I’ve been exploring with the Partch 43-tone scale and one of the things I’ve been curious about is how one might go about navigating a scale that has so many degrees.
My first step has been to add a colour scheme to the overlay that I created for the Sensel Morph, based on the colours that Partch himself used on his Chromolodeons.
With that the symmetry of the scale becomes immediately apparent. The coloured hexagons are the ratios from the 11-limit tonality diamond that Partch has at the core of his scale, and the grey hexagons are the additional tones that he added in-between those core ratios as a way of filling in some of the wider gaps, and making a wider range of harmonies possible.
So the ratios in the top right hand quadrant will be mirrored in the bottom left, and vice versa. To demonstrate: a pure fifth
1/1:3/2 will correspondingly give me a pure fifth here
2/1:4/3. I can also go to another degree of the scale,
16/15:8/5 will corresponding give me a pure fifth here
15/8:5/4. You can also do that on other degrees of the scale
81/80:32/21, but here you won’t get a pure fifth, you can hear some beating, and the same thing here
33/32:14/9 slightly faster beating. But if I go back to one of the pure fifths
1/1:3/2 and add a third
5/4 you get a nice pure major triad, or minor
1/1:6/5:3/2. There are also two ‘alternative’ degrees of the scale, e.g. here
10/9:4/3 I get a minor third, but if I take this one
11/10:4/3 it’s no longer in tune, but what it does give me is a purely tuned major second (
10/9), and correspondingly
20/11:18/11, I get the pure major second over there.
So that’s a little start in how one might go about navigating the 43 tones of the scale. I find the the symmetries are really useful in reducing the amount of information that one has to deal with.