To run TTS-1 at high sample rates the TTS-1 "Light Load Mode" must be enabled.
On the TTS-1 UI click the SYSTEM button,
On the TTS-1 SYSTEM SETTINGS dialog click the OPTION button,
On the TTS-1 OPTIONS dialog click the Options tab and check the "Light Load Mode"
 
Note: TTS-1 does not support 88.2 but I believe it will run at 96 Light Load Mode enabled.

or use a different synth...

BOIBHAVA
Yes Mudgel, its when I am playing a midi project that I then assign to Cakewalk-TTS1 for example.
I just did some more experimenting and found that it is only the Direct X soft synth plug ins that sound
distorted, the VST ones are ok. So I wonder how to fix that?

 
What happens when you assign a different synth (to replace the TTS-1)?
It should sound fine.
If audio playback is clean... synth playback should also be clean.
For the audio interface, it's all "audio"... 

Thanks SCook. Clicking on the light load setting seems to have worked. I was also having the same problem with another Direct X one which was the Roland Groove Synth, so I will look for something similar in that one.
By the way, I found this link where Scott Garigus makes the same suggestion as you have but at the end says he has not tested whether it plays at the same quality. To my ears it does, but maybe he has better ones..

There is not an equivalent option to "Light Load Mode" for GrooveSynth. While the documentation claims it supports 96KHz, there have been other unresolved reports of failure at that sample rate.
 
The TTS-1 "Light Load Mode" setting is per instance, per session. Each time a project is opened each instance of TTS-1 must have the "Light Load Mode" set.

Yes I noticed that I have to reset it everytime I open a project. That should be fixed in an upgrade
I hope. As for the Groove Synth, oh well, I'll just use another one I guess.