Parapyth: Difference between revisions
+ norm-based tunings & target tunings |
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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, | | 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 | '''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 == | ||