Parapyth
Parapyth is the rank-3 temperament tempering out 352/351 and 364/363 in the 2.3.7.11.13 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 peppermint. Parapyth encapsulates peppermint, 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
Both diagrams are tuned in 2.3.7.11.13 subgroup CTE tuning, but they differ in the lattice basis. {~2, ~3, ~7/4} in the first diagram corresponds to the octave-reduced form of the mapping. {~2, ~3, ~33/32} in the second diagram is preferred in Margo Schulter's neoclassical tuning theory.
See also
External links
- Xenharmonikon | MET-24: A Milder Extended Temperament by Margo Schulter
- A Friendly Introduction to "Rank-3" Temperaments: Designing a System with Three Degrees of Freedom by Margo Schulter, with an introduction to parapyth