Ha! I remember writing this code. It is al based on the basicode standard, an attempt of a group of people to create a cross-platform basic. With it came a digital format to stream programs from/to tape, and I figured out how to read/write (actually, I created the reader while a friend of mine, also called Ton, created the initial version of the writer). Then I started modifying the timings to create turbo loaders/savers, utilities to stream program files to tape, and this full disk backup program. I remember also reverse engineering the ZX-Spectrum tape protocol, so ZX-Spectrum bitmaps pictures (which could be saved separately) could be loaded on TI. One key improvement was that I use the leader tone to calibrate the algorithm, so timing constants could be removed and the program would work when I increased the tape pitch (had a player with a speed wheel). I also built in a second crystal with a switch in my console to clock it to 3MHz. The VDP got confused by this speed at times, but the tape loader actually worked better. So you could set the computer to turbo, and crank up the speed of the tape...
Funny enough, this was like 30 years ago, and today I'm working on reverse engineering a variant of SPDIF. Same box of tricks, only kHz have become MHz...