Lumma stability: Difference between revisions

Imagine a log-frequency ruler whose total length is the interval of equivalence of our periodic scale (e.g. 1200 cents).  Mark off each interval in the IM on this ruler.  Now we'll draw line segments on the ruler with colored pencil, using the marks as endpoints.  We'll connect all marks belonging to the same interval class with a single line, using a different color for each interval class.  Lumma stability is the portion of the ruler that has no pencil on it.  The impropriety factor is the portion that's more than singly covered -- where different colors overlap.  The idea being that when two interval classes overlap, listeners will not be able to distinguish them in all cases.  Lumma stability measures how easily distinguishable the non-overlapping classes will be.  Rothenberg stability is very similar, except it counts the number of overlaps, so it can't distinguish a gross overlap (in cents) from a small one, or detect when two interval classes are arbitrarily close to overlapping.

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