I think that we should look really carefully at what Dick has said here, because, as he says, all of these explanations of modes relies on tempered scales, and modes, in the sense of folk music and early music, really have nothing to do with the tempered scale--

The tempered scale is an artificial device that was introduced into Western Classical Music relatively recently, and really evolved from modes--the modal scale had irregular intervals--for instance, the interval between D and A was a perfect fifth, but the interval between A and E wasn't, and because the scale was not chromatic, it wasn't possible to play, say, an Ionian mode, starting on any other step of the scale than the C--

When Mousethief talks about sharps and flats in relation to modes, technically, he makes a mistake, because the modal scale had no sharps and flats--also, the piano has always been a tempered instrument, at first it used "mean temperament", so you could play the same scales on both C and D, though mean temperament started going out of tune after about three flats--

Technically speaking, it was never possible to play actual modes on the piano, because the modal system used scale pitches that were not on a piano, and the major/minor scales(and a tuning system that allowed them) had replaced modes in classical music by that time anyway--

I hate the discussions about modes and tempering, because most of the questions that come up have answers that require a lot better understanding of the technicalities of music than most people (even classical trained musicians) have, and, even more important, it is not very useful for most people (including musicians) to understand those answers anyway--

If the truth were told, I believe that PeterT's admirable effort still doesn't address the basic issue that he was trying to deal with, which had to do with trying to figure out what certain guitar books meant when they talked about modes--

I think a lot of confusion could be eliminated if modern guitar and jazz teachers(and the authors of instruction books) didn't use the term "mode"which is technically inaccurate) and instead said "Dorian Scale"(etc) which accurately describes both the scale and fingering positions that their students can use to improvise over dominant chord progressions--