Matching this window balance

A home owner from Ridgefield Park NJ says:
This is for the left side of the window. The balance popped out and I guess the spring sprung up. Will you be able to help me match what I need? Thank you
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A home owner from Ridgefield Park NJ says:
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Casey from SWISCO responded:

Hello,

Your channel balances resembles the S770, which attaches to the top of the window with a screw and anchors to the pivot shoe with a terminal clip at the end of the pulley cord. 

Close up view of the Series 770 balance top.
Close up view of the Series 770 balance top.

Close up view of the Series 770 balance bottom.
Close up view of the Series 770 balance bottom.

If the pivot shoe is the part that broke, I would recommend removing yours from the window to compare to the 15-129 shown below. Take a look and thanks for posting! 

Detail of 15-129
Detail of 15-129

A home owner from Ridgefield Park NJ says:
Hello
The length of my channel balance is 19" and the width is 1/2". The best I could read on the back looks like 19B BSI Does your S770 still resemble mine? And do you think the Pivot Shoe 15-129 would work? It looks a little bit too big. Thank you for helping me
A home owner from Ridgefield Park NJ says:
Could it possibly be called a Block and Tackle Balance??
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Casey from SWISCO responded:

We do offer a 19B strength option for the S770-19 channel balance, which is also referred to as a block and tackle balance in the industry. The 15-129 is often used with the S770 but we would need to see your pivot shoe uninstalled, along with written-out dimensions, to confirm if a closer match is available. 

How to replace a tilt-window channel balance.
How to replace a tilt-window channel balance.
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How to Remove a Pivot Shoe (Cutout Method)
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How to remove window pivot shoes
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Anatomy of a tilt window
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