[cechner]

actually, beta is less useful than that! I think it represents the median difference between the two distances, its not a tolerance (at least as far as I can recall after experimenting with tuning this value).

As with you, I have found that it still often gives ok results with slower frequencies, as long as the transition probabilities are still relatively in the same scale as each other for a particular observation pair. However it means that there's no point trying to 'tune' using the gamma and beta parameters