When you said "old rotary dial phone", I assumed it was an old Western Electric 500 model or older, which had an electromagnetic clapper and bell ringer. The OBi devices may have trouble powering those ringers. I now hear that you have a newer phone with an electronic ringer, so my comment doesn't apply.
Thanks for posting the sound files. I suppose it's a corollary to the old saying, "a picture speaks a thousand words"; in this case, the sound files show that the rings aren't "clipped", meaning that there is no abnormal loss of ringing power causing a muffled or defective-sounding ring. What you're hearing is a different ring pattern, commonly used to help the customer tell the difference between an incoming call to one of their phone numbers vs. a second, different number. The phone companies called this feature "Distinctive ring", back in the day when you could have one physical phone line that would receive calls from two different numbers.
On the OBi, this is controlled by Ring profiles. Each ring profile, A or B, has a set of definitions for the various frequencies and duration used by the different types of ring sounds. You've probably either changed the pattern yourself, or you're using ring profile B instead of A.
The ring profile is specified in the Voice Service section, separately for each SPx, as "X_RingProfile".
The settings for each ring profile are under Ring Settings.
Go to the OBiTALK portal page for your device, get into Expert configuration mode, and then edit the settings as you wish. Note that you need to un-check both check-boxes to the right of a setting before it will allow you to change the setting.