Musical cells: Difference between revisions

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-'''Musical cells''' is a system of [[Mario Pizarro]] for constructing [[circulating temperament]]s. Recently he has connected this to a system of stretched octaves he calls "'''toctaves'''". This is discussed on ''[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100427.html The corrected progression of musical cells]''.
+'''Musical cells''' are a system of [[Mario Pizarro]] for constructing [[well temperament]]s. Recently he has connected this to a system of stretched octaves he calls "'''toctaves'''". This is discussed on ''[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_100427.html The corrected progression of musical cells]''.
+== Musical cells ==
+Pizarro's musical cells are based on a set of three [[comma]]s:
+* M: (3<sup>8</sup> × 5)/2<sup>15</sup> ([[schisma]]);
+* J: (2<sup>25</sup> × 2<sup>1/4</sup>)/(3<sup>13</sup> × 5<sup>2</sup>);
+* U: (2<sup>12</sup> × 5<sup>2</sup> × 3<sup>1/2</sup>)/3<sup>11</sup>.
+Using combinations of these commas, he defined two "semitone factors" K and P, which he then put together to from the Piagui scale. This well-tempered scale follows an [[8L 4s]] pattern, with large steps K and small steps P. There are three variants (rotations) of this scale: Piagui I (KKP KKP KKP KKP), Piagui II (KPK KPK KPK KPK) and Piagui III (PKK PKK PKK PKK).
 == Toctave ==