The Zoom H2 is capable of giving adequate recordings provided you use 24-bit linear PCM recording and don't use the automatic gain control. However, it's got all sorts of gimmicky panning and surround functions, so you should make sure you are using only the front two microphones in the "front 90 degree cardioid" configuration.

Where I suspect your problem arises is that the acoustic environment in which you are making these recordings is not up to the job. You talk about wanting to record lessons, implying that you may be in a teaching space, and these can be difficult places to get any sort of decent recordings free of reflections and other distractions that the ear ignores at the time but not when hearing a recording. You also don't say whether these recordings are vocal solos or whether you have a pianist or other form of accompaniment that you need to capture at the same time.

For the moment, I don't see any need to go and spend money on another recorder to get the result of a more expensive muddy sound. You should instead check that you are setting up and using the H2 to the best of its capabilities, and identify problems with the acoustic environment in which you are making these recordings. When you have got good recordings using the H2 you can start to consider whether the technical shortcomings of that particular model of recorder are limiting the quality of what you produce, and, if so, decide what your next purchase should be.

Exactly as Boswell states. The H2 is perfectly adequate for your task of lesson archival. Mic positioning is about 95% of any recording whether it is stand alone microphones or an all in one unit like the Zoom/Korg/. Make sure the microphones are pointed at your throat area erring toward your upper chest and not your mouth. Make sure as Boswell states that you are actually in the 90 degree pattern and not pointing it at the ceiling or your knee caps. Another common error with these units is to set them laying on a table or shelf (including the mic portions) which greatly detract from the quality of the recording. When I have used the H4n in down and dirty situations for my wife, I try to place the unit so the mics are as free from the support surface as possible without it falling off. There are miniature tripods which do a better job of elevating the unit off of the table/shelf/music stand.

Thanks so much for the detailed replies, and especially for helping out a beginner! I have a degree in computer science and understand what it's like reading questions from someone outside the field, so thank you very much for your help.

So far in all cases I'm recording with the device standing vertically and facing me, in front 90º mode (had done some recording in 4ch surround but ignoring the "rear" file; is that equivalent or different). Rec level is at 90 of 127 and mic gain was at High (choices were L/M/H). I'm not sure why I settled on high mic gain. When the device was just ~3 feet away from me, like in a previous lesson, sometimes these settings were causing distortion when I got really loud. Perhaps you can help me come up with configurations for my common use cases:

1) Lesson. I've been keeping the recorder about at waist height, sitting vertically on a table. I'm tall and it's going to be very tough to get this to throat or even chest level but I can try. Is this a big deal? Perhaps a tripod that lets me angle the device up is helpful. How far away is ideal for opera singing?

2) Chamber performance. Typically trying to record me plus piano/harpsichord. I've been setting the device pretty far away, like 15-20 feet. It sounds better closer but I get worried about picking up too much of one or the other, and there typically isn't setup time to verify the setup. Is there an ideal distance?

3) Orchestra performance. I recorded myself singing as soloist with a full orchestra and ~80-voice chorus, with the recorder on the floor of the stage, basically in front of me and to the left (since soloists were standing stage right but I wanted the recorder in the center). How would you change this setup? I realize it's ridiculous to ask a little tiny device to pick up a whole stage...

Again, in all these cases, the goal is first for me to hear my voice (since we don't hear ourselves accurately in our heads), second to hear how the whole group fits together, and third, ideally, to have some recordings that I can send to conductors, put on my web site, etc.

So, please rip into my setup and tell me how to make it awesome!

You need to get a stand for the H2. Waist height is completely unacceptable. Period. You should be at a distance of six to ten feet away and the mic setting likely should be on medium or less. Mic position is THE MOST IMPORTANT aspect of your setup. Shooting yourself in the ass starting out is not the way to a good recording. The H2 came with an adapter for a microphone clip. This can be utilized with any standard mic stand to get your positioning. The H4 and H6 have adjustable gain on the microphones making them a better option if the H2 really only has three settings.