A home owner from CHICAGO says:
Windows are double hung and tilt.
Pretty sure windows use the 5/8" tube diameter and the length of the cylinder is 31 5/8. (so 32"?)
Pretty sure pivot shoe is 1/2 inch.
Tip is black.
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Bob from SWISCO responded:

Thanks for writing in, and apologies for the wait. If the diameter of your spiral balance is 5/8", and the tube is about 31-1/2" long not including the tip, then the S600-32 should work for you. I can't say for sure if this is a black tip spiral balance from these photos; it looks like there's a clip of some sort obscuring the bottom tip. If you're uncertain, weigh the window sash. You can then match that exact weight with one of the weight ranges listed alongside each color tip option on the product page. For your pivot shoe, our 15-046 might be what you need; but it will be wisest to remove the pivot shoe from the window and obtain the exact width and thickness to confirm. Let me know what you think.

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