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 {{Optimal ET sequence|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: {{Optimal ET sequence|87, 104, 121, 128, 133, 145, 150, 167, 184, 191, 196, ''208'', 213, 230, 232, 237, 254, 259, 271, 278, 283, 295}}. (Note: 208edo is contorted in 2.3.7.11.13 subgroup but not in the full 13-limit.)

== Interval lattice ==

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* [[Pepperoni7]] – 7-tone single chain of fifths in 271edo tuning

* [[Pepperoni12]] – 12-tone single chain of fifths in 271edo tuning

== Tunings ==

The most important tuning for parapyth is that given by MET-24 (''milder extended temperament''): ~2/1 = 1\1, ~3/2 = 703.711, ~33/32 = 57.422. Another tuning is taking a 24-tone subset of [[George Secor]]'s 29-HTT, thus a "24-HTT". Yet another possible tuning is that given by [[Peppermint-24]].

=== Edo tunings ===

The parapyth edos below 311 that are not contorted in 2.3.7.11.13 are {{Optimal ET sequence| 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: {{Optimal ET sequence| 87, 104, 121, 128, 133, 145, 150, 167, 184, 191, 196, ''208'', 213, 230, 232, 237, 254, 259, 271, 278, 283, 295 }}. (Note: 208edo is contorted in 2.3.7.11.13 subgroup but not in the full 13-limit.)

== See also ==

@@ Line 12: / Line 12: @@
 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 {{Optimal ET sequence|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: {{Optimal ET sequence|87, 104, 121, 128, 133, 145, 150, 167, 184, 191, 196, ''208'', 213, 230, 232, 237, 254, 259, 271, 278, 283, 295}}. (Note: 208edo is contorted in 2.3.7.11.13 subgroup but not in the full 13-limit.)
 == Interval lattice ==
@@ Line 31: / Line 26: @@
 * [[Pepperoni7]] – 7-tone single chain of fifths in 271edo tuning
 * [[Pepperoni12]] – 12-tone single chain of fifths in 271edo tuning
+== Tunings ==
+The most important tuning for parapyth is that given by MET-24 (''milder extended temperament''): ~2/1 = 1\1, ~3/2 = 703.711, ~33/32 = 57.422. Another tuning is taking a 24-tone subset of [[George Secor]]'s 29-HTT, thus a "24-HTT". Yet another possible tuning is that given by [[Peppermint-24]].
+=== Edo tunings ===
+The parapyth edos below 311 that are not contorted in 2.3.7.11.13 are {{Optimal ET sequence| 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: {{Optimal ET sequence| 87, 104, 121, 128, 133, 145, 150, 167, 184, 191, 196, ''208'', 213, 230, 232, 237, 254, 259, 271, 278, 283, 295 }}. (Note: 208edo is contorted in 2.3.7.11.13 subgroup but not in the full 13-limit.)
 == See also ==