The fifive pump and a few thoughts

Hi all.

Honestly, when I was thinking of the names like "sixix" and "fifive", I had absolutely no idea that the two temperaments had some similar harmonic properties. Surprisingly enough, while I was making a comma pump example for fifive, I realized that the following was the case for both sixix and fifive:
- A) When going from major to minor, the root pitch falls by a minor third.
- B) When going back to major, the root pitch rises by a fourth.
When I tried to find out what was going on here, I discovered this:
If you make a pitch progression like "2/1, 5/6, 5/6, 5/6, 4/3, 5/6, 5/6", you end up at 3125/2916, which is tempered out in sixix. If you then rise by one more 4/3, you arrive at 3125/2187, which is one untempered half-octave period in fifive. I really didn't know that that was the case at the time I first thought of "fifive". And now I'm just surprised. Well, that's the way things happen, sometimes.

Anyway, I've promissed to let you hear a comma pump example in fifive. So here it is:
/tuning/files/PetrParizek/Fifive_pump.mid

Petr

I wrote:

> - A) When going from major to minor, the root pitch falls by a minor > third.
> - B) When going back to major, the root pitch rises by a fourth.

I should have said:
When going from minor to major, the root pitch rises by a fourth, while in all the other cases it falls by a minor third.
Interestingly enough, this seems to be true for sixix, porcupine, unicorn, and semisixths as well -- and I'll surely find other examples if I go on making MIDI renditions of comma pumps.

Petr