Parapyth: Difference between revisions

+ norm-based tunings & target tunings
m Linking
 
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| Edo join 1 = 17 | Edo join 2 = 41 | Edo join 3 = 46
| Edo join 1 = 17 | Edo join 2 = 41 | Edo join 3 = 46
| Mapping = 1; 1 0 -4 -7; 0 1 1 1
| Mapping = 1; 1 0 -4 -7; 0 1 1 1
| Generators = 3/2, 5/4
| Generators = 3/2, 7/4
| Generators tuning = 703.8, 969.2
| Generators tuning = 703.8, 969.2
| Optimization method = CWE
| Optimization method = CWE
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| Odd limit 2 = 2.3.7.11.13 21 | Mistuning 2 = 3.28 | Complexity 2 = ?
| Odd limit 2 = 2.3.7.11.13 21 | Mistuning 2 = 3.28 | Complexity 2 = ?
}}
}}
'''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]].  
'''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.  
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.  
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This temperament is now known as [[pepperoni]]. Parapyth encapsulates pepperoni and adds a {{nowrap| 28/27 ~ 33/32 }} spacer interval such that harmonics 7, 11, and 13 are all made available simply by using two chains of fifths.  
This temperament is now known as [[pepperoni]]. Parapyth encapsulates pepperoni and adds a {{nowrap| 28/27 ~ 33/32 }} spacer interval such that harmonics 7, 11, and 13 are all made available simply by using two chains of fifths.  


See [[Pentacircle clan#Parapyth]] for technical data.
See [[Pentacircle clan #Parapyth]] for technical data.


== Interval lattice ==
== Interval lattice ==