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Is it possible to write a phase-shifted pattern in the style of Minimalist phased looping on Gibson Echoplex Digital Pro that obeys all the classical counterpoint rules? Each note of the pattern will eventually play against every other note.

If it is possible, which diatonic scale degrees are permissible?

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  • nb Reich uses the word "counterpoint" in a lot of his works. Maybe the point is that a broader use of the word just involves "point against point," as the shifting phases bring points into contact with other points, creating a new "counterpoint" with every shift. Meanwhile, sure, I imagine just about any challenge is possible. Retrograde canons, duets that can be executed by two people facing one sheet of music from either end, etc. It's kind of a "negative-proof" question; it's hard to prove an impossibility. Apr 18, 2023 at 17:32

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Yes.

  1. One part that repeats a single pitch for the entire tune, and another part repeats a pitch a major or minor third away.

  2. One part oscillates between the root and third of a major or minor chord, and another part oscillates between the third and fifth.

I think the "real" question is whether a musically "interesting" counterpoint can be written. And in this case, I believe the answer is no.

In this particular case, we're talking about a canon: a single pattern that plays against itself. So we need to construct a musically interesting melody that can be phase shifted against itself and remain a classically rule-adherent canon.

The melody, in this case, will be required to include seconds — a classical melody entirely of skips would not be aesthetically acceptable. Further, to avoid just oscillating between the same two pitches (which wouldn't meet the "rules"), there will have to be a passage with at least two consecutive seconds, either both ascending or both descending. Let's make them both ascending, since the descending case will lead to the same problem.

In classical counterpoint, when two voices form a second, the should either resolve to a third or a unison. However, there will be phases in which the seconds between the two voices do not resolve properly: for example when the first and second notes in one voice overlap with the second and third notes in the other voice.


There is a related topic that might be of interest: tiling rhythmic canons. These are rhythmic patterns which, when presented in canon with themselves, fill the entire metric space. For more see: What is rhythmic counterpoint? and What's "species counterpoint"? Are there any other types of counterpoint?.

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  • Thank you for your detailed answer! I'm not sure what you mean by part here. Are you referring to two parts of the same phrase? In the phase-shifting I'm thinking about, the phrase is identical in both parts except that one part has a simple 8/8 time signature, and the other part has an 8/9 time signature with same phrase but with an extra eighth note or eighth note rest tacked on.
    – empty
    Apr 18, 2023 at 20:17
  • @empty My answer actually shifts between two separate voices and a single voice that is phase shifted with itself in the manner of Steve Reich. The 8/8 vs. 9/8 case would have similar problems, but it wasn't clear that's what your question referred to. As a side note, it's not reasonable to expect people to read the entire web page you linked to, which is why this site asks for videos, for example, to be summarized. (Also because links go dead.)
    – Aaron
    Apr 18, 2023 at 20:47
  • I just wanted a quick disambiguating link for answerers. Do you think I should add a full explanation of phased-shifted loops?
    – empty
    Apr 18, 2023 at 22:08
  • @empty I don't think a full explanation is necessary (for that, you can include the link), but a clearer explanation of your question would help. What you're describing in your comment sounds like polymeter rather than phase shifting, so the specific kind of phasing you'rr asking about should be clarified.
    – Aaron
    Apr 18, 2023 at 22:12
  • Thanks, I've changed the link to an MSE link with an appropriate example.
    – empty
    Apr 18, 2023 at 22:13

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