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Im glad I read this as I was very familiar with the sound but didnt know what it was called. Just out of curiosity why is this sound called the singing sword?
To my ears it really really sounds like a feedback look, like they got to sound emitting objects real close together that also recorded. Like what you can do with two phones on a call with each other. What they used exactly? I don't know, but there's a whole expo (shame I can't find a link) of feedback sound creators. Look at what they did and you might find a cheap solution to your problem.