I need a horn players help

[wonder]

I'm doing an arrangement and have a question about notation.

This passage (audio file linked below) ... what's the proper way to notate this? 3-4 grace notes before each note looks like overkill but is it correct? How do you tell the player to "run up/down to each note"?

Pictured below is what I have ... but it doesn't feel/look well thought out. Especially since later in the tune, the horns do the same thing but the passage is much quicker so the measure just looks like a mess!

Here is the Finale file in case ANYONE has time to show me how you'd notate this ... or how you'd like to see it notated as a horn player ...

HORN CLIPPING.musx

(143.23 KiB) Downloaded 46 times

Here's what it should sound like
https://www.dropbox.com/s/ppebqc17zd534 ... P.mp3?dl=0

[motet]

It's essentially fine. Common practice now is to use just two beams (16ths) for multiple grace notes, and a single slashed eighth note for a single grace note; and to slur the grace note(s) to the main note:

[wonder]

When I played the 16th's grace notes back in Finale ... it was sounding like it was too "timed" ... like it was playing back at a specific rhythmic value ... which I didn't/don't want. I just want them to be fast and sound like they're falling (or ripping/raising) to the desired note.
That's why I used 32nd's. I'll switch it to 16ths.

[N Grossingink]

The way I see it, this is basically jazz notation. I have experience (37 years) copying jazz charts and have rarely seen these kind of figures written out. The attached screenshot shows how it's usually done. Each player will play slightly different timing, which is what you want - creating a kind of greasy "slide". Incidentally, you could replace the dotted eighth/sixteenth with 2 eighths, specifying "swing eighths" in the tempo header. I'll attach the Finale file as well.

[wonder]

Ah yes. That makes sense to me and it looks much cleaner than a bunch of grace notes.