RE Tunings and Scales are different animals from digest 6151

I haven't followed this discussion until today, so I don't know if this suggestion has been made already or not, so I'll make it here. It seems to me that a scale should be defined as a Rothenberg Equivalence Class, not just a list of 2nds in ascending or descending order, whether or not in "normal" order.

For example, different tunings of the familiar diatonic scale fall into different Equivalence Classes when all their intervals are considered. Some are Strictly Proper, others Proper, still others Improper to various extents, though we usually think of them as simply retunings of one diatonic scale. The cyclic version of the diatonic scale is Strictly Proper in 19 and 31 tet, Proper in 12, and Improper in 17, 22 and other positive systems as well as in Pythagorean tuning. Hence the difference matrix or the rank-order matrix should be used to define the scale.

It is probably useful to consider the variety of the diatonic scale that is generated by a cycle of fifths or fourths as a different scale from the one that is the union of 3 triads on the 1st, 4th and 5th degrees even though they are merged or confused in meantone and 12-tet tuning. This point is clear in 53-tet, where both forms of the diatonic scale occur. The pseudo-JI version 9 8 5 9 8 9 5 is Strictly Proper, the "Pythagorean" version, Improper.

Of course, there is a listener-dependent 'delta' as Rothenberg states, so some tunings might be considered equivalent by some listeners and not by others depending upon their ear, training, or musical context. I think this point is worth raising as often Rothenberg's descriptors are thought of as absolute, though in practice, they may depend on the listener's perception, pitch discrimination and/or memory.

--John