Last week, my question about what was greater than augmented was wonderfully answered by people participating in this forum.
Also posted was fascinating information about a 53-note-per-octave organ.
When I told my student today about the double augmented interval, I also told him about the organ. He asked me more questions I couldn't answer (what did it look like? what were the mathematics involved in the differences in tones?). When he went home, after wondering as he walked, he proceeded to do lucrative research about it which yielded information and a photo. I have described the websites where these can be found in the TEACHERS forum.
I thank all of you who gave such thoughtful and thought-provoking replies to my initial question about intervals. I hope you like the photo and information about Bosanquet's 53-note-per-octave reed organ (1872).