Parapyth: Difference between revisions
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'''Parapyth''' is the rank-3 [[temperament]] tempering out [[352/351]] and [[364/363]] in the 2.3.7.11.13 [[subgroup]]. | |||
Inspired by [[Secor29htt|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. | |||
== Interval lattice == | |||
<gallery> | |||
File:Lattice Parapyth RTT.png | |||
File:Lattice Parapyth NTT.png | |||
</gallery> | |||
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 == | |||
* [https://www.xenharmonikon.org/2022/07/15/met-24-a-milder-extended-temperament/ Xenharmonikon | ''MET-24: A Milder Extended Temperament''] by Margo Schulter | |||
* [https://www.bestii.com/~mschulter/tn101812-3degrees.txt ''A Friendly Introduction to "Rank-3" Temperaments: Designing a System with Three Degrees of Freedom''] by Margo Schulter, with an introduction to parapyth | |||
[[Category:Temperaments]] | [[Category:Temperaments]] | ||
[[Category:Pentacircle clan]] | [[Category:Pentacircle clan]] | ||
Revision as of 15:25, 9 December 2022
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.
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