I've only listened to the roadside recording, but you might want to check that the limiter is off. I can definitely hear some agressive limiter action taking place there.
This is going to be a long post, but this should be everything you should need to know about setting the microphone gain, and the limiter and low cut settings.
I have an lsp2 which is fairly similar to your LS14 I think. Just a bit of general advice: regardless of recorder choice, the first thing you should do when recordings come out distorted is to lower the volume, so setting your mic gain to low might be of benefit. Iirc medium mic gain on Olympus recorders is meant for speech-level recordings with the internal mics, and I have a set of in-ear mics similar to what I think you have, and medium is probably going to be far too loud for those mics as they're considerably louder than the internals when using the same microphone gain setting. Admittedly I haven't tried setting to medium with those mics to actually see what I get, so I'm just going off of memory and some speculation here.
You can also probably set the Olympus to manual mode, which basically lets you fine tune the microphone gain between the low, medium and high settings, except you can do it in much finer steps. On my lsp2, for example, the manual mode gives me 30 steps of adjustment, from very low to very high. I generally set all my recorders to this mode if possible because I like having fine control of the gain. If something is a touch too loud and I fear it will be distorted or is coming close to being distorted, I can just lower the gain by 5 clicks or so and feel reasonably safe that the levels will be better, but not too low.
Hypothetically, the solution to avoid all distortion is to just use the lowest microphone gain available in manual mode. I used to do that, in fact, and while that is generally fine on Olympus recorders from my brief testing anyway, on other recorders you have to be careful, sometimes especially so.
If you record at a level that's too low, you will end up with an inaudible recording, especially if there are no loud sounds. That's not really a problem, as you can boost it as much as you want with audio editors. But when you do that, a big problem can surface. Along with the audio you recorded, you may also begin to hear hiss and circuitry noise (and quantization noise if you're recording at 16 bit, and other compression artifacts if recording in mp3). You don't hear these when recording at normal microphone gain settings because the sounds you're recording cover it up, but at lower microphone gain settings, all that quiet crud isn't being covered up anymore, and once that happens, there is no clean or magical procedure that can save it.
Fortunately with most Olympus recorders, or at least the few I've seen, they won't let you set your microphone gain low enough to put you in any real danger of that. You'll certainly be able to go low enough to avoid distortion in all but the loudest of situations, but there's a reasonable limit as to how low it can go. I haven't extensively checked to see whether really quiet recordings on my LSP2 sound as clean as they would at a more reasonable microphone gain. I might check this out in detail one day, as I really do want to know.
As for the limiter and low cut settings. First I'll explain what they are, and then where I stand on their use. The limiter setting helps to prevent distortion by lowering the microphone gain automatically when the sound is just about to be distorted, then raising it gradually when the loud sound has passed, until it is safe again to record at the gain you have set. The low cut setting removes low frequencies such as deep rumble of wind/traffic that will make subwoofers and big speakers/headphones go crazy.
I generally recommend keeping both settings off. Not because they aren't useful, but because they remove a lot of control you would otherwise have over the sound of your recordings. Using them is fine when you're in a pinch, or if you want to alleviate yourself the task of doing these things later in audio editing. But if you're like me and you like to edit and tweak using audio editors, then it's best to leave them off, since you can always add limiting to your heart's content in an audio editor, or cut the bass, but it is far more difficult to undo a limiter or a low cut after the fact.
If you do elect to use the limiter on the recorder, make sure your microphone gain is reasonable. If the microphone gain is too loud, yes the limiter will still avoid distortion but it'll be caught between a rock and a hard place. It'll constantly be lowering the microphone gain to avoid distortion, then trying to bring it back to where you set it. If you set the gain high, then the limiter may hardly ever make it all the way up before something pushes it back down. The gain will be changing in an erratic up-down up-down cycle, which leads to an unnatural sound. To avoid this unnatural sound, lower the gain until most things are not distorted, then the limiter only has to step in on the unusually loud bits.
So to sum up and to bring this back to the simple question you proposed instead of continuing to lengthen my already 5000 character dissertation: First, try lowering your microphone gain before doing anything else. Then, maybe try investigating the manual microphone gain setting if you want to fine tune the gain. Keeping the limiter and low cut turned off is a good idea, at least in my opinion, but if you think you'll need them, give them a try.
Few, I believe that's everything. Feel free to pose more questions or yell at me if I completely went over your head lol
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