Ptolemismic chords: Difference between revisions

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-The '''ptolemismic triad''' is an [[essentially tempered chord]] which is the [[100/99]] tempering of 1-[[11/8]]-[[5/3]], with steps of 11/8-[[6/5]]-6/5. Equal divisions with ptolemismic triads include [[19edo]], [[22edo]], [[37edo]], [[41edo]] and [[104edo]].
+'''Ptolemismic chords''' are [[essentially tempered chord]]s tempered by the ptolemisma, [[100/99]].
+The ptolemismic triad consists of [[11/8]] and a stack of two [[6/5]]'s closing at the octave:
+* 1-11/8-5/3 with steps of 11/8-6/5-6/5.
+It can be extended to tetrads as
+* 1-11/8-3/2-5/3 with steps 11/8-12/11-11/10-6/5, and its inverse
+* 1-11/8-5/3-11/6 with steps 11/8-6/5-11/10-12/11;
+* 1-5/4-11/8-5/3 with steps 5/4-11/10-6/5-6/5, and its inverse
+* 1-11/10-11/8-5/3 with steps 11/10-5/4-6/5-6/5.
+They can be extended to pentads as
+* 1-5/4-11/8-3/2-5/3 with steps 5/4-11/10-12/11-11/10-6/5, and its inverse
+* 1-11/10-11/8-5/3-11/6 with steps 11/10-5/4-6/5-11/10-12/11.
+Equal divisions with ptolemismic triads include [[19edo]], [[22edo]], [[37edo]], [[41edo]] and [[104edo]].
 [[Category:11-odd-limit]]
 [[Category:Essentially tempered chords]]
 [[Category:Triads]]
+[[Category:Tetrads]]
+[[Category:Pentads]]
 [[Category:Ptolemismic]]