How Different Should Your Left Side Ride Be?

JDA

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Both Rides may be the key.
but am worried that it will mostly provide a crash
900 between a 22 and 19. Both Rides. Sorry I just threw that out wasn't clear.
What weight is your 20 again? and you want/are looking at/for/ an 18 correct correct?
 

zenstat

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Why? I'm contemplating a left side 18" about this much lighter than my main ride, but am worried that it will mostly provide a crash and a quieter/washier ride sound when I like a brasher and louder left side ride. What are you getting out of a 900 gram difference?
I think you will find Joe is talking a difference in grams but that will be specific to two particular diameter cymbals. The more general form of the relationship (for different diameters) is to use some sort of percentage. Otherwise you get non useful answers. For example trying to find a LSR to go with this 16" 1124g Medium Bounce from the late 50s.

16-1134-ink.jpg


16-1134-top.jpg


or a main ride to go with the 16" Medium Bounce on the left.

BTW that graph of predictions from the three models is for ride cymbals. There are different curves for Crash, Crash Ride, and Ping Ride.
 

JDA

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The thought occurred to me that there is a more scientific (or maybe just math) way to choose a left side cymbal. This is to first find a main ride you love and then buy the SAME cymbal in a proportionately smaller diameter and weight for the left side. This way, the two cymbals would have the same overall sound and complement each other, yet differ in pitch, volume, and crashability.
The key-Key- to that is- and it's sometimes difficult and takes time and perseverance---is for the second cymbal to Also be a dedicated Ride not Crash parlez-vous?
there's a few 18" rides (and I think I've had or still own (choice ones) them all)
 

Old Drummer

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Both Rides may be the key.


900 between a 22 and 19. Both Rides. Sorry I just threw that out wasn't clear.
What weight is your 20 again? and you want/are looking at/for/ an 18 correct correct?
Thanks for the clarification. My 20" Agop Traditional Medium ride is 2470 grams. This strikes me as a bit heavy, but it's what I have and at the moment it's the one that works best for me. It's a nice middle-of-the-road ride that handles everything without annoying me.

I'm using an 1838 gram 18" old A as left side now, which although the relative weight is in the ballpark, is overpoweringly loud as a crash and not the greatest alternative ride either. I think it's the design of the cymbal rather than the size and weight. Both Agop and Mehmet (I doubt it makes much difference) have several 18" choices in their Traditional lines weighing between under 1300 to around 1650 grams. The prices are pretty low too. Unfortunately, there aren't many sound files and those that exist rarely ride the cymbal, they just crash it. Well OK, pretty much all of them crash decently, but how's the ride? And how would the ride fit with my current one? It seems like the lighter 18" Istanbul cymbals have a quieter, washier ride sound, but as said I think I want brasher ride sound on the left.

Maybe I'm looking for a horse of a color that doesn't exist. I'm quite familiar with thinner 18" left side cymbals that both crash and ride well, but the ride sounds are quieter and washier than I want. In theory, an 18" Istanbul in the 1900+ gram range would give me the different colored horse I want, and I can't see how that weight wouldn't crash. My 2470 gram 20" crashes OK at loud volumes. Wouldn't a 1970 gram 18" cymbal from the same family crash proportionately as well while providing a brasher ride sound? I would think so. But getting an 18" Istanbul this heavy is a real risk as well as hard to find. What would an 18" Istanbul at say 1500-1600 grams do?

It's just all a puzzle, at the moment my old A 18" is OK, and buying cymbals on spec isn't in my budget.
 
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JDA

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I think you're on the right track. Taking your info Istanbul what model? ok Traditional Medium 2470 I would...based on my experience recent experience and a darn good roll of the Dice Recommend. An 18" Sultan. Yes. The one "with the Rings" on top. If you find one marked "Jazz Ride" jump on it be wary -even of- the Thin crashes (I might be wrong- but doubt it) They -Sultan- will "open up" but they won't go too far.....One marked " medium" ok..but I recommend an 18" Sultan I recommend (free no charge..Used second hand low price..
 

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I think you will find Joe is talking a difference in grams but that will be specific to two particular diameter cymbals. The more general form of the relationship (for different diameters) is to use some sort of percentage. Otherwise you get non useful answers. For example trying to find a LSR to go with this 16" 1124g Medium Bounce from the late 50s.

View attachment 408573

View attachment 408574

or a main ride to go with the 16" Medium Bounce on the left.

