Tourist visa question

This might help you https://www.schengenvisainfo.com/visa-calculator/

@Silver Nomad

Welcome to the expat.com forum, and best wishes for your travels to Spain and Europe.

There is a Schengen Tourist Visa, but I think you'll find that, as an American, you have visa-free entry to most/all the EU (and many others), so you won't need to apply for one. However, you are correct that you still have to comply with the 90 in 180 Schengen rule. While visits to any Schengen country (e.g. Spain, Germany) get counted together, you have separate allowances for non-EU countries (e.g. Serbia, Turkey, UK) or EU countries not currently part of the Schengen Zone (e.g. Cyprus).

"Is the following scenario allowed under current rules?"

Nope! :-)

@SimCityAT gave us a very helpful info link with a calculator to check.

Firstly, it's (up to) 90 in 180, so you can never (legally) stay more than 90 consecutive days.

And the 180 days isn't a fixed period as you describe it (first half of year, second half of year). Rather it's a rolling count of your last 180 days. If today, you have 90 days (or less) inside Schengen during this period, then you've complied with the rules. If, instead, you have 91 days (or more), then you have overstayed, and broken your visa (or visa-free) conditions.

Here's a way to think of it. There is a counter, which starts at 90. Every day you are in the zone in the 180 day window and 180 days ago you were out, it decrements by 1. Every day you stay out of the zone in that window and 180 days ago you were in, it increments by 1, to a max of 90. If the outgoing day in the window is the same type as the incoming day, that is both in or both out, the counter dies not change. If ever the counter reaches 0, you have to leave.