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Encyclopedia of Microtonal Music Theory

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Rothenberg stability

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

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

For example, the major scale in 12-ET 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. -- (in Scala, do SHOW INTERVALS or SHOW/TOTAL INTERVALS to see this) -- There are 6*7 intervals so the stability is (42-2)/42.

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[Carl Lumma, Yahoo tuning, message 12597 (Sun Sep 10, 2000 11:23am)]

...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 -- in other words, how long it takes the listener with "perfect pitch" to figure out what key the average melody is in.

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