Lisa Hirsch's "help wanted" query for help with listening to microtonal music has been scratching the insides of my intervals for a few days. In a comment on her post, I suggested that she listen to Easely Blackwood's microtonal keyboard music, which, being played by the composer on a dedicated microtonal keyboard, gives a reliable and consistent picture of what is possible to do when you divide an octave into more than 12 parts.
I believe that a person doesn't need to "learn" to listen to microtonal music, but it is a good idea to understand that all microtonal music is not equal (though, of course, some is). It has been my experience that playing microtonal music on an instrument other than a keyboard instrument can be a hit or miss proposition. Much of the time you can get away with "almost" in microtonal music without anyone in the audience really knowing (unless someone with ears like Blackwood is in the audience, with a score).
The problem that I find with the world of microtonal music is that it really only makes sense when it is played on an instrument built to allow the intervals to have points of reference. Two like wind instruments instructed to play microtones (whether they are exact or not) can cause a pretty "loud" difference tones, generating all kinds of interesting sounds not otherwise found in nature (one desirable product of microtonal writing), but it is difficult to duplicate exactly the same noise or the same microtonal difference tone pitch that a composer wants to be sounded every time you play a particular piece.
Microtonal double stops on a stringed instrument (or even single microtones themselves) do not resonate well on acoustic string instruments. It has everything to do with the way stringed instruments are built. I have found that the effect of playing microtones on an acoustic string instrument is the opposite of the wind effect: the product is a kind of overtoneless dullness, unless it happens to be two fiddles playing in the high register (but it is the non-microtonal intervals that generate the most sympathetic sound).
When string players playing tonal music play out of tune in the normal ranges of the instruments, we recognize out-of-tune pitches as being out of tune partially because of their un-resonant color. An out of tune pitch simply does not excite the harmonic series that stringed instrument (tuned in the standard manner) is built to excite. (I haven't tried intervals smaller than a half step on an electric violin, or on a violin with an amplifier. Once you add electronics, there are certainly other elements at play.)
Microtonal music systems have nothing to do with the constant adjustments that string players have to make when playing tonal music: we always have to adjust our thirds, our leading tones, and our perfect intervals, and then, when we play with other instruments with fixed tempered tuning (like the piano), we need to adjust to those instruments. Just intonation can be discussed mathematically, and people can claim to use systems of just and mean tone tuning, but it is the ear and the color of the intervals at play (and not mathematical adjustments by the players) that allow us to have some point of reference. You can mess with an electronic tuner in rehearsal, but in a performance you are on your own (unless the use of an electronic tuner is written into the piece)!
All wind instruments are built to a particular schema. Instruments without keys, like recorders, can have their holes voiced to favor a particular tuning. Boehm used one to make the modern flute, and I imagine he used one to make the Boehm system clarinet. Boehm's schema has been improved upon by several 21st-century flute makers, and new-flute players like Robert Dick have figured out foolproof fingerings to play pitches that lie in between Boehm's 19th-century sense of the half step. Loads of 20th- and 21st-century composers have written flute music using these "new" pitches and non-pitches (extended techniques involving percussive effects), and they have become staples of a modern flute player's paintbox.
Instruments from cultures that use different scale systems from the diatonic scale systems used in the west, are probably built to resonate optimally with their specific scale systems. Unfortunately I haven't had the opportunity to hear an un-amplified western string instrument play non-western music (It seems that everybody uses microphones to perform these days, and everyone must use a microphone to record).
It is important to remember that all non-western scale systems are not alike. I remember trying to wrap my head around a set of 10 Karnatic Etudes by Bozza (for the flute) that used Indian scales (the divisions of the octave were indicated in a set of scales in the beginning of the book). I could not, for the life of me, figure out how I was supposed to "hear" them. Gee, when I listen to this woman teaching a group of kids to sing a Carnatic minor scale, it just sounds like a minor scale to me, with a bit of vocal inflection and strikingly non-western sound production. This first lesson shows how difficult it is for the kids this woman is teaching to match her pitches--or even come close.