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According to https://en.wikipedia.org/wiki/Group_coded_recording the Commodore 1541 disk drive used a particularly efficient GCR encoding scheme to cram 170K onto the same 5.25" disks that in an Apple drive only stored 140K.

However, for the Amiga 3.5" disks, they reverted to MFM, a lower density encoding. Why abandon something that worked so well?

According to 'Amiga Disk Encoding Schemes MFM? GCR? Please explain!' by Betty Clay,

"[GCR] would appear to let a disk hold far more information than could be stored under most other methods. However, since GCR permits the use of as many as eight on-bits in a row, the drive cannot interpret them at full speed. It is necessary to write or read at only half the normal speed, in order to insure accuracy. When the writing speed is slowed to four microseconds per bit instead of the normal two, the density of the data is only half as much, cutting drastically into the storage advantage."

That would indeed seem to eliminate the advantage of GCR. but then why did that disadvantage not apply to its use for 5.25" disks? Is it a limitation of the rate at which the electronics can process the bits, or of the physics of the interaction of the drive head with the magnetic fields?

On a floppy disk, each 'bit' is a flux reversal — a magnetic event. If those bits are too close together, they'll leak into one another and data will be lost.

Disk controllers use a regular clock and either write a transition or write nothing at each clock tick.

There's also a lower limit on how far apart transitions can be. Disk rotation speed varies according to the whims of the motor, aerodynamic drag, etc, and drives contain automatic gain controls — if they think they aren't seeing data but should be, they turn up their own volume.

So bits need to be regular enough that the controller doesn't have to make too many guesses about rotation speed, and the drive doesn't turn up its gain so far that it's reading noise.

As a result, the bit patterns that drives actually write are a translation of the bytes to be stored into some other encoding, that guarantees bits aren't too far apart, and aren't too close together.

FM and the GCR schemes solve for too far apart differently, but use the same solution for ensuring bits can't be too close together: their data clock is picked so that each tick is far enough apart that two will never be too close. The GCR schemes then do a better job of making sure that they're not too far apart than does FM: FM encoding uses two output bits per input bit, but e.g. Apple's second GCR encoding uses only eight output bits for six inputs.

MFM is a later development than GCR and provides a different solution to the too-close-together problem: it guarantees that there are no sequences that lead to two bits being output consecutively. So, you can double the data clock without fear of magnetic collision. Like FM it also produces two output bits per input, but those two fit into the same physical space as one FM bit. Hence: double density.

MFM is an equally valid improvement for 5.25" drives as it is for any other, and is better than both company's GCRs; the reason that Apple and Commodore each came up with GCR schemes is that they were coming up with something better than FM, not rejecting MFM — both companies released drives before MFM controllers were available.

No answer yet told about the four different writing speeds the Commodore 8-Bit floppies used. That way, it could store

 Track Sectors/track Sum Sectors Storage in Bytes/track
 ----- ------------- ----------- ----------------------
 1-17 21 357 7820
 18-24 19 133 7170
 25-30 18 108 6300
 31-40(*) 17 85 6020
 ---
 683 (for a 35 track image)

while one-speed FM/MFM floppies have to use the smaller number of bytes per track on the outer tracks, too.

The only other system I know which did that was an Olivetti PC with FM floppies. Totally incompatible to anything. Other than the Commodore 8-Bit floppies, it changed the physical drive speed instead of the writing speed.

I think that the reason was simple: amiga used standard (well, nearly standard) double-density disk drives. This is untrue for 1541, that used non-standard disk drive (consisting of only mechanical parts) and quite sophisticated controller circuity, that includes analog parts (read and write amplifiers, disk motor driver).

The standard drive was optimized for standard bitrate -- so no even emulation of CLV by switching bit frequency is possible -- as 1541 did.

The MFM/GCR difference is actually less important part since again disk drive is not aware of the specific encoding. If you wish, you can use GCR encoding with amiga as well -- because amiga FDC does not do any MFM encoding or decoding. That is done by either CPU or blitter.

Aside from the technical aspects: when early floppy systems came out, disks were expensive and higher capacity was a selling point. By the time that 3½" disks were popular, the media was cheaper and it wasn't worth the effort of having complex controllers to save a few bytes.