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

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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

• Peppermint-24

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
• The MET-24 temperament for Maqam music: Partitions or divisions of the apotome in context by Margo Schulter