Blumeyer Comma JI Unpump

11.23.2015 § Leave a comment

Four years ago I invented a tuning system based on the pun whereby movement by a 19th harmonic almost exactly cancels out movement by an 11th, 13th, and 17th (2432:2431). Finally, I’ve written a piece in it:

I call it an “unpump” because rather than spiraling out in looping increments of the comma as JI pumps tend to do, I instead modulate by the tiny intervals in the tuning in order to return back to the home pitch as tempered pumps tend to do.

Here are two different maps of the bass to the track:

2431tuning_with_cheats_and_paths blumeyer_ji_with_cheats_and_path

Basically I found the three instances of the pump I used for the tempered version (here) and noticed that they each shared one pitch with each other, so I decided to give each one at least one full loop around itself before switching tracks to the next, looping back around the full three-pump cycle in a total of 23 bars. The exact pattern is:


As you can see, ABCD, DEFG, and GHBE are the pumps. The first two links are seamless, but the link from the pump starting with G back to the one starting with A requires a little more connective tissue. It’s fine, though, I think, since it results in a nearly even distribution of presence of chords per pump (that is, while individual chords appear between 2 and 4 times each – a factor of 2x difference – sets of chords appear in more similar amounts: A’s, B’s, C’s, and D’s together appear 13 times; D’s, E’s, F’s, and G’s together appear 12 times; G’s, H’s, B’s, and E’s together also appear 12 times).

The chords are built from the pitches directly connected to each of these bass notes but which were not captured along this path. I guess you could call these the “left-out” notes.

The harmony comes from choosing from left-out notes, too. But instead of building a stack of all such notes for each bass note, what I did was pick a single note, then connected them by moving step-wise through the left-out notes. How long I hold each harmony note just depends on how many steps it takes to get between one bass note’s harmony note and its next’s using the shortest possible path. Only one note has no neighbor left-out notes: the unison.

I did some other tricky things that I don’t exactly remember and won’t attempt to explain. Enjoy!



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