BTW that graph of predictions from the three models is for ride cymbals. There are different curves for Crash, Crash Ride, and Ping Ride.
Oh no. Care to post the other curves? I'd be especially interested in the curve for crash/rides. Also, if there's an understandable way to explain it, I'm curious why the curves are different for different cymbal styles.
 

Old Drummer

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I think you're on the right track. Taking your info Istanbul what model? ok Traditional Medium 2470 I would...based on my experience recent experience and a darn good roll of the Dice Recommend. An 18" Sultan. Yes. The one "with the Rings" on top. If you find one marked "Jazz Ride" jump on it be wary -even of- the Thin crashes (I might be wrong- but doubt it) They -Sultan- will "open up" but they won't go too far.....One marked " medium" ok..but I recommend an 18" Sultan I recommend (free no charge..Used second hand low price..
This is a fascinating recommendation that I really appreciate. Yeah, I know the Sultans, having briefly owned a pair of the hats (and liked them), but I never would have thought of an 18" Sultan in my situation. I know from other of your posts that you know cymbals well, so I'm going to listen to the Sultans. Thanks again.
 

JDA

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(Youre' of course welcome) but here's a Problem I see (not fatal..) The price of used Agops is not as let's say liberal as "that other brand from Turkey (starts with a 'B" ) I did a quick search thru ebay and reverb and came up with No used 18 Agop (beside some lower lines but even they were new and expensive) So unless a friend has an 18" Agop to help you out- I see u may be in a bit of an Agop box (The "B" brand used are plentiful, variety, & a steal sometimes)
So...keep looking, there was video of an 18" Sultan Crash on Reverb didn't think it was what you/me/the other guy/ would want in a Ride. (you can search it It's a Crash dances too much to ride on imo) (same as any brand would respond(being) built as a crash)
 

zenstat

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Oh no. Care to post the other curves? I'd be especially interested in the curve for crash/rides. Also, if there's an understandable way to explain it, I'm curious why the curves are different for different cymbal styles.
I haven't graphed them yet. But the crash ride data goes

13 630
14 770
15 850
16 990
17 1150
18 1350
19 1550
20 1780
21 2050
22 2370
23 2750
24 3180

From memory the sequence is the same but offset by 100g from the ride sequence at the 13" start. So 630g for the crash ride rather than 730g for the ride. You can use the original graph but go down 1 inch to get your weight for a crash ride, and 2 inches to get a suggested crash weight.

What is promising to me about the P15R model isn't the exact weights it produces but that the general approach offers a nice way to make it easy to use and easy to integrate all the information in one place. I'm still working on checking the estimated weights out against all the weights for specific diameters and models I've got in my database (which span a few decades). Like that late 50s 16" Medium Bounce (which is a ride) I showed before. Then I also want to see what adjustments might be needed for a similar model to work on Paiste, Sabian, K Zildjian Istanbul, other modern Turkish brands, etc.

The name P14R for the model comes from it being percentage based where each increasing inch of diameter is associated with increment of about 14 to 15 percent on the previous diameter. The weight displayed is also rounded (and or bumped up -- not sure yet) to end up with the nice even numbers you see. Somebody else came up with the model based on A Zildian cymbals and I've been investigating how it performs relative to the Allometric and Ratio of Areas methods. I've also been trying to reproduce the calculations working back from the rounded/bumped up results.

What I'm pairing by way of rides:

22" Lauritsen 2489g with a 20" Lauritsen at 1730g
22" Paiste Trad Medium Light at 2840g with a 20" Paiste Trad Medium Light at 2162g
21" Paiste Silver Mellow at 2504g with an 18" Paiste Extra Light at 1290g
20" Zildjian mid 50s LS2 at 2318g with an 18" 60s Zildjian crash at 1240g

but I've got other options for either a LSR or somehting more crashy. Not all fit the expected patterns.
 
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Seb77

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I'm using an 1838 gram 18" old A as left side now, which although the relative weight is in the ballpark, is overpoweringly loud as a crash and not the greatest alternative ride either. I think it's the design of the cymbal rather than the size and weight.

... I think I want brasher ride sound on the left.

