Parapyth: Difference between revisions

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

== Parapyth edos ==

The parapyth edos below 311 that are not contorted in 2.3.7.11.13 are {{EDOs|17, 22, 24, 29, 41, 46, 58, 63, 65, 80, 87, 104, 109, 121, 128, 133, 145, 150, 167, 172, 184, 191, 196, 213, 230, 232, 237, 254, 259, 271, 278, 283, and 295}}~~. Note that 17, 24, 41, 58, and 65 additionally temper out 144/143, thereby equating 16/13 and 11/9 to exactly one-half of 3/2~~.

The parapyth edos below 311 that are not contorted in 2.3.7.11.13 are {{EDOs|17, 22, 24, 29, 41, 46, 58, 63, 65, 80, 87, 104, 109, 121, 128, 133, 145, 150, 167, 172, 184, 191, 196, 213, 230, 232, 237, 254, 259, 271, 278, 283, and 295}}.

[[87edo]] is special for being the smallest "strict parapyth edo" (tempers out 352/351 and 364/363 and maps all of 121/120, 144/143, and 169/168 positively, meeting [[Margo Schulter]]'s criterion for "middle parapyth in the strict sense"). The following are strict parapyth edos below 311 that are not contorted in the 13-limit: {{EDOs|87, 104, 121, 128, 133, 145, 150, 167, 184, 191, 196, 208\*, 213, 230, 232, 237, 254, 259, 271, 278, 283, 295}}.

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 See [[Pentacircle clan #Parapyth]] for technical data.
 == Parapyth edos ==
-The parapyth edos below 311 that are not contorted in 2.3.7.11.13 are {{EDOs|17, 22, 24, 29, 41, 46, 58, 63, 65, 80, 87, 104, 109, 121, 128, 133, 145, 150, 167, 172, 184, 191, 196, 213, 230, 232, 237, 254, 259, 271, 278, 283, and 295}}. Note that 17, 24, 41, 58, and 65 additionally temper out 144/143, thereby equating 16/13 and 11/9 to exactly one-half of 3/2.
+The parapyth edos below 311 that are not contorted in 2.3.7.11.13 are {{EDOs|17, 22, 24, 29, 41, 46, 58, 63, 65, 80, 87, 104, 109, 121, 128, 133, 145, 150, 167, 172, 184, 191, 196, 213, 230, 232, 237, 254, 259, 271, 278, 283, and 295}}.
 [[87edo]] is special for being the smallest "strict parapyth edo" (tempers out 352/351 and 364/363 and maps all of 121/120, 144/143, and 169/168 positively, meeting [[Margo Schulter]]'s criterion for "middle parapyth in the strict sense"). The following are strict parapyth edos below 311 that are not contorted in the 13-limit: {{EDOs|87, 104, 121, 128, 133, 145, 150, 167, 184, 191, 196, 208\*, 213, 230, 232, 237, 254, 259, 271, 278, 283, 295}}.