Palingenetic chords

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A palingenetic chord is an essentially tempered dyadic chord tempered by 1701/1700, the palingenetic comma. Currently, there are only a handful of palingenetic chords known.

There is a 21-odd-limit palingenetic triad:

  • 1-10/9-9/5 with steps 10/9-34/21-10/9.

Assuming we stick to the 27-odd-limit, we have two known triads and one known tetrad.

The known 27-odd-limit palingenetic triads are:

  • 1-34/27-3/2 with steps 34/27-25/21-4/3, and its inversions; dubbed the "palingenetic major triad"
  • 1-25/21-3/2 with steps 25/21-34/27-4/3, and its inversions; dubbed the "palingenetic minor triad"
  • 1-18/17-32/27 with steps 18/17-28/25-27/16, and its inversions
  • 1-28/25-32/27 with steps 28/25-18/17-27/16, and its inversions

The known 27-odd-limit palingenetic tetrads are:

  • 1-18/17-32/27-8/5 with steps 18/17-28/25-27/20-5/4, and its inversions
  • 1-28/25-32/27-40/27 with steps 28/25-18/17-5/4-27/20, and its inversions