Rothenberg stability

The portion of the intervals which are unique to one interval class, out of all possible intervals.

For example the major scale in 12-tET has a stability of 20/21, because there are 2 occurrences of the 600 cents tritone, one for interval class 3 and one for 4. -- (do SHOW INTERVALS or SHOW/TOTAL INTERVALS in Scala to see this) -- There are 6*7 intervals so the stability is (42-2)/42.

[from Manuel Op de Coul, Scala file "tips.par"; view in Scala with command "SHOW DATA"]

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...Stability measures how easy it is for a listener to determine which interval class an interval belongs to. Efficiency measures how difficult it is for her to determine what scale position a pitch represents -- IOW, how long it takes the listener with "perfect pitch" to figure out what key the average melody is in.

[from Carl Lumma, Tuning List posting, Sun Sep 10, 2000 11:23am]

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See also:

Lumma stability
Rothenberg efficiency
Rothenberg redundancy
Lumma impropriety