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]].

'''Parapyth''', also known as '''parapythagorean''', 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:

In the early prototype, there was only a single chain of fifths, tuned slightly sharp such that:

* ~~the major sixth~~ (+3 fifths) ~~hits~~ [[22/13]], tempering out 352/351;

* The minor third (−3 fifths) is [[13/11]], tempering out 352/351;

* ~~the~~ major third (+4 fifths) hits [[14/11]], tempering out [[896/891]];

* The major third (+4 fifths) hits [[14/11]], tempering out [[896/891]];

* ~~the~~ augmented unison (+7 fifths) hits [[14/13]], tempering out [[28672/28431]].

* 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.

This temperament 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.

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[[Category:Temperaments]]

[[Category:Parapyth| ]]

[[Category:Parapyth| ]]

[[Category:Pentacircle clan]]

@@ Line 1: / Line 1: @@
-'''Parapyth''' is the rank-3 [[temperament]] tempering out [[352/351]] and [[364/363]] in the 2.3.7.11.13 [[subgroup]].
+'''Parapyth''', also known as '''parapythagorean''', 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:
+In the early prototype, there was only a single chain of fifths, tuned slightly sharp such that:
-* the major sixth (+3 fifths) hits [[22/13]], tempering out 352/351;
+* The minor third (&minus;3 fifths) is [[13/11]], tempering out 352/351;
-* the major third (+4 fifths) hits [[14/11]], tempering out [[896/891]];
+* The major third (+4 fifths) hits [[14/11]], tempering out [[896/891]];
-* the augmented unison (+7 fifths) hits [[14/13]], tempering out [[28672/28431]].
+* 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.
+This temperament 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.
@@ Line 56: / Line 56: @@
 [[Category:Temperaments]]
-[[Category:Parapyth| ]] <!-- main article -->
+[[Category:Parapyth| ]] <!-- Main article -->
 [[Category:Pentacircle clan]]