Maybe I'm looking for a horse of a color that doesn't exist. I'm quite familiar with thinner 18" left side cymbals that both crash and ride well, but the ride sounds are quieter and washier than I want. In theory, an 18" Istanbul in the 1900+ gram range would give me the different colored horse I want, and I can't see how that weight wouldn't crash. My 2470 gram 20" crashes OK at loud volumes. Wouldn't a 1970 gram 18" cymbal from the same family crash proportionately as well while providing a brasher ride sound? I would think so. But getting an 18" Istanbul this heavy is a real risk as well as hard to find. What would an 18" Istanbul at say 1500-1600 grams do?
There are few designated 18" rides overall these days, that's the problem. Both Istanbul branches have the Mel Lewis /Legend 19", which isn't really brash, but works well. Agop also has the Mel lewis 1982 series with an 18" crash ride, most are around 1600g I think. One of those might be the ticket.

I also have two 19" cymbals around 1950 grams that ride nicely, one is a Mehmet Sultan, the other is a Paiste 602 Medium. On both, the crash doesn't really open up easily, but it also doesn't overpower because of that.

Since the advent of Sabian Omnis I'd say you can have any combination of thin crash and pingy ride in one cymbals; anything is possible.
 

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I use a flat ride as left hand ride and that gives me the difference I need in my jazz gigs. Both that and the right hand ride are Bosphorus Turk series so blend well tonally but have of course different stick definition and volume.
 

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My main ride is a UFIP class medium 22” and it’s heavy and pingy. My second ride is a 22” zildjian k light ride and it’s dark and washy. Different voices for different parts of the song.
 

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I haven't graphed them yet. But the crash ride data goes

13 630
14 770
15 850
16 990
17 1150
18 1350
19 1550
20 1780
21 2050
22 2370
23 2750
24 3180

From memory the sequence is the same but offset by 100g from the ride sequence at the 13" start. So 630g for the crash ride rather than 730g for the ride. You can use the original graph but go down 1 inch to get your weight for a crash ride, and 2 inches to get a suggested crash weight.

What is promising to me about the P15R model isn't the exact weights it produces but that the general approach offers a nice way to make it easy to use and easy to integrate all the information in one place. I'm still working on checking the estimated weights out against all the weights for specific diameters and models I've got in my database (which span a few decades). Like that late 50s 16" Medium Bounce (which is a ride) I showed before. Then I also want to see what adjustments might be needed for a similar model to work on Paiste, Sabian, K Zildjian Istanbul, other modern Turkish brands, etc.

The name P14R for the model comes from it being percentage based where each increasing inch of diameter is associated with increment of about 14 to 15 percent on the previous diameter. The weight displayed is also rounded (and or bumped up -- not sure yet) to end up with the nice even numbers you see. Somebody else came up with the model based on A Zildian cymbals and I've been investigating how it performs relative to the Allometric and Ratio of Areas methods. I've also been trying to reproduce the calculations working back from the rounded/bumped up results.

What I'm pairing by way of rides:

22" Lauritsen 2489g with a 20" Lauritsen at 1730g
22" Paiste Trad Medium Light at 2840g with a 20" Paiste Trad Medium Light at 2162g
21" Paiste Silver Mellow at 2504g with an 18" Paiste Extra Light at 1290g
20" Zildjian mid 50s LS2 at 2318g with an 18" 60s Zildjian crash at 1240g

but I've got other options for either a LSR or somehting more crashy. Not all fit the expected patterns.
Thanks. Without examining it in detail, it looks like the crash/ride distribution is all lighter than the ride distribution. That makes sense, since the crash/ride is a hybrid. I suppose the full picture would require including the crash distribution alongside the other two to try to figure out what's going on overall, but I'll leave that up to you.

I get what you're saying about P14R but don't understand the rationale for departing from the area method (unless the departure is a fudge factor attempting to offset the effects of the bells). I assume the allometric method is also a departure with a rationale I don't understand. But then I don't need to understand. It's interesting that there are these different methods out there.

Also interesting is that you aren't pairing cymbals of analogous weights and a dimensions. That's still the player's decision. Do we even want cymbals that match in these ways? Maybe we don't.
 

Old Drummer

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There are few designated 18" rides overall these days, that's the problem.
I'm finding this too. Most 18" cymbals are labeled crashes, but this raises the question of whether they're designed differently than rides or just have different ink on them. I fear that it could be either. Since it's hard to know when shopping online, a lot of sound files displaying both the crash and the ride are crucial. Unfortunately, there often aren't many and sometimes aren't any. I'm not buying based on a label even if I do know the weight!
 

