machines and see what I can do to address them...reluctantly.
The formulas used are there in the spreadsheet. I haven't yet had a chance to analyze your weights (based on a 15.8% increase) so I can show how they all fit together in terms of predictions.
An historical note. This all began with somebody putting forward names for particular weight bands for 22" cymbals. This was an effort to get people to standardize their naming conventions based on specific weight ranges for 22" cymbals. I don't even consider that a good idea in terms of reporting because it is better to give the actual weight. If you substitute a named band for a weight you just lose information. I don't mind if people choose to report both.
As far as I know these original weight bands were just somebody's personal suggestion and didn't reflect any statistical analysis of weight data. There is also no necessary universality about the weight band names. It is silly to apply the same named bands to 1950s K Zildjian Istanbul cymbals and 1980s A Zildjian cymbals. We know this because enough of that brand, series, and production era specific work has now been done. But we always sort of "knew it" less formally.
Next somebody asked how to apply these named weight bands to cymbals of different diameters. That led to a few suggestions of how to "scale" the weights to work for a different diameter cymbal. The ratio of areas method was the winner back in the day. Fortunately it also happens to be the correct mathematical formulation for the question asked. And that's what the calculator linked to earlier was intended to do. I found it much easier to get an overview by creating a table which gave weight class boundaries rather than try and work them out iteratively by trying out different combinations in that calculator. Hence my spreadsheet.
My own work is trying to move us to make use of specific cymbal model info (where identifiable) in addition to just weights. Plus I'm working on the actual weight ranges which are found in different diameters of different brands and series in different production eras, rather than presuming a one size fits all approach. I've also been working (slowly since it isn't a high priority) on more sophisticated mathematical modelling of how cymbals will sound based on including things like profile (curvature), taper (metal thinning at the edge), bell size and shape, lathing style, hammering attributes, and weight. While this is interesting modelling work, it is no substitute for just playing a cymbal on a stand in front of you. Hence the lower priority than some other work. :)
