Rowan, the first bit about your experience on the melodeon is spot-on. But the bit about Bach and modes is completely out to lunch.

Firstly, it's an urban legend that Bach ever used equal temperament. Nobody started using it in a significant way until decades after he was dead. The temperament he probably used most of the time was Werckmeister 3, an adaptation of meantone which makes all keys acceptable but not all the same. His collection is called the WELL Tempered Keyboard, not the EQUAL Tempered Keyboard. (The fact that he writes very different kinds of music in the pieces in the more extreme keys, like the E flat minor ones from Book 2, should be a rather strong hint that he did *not* expect all keys to sound the same).

Secondly, the modal systems of Western music are independent of its tuning systems. You only need an accuracy of a semitone to say what mode a tune is in. Tuning systems are far more fine-grained than that - the differences you're talking about are about a sixth of a tone at most. A Dorian tune played in equal temperament, meantone, Pythagorean, or just intonation will sound Dorian in all of them. It won't be the same sound but it will be the same mode.

These different tuning systems can all be heard on record in different types of music. Most performers of mediaeval music (like Perotin or Machaut) use the Pythagorean system, in which all fourths and fifths are pure. It gives a hard, bright sound in which thirds are never lingered on because they always sound dissonant. People playing or singing Renaissance and Baroque music (like Byrd, Monteverdi or Purcell) use systems closer to just intonation or meantone, which makes the thirds pure and gives a softer and more emotional effect. Equal temperament is in between these extremes and it can be hard to tell it apart from either at times - modern minimalist music will often be in the Dorian mode in equal temperament.

In Middle Eastern music, you do sometimes get two modes that only have microtonal differences between their sets of pitches. But a listener has more than the pitch set to go on - the two modes will use different repertoires of melodic cadences and different large-scale melodic structures. Even in this music with all its shades of microtonality, a listener isn't expected to tell two modes apart by employing any greater pitch discrimination than you need when listening to somebody playing Irish tunes on an accordion.