- Does this match how other people's boards behave?
- Am I right that there's no way to get a good, loud sound over my headphones without using a mixer?
- Does this indicate that the CP4 has a combination of high signal levels and a weak headphone amplifier that doesn't work very well?
- Does everybody keep their volume at 50% or less all the time?

Yes. They all work fairly similarly.
No.
No.
I seriously doubt it.

Okay, let's see if we can straighten this out for you. It could simply be the efficiency of the particular headphones... I'll try to find out the impedance of the headphone jack. But until then...

We are dealing with the MAIN Part. A "CFX Grand"
There are several settings that control just how loud the sound is and where you choose to turn it up or down DOES matter.

Press [EDIT]
Select 02:Part
Cursor up to the top screen:

The "GAIN" is the a setting that affects the output level of the piano in the MAIN Part.
If GAIN is turned up and distorts, it will not matter if you turn the level down at a later stage, you simply have a distorted sound you are hearing less load. Much like a guitar player overdriving the pre-amp stage of their amp creates distortion, then they use a later stage to increase or decrease the overall volume. Try not to distort at the GAIN setting. If you are getting distortion reduce the GAIN.

The "VOLUME" setting on the same screen is used to balance the Piano (Main) with the Layer and Split Parts when using multiple Parts.
This is very much like the fader on a mixer channel. You set it subjectively to balance how much piano to string, for example.

Finally, the analog VOLUME knob on the front panel should be set totally subjectively to your listening volume in headphones - it is the final stage - it determines the overall output from the instrument both for headphones and the main L/R outputs.

A mixer should be able to handle the CP4 turned all the way up... the next stage in the audio chain will need to be able to handle +4dB coming in. What you send the next stage be it headphones or speakers or a mixer channel, you want to send this next stage enough signal for it to do its job.

Gain staging is the process of ensuring that each step (called a "stage") in the chain puts out clean signal so that the next stage has enough signal to cleanly output to the following stage. If you introduce distortion, every step farther down the chain simply reproduces it. The key is, if there is distortion you must FIND at what step is it introduced?

You can determine this easily enough. Plug in your headphones, make the sound right for these.
You should be able to plenty of clean signal to your headphones between the GAIN and Volume. Make sure it does not distort. Set the analog volume knob to make the sound clean and loud in your headphones.

From this point, if you are connecting to a mixer, set the Gain control on the channel so the peak meter flashes on only at the very loudest peak signal. Then raise the channel fader to taste to make your speakers loud. If you need it louder in the room turn up the amplifier feeding your speaker system
... Not anything earlier in the chain.

Setting the front panel knob to any % is simply non-sense. Set it as necessary for the output you require whether that is halfway or fill on. This is not a "by eye" thing, this is a 'by ear' thing!

Final note: you can distort the internal gain structure of the instrument, be careful using EQ's to boost signal. If you are doing any extreme EQ'ing, make sure it is not overloading the internal mixer of the instrument. Adjust the GAIN lower if you are into extreme EQ at the Piano's pre-amp stage.

The Rhodes pre-amps do distort (on purpose) as did the real things. I've never done it but the Mic Pre-amp models on the acoustic piano models could probably overdrive the GAIN.

Different headphone impedance can cause huge differences in how loud they sound. Some are more efficient than others. Efficient has little to do with quality, it has to do with how loud they get on a given signal.

Thanks for the detailed answer. Everything you say makes sense.

I tried reducing the gain from the edit -> 02:part -> 01:play mode screen as you suggested. But however much I reduce the gain there, the corresponding increase needed in the part volume and/or the overall volume to get the sound back to a good listening level brings the distortion back. This is going directly from the CP4 to the headphones. Is there some other gain that I'm missing?

In case you or anyone else wants to go farther into this rabbit hole with me (and no worries if you don't), here are a few more details:

-The EQ is completely flat.
-I turned off all effects and reverb just to rule them out.
-I tried another pair of headphones with the same result.
-the distortion is present in other sounds (e.g. organ), but the acoustic pianos are the only ones where the distortion is present at a normal comfortable listening volume, due to the big difference between attack volume and the rest of the sound.
-I tried my headphones in my korg SV-1, and the piano soumds can go way louder than comfortable without any distortion.

Thanks again...

But however much I reduce the gain there, the corresponding increase needed in the part volume and/or the overall volume to get the sound back to a good listening level brings the distortion back. This is going directly from the CP4 to the headphones. Is there some other gain that I'm missing?

Although you do not sound confident in the process of gain staging, I suggest if this statement is true you take your CP4 Stage to an authorized service center for a thorough inspection. You are saying that however much you reduce the GAIN you are getting distortion. Well that's just not right. Please have it serviced.