New conclusions about comma pump models and some more examples

Hi tuners.

Just to inform you about my evolving theory, today I've compared my triadic comma pump model to the tetradic one in various 2D temperaments. And my conclusion is that the triadic model can happily be used also for making progressions of tetrads and that doing it this way often gives better results than trying to find a model specifically based on tetrads. This "tetradic application" of the triadic model works okay as long as the interval between pitches which are 3 steps apart in the sequence isn't 25/24 or an octave equivalent/complement of that. After all, you might have heard for yourselves when I made the example in amity, first with triads, then with tetrads.

Some temperaments even make it possible to play pentads using the same model, a good example of which may be superpyth or schismatic. Incidentally, superpyth and schismatic are related to each other in a similar fashion as meantone and mavila. Therefore, if we make a pump by 20480/19683 in one case and 32768/32805 in the other (I'm using a falling schisma in order the progression of fifths went in the same direction in both cases), we can not only use tetrads and even pentads but we can also retune it from one temperament to the other. This means that if someone wrote a piece in schismatic, for example, it may be easy to retune it to superpyth or vice versa as long as we're able to retune meantone to mavila.

To hear for yourselves, you can go to /tuning/files/PetrParizek and look for "pp_spyth.mid" and "pp_schis.mid". In both of these examples, the sequence file used was the same, only the scale files were different.

Petr