Temperament addition: Difference between revisions

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Revision as of 19:47, 24 June 2024 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,160 edits →Third example: reordering of canonical form ← Older edit		Revision as of 19:48, 24 June 2024 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,160 edits →Fourth example: other side of duality Newer edit →
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	In order to compare this result directly with our other three results, let's take the dual of this {{rket\|{{map\|6 8 -4 1}} {{map\|0 1 5 10}}}}, which is [{{vector\|22 -15 3 0}} {{vector\|41 -30 2 2}}] (in canonical form), so we can see that's yet a fourth possible result<ref>		In order to compare this result directly with our other three results, let's take the dual of this {{rket\|{{map\|6 8 -4 1}} {{map\|0 1 5 10}}}}, which is [{{vector\|22 -15 3 0}} {{vector\|41 -30 2 2}}] (in canonical form), so we can see that's yet a fourth possible result.<ref>
	It is possible to find a pair of mapping forms for septimal meantone and septimal blackwood that sum to a mapping which is the dual of the comma basis found by summing their canonical comma bases. One example is {{rket\|{{map\|97 152 220 259}} {{map\|-30 -47 -68 -80}}}} + {{rket\|{{map\|-95 -152 -212 -266}} {{map\|30 48 67 84}}}}.</ref>		It is possible to find a pair of mapping forms for septimal meantone and septimal blackwood that sum to a mapping which is the dual of the comma basis found by summing their canonical comma bases. One example is {{rket\|{{map\|97 152 220 259}} {{map\|-30 -47 -68 -80}}}} + {{rket\|{{map\|-95 -152 -212 -266}} {{map\|30 48 67 84}}}}.</ref>