Are "tile pixels" the same size as "sprite pixels", and are they both square (ignoring the rule that multicolor sprites can only be colored in groups of two pixels)?
By "square" I mean that the pixels have a 1:1 aspect ratio.
If the answer depends on the display, then I am asking about the ubiquitous 1702 monitor.
EDIT: I am asking so that I can configure the graphics editor on my modern laptop for creating Commodore 64 artwork. In my case, I am using an NTSC system.
The pixels are not exactly square, the actual aspect ratio depends on the TV system. For PAL-B, the pixel aspect ratio is 0.937:1, the pixels are a bit higher than they are wide. For NTSC, the ratio is 0.75:1. At this ratio it can be clearly seen that the cursor block is definitely higher than wide.
In standard bitmap mode the C64 outputs 320 pixels in 40µs.
The visible portion of a line is ~52µs; in 60Hz regions ~240 lines are considered 'visible', but in PAL regions it's ~288 lines.
So if there were no borders, there'd be around 52/40*320 = 416 pixels across the visible portion of a line.
Given that each line is 4/3rds as wide as a hypothetical vertical scan, you can compute that 416 * 3/4 = 312, implying that so you would have square pixels in a hypothetical 312 line display.
A PAL screen has only 288 lines, so it's like taking that 312 line display and stretching out only 288 lines of it. Therefore the pixels will be very slightly taller than wide. Around 288/312 = ~92% as wide as tall.
An NTSC screen has only 240, so its pixels would be more like 240/312 = ~77% as wide as tall.
Heavy caveats apply: different screens are calibrated differently, to numbers usually near to those above but subject to being only as close as the engineer turning the dials could get.
A further nuance is that total line time may be 64µs or 65µs (depending on revision) in 60Hz world, but will be 63µs in 50Hz world. Your screen will have a PLL of some sort to bring itself into synchronisation with the horizontal sync period, but often that'll result in the line contents being slightly stretched or slightly compressed, further throwing off the arithmetic.
You therefore might as well say that PAL pixels are square, as 92% is within the margin of error given the effective approximations of all the other numbers. But NTSC pixels shouldn't be close.
As for the first part of your question, yes, for sprites as well as characters or bitmap images the same principle holds: either you can be in single colour/hi-res mode (320x200, 1 bit of foreground colour info per logical pixel) or multi colour mode (160x200, 2 bits of colour info per logical pixel).
In practice, for PAL, a single colour pixel that is rendered is very close (0.936:1) to being a square.
EDIT: Disregard the stuff below as regards PAL. I failed to take account of the fact that the PAL C64 uses a slightly non-standard line frequency, which causes the lines on an an analogue PAL screen to be slightly further apart from each other than the standard has them. See here: Pixel Aspect Ratio
Taking that into account, the pixel aspect ratio for a PAL C64 is a much simpler value. It is 59:63.
Here's a table of pixel aspect ratios of different Commodore and Apple machines (as they are after power on without any register tweaking), taking this into account. E.g. "118:71" means, 118 lines high equals 71 pixels wide. I've also given the maximum sized perfect square you can draw on the main screen area of that machine, with the register settings as they are after normal power on reset (i.e. without tricks such as opening borders, changing frequencies, adjusting timing registers, putting the VDC in 40-chars-per-line mode etc.). You can use that to adjust your screen height and width.
| Machine | TV System | Pixel aspect ratio | Maximum Square |
|---|---|---|---|
| VIC-20 | NTSC | 3:2 | X=122 Y=183 |
| VIC-20 | PAL | 118:71 | X= 71 Y=118 |
| C64,C128 | NTSC | 3:4 | X=264 Y=198 |
| C64,C128 | PAL | 59:63 | X=189 Y=177 |
| C128 VDC | NTSC | 195:508 | X=508 Y=195 |
| C128 VDC | PAL | 59:128 | X=384 Y=177 |
| C16,Plus/4 | NTSC | 65:76 | X=228 Y=195 |
| C16,Plus/4 | PAL | 59:57 | X=171 Y=177 |
| Apple II+ | NTSC | 65:76 | X=152 Y=130 |
| Apple II+ | PAL | 59:57 | X=171 Y=177 |
The Apple II+ values are also valid for all other Apple II machines (including the IIgs) as long as they are in II+ compatible display modes, i.e., 40-column text, standard hires, and the mixed mode combining those two. In the //e and above Double-Hires or the IIgs Super-Hires modes, double the 76 or the 57.
The values for PET (with and without CRTC) and CBM-II are missing. I'm not sure about their dot-clock and cycles-per-line values.
DISREGARD THE FOLLOWING AS REGARDS PAL: The best way to calculate the answer is by using the dot clock values. Industry standards mandate that for a full-frame 480 line NTSC picture at a dot clock of exactly 13.5 MHz, the pixel aspect ratio is exactly defined as 11 dots wide equal 10 lines high, so for square pixels, you need a dot clock of 135/11≈12.27272 MHz. For a 576-line PAL frame, the same dot clock gives pixels where 54 dots wide equal 59 lines high, so for square pixels the required dot clock is 59/4=14.75 MHz. With the C64 dot clocks, PAL color clock times sixteen over nine, which is 709379/90000≈7.882 MHz, or NTSC color clock times sixteen over seven which gives 90/11≈8.182 MHz, and the fact that the Commodores use non-interlaced modes that are half as many lines high as full frames, the NTSC C64’s pixel aspect ratio comes out as (135/11)/(90/11)/2, exactly 3:4 or 0.75, three lines high equal four pixels wide. The PAL C64 gives (59/4)/(709379/90000)/2, the rather unwieldy exact value of 663750:709379, which comes out at about 0.93568; that means that 160 lines high almost exactly equal 171 pixel wide; the error is less than 1/1000 pixel, far below the limit of how well even professional equipment can be adjusted.
