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Parapyth is the rank-3 temperament tempering out 352/351 and 364/363 in the subgroup.

Inspired by George Secor's 29-tone high tolerance temperament, parapyth was found by Margo Schulter in 2002, and it continued to be developed as part of her neoclassical tuning theory (NTT), although a regular temperament perspective is as viable.

In the early prototype, there was only a single chain of fifths, tuned a little sharp such that:

  • the major sixth (+3 fifths) hits 22/13, tempering out 352/351;
  • the major third (+4 fifths) hits 14/11, tempering out 896/891;
  • the augmented unison (+7 fifths) hits 14/13, tempering out 28672/28431.

This is now known as pepperoni. Parapyth encapsulates pepperoni, and adds a spacer representing 28/27~33/32. Prime harmonics 7, 11 and 13 are all made available simply using two chains of fifths.

See Pentacircle clan #Parapyth for technical data.

Interval lattice

These diagrams differ by lattice bases and tunings. The first diagram is generated by {~2, ~3, ~7/4}, corresponding to the octave-reduced form of the mapping, and tuned to the subgroup CTE tuning. The second diagram shows the preferred settings in Margo Schulter's neoclassical tuning theory, where it is generated by {~2, ~3, ~33/32}, and tuned to MET-24.


  • Parapyth12 – 12-tone Fokker block in TOP tuning
  • Pepperoni7 – 7-tone single chain of fifths in 271edo tuning
  • Pepperoni12 – 12-tone single chain of fifths in 271edo tuning

See also

External links