Prodigy chords

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A prodigy chord is an 11-odd-limit essentially tempered chord in prodigy temperament. Since 441/440 is tempered out in prodigy, werckismic chords are also prodigy chords, and since 225/224 is tempered out, the 9-odd-limit marvel chords are prodigy chords. Aside from these, there are three more prodigy chords:

  • a 1-5/4-7/5-16/9 tetrad with steps 5/4-9/8-14/11-9/8;

and a pair of inversely related pentads:

  • 1-5/4-7/5-8/5-16/9 with steps 5/4-9/8-8/7-10/9-9/8;
  • 1-5/4-7/5-14/9-16/9 with steps 5/4-9/8-10/9-8/7-9/8.

Miracle essentially tempered chords

Main article: Miracle chords

11-limit miracle temperament tempers out an astonishing five commas which allow essential tempering: 540/539, 441/440, 385/384, 243/242 and 225/224, and hence has all of the essentially tempered chords of each of them. Further chords come from jove and undecimal marvel chords. Then there are the three listed above, and ten essentially miracle chords.

Three chords may not seem to be many, but consider this: the POTE tuning for prodigy shrinks 540/539 and 243/242 to a third of a cent, and 385/384 to -1/3 cent. Other optimizations are similar. Hence, the miracle essentially tempered chords are already available in prodigy, we just aren't counting them; in effect, we can more or less equate prodigy with miracle. In miracle, we may put the eight different kinds of essentially tempered chords together, for a total of triads: 21, tetrads: 76, pentads: 38, and hexads: 12. There are therefore actually more essentially tempered chords than just ones.

EDOs supporting prodigy/miracle include 31, 41, 72, 103, 175, 216c, 247c, 319bcde, 391bcde, 463bcde.

See also