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@jack_b, there is no right or wrong way for crosspicking. The tonal difference is marginal but it is there. Tony Rice (RIP) had an odd cross picking style but seemed to favor the down down up method. Molly Tuttle favors the alternating method. I’m not that good at it and often mix the two or get them mixed up. Currently I’m cleaner with the down down up method. But the alternating method is faster. It’s like anything else, as you get better at it, it will become automatic and you won’t even think about it.
Here is a lesson by Molly tuttle. It’s a bit long but she also goes over a song Tony teaches in the song vault. Tony mixes the two styles but Molly used alternating only.. https://youtu.be/sHT4HibXPeA