I have now deleted all of the music files from the phone, converted all of the music files on my computer to MP3 format and then transferred them to the HTC One.
Same problem. Now HTC tech support tells me that I have to flush the cache. We did that. I will try again in the morning. The phone works fine in a stable environment such as on my desk. The problem only occurs when I am outside in a varying electronic environment. I still think there is an EMI problem but so far HTC does not want to go down that path.