I think I need a hardware geek. Here's a diagram of my setup:
 

 
Sonar X3, which is sending the MIDI data to the harmonizer via the AKAI's USB. The harmonizer is sending the result BACK to Sonar via the line in/out and the AKAI USB. I can verify by speaking into the mic. (There's a mic volume and a separate harmonizer volume control.) While Sonar can record the mic's feed, it can't read the harmonies interpreted by its own MIDI data.
 
Before, I used two computers; one strictly for MIDI output. So I'm thinking that Sonar is "eating its own tail" by sending both the MIDI and trying to receive the harmonies back through the same interface.
 
Keep in mind that I've got to be able to hear the MIDI music while singing through the harmonizer. But then, you guys know that.

OK. Not much information to go on, but I'll try.

What is the harmoniser?

Why do you have the controller keyboard (if that's what it is) connected to both the PC via USB and to the EIE's MIDI in? Does the controller receive/send MIDI over that USB cable or audio?

The synth. Is it meant to be passing MIDI from the EIE through to the harmoniser? If so is it correctly configured to do this? Usually MIDI through is sent from a MIDI Thru connection, not MIDI out, though there are exceptions.

Sonar can handle audio and MIDI at the same time with no problems at all.

I suspect you might have a routing problem with the way the hardware is connected and possibly within Sonar as well but without more information I can't tell.

Ditto, I noticed the midi out from the Synth too. Normally that would have to be a thru jack or nothing will happen, Unless it's a out jack that can be told to be a thru jack. And your not showing the audio connection from the synth module if there is one anyway so what does it do? 
 Why not use a soft synth in Sonar to play the music? 
Nice diagram by the way. 

It's after midnight, so I'll not go into a lot of detail.
 
All the synth module does is send MIDI data to the harmonizer. It doesn't send "music." That data is then interpreted by the harmonizer as vocal parts. So when you sing into the mic, it makes your voice sound like a 4-part singing group. The synth is getting its info from Sonar. (The keyboard you see isn't involved in any of this.) Now if I plug the keyboard into the harmonizer and play manual chords, then it works fine. But for complicated harmonies that are jumping all over the place, it isn't practical. The hands-off method, letting Sonar do all the heavy lifting, is preferred.
 
The MIDI OUT is actually MIDI THRU. Sorry. I pulled out a lot hair figuring that one out years ago.
 
 

OK - now I am a bit confused.
 
If the synth module is not sending any audio output, only midi, what midi would it be sending, other than the same midi that was already coming from the audio interface.
 
And if the above is correct, then what purpose does the synth module serve at all?  You indicated that the note information (midi data) is coming from Sonar, so why not just pass that straight to the Harmonizer?
 
I don't know if any of the above is connected to the problem - it's just an observation that you have a useless device in the data chain - that being the synth module.
 
The only way it would seem relevant is if it is generating additional notes than what it is receiving from the data it is getting from Sonar.  If so, please confirm that.
 
As far as not getting any of the chord notes to be present in the Harmonizer, you need to see where the midi data is failing to be passed to each device in the data chain.  It seems logical that one or more of the following would be occurring
 
1.  The data is not being sent out from Sonar to the synth module
2.  The synth module is not passing the data THROUGH to the Harmonizer
3.  The Harmonizer is failing to react to the data it is seeing.
 
If 1, then make sure you have the MIDI OUT box checked for the soft synth that is involved.  Also, make sure your synth module (external one) is 'seen' by Sonar by making sure it is checked as a MIDI Output Device in Sonar Preferences.
 
If it is number 2 above, then check the settings on the external synth module to make sure it is in fact passing the midi data to its midi Through port.  (I still do not see why this external synth module is present in your data chain, from what I have read thus far).
 
If number 3 is occurring, perhaps the Harmonizer is looking for data on a particular midi channel, and the midi data it is receiving is on a different midi channel.
 
Bob Bone
 

Thanks for the info, Bob. I got to thinking the same thing about the synth module's redundancy. Getting used to this new way of recording is unfamiliar territory. (I'm 62 and prefer the old TEAC 8-track reel-to-reel brutes.) Still, I'm fairly tech savvy.
 
I will check your suggestions. If I can get rid of that synth module, I'll gladly do so. I'll take it out of the chain, route the AKAI interface MIDI out to the harmonizer, and see what happens.  The harmonizer is set to receive on MIDI channel 1. Now, I just have to figure out how to tell Sonar where to put the harmonizer audio output flow. But my wife is glaring at me and I have to take my daughter to school.

I do this with a TC Helicon VoiceWorks+.   In my case, the MIDI goes to the TC from a MIDI interface connected to my PC and to external synths.  Lately I have been taking digital out of the TC but I have used line outs before.
 
Most of the issues I have had were with the internal settings of the TC rather than with the physical setup and these may not apply to the unit you have, unless it is specifically a TC Helicon.  Using the Digital Out from the TC into the VS-700 I/O also took a bit of experimenting, but that doesn't apply to your diagram.
 
Let me know if I can help.
 
 

Right. Try this.

Connect the EIE MIDI out to the harmoniser MIDI in.

Assuming you have installed the driver for the EIE if you open Sonar's preferences and look under the MIDI section you should see the EIEs MIDI in and out ports listed. Make sure they are ticked. If you need to use the controller keyboard at all then install its drivers and again tick the relevant boxes. Unless it is very, very unusual the controller almost certainly only needs to be connected by USB, not a MIDI cable as well.

Under preferences/project there are other MIDI settings to do with sending MIDI clock. If the harmoniser needs to receive clock switch those preferences on.

Open a new project and insert a MIDI track. In the track inspector view (left side of the screen by default) there are pull-down menus for MIDI input and output. Set the output to the EIE MIDI and the input to the keyboard if you need to use it to record MIDI parts. You can write the MIDI in the piano roll, step sequencer and notation views as well. Set that MIDI channel to the same channel as the harmoniser.

Try a few notes an the keyboard if connected. You should see the meter on the MIDI track respond, the dreen bar showing velocity and a red light above which blinks when the channel receives MIDI. If not try arming the track for record and try a few more notes.

Record or edit in some MIDI, play it back and see what happens. With any luck that will work, unless I've forgotten something.

On the audio side of things you need to insert an audio track and point its inputs at whichever EIE sockets the harmoniser is plugged in to, and the teack should output to the master bus. You may need to go into the preferences audio settings to enable the EIE inputs and outputs.

The "getting started" section in Sonar help is a good way to work through the basics of getting Sonar up and running, though it is a little sparse regarding the MIDI hardware side of things.

When trouble shooting it is wise to work your way through the signal chain, be it MIDI or Audio and eliminate or swap components. 
I can see that the Synth module would be there for when you wanted it to be a sound source. 
But daisy chaining MIDI devises has always had it's pitfalls. Added latency being one of them.
 I built a little switch box a million years ago that allows me to swap between my Korg 05/RW and my Roland TR505. Radio shack project box and 3 MIDI jacks and a STDP toggle. $ 12.Not sure if they sell midi ( DIN) jacks anymore. 

@konradh: Yepper. It's a TC-Helicon Voice Prism Plus (with the extra card). A month after I bought it ($1,000) it became a "discontinued" item. But it's pretty reliable.
 
I have the Komplete 9 Ultimate. And while it has a bunch of classic pianos, my Roland MGS-64's piano sound is superior. I'll figure out a way to keep it in thar.