The upper left picture on Page 43 shows Velocity and Note Ranges near the bottom of the screen and side by side.   These are at the Part level.  So if you wanted to split based on key range you'd use the note side and assign a range of notes for the Part to respond to.   If you want to have a split based on velocity you would give velocity a range of values.  1 being the lowest velocity "softest touch" and 127 being the maximum (banging keys).

And split would imply a unique range.  So one Part would have some range and another Part would have a different non-overlapping range.  Each part would only sound if notes are played in the limited velocity range.

On page 40 of my owner's manual, it talks about split by velocity range, but it is not described any further in the manual.

The owner doc typically tells you what CAN BE done on the instrument but not necessarily how to do it.

But where are the instructions to SPLIT BY VELOCITY RANGE?

Those would be in the Reference Manual. And you will find them in several places.

1. page 32 - 'Velocity - Note view' - this page has a graphic that shows an overview of the performance and its parts. This particular view shows, for each part, BOTH the note range settings and the velocity range settings. You can change those settings using that view.

2. page 66 - 'Edit - Partn - Common' screen (n is the part number) - this page has a graphic that shows the 'Velocity Limit' and 'Note Limit' parameters on the bottom of the screen. You can change those settings here also.

3. page 107 - 'Edit - Partn - Elementp' screen (n is the part number, p is the element number) - this page has a graphic that shows the two sets of limit parameters for 'Velocity' and 'Note' that are identical to the ones on the 'part common' edit screen EXCEPT these apply to ONLY this one element.

After selecting a Performance, the PARTS touch screen is not intuitive enough, at least for me, to show me how to do this. It's easy to split by note range, this is pretty obvious.

Hopefully those screens mentioned above will be 'intuitive enough'. If not just post any other questions.

CAVEAT! - what may not be intuitive is that the part settings restrict both the what is seen by the elements of the part.

1. part note limit - C-2 to C3 but element note limit setting is C#3 to G8 - nothing will sound if you play notes C3 or below because the element will never see the note.

2. part velocity limit 1-64 but element velocity limit is 65 - 127 - nothing will sound if you play with a velocity of 1-64 because those velocities are outside the element range.

3. the element settings need to be WITHIN the boudaries of the part settings for the elements to have any effect. This is one area where is it can be less problematic if you define the part level settings before the element level settings.

But anytime you change one of these parameters it is good to get into the habit of double-checking all of the related parameters to make sure all of the element range settings are still within the part range settings.

If you actually try the simple tests above it will help it sink in.

EXTRA CREDIT - there is actually one exception to the above which I posted about in this thread

https://yamahasynth.com/community/montage-series-synthesizers/m8x-portamento-groups-allow-multiple-parts-to-work-together-but-element-note-boundaries-are-not-respected-in-a-part/#post-123929

In that thread I reported that

Portamento does NOT respect the element note range boundaries within a part

But I have never received an answer from Support as to whether that is a bug or 'working as designed'.