Chromatic? That's an atypical siren. Most would be more like a frequency sweep and not have chromatic notes only (such as C, C#, D, D#, etc ...)

If you want a sweep then a pitch LFO is the typical way to do this. A sweep would sound more like portamento than individual chromatic notes.

If you really did need chromatic notes then an ARP would probably be the easiest way to go. Although you could approximate chromatic notes and use user step curves targeting pitch (motion sequence). Or just use standard curves and have a really loose approximation of "chromatic" notes. The motion sequence could be tied to superknob automation or not (use Part-level MS Lanes instead). I wouldn't use superknob automation in order to free up superknob for something else.

Yes, a sweep! How may I set this up?

Pitch LFO with slow speed and wide range.

I loaded "Early Lead" then edited the Part. Under Common - "Mod / Control" -> "Part LFO". Set LFO wave to Trapezoid (although you can set to another waveform or create your own). Set speed to 30 and destination=Pitch with depth of 112. Bigger goes wider, smaller is less wide of pitch variation.

Each element can get a different depth - so in this example you can set element 1 to 124 and element 2-8 to the default of 128 which will detune one of the elements and give its own effect. Sounds like multiple sirens going off.

You can "play" with these values to achieve the end result you're after.

MODX Reference Manual

User LFO:- Page 99.

Or...

Control Assign User Curve:- Page 103. Then as Jason suggests, automate it with a Motion Sequence Lane. You can make multiple User Curves such that you can string them all together in a Motion Sequence, each new curve starting where the previous curve left off. There are some Presets that already do this (known as "Risers") - but you'll have to go look for them yourself.

Example
User Curve #/ Function
1/Raise Pitch by +1 through +7 semitones
2/Raise Pitch by +8 through +14 semitones
3/Raise Pitch by +15 through + 22 semitones
etc

You can use PEGs for continuous Risers (non-chromatic, non-stepped).

BASIC
https://youtu.be/tg7ixg-7xNQ

ADVANCED
https://youtu.be/7i6vB67Baz8

Note how Dom uses LFO to "chop up" the continuous Rise to make it sound Chromatic or Stepped.

Have a look at Performance named : "FM MotionSeq Ld DA"

Sorry, I don't know where this came from. Probably Montage Extended, but could also be from SoundMondo.

It uses the SuperKnob to do a siren-like pitch change, you'll just need to speed up the Animation to get it more like a siren.

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Another, perhaps easier way to make warning sirens of all sorts, like in factories and shopping centres etc:

Add Effect named: Pitch Change to any long sounding part, particularly good with saw wave sounds, and then set the Feedback to max (63) and this will loop. Set wetness to full, so you don't hear the original sound.

You can make complex evolving ones this way, by setting one side of the pitch changer to a slightly different amount of pitch change to the other.

Antony, According to the Basic YouTube link above, I've created the falling siren all right, but the original pitch is retained and still sounding. It is not coming from another part; happens when I solo this part. How can I eliminate it?

This is a matter of more than one element sounding - you need to apply the same envelope to both elements (Elem1 and Elem2).

You initially asked about ascending (pitch rising) and now you're implementing descending (pitch falling).

And then I went the usual "siren" route and gave you oscillating falling+rising.

Jason, that fixed it--thank you so much!

Thanks, everybody--your expertise makes ALL THE DIFFERENCE to me!