The pythagorean scale has perfect fifths while the octave is off and the third is further off than standard 12tet.
http://www.pianofundamentals.com/book/en/2.2.3
Experimental. Sometimes emphasizing the perfect fifths. Other times not in any key at all.
I like the keyless stuff. But the transitions and overall flow isn't so great.

To summarize that link:
Meantone Temperament has perfect thirds (the freq ratio between c and e being 5/4 for example.)
12 tone Pythagorean Temperament has perfect fifths (c and g being 3/2)
12 tone Equal Temperament fudges both thirds and fifths and instead has a perfectly smooth step up for each note. It only has a perfect octave.
12 tone Well Temperaments are a variety of alternate compromises between meantone and pythagorean, the primary goal being to have both good thirds and good fifths. Supposedly the best WTs are by Werckmeister and Young. And supposedly Moonlight Sonata sounds better in WT for example. I had already been thinking about doing the midi for moonlight and listening to it with various temperaments. WTs additionally keep it meaningful to have all the different keys as each has it's own 'color'. Which is the same idea as what just intonation would do. Although just intonation may be too extreme.

I do think that I sort of like having the octave off a bit. If I had to choose, I'd choose fifths or thirds over the octave. I guess somewhat like this link I earlier had read was saying:
http://www.nonoctave.com/tunes/