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Put a piece of gaffer tape under one or the other.
Clamp a rivet onto a piece of string or a light shoelace and drape it on the other one.

Ta da! You've got two different cymbals.

I knew a guy who used to gig two 22" K Cons-- a Medium Thin HIgh and a Medium Thin Low. You put a piece of gaff tape underneath one of them and you're ready to go.
 

Old Drummer

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(Youre' of course welcome) but here's a Problem I see (not fatal..) The price of used Agops is not as let's say liberal as "that other brand from Turkey (starts with a 'B" ) I did a quick search thru ebay and reverb and came up with No used 18 Agop (beside some lower lines but even they were new and expensive) So unless a friend has an 18" Agop to help you out- I see u may be in a bit of an Agop box (The "B" brand used are plentiful, variety, & a steal sometimes)
So...keep looking, there was video of an 18" Sultan Crash on Reverb didn't think it was what you/me/the other guy/ would want in a Ride. (you can search it It's a Crash dances too much to ride on imo) (same as any brand would respond(being) built as a crash)
Is there a reason you're not looking at Mehmets? I'm finding more of them for sale than Agops, often at lower prices, and understand that similar cymbals made by each company are close to the same.

I spent some time listening to sound files of 18" Sultans and Traditionals today (probably mostly Mehmets).

I really liked the Sultans as rides, but found myself thinking that their ride sound was more what I want in a main ride than a left side ride. They were kind of subdued, woody, earthy. The crash was OK, but a little bold, leaving me to wonder how well riding and crashing at the same time (to make some white noise) would work. I didn't think it would work well. The exception was the lightest of the Sultans I listened to. At 1325 grams it seemed a bit washier than the others (1400+ grams) and more able to fill the air with some left side white noise, while also a decent crash and subdued ride if played those ways.

By contrast, the Traditionals I listened to (all labeled crashes) seemed better able to achieve my objective. Their ride sound wasn't as appealing, but their crash sound was more appealing. Mostly, it sounded like riding and crashing together would work well. Interestingly, it seemed that the heavier Traditional crashes (knocking on the door of 1600) were more to my liking than the lighter ones, whereas with the Sultans the opposite was the case.

Puzzling is that an 18" Traditional Original Ride is for sale on Reverb. There is no weight listed and I couldn't find a sound file for it. It's the only Traditional 18" I found labeled a ride rather than a crash, so I naturally wonder if it's different from the crashes and if so how.

Meanwhile, in the buying department, I did find an 18" Mehmet Sultan Jazz Ride for sale on eBay that would cost me about $285. But it included no information on weight and I couldn't find information anywhere explaining how the jazz ride is different from the same cymbal in thin, if there is a difference, I also found an 18" Mehmet Sultan Thin Crash in a local store for $225 brand new. Obviously I'd like to know if the jazz ride differs from the thin crash, and if so how. Additionally, I found a year-old classified ad posted by a guy selling an 18" Mehmet Sultan Medium. He was asking $160 then. Who knows what he would take if he still has it. Then again, based on my listening, I'm not sure I'd want the Sultan in Medium. The Sultans seem to need to be lighter to suit me.

As for buying a Traditional, there are half a dozen viable choices listed on Reverb, but I'm not yet comfortable zeroing in on exactly the one I might want without more information than I have. Also, they're all new, the least I could pay is $225, and the seller with the lowest prices just joined Reverb this month and has only one feedback.

Maybe I should go to the shop with the Sultan thin crash and bang on it. That or maybe the one in the classified ad is the only one I can personally play, so I probably should. It would be fun to have a room full of different cymbals to experiment with, but since I don't have that, I probably ought to go listen to the one I can.
 

JDA

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ride rather than a crash, so I naturally wonder if it's different from the crashes and if so how
How crashes are made different than Rides. Would someone like to tackle that.
Go from the beginning a Historical perspective. I'm a little exhausted atm. and chose to relax.
831AugustHonda 008.JPG


Don't let that last sentence confuse you. as much as it could..
There are medium-thin "rides" that are near identical thickness at the cup as at the edge . Generally you see, it's Taper (build) that lends to lead lean either Ride or Crash
 
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zenstat

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Thanks. Without examining it in detail, it looks like the crash/ride distribution is all lighter than the ride distribution. That makes sense, since the crash/ride is a hybrid. I suppose the full picture would require including the crash distribution alongside the other two to try to figure out what's going on overall, but I'll leave that up to you.

