Parapyth: Difference between revisions

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~~#redirect~~ [[~~Pentacircle clan #~~Parapyth]]

'''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 ==

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:Pentacircle clan]]

@@ Line 1: / Line 1: @@
-#redirect [[Pentacircle clan #Parapyth]]
+'''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:Pentacircle clan]]