# 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 **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.

## Parapyth EDOs

The parapyth EDOs below 311 that are not contorted in 2.3.7.11.13 are 17, 22, 24, 29, 41, 46, 58, 63, 65, 80, 87, 104, 109, 121, 128, 133, 145, 150, 167, 172, 184, 191, 196, 213, 230, 232, 237, 254, 259, 271, 278, 283, and 295.

87edo is special for being the smallest "strict parapyth EDO" (tempers out 352/351 and 364/363 and maps all of 121/120, 144/143, and 169/168 positively, meeting Margo Schulter's criterion for "middle parapyth in the strict sense"). The following are strict parapyth EDOs below 311 that are not contorted in the 13-limit: 87, 104, 121, 128, 133, 145, 150, 167, 184, 191, 196, *208*, 213, 230, 232, 237, 254, 259, 271, 278, 283, 295. (Note: 208edo is contorted in 2.3.7.11.13 subgroup but not in the full 13-limit.)

## 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 2.3.7.11.13 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.

## Scales

- Parapyth12 – 12-tone Fokker block in 2.3.7.11.13 TOP tuning
- Parapyth17 – 17-tone Fokker block in 2.3.7.11.13 TOP tuning
- Pepperoni7 – 7-tone single chain of fifths in 271edo tuning
- Pepperoni12 – 12-tone single chain of fifths in 271edo tuning