I get what you're saying about P14R but don't understand the rationale for departing from the area method (unless the departure is a fudge factor attempting to offset the effects of the bells). I assume the allometric method is also a departure with a rationale I don't understand. But then I don't need to understand. It's interesting that there are these different methods out there.

Also interesting is that you aren't pairing cymbals of analogous weights and a dimensions. That's still the player's decision. Do we even want cymbals that match in these ways? Maybe we don't.
The history of the weight scaling research explains more about the situation as far as I'm concerned. Once upon a time LuvMyLeedy on Cymbalholic came up with some weight ranges for 22" cymbals and the name of that weight category. The table was

22" cymbals
1900 - 2100 Extra Light
2100 - 2300 Light
2300 - 2500 Med Light
2500 - 2800 Medium
2800 - 3100 Med Heavy
3100 - 3500 Heavy
3500 and up Very Heavy

I don't know if it was validated by getting weights for actual cymbals with model ink. I don't know how large a sample of cymbals they were working from. I don't know if they were just talking "ride cymbals" and had explicitly excluded crashes and crash rides. I don't know if the sample included different brands and different production eras. I don't know if they even considered whether a single table was useful to represent such disparate cymbals as old Ks from the 1940s, A Zildjians from the 1960s, A Zildjians from the 1990s, UFIP, Paiste, etc.

The table caught on and the peeps started asking versions of the question I quoted above: what are the ranges for a 20"? Or an 18"? Somebody proposed the ratio of areas method and it caught on. It became available as an online calculation and is preserved here


in the Cymbalholic color scheme. :glasses8:

One of the problems is that it produces ranges which aren't simplified and these became gospel. So for a 20" if your cymbal is

1901 - 2066 Med Light
2066 - 2314 Medium

And don't get me started on the rookie statistician mistake of having the end of one category match the beginning of the next category. They should probably be more like

1900 - 2060 Med Light
2061 - 2315 Medium

You can verify that the online calculator is implemented with non overlapping ranges and does use 2061 for the lower bound of 20" Medium.

Nobody ever said that the calculations were to provide an answer to pairing up two ride cymbals of different diameters to get a contrasting or harmonious LSR.

The next exploratory improvement was a modification to the ratio of areas based on the observation that the ratio of areas method didn't give accurate results in terms of cymbals having a similar sound and feel when applied to different diameters. You can read up on allometry here


The main reason for using allometry with cymbals is that the thickness of a cymbal has to scale a bit with increasing diameter otherwise the cymbal would behave (and sound) too different. This introduces certain a bit of non linearity into the model. The estimates for the coefficients came from a series of Bos cymbals at different diameters so they were within one Brand. Again I didn't do the original research, but I've used the model. If you go back to that graph you will see that larger diameters get relatively heavier compared to the ratio of areas. That's the thicker metal at work for larger diameters. For smaller diameters the Allometric model is a little thinner than the corresponding ratio of areas.

If you compare this to the P15R method, smaller diameters are the same as the Allometric model but P15R gets "carried away" at larger diameters and gives increasingly heavier weights. How much more "carried away"? And is it closer to what we actually find on cymbals? Nobody really knows yet. This is one of the reasons I started collecting weights on cymbals with model ink. I've got many thousands of data points across many brands, production eras, etc. but I've been working on other things. There is a place reserved for this in Cymbal Wiki for when I get to it.
 
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Old Drummer

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The history of the weight scaling research explains more about the situation as far as I'm concerned. Once upon a time LuvMyLeedy on Cymbalholic came up with some weight ranges for 22" cymbals and the name of that weight category. The table was

22" cymbals
1900 - 2100 Extra Light
2100 - 2300 Light
2300 - 2500 Med Light
2500 - 2800 Medium
2800 - 3100 Med Heavy
3100 - 3500 Heavy
3500 and up Very Heavy

I don't know if it was validated by getting weight for actual cymbals with model ink. I don't know how large a sample of cymbals they were working from. I don't know if they were just talking "ride cymbals" and had explicitly excluded crashes and crash rides. I don't know if the sample included different brands and different production eras. I don't know if they even considered whether a single table was useful to represent such disparate cymbals as old Ks from the 1940s, A Zildjians from the 1960s, A Zildjians from the 1990s, UFIP, Paiste, etc.

The table caught on and the peeps started asking versions of the question I quoted above: what are the ranges for a 20"? Or an 18"? Somebody proposed the ratio of areas method and it caught on. It became available as an online calculation and is preserved here


in the Cymbalholic color scheme. :glasses8:

One of the problems is that it produces ranges which aren't simplified and these became gospel. So for a 20" if your cymbal is

1901 - 2066 Med Light
2066 - 2314 Medium

And don't get me started on the rookie statistician mistake of having the end of one category match the beginning of the next category. They should probably be more like

1900 - 2060 Med Light
2061 - 2315 Medium

You can verify that the online calculator is implemented with non overlapping ranges and does use 2061 for the lower bound of 20" Medium.

Nobody ever said that the calculations were to provide an answer to pairing up two ride cymbals of different diameters to get a contrasting or harmonious LSR.

The next exploratory improvement was a modification to the ratio of areas based on the observation that the ratio of areas method didn't give accurate results in terms of cymbals having a similar sound and feel when applied to different diameters. You can read up on allometry here


The main reason for using allometry with cymbals is that the thickness of a cymbal has to scale a bit with increasing diameter otherwise the cymbal would behave (and sound) too different. This introduces certain a bit of non linearity into the model. The estimates for the coefficients came from a series of Bos cymbals at different diameters so they were within one Brand. Again I didn't do the original research, but I've used the model. If you go back to that graph you will see that larger diameters get relatively heavier compared to the ratio of areas. That's the thicker metal at work for larger diameters. For smaller diameters the Allometric model is a little thinner than the corresponding ratio of areas.

If you compare this to the P15R method, smaller diameters are the same as the Allometric model but P15R gets "carried away" at larger diameters and gives increasingly heavier weights. How much more "carried away"? And is it closer to what we actually find on cymbals? Nobody really knows yet. This is one of the reasons I started collecting weights on cymbals with model ink. I've got many thousands of data points across many brands, production eras, etc. but I've been working on other things. There is a place reserved for this in Cymbal Wiki for when I get to it.
Ah, I've myself pondered what I now gather is allometry when mulling the ratio of people's heights and weights. They aren't directly proportional. I've wondered why and suspected that there must be a different formula operating, just didn't know what it is. Anyway, I see what you're saying about needing allometry for cymbals too.

Yeah, I've used the online cymbal weight calculator multiple times--but more as a guide than as gospel. My questions about it have long been: How does it know and are we talking rides or crashes or what? But my guess is that when a manufacturer labels a cymbal say "medium" it will probably fall into the medium range of the cymbal weight calculator--though my sense is that the calculator is geared to rides rather than crashes. To confirm my suspicion, I just punched in a medium crash and the calculator said it is light. No. It would be light for a ride, but it's medium for a crash.

Regarding the issue of validating a method, I think ultimately someone ought to concoct some sonic test. Using empirical data from cymbals only tells us the weights of the cymbals we can find (a poor sampling method, since presumably lighter cymbals crack more easily than heavier cymbals) but it doesn't tell us how the different weights sound, much less how different weights sound together. This though is what we want to know. I also doubt that sound is purely subjective. Very little in life is really subjective, and usually when people believe something is subjective, that only means that they're unaware of the objective bases for their opinions. Surely there's some sort of objective way to measure cymbal sounds, and thus calculate their sounds relative to one another. Mind, my guess is that an objective measurement won't lead to one right cymbal matching. I bet there are multiple matches that sound fine. However, I bet there are more matches that sound bad than sound good. Needed though is some way to assess cymbal sound objectively, and I have no idea what that way is.
 

Old Drummer

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How crashes are made different than Rides. Would someone like to tackle that.
Go from the beginning a Historical perspective. I'm a little exhausted atm. and chose to relax. View attachment 408691

Don't let that last sentence confuse you. as much as it could..
There are medium-thin "rides" that are near identical thickness at the cup as at the edge . Generally you see, it's Taper (build) that lends to lead lean either Ride or Crash
Thanks, but actually the last sentence doesn't follow from the first two. The issue of taper is said to distinguish crashes from rides, but we aren't told which one tapers more. Instead we're given an example of a medium-thin ride tapering a lot, though weight in relation to taper wasn't mentioned. Maybe earlier on these issues are clarified, but I can make no sense out of this last sentence and have no idea why it's even in the paragraph.
 

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