Why does the Amiga 500 have half the HSYNC pulses seperately compared to those in CSYNC?

In an analog television set, the vertical and horizontal sync circuits are independent, but both need to derive their trigger signals from a common source. As a general concept, a short "low-going" pulse [which is modulated for broadcast as an increase in signal level] will trigger the horizontal sync circuit, while a long pulse will trigger the vertical circuit.

In order to improve apparent resolution, the horizontal frequency is 525/2 times the vertical frequency, so that on every other vertical scan the horizontal scans will be shifted by half a scan line. If a television set were to simply transmit horizontal sync triggers as short pulses and vertical ones as long ones, this would cause a couple of problems:

1. To facilitate separation, the vertical sync pulse is multiple scan lines long. If there were no horizontal sync pulses within that time, television sets would be prone to lose horizontal synchronization. Although sets would regain horizontal synchronization eventually, the time required for them to do so might be longer than the vertical blanking interval; the failure to reestablish synchronization within the blanking interval could cause "tearing" on the top part of the display.

2. The amount of time required for a set to detect a vertical scanning pulse might be affected by the time that elapsed since the end of the preceding horizontal pulse. Typically, the vertical detector circuit will derive a rough "time averaged" version of the sync signal and trigger when the average voltage falls below a certain threshold. While a horizontal sync pulse is active, the average will drop, and when it's inactive it will rise. If the time required for the average to fully recover is more than half a scan line, this would affect the amount of time required for the set to detect the vertical sync.

To alleviate these issues, the rate of horizontal sync pulses is doubled a shortly before the start of the vertical sync pulse. Television sets will ignore a horizontal sync pulse that occurs before a point somewhere between 60% and 98% of the way through a scan line, but by the time the sync pulse arrives, the averaging circuit would have settled onto a level which would be the same on each pulse, whether or not it lined up with the vertical sync.

I would expect that a signal which is intended for use with the kind of decoding circuitry found in a television set would include these extra pulses, though many computers and video game systems omit them. A signal which is intended to directly drive a horizontal-sync trigger circuit, however, should omit them. Some monitors might attempt to respond to the double-speed pulses by scanning twice as fast, even if this would cause damaging levels of stress on their components, or would cause them to needlessly adjust their deflection currents to double the rate at which the beam moves (without such adjustment, doubling the scan rate would squish the image by 50%). If the sets start increasing the deflection current when the rate doubles, and then start dropping it when the rate goes back to normal, the time required for the current to stabilize at a level appropriate to the normal scan rate might exceed the vertical blanking interval, causing tearing.

The CSYNC looks perfectly normal for a standard 576i or 480i composite signal, just like how sync signals on composite video and analog TV transmissions work.

The video signal standards define that serrated equalizing sync pulses are sent at twice the HSYNC rate during the VSYNC and few lines before and after it. This is to allow the VSYNC to be detected better and it also gives a handy reference for starting the VSYNC at the start of a line or in the middle of a line to provide timings for odd and even frames for interlaced video.

The VSYNC is not sent as a single long pulse that would block HSYNC, nor as a series of long sync pulses at HSYNC frequency.

Also, the A500 outputs video at 15kHz interlaced rate and has no support for VGA compatible timings. It is extremely unlikely that a monitor would support 15kHz interlaced 480i/576i video on VGA connector. Most monitors support 31kHz progressive video at